Collection volume I

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Articles Abstraction 1 Analogy 6 Bricolage 15 Categorization 19 Computational creativity 21 Data mining 30 Deskilling 41 Digital morphogenesis 42 Heuristic 44 Hidden curriculum 49 Information continuum 53 Knowhow 53 Knowledge representation and reasoning 55 Lateral thinking 60 Linnaean taxonomy 62 List of uniform tilings 67 Machine learning 71 Mathematical morphology 76 Mental model 83 Montessori sensorial materials 88 Packing problem 93 Prior knowledge for pattern recognition 100 Quasi-empirical method 102 Semantic similarity 103 Serendipity 104 Similarity (geometry) 113 Simulacrum 117 Squaring the square 120 Structural information theory 123 Task analysis 126 Techne 128 Tessellation 129 Totem 137 Trial and error 140 Unknown unknown 143 References Article Sources and Contributors 146 Image Sources, Licenses and Contributors 149 Article Licenses License 151 Abstraction 1 Abstraction

Abstraction is a conceptual process by which higher, more abstract concepts are derived from the usage and classification of literal, "real," or "concrete" concepts. An "abstraction" (noun) is a concept that acts as super-categorical noun for all subordinate concepts, and connects any related concepts as a group, field, or category. Abstractions may be formed by reducing the information content of a concept or an observable phenomenon, typically to retain only information which is relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball retains only the information on general ball attributes and behavior, eliminating the characteristics of that particular ball.

Origins The first symbols of abstract thinking in humans can be traced to fossils dating between 50,000 and 100,000 years ago in Africa.[1] [2]

Thought process In philosophical terminology, abstraction is the thought process wherein ideas[3] are distanced from objects. Abstraction uses a strategy of simplification, wherein formerly concrete details are left ambiguous, vague, or undefined; thus effective communication about things in the abstract requires an intuitive or common experience between the communicator and the communication recipient. This is true for all verbal/abstract communication. For example, many different things can be red. Likewise, many things sit on surfaces (as in picture 1, to the right). The property of redness and the relation sitting-on are therefore abstractions of those objects. Specifically, the conceptual diagram graph 1 identifies only three boxes, two ellipses, and four arrows (and their nine labels), whereas the picture 1 shows much more pictorial detail, with the scores of implied relationships as implicit in the picture rather than with the nine explicit details in the graph. Cat on Mat (picture 1)

Graph 1 details some explicit relationships between the objects of the diagram. For example the arrow between the agent and CAT:Elsie depicts an example of an is-a relationship, as does the arrow between the location and the MAT. The arrows between the gerund SITTING and the nouns agent and location express the diagram's basic relationship; "agent is SITTING on location"; Elsie is an instance of CAT. Although the description sitting-on (graph 1) is more abstract than the graphic image of a cat sitting on a mat (picture 1), the delineation of abstract things from concrete things is somewhat ambiguous; this ambiguity or vagueness is characteristic of abstraction. Thus Conceptual graph for A Cat sitting on the Mat (graph 1) something as simple as a newspaper might be specified to six levels, as in Douglas Hofstadter's illustration of that ambiguity, with a progression from abstract to concrete in Gödel, Escher, Bach (1979):

(1) a publication (2) a newspaper (3) The San Francisco Chronicle (4) the May 18 edition of the Chronicle Abstraction 2

(5) my copy of the May 18 edition of the Chronicle (6) my copy of the May 18 edition of the Chronicle as it was when I first picked it up (as contrasted with my copy as it was a few days later: in my fireplace, burning) An abstraction can thus encapsulate each of these levels of detail with no loss of generality. But perhaps a detective or philosopher/scientist/engineer might seek to learn about some thing, at progressively deeper levels of detail, to solve a crime or a puzzle.

Referents Abstractions sometimes have ambiguous referents; for example, "happiness" (when used as an abstraction) can refer to as many things as there are people and events or states of being which make them happy. Likewise, "architecture" refers not only to the design of safe, functional buildings, but also to elements of creation and innovation which aim at elegant solutions to construction problems, to the use of space, and to the attempt to evoke an emotional response in the builders, owners, viewers and users of the building.

Instantiation Things that do not exist at any particular place and time are often considered abstract. By contrast, instances, or members, of such an abstract thing might exist in many different places and times. Those abstract things are then said to be multiply instantiated, in the sense of picture 1, picture 2, etc., shown above. It is not sufficient, however, to define abstract ideas as those that can be instantiated and to define abstraction as the movement in the opposite direction to instantiation. Doing so would make the concepts "cat" and "telephone" abstract ideas since despite their varying appearances, a particular cat or a particular telephone is an instance of the concept "cat" or the concept "telephone". Although the concepts "cat" and "telephone" are abstractions, they are not abstract in the sense of the objects in graph 1 above. We might look at other graphs, in a progression from cat to mammal to animal, and see that animal is more abstract than mammal; but on the other hand mammal is a harder idea to express, certainly in relation to marsupial or monotreme.

Physicality A physical object (a possible referent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies a particular place and time. Abstract things are sometimes defined as those things that do not exist in reality or exist only as sensory experiences, like the color red. That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like God, the number three, and goodness are real, abstract, or both. An approach to resolving such difficulty is to use predicates as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g. good). Questions about the properties of things are then propositions about predicates, which propositions remain to be evaluated by the investigator. In the graph 1 above, the graphical relationships like the arrows joining boxes and ellipses might denote predicates. Different levels of abstraction might be denoted by a progression of arrows joining boxes or ellipses in multiple rows, where the arrows point from one row to another, in a series of other graphs, say graph 2, etc. Abstraction 3

Abstraction used in philosophy Abstraction in philosophy is the process (or, to some, the alleged process) in concept-formation of recognizing some set of common features in individuals, and on that basis forming a concept of that feature. The notion of abstraction is important to understanding some philosophical controversies surrounding empiricism and the problem of universals. It has also recently become popular in formal logic under predicate abstraction. Another philosophical tool for discussion of abstraction is thought space.

Ontological status The way that physical objects, like rocks and trees, have being differs from the way that properties of abstract concepts or relations have being, for example the way the concrete, particular, individuals pictured in picture 1 exist differs from the way the concepts illustrated in graph 1 exist. That difference accounts for the ontological usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that instances of them can exist, potentially in many different places and times. Perhaps confusingly, some philosophies refer to tropes (instances of properties) as abstract particulars. E.g., the particular redness of a particular apple is an abstract particular. Akin to qualia and sumbebekos.

In linguistics Reification, also called hypostatization, might be considered a formal fallacy whenever an abstract concept, such as "society" or "technology" is treated as if it were a concrete object. In linguistics this is called metonymy, in which abstract concepts are referred to using the same sorts of nouns that signify concrete objects. Metonymy is an aspect of the English language and of other languages. It can blur the distinction between abstract and concrete things: 1805: Horatio Nelson (Battle of Trafalgar) - "England expects that every man will do his duty"

Compression An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction "CAT". This conceptual scheme emphasizes the inherent equality of both constituent and abstract data, thus avoiding problems arising from the distinction between "abstract" and "concrete". In this sense the process of abstraction entails the identification of similarities between objects and the process of associating these objects with an abstraction (which is itself an object). For example, picture 1 above illustrates the concrete relationship "Cat sits on Mat". Chains of abstractions can therefore be constructed moving from neural impulses arising from sensory perception to basic abstractions such as color or shape to experiential abstractions such as a specific cat to semantic abstractions such as the "idea" of a CAT to classes of objects such as "mammals" and even categories such as "object" as opposed to "action". For example, graph 1 above expresses the abstraction "agent sits on location". This conceptual scheme entails no specific hierarchical taxonomy (such as the one mentioned involving cats and mammals), only a progressive exclusion of detail. Abstraction 4

The neurology of abstraction A recent meta-analysis suggests that the verbal system has greater engagement for abstract concepts when the perceptual system is more engaged for processing of concrete concepts. This is because abstract concepts elicit greater brain activity in the inferior frontal gyrus and middle temporal gyrus compared to concrete concepts when concrete concepts elicit greater activity in the posterior cingulate, precuneus, fusiform gyrus, and parahippocampal gyrus.[4] Other research into the human brain suggests that the left and right hemispheres differ in their handling of abstraction. For example, one meta-analysis reviewing human brain lesions has shown a left hemisphere bias during tool usage.[5]

Abstraction in art Typically, abstraction is used in the arts as a synonym for abstract art in general. Strictly speaking, it refers to art unconcerned with the literal depiction of things from the visible world[6] —it can, however, refer to an object or image which has been distilled from the real world, or indeed, another work of art. Artwork that reshapes the natural world for expressive purposes is called abstract; that which derives from, but does not imitate a recognizable subject is called nonobjective abstraction. In the 20th century the trend toward abstraction coincided with advances in science, technology, and changes in urban life, eventually reflecting an interest in psychoanalytic theory.[7] Later still, abstraction was manifest in more purely formal terms, such as color, freed from objective context, and a reduction of form to basic geometric designs.[8] In music, the term abstraction can be used to describe improvisatory approaches to interpretation, and may sometimes indicate abandonment of tonality. Atonal music has no key signature, and is characterized the exploration of internal numeric relationships.[9]

Abstraction in psychology Carl Jung's definition of abstraction broadened its scope beyond the thinking process to include exactly four mutually exclusive, opposing complementary psychological functions: sensation, intuition, feeling, and thinking. Together they form a structural totality of the differentiating abstraction process. Abstraction operates in one of these opposing functions when it excludes the simultaneous influence of the other functions and other irrelevancies, such as emotion. Abstraction requires selective use of this structural split of abilities in the psyche. The opposite of abstraction is concretism. Abstraction is one of Jung's 57 definitions in Chapter XI of Psychological Types. There is an abstract thinking, just as there is abstract feeling, sensation and intuition. Abstract thinking singles out the rational, logical qualities ... Abstract feeling does the same with ... its feeling-values. ... I put abstract feelings on the same level as abstract thoughts. ... Abstract sensation would be aesthetic as opposed to sensuous sensation and abstract intuition would be symbolic as opposed to fantastic intuition. (Jung, [1921] (1971):par. 678). Abstraction 5

Abstraction in computer science Computer scientists use abstraction to understand and solve problems and communicate their solutions with the computer in some particular computer language.

Abstraction in mathematics Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. The advantages of abstraction in mathematics are: • it reveals deep connections between different areas of mathematics • known results in one area can suggest conjectures in a related area • techniques and methods from one area can be applied to prove results in a related area The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

See also

• Abstract art • Leaky abstraction • Abstract structure • List of thinking-related topics • Abstract (summary) • Model (abstract) • Abstract interpretation • Object of the mind • Abstract object • Ontology • Gottlob Frege • Charles Sanders Peirce • Hypostatic abstraction • Platonic realism • Portal: thinking • Symbolism (disambiguation)

Bibliography • Eugene Raskin, Architecturally Speaking, 2nd edition, a Delta book, Dell (1966), trade paperback, 129 pages • The American Heritage Dictionary of the English Language, 3rd edition, Houghton Mifflin (1992), hardcover, 2140 pages, ISBN 0-395-44895-6 • Jung, C.G. [1921] (1971). Psychological Types, Collected Works, Volume 6, Princeton, NJ: Princeton University Press. ISBN 0-691-01813-8. Abstraction 6

External links • Internet Encyclopedia of Philosophy: Gottlob Frege [10] • Stanford Encyclopedia of Philosophy: Abstract Objects [11] • Discussion at The Well concerning Abstraction hierarchy [12]

References

[1] Abstract Engravings Show Modern Behavior Emerged Earlier Than Previously Thought (http:/ / www. scienceinafrica. co. za/ 2002/ january/

ochre. htm)

[2] Ancient Engravings Push Back Origin of Abstract Thought (http:/ / www. sciam. com/ article. cfm?articleID=000629D0-B23F-1CCE-B4A8809EC588EEDF) [3] But an idea can be symbolized. "A symbol is any device whereby we are enabled to make an abstraction." -- p.xi and chapter 20 of Suzanne K. Langer (1953), Feeling and Form: a theory of art developed from Philosophy in a New Key: New York: Charles Scribner's Sons. 431 pages, index. [4] Jing Wang, Julie A. Conder, David N. Blitzer, and Svetlana V. Shinkareva "Neural Representation of Abstract and Concrete Concepts: A

Meta-Analysis of Neuroimaging Studies" Human Brain Mapping (2010). http:/ / dx. doi. org/ 10. 1002/ hbm. 20950 [5] James W. Lewis "Cortical Networks Related to Human Use of Tools" 12 (3): 211-231 The Neuroscientist (June 1, 2006).

[6] Encyclopaedia Britannica (http:/ / www. britannica. com/ eb/ article-9003405/ abstract-art) [7] Catherine de Zegher and Hendel Teicher (eds.), 3 X Abstraction. NY/New Haven: The Drawing Center/Yale University Press. 2005. ISBN 0-300-10826-5

[8] National Gallery of Art: Abstraction. (http:/ / www. nga. gov/ education/ american/ abstract. shtm)

[9] Washington State University: Glossary of Abstraction. (http:/ / www. wsu. edu/ ~dee/ GLOSSARY/ ABSTRACT. HTM)

[10] http:/ / www. utm. edu/ research/ iep/ f/ frege. htm

[11] http:/ / plato. stanford. edu/ entries/ abstract-objects/

[12] http:/ / originresearch. com/ sd/ sd1. cfm

Analogy

Analogy (from Greek "ἀναλογία" - analogia, "proportion"[1] [2] ) is a cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. In a narrower sense, analogy is an inference or an argument from one particular to another particular, as opposed to deduction, induction, and abduction, where at least one of the premises or the conclusion is general. The word analogy can also refer to the relation between the source and the target themselves, which is often, though not necessarily, a similarity, as in the biological notion of analogy. Analogy 7

Analogy plays a significant role in problem solving, decision making, perception, memory, creativity, emotion, explanation and communication. It lies behind basic tasks such as the identification of places, objects and people, for example, in face perception and facial recognition systems. It has been argued that analogy is "the core of cognition".[3] Specific analogical language comprises exemplification, comparison s, metaphors, similes, allegories, and parables, but not metonymy. Phrases like and so on, and the like, as if, and the very word like also rely on an analogical understanding by the receiver of a message including them. Analogy is important not only in ordinary language and common sense (where proverbs and idioms give many examples of its application) but also in science, philosophy and the humanities. Niels Bohr's model of the atom, though inaccurate, The concepts of association, comparison, correspondence, made an analogy between the atom and the solar mathematical and morphological homology, homomorphism, system. iconicity, isomorphism, metaphor, resemblance, and similarity are closely related to analogy. In cognitive linguistics, the notion of conceptual metaphor may be equivalent to that of analogy.

Analogy has been studied and discussed since classical antiquity by philosophers, scientists and lawyers. The last few decades have shown a renewed interest in analogy, most notable in cognitive science.

Usage of the terms source and target With respect to the terms source and target there are two distinct traditions of usage: • The logical and mathematical tradition speaks of an arrow, homomorphism, mapping, or morphism from what is typically the more complex domain or source to what is typically the less complex codomain or target, using all of these words in the sense of mathematical category theory. • The tradition that appears to be more common in cognitive psychology, literary theory, and specializations within philosophy outside of logic, speaks of a mapping from what is typically the more familiar area of experience, the source, to what is typically the more problematic area of experience, the target.

Models and theories

Identity of relation In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio. From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant's Critique of Judgment held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the US-based SAT tests, that included "analogy questions" in the form "A is to B as C is to what?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format: HAND : PALM : : FOOT : ____ While most competent English speakers will immediately give the right answer to the analogy question (sole), it is more difficult to identify and describe the exact relation that holds both between hand and palm, and between foot and sole. This relation is not apparent in some lexical definitions of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot. Analogy and abstraction are different cognitive Analogy 8

processes, and analogy is often an easier one. Recently a computer algorithm has achieved human-level performance on multiple-choice analogy questions from the SAT test.[4] The algorithm measures the similarity of relations between pairs of words (e.g., the similarity between the pairs HAND:PALM and FOOT:SOLE) by statistical analysis of a large collection of text. It answers SAT questions by selecting the choice with the highest relational similarity.

Shared abstraction

Greek philosophers such as Plato and Aristotle actually used a wider notion of analogy. They saw analogy as a shared abstraction.[5] Analogous objects did not share necessarily a relation, but also an idea, a pattern, a regularity, an attribute, an effect or a function. These authors also accepted that comparisons, metaphors and "images" (allegories) could be used as arguments, and sometimes they called them analogies. Analogies should also make those abstractions easier to understand and give

confidence to the ones using them. In several cultures, the sun is the source of an analogy to God.

The Middle Ages saw an increased use and theorization of analogy. Roman lawyers had already used analogical reasoning and the Greek word analogia. Medieval lawyers distinguished analogia legis and analogia iuris (see below). In Islamic logic, analogical reasoning was used for the process of Qiyas in Islamic sharia law and fiqh jurisprudence. In Christian theology, analogical arguments were accepted in order to explain the attributes of God. Aquinas made a distinction between equivocal, univocal and analogical terms, the latter being those like healthy that have different but related meanings. Not only a person can be "healthy", but also the food that is good for health (see the contemporary distinction between polysemy and homonymy). Thomas Cajetan wrote an influential treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved.

Special case of induction On the contrary, Ibn Taymiyya,[6] [7] [8] Francis Bacon and later John Stuart Mill argued that analogy is simply a special case of induction.[5] In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form: Premises a is C, D, E, F, G b is C, D, E, F Conclusion b is probably G. Alternative conclusion every C, D, E, F is probably G. This view does not accept analogy as an autonomous mode of thought or inference, reducing it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, Analogy 9

while analogy looks for particular ones.

Hidden deduction The opposite move could also be tried, reducing analogy to deduction. It is argued that every analogical argument is partially superfluous and can be rendered as a deduction stating as a premise a (previously hidden) universal proposition which applied both to the source and the target. In this view, instead of an argument with the form: Premises a is analogous to b. b is F. Conclusion a is plausibly F. We should have: Hidden universal premise all Gs are plausibly Fs. Hidden singular premise a is G. Conclusion a is plausibly F. This would mean that premises referring the source and the analogical relation are themselves superfluous. However, it is not always possible to find a plausibly true universal premise to replace the analogical premises.[9] And analogy is not only an argument, but also a distinct cognitive process.

Shared structure

Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by Gentner's (1983) structure mapping theory.[10] The same idea of mapping between source and target is used by conceptual metaphor theorists. Structure mapping theory concerns both psychology and computer science. According to this

According to Shelley (2003), the study of the coelacanth drew heavily on analogies view, analogy depends on the mapping or from other fish. alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target. Structure mapping theory has been applied and has found considerable confirmation in psychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as metaphor and similarity.[11]

Keith Holyoak and Paul Thagard (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "coherence" of an analogy depends on structural consistency, semantic similarity and purpose. Structural consistency is maximal when the analogy is an isomorphism, although lower levels are admitted. Analogy 10

Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose insofar as it helps solve the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome.[5] Hummel and Holyoak (2005) recast the multiconstraint theory within a neural network architecture. A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some identical attributes or relations at some level of abstraction. Human analogy does not, or at least not apparently. Mark T. Keane and Brayshaw (1988) developed their Incremental Analogy Machine (IAM) to include working memory constraints as well as structural, semantic and pragmatic constraints, so that a subset of the base analog is selected and mapping from base to target occurs in a serial manner[12] [13] . Empirical evidence shows that human analogical mapping performance is influenced by information presentation order [14] .

High-level perception Douglas Hofstadter and his team[15] challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make representations by selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et al. conclude that analogy is high-level perception. Forbus et al. (1998) claim that this is only a metaphor. It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.

Analogy and Complexity Antoine Cornuéjols[16] has presented analogy as a principle of economy and computational complexity. Reasoning by analogy is a process of, from a given pair (x,f(x)), extrapolating the function f. In the standard modeling, analogical reasoning involves two "objects": the source and the target. The target is supposed to be incomplete and in need for a complete description using the source. The target has an existing part S and a missing t part R . We assume that we can isolate a situation of the source S , which corresponds to a situation of target S , and t s t the result of the source R , which correspond to the result of the target R . With B , the relation between S and R , we s t s s s want B , the relation between S and R . t t t If the source and target are completely known: Using Kolmogorov complexity K(x), defined as the size of the smallest description of x and Solomonoff's approach to induction, Rissanen (89),[17] Wallace & Boulton (68) proposed the principle of Minimum description length. This principle leads to minimize the complexity K(target| Source) of producing the target from the source. This is unattractive in Artificial Intelligence, as it requires a computation over abstract Turing machines. Suppose that M and M are local theories of the source and the target, available to the observer. The best analogy between a s t source case a and target case is the analogy that minimizes: K(M ) + K(S |M ) + K(B |M ) + K(M |M ) + K(S |M ) + K(B |M ) (1). s s s s s t s t t t t If the target is completely unknown: All models and descriptions M , M , B , S , and S leading to the minimization of: s t s s t K(M ) + K(S |M ) + K(B |M ) + K(M |M ) + K(S |M ) (2) s s s s s t s t t are also those who allow to obtain the relationship B , and thus the most satisfactory R for formula (1). t t The analogical hypothesis, which solves an analogy between a source case and a target case, has two parts: Analogy 11

• Analogy, like induction, is a principle of economy. The best analogy between two cases is the one which minimizes the amount of information necessary for the derivation of the source from the target (1). Its most fundamental measure is the computational complexity theory. • When solving or completing a target case with a source case, the parameters which minimize (2) are postulated to minimize (1), and thus, produce the best response. However, a cognitive agent may simply reduce the amount of information necessary for the interpretation of the source and the target, without taking into account the cost of data replication. So, it may prefer to the minimization of (2) the minimization of the following simplified formula: K(M ) + K(B |M ) + K(M |M ) (3). s s s t s

Applications and types

In language

Rhetoric • An analogy can be a spoken or textual comparison between two words (or sets of words) to highlight some form of semantic similarity between them. Such analogies can be used to strengthen political and philosophical arguments, even when the semantic similarity is weak or non-existent (if crafted carefully for the audience). Analogies are sometimes used to persuade those that cannot detect the flawed or non-existent arguments.

Linguistics • An analogy can be the linguistic process that reduces word forms perceived as irregular by remaking them in the shape of more common forms that are governed by rules. For example, the English verb help once had the preterite holp and the past participle holpen. These obsolete forms have been discarded and replaced by helped by the power of analogy (or by widened application of the productive Verb-ed rule.) This is called leveling. However, irregular forms can sometimes be created by analogy; one example is the American English past tense form of dive: dove, formed on analogy with words such as drive: drove. • Neologisms can also be formed by analogy with existing words. A good example is software, formed by analogy with hardware; other analogous neologisms such as firmware and vaporware have followed. Another example is the humorous term underwhelm, formed by analogy with overwhelm. • Analogy is often presented as an alternative mechanism to generative rules for explaining productive formation of structures such as words. Others argue that in fact they are the same mechanism, that rules are analogies that have become entrenched as standard parts of the linguistic system, whereas clearer cases of analogy have simply not (yet) done so (e.g. Langacker 1987.445-447). This view has obvious resonances with the current views of analogy in cognitive science which are discussed above.

In science Analogues are often used in theoretical and applied sciences in the form of models or simulations which can be considered as strong analogies. Other much weaker analogies assist in understanding and describing functional behaviours of similar systems. For instance, an analogy commonly used in electronics textbooks compares electrical circuits to hydraulics. Another example is the analog ear based on electrical, electronic or mechanical devices.

Mathematics Some types of analogies can have a precise mathematical formulation through the concept of isomorphism. In detail, this means that given two mathematical structures of the same type, an analogy between them can be thought of as a bijection between them which preserves some or all of the relevant structure. For example, and are isomorphic as vector spaces, but the complex numbers, , have more structure than does - is a field as Analogy 12

well as a vector space. Category theory takes the idea of mathematical analogy much further with the concept of functors. Given two categories C and D a functor F from C to D can be thought of as an analogy between C and D, because F has to map objects of C to objects of D and arrows of C to arrows of D in such a way that the compositional structure of the two categories is preserved. This is similar to the structure mapping theory of analogy of Dedre Gentner, in that it formalizes the idea of analogy as a function which satisfies certain conditions.

Artificial intelligence See case-based reasoning.

Anatomy See also: Analogy (biology) In anatomy, two anatomical structures are considered to be analogous when they serve similar functions but are not evolutionarily related, such as the legs of vertebrates and the legs of insects. Analogous structures are the result of convergent evolution and should be contrasted with homologous structures.

Engineering Often a physical prototype is built to model and represent some other physical object. For example, wind tunnels are used to test scale models of wings and aircraft, which act as an analog to full-size wings and aircraft. For example, the MONIAC (an analog computer) used the flow of water in its pipes as an analog to the flow of money in an economy.

In normative matters

Morality Analogical reasoning plays a very important part in morality. This may be in part because morality is supposed to be impartial and fair. If it is wrong to do something in a situation A, and situation B is analogous to A in all relevant features, then it is also wrong to perform that action in situation B. Moral particularism accepts analogical moral reasoning, rejecting both deduction and induction, since only the former can do without moral principles.

Law In law, analogy is used to resolve issues on which there is no previous authority. A distinction has to be made between analogous reasoning from written law and analogy to precedent case law.

Analogies from codes and statutes In civil law systems, where the preeminent source of law is legal codes and statutes, a lacuna (a gap) arises when a specific issue is not explicitly dealt with in written law. Judges will try to identify a provision whose purpose applies to the case at hand. That process can reach a high degree of sophistication, as judges sometimes not only look at a specific provision to fill lacunae (gaps), but at several provisions (from which an underlying purpose can be inferred) or at general principles of the law to identify the legislator's value judgement from which the analogy is drawn. Besides the not very frequent filling of lacunae, analogy is very commonly used between different provisions in order to achieve substantial coherence. Analogy from previous judicial decisions is also common, although these decisions are not binding authorities. Analogy 13

Analogies from precedent case law By contrast, in common law systems, where precedent cases are the primary source of law, analogies to codes and statutes are rare (since those are not seen as a coherent system, but as incursions into the common law). Analogies are thus usually drawn from precedent cases: The judge finds that the facts of another case are similar to the one at hand to an extent that the analogous application of the rule established in the previous case is justified.

See also • List of thinking-related topics • Conceptual metaphor • Conceptual blending • False analogy • Portal: thinking • Metaphor • Allegory

References • Chalmers, D.J. et al. (1991). Chalmers, D.J., French, R.M., Hofstadter, D., High-Level Perception, Representation, and Analogy [18]. • Cornuéjols, A. (1996). Analogie, principe d’économie et complexité algorithmique [19]. In Actes des 11èmes Journées Françaises de l’Apprentissage. Sète. • Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. [20] Cognitive Science, 7, 155-170. (Reprinted in A. Collins & E. E. Smith (Eds.), Readings in cognitive science: A perspective from psychology and artificial intelligence. Palo Alto, CA: Kaufmann). • Forbus, K. et al. (1998). Analogy just looks like high-level perception [21]. • Gentner, D., Holyoak, K.J., Kokinov, B. (Eds.) (2001). The Analogical Mind: Perspectives from Cognitive Science. [22] Cambridge, MA, MIT Press, ISBN 0-262-57139-0 • Hofstadter, D. (2001). Analogy as the Core of Cognition [23], in Dedre Gentner, Keith Holyoak, and Boicho Kokinov (eds.) The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: The MIT Press/Bradford Book, 2001, pp. 499–538. • Holland, J.H., Holyoak, K.J., Nisbett, R.E., and Thagard, P. (1986). Induction: Processes of Inference, Learning, and Discovery [24]. Cambridge, MA, MIT Press, ISBN 0-262-58096-9. • Holyoak, K.J., and Thagard, P. (1995). Mental Leaps: Analogy in Creative Thought [25]. Cambridge, MA, MIT Press, ISBN 0-262-58144-2. • Holyoak, K.J., and Thagard, P. (1997). The Analogical Mind [26]. • Hummel, J.E., and Holyoak, K.J. (2005). Relational Reasoning in a Neurally Plausible Cognitive Architecture [27] • Itkonen, E. (2005). Analogy as Structure and Process. Amsterdam/Philadelphia: John Benjamins Publishing Company. • Juthe, A. (2005). "Argument by Analogy" [28], in Argumentation (2005) 19: 1–27. • Keane, M.T. Ledgeway, T. & Duff, S, (1994). Constraints on analogical mapping: a comparison of three models. Cognitive Science, 18, 287-334. • Keane, M.T. (1997). What makes an analogy difficult? The effects of order and causal structure in analogical mapping. Journal of Experimental Psychology: Learning, Memory and Cognition, 123, 946-967 • Kokinov, B. (1994). "A hybrid model of reasoning by analogy." [29] • Kokinov, B. and Petrov, A. (2001). "Integration of Memory and Reasoning in Analogy-Making." [30] • Lamond, G. (2006). Precedent and Analogy in Legal Reasoning [31], in Stanford Encyclopedia of Philosophy. Analogy 14

• Langacker, Ronald W. (1987). Foundations of Cognitive grammar. Vol. I, Theoretical prerequisites. Stanford: Stanford University Press. • Little, J. (2000). Analogy in Science: Where Do We Go From Here? Rhetoric Society Quarterly, 30, 69-92. • Little, J. (2008). The Role of Analogy in George Gamow's Derivation of Drop Energy. Technical Communication Quarterly, 17, 1-19. • Morrison, C., and Dietrich, E. (1995). Structure-Mapping vs. High-level Perception [32]. • Shelley, C. (2003). Multiple analogies in Science and Philosophy. Amsterdam/Philadelphia: John Benjamins Publishing Company. • Turney, P.D., and Littman, M.L. (2005). Corpus-based learning of analogies and semantic relations [33]. Machine Learning, 60 (1-3), 251-278. • Turney, P.D. (2006). Similarity of semantic relations [34]. Computational Linguistics, 32 (3), 379-416. • Cornuéjols, A. (1996). Analogy, principle of economy and computational complexity [19].

External links • Dictionary of the History of Ideas: [35] Analogy in Early Greek Thought. • Dictionary of the History of Ideas: [36] Analogy in Patristic and Medieval Thought. • Stanford Encyclopedia of Philosophy: [37] Medieval Theories of Analogy. • Dedre Gentner's publications page [38], most of them on analogy and available for download. • Shawn Glynn’s publications page [39], all on teaching with analogies and some available for download. • Keith Holyoak's publications page [40], many on analogy and available for download. • Boicho Kokinov's publications page [41], most of them on analogy and available for download. • jMapper - Java Library for Analogy/Metaphor Generation [42]

References

[1] ἀναλογία (http:/ / www. perseus. tufts. edu/ hopper/ text?doc=Perseus:text:1999. 04. 0057:entry=a)nalogi/ a), Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus Digital Library

[2] analogy (http:/ / www. etymonline. com/ index. php?term=analogy), Online Etymology Dictionary [3] Hofstadter in Gentner et al. 2001. [4] Turney 2006 [5] Shelley 2003 [6] Hallaq, Wael B. (1985-1986), "The Logic of Legal Reasoning in Religious and Non-Religious Cultures: The Case of Islamic Law and the Common Law", Cleveland State Law Review 34: 79-96 [93-5]

[7] Ruth Mas (1998). "Qiyas: A Study in Islamic Logic" (http:/ / www. colorado. edu/ ReligiousStudies/ faculty/ mas/ LOGIC. pdf). Folia Orientalia 34: 113–128. ISSN 0015-5675. .

[8] John F. Sowa; Arun K. Majumdar (2003). "Analogical reasoning" (http:/ / www. jfsowa. com/ pubs/ analog. htm). . Berlin: Springer-Verlag. ., pp. 16-36 [9] See Juthe 2005 [10] See Dedre Gentner et al. 2001 [11] See Gentner et al. 2001 and Gentner's publication page. [12] Keane, M.T. and Brayshaw, M. (1988). The Incremental Analogical Machine: a computational model of analogy. In D. Sleeman (Ed). European working session on learning. (pp.53-62). London: Pitman. [13] Keane, M.T. Ledgeway, T. & Duff, S, (1994). Constraints on analogical mapping: a comparison of three models. Cognitive Science, 18, 287-334. [14] Keane, M.T. (1997). What makes an analogy difficult? The effects of order and causal structure in analogical mapping. Journal of Experimental Psychology: Learning, Memory and Cognition, 123, 946-967 [15] See Chalmers et al. 1991

[16] Cornuéjols, A. (1996). Analogie, principe d’économie et complexité algorithmique (http:/ / www. lri. fr/ ~antoine/ Papers/ JFA96-final-osX. pdf). In Actes des 11èmes Journées Françaises de l’Apprentissage. Sète. [17] Rissanen J. (1989) : Stochastical Complexity and Statistical Inquiry. World Scientific Publishing Company, 1989.

[18] http:/ / consc. net/ papers/ highlevel. pdf

[19] http:/ / www. lri. fr/ ~antoine/ Papers/ JFA96-final-osX. pdf

[20] http:/ / groups. psych. northwestern. edu/ gentner/ papers/ Gentner83. pdf Analogy 15

[21] http:/ / www. psych. northwestern. edu/ psych/ people/ faculty/ gentner/ newpdfpapers/ ForbusGentner98. pdf

[22] http:/ / cognet. mit. edu/ library/ books/ view?isbn=0262571390

[23] http:/ / prelectur. stanford. edu/ lecturers/ hofstadter/ analogy. html

[24] http:/ / cognet. mit. edu/ library/ books/ view?isbn=0262580969

[25] http:/ / cognet. mit. edu/ library/ books/ view?isbn=0262581442

[26] http:/ / cogsci. uwaterloo. ca/ Articles/ Pages/ Analog. Mind. html

[27] http:/ / reasoninglab. psych. ucla. edu/ KH%20pdfs/ hummel& holyoak_cdips_2005. pdf

[28] http:/ / www. cs. hut. fi/ Opinnot/ T-93. 850/ 2005/ Papers/ juthe2005-analogy. pdf

[29] http:/ / nbu. bg/ cogs/ personal/ kokinov/ ambr94. pdf

[30] http:/ / nbu. bg/ cogs/ personal/ kokinov/ Analogy& Memory(2002). pdf

[31] http:/ / plato. stanford. edu/ entries/ legal-reas-prec/

[32] http:/ / eksl. cs. umass. edu/ ~clayton/ publications/ CogSci95/ SM-v-HLP. pdf

[33] http:/ / arxiv. org/ abs/ cs. LG/ 0508103

[34] http:/ / arxiv. org/ abs/ cs. CL/ 0608100

[35] http:/ / etext. lib. virginia. edu/ cgi-local/ DHI/ dhi. cgi?id=dv1-09

[36] http:/ / etext. lib. virginia. edu/ cgi-local/ DHI/ dhi. cgi?id=dv1-10

[37] http:/ / plato. stanford. edu/ entries/ analogy-medieval/

[38] http:/ / www. psych. northwestern. edu/ psych/ people/ faculty/ gentner/ publications2. htm

[39] http:/ / www. coe. uga. edu/ twa/

[40] http:/ / reasoninglab. psych. ucla. edu/ KeithPublications. htm

[41] http:/ / nbu. bg/ cogs/ personal/ kokinov/ index. html

[42] http:/ / student. dei. uc. pt/ ~racosta/ jmapper

Bricolage

Bricolage (pronounced /ˌbriːkɵˈlɑːʒ/ or /ˌbrɪkɵˈlɑːʒ/) is a term used in several disciplines, among them the visual arts and literature, to refer to the construction or creation of a work from a diverse range of things that happen to be available, or a work created by such a process. The term is borrowed from the French word bricolage, from the verb bricoler, the core meaning in French being, "fiddle, tinker" and, by extension, "to make creative and resourceful use of whatever materials are at hand (regardless of their original purpose)". In contemporary French the word is the equivalent of the English do it yourself, and is seen on large shed retail outlets throughout France. A person who engages in bricolage is a bricoleur.

Art • Michel Gondry, music video producer.

Music Instrumental bricolage in music includes the use of found objects as instruments, such as in the cases of: • Irish Spoons • Australian slap bass made from a tea chest • comb and wax paper for humming through • gumleaf humming • Largophone (made from a stick and bottle tops) • Trinidadian Steel drums (made from industrial storage drums) • African drums and thumb pianos made from recycled pots and pans. • American super instruments made from recorders and bicycle bells or metal rods and keys • Stomp (dance troupe) is an example of the use of bricolage in music and dance. They utilize everyday objects, such as trash cans and broom sticks, to produce music. Stylistic bricolage is the inclusion of common musical devices with new uses. Shuker writes "Punk best emphasized such stylistic bricolage".[1] Bricolage 16

Musical Bricolage flourishes in music of sub-cultures where: • experimentation is part of daily life (pioneers, immigrants, artistic communities), • access to resources is limited (such as in remote, discriminated or financially disconnected sub-cultures) which limits commercial influence (e.g. acoustic performers, gypsies, ghetto music, hippie, folk or traditional musicians) and • there is a political or social drive to seek individuality (e.g. Rap music, peace-drives, drummers circles) Unlike other bricolage fields the intimate knowledge of resources is not necessary. Many punk musicians, for instance, are not musically trained, since training can discourage creativity in preference for accuracy. Also, careful observation and listening is not necessary, it is common in spontaneous music to welcome 'errors' and disharmony. Like other bricolage fields, Bricolage music still values trusting one's ideas and self-correcting structures such as targeted audiences.

Visual art In art, bricolage is a technique where works are constructed from various materials available or on hand, and is seen as a characteristic of postmodern works. These materials may be mass-produced or "junk". See also: Merz, polystylism, collage, assemblage. Bricolage can also be applied to theatrical form of improvisation. More commonly known as Improv. The idea of using one's environment and materials which are at hand is the main goal in Improv. The environment is the stage and the materials are often pantomimed. The use of the stage and the imaginary materials are all made up on the spot so the materials which are at hand ar actually things that the players know from past experiences. (i.e. an improvisation of ordering fast food: One player would start with the common phrase "How May I help You"). Bricolage is also applied in interior design, through blending styles and accessorizing spaces with what is "on hand". Many designers use bricolage to come up with innovative and unique ideas.

Academics

Cultural studies In cultural studies bricolage is used to mean the processes by which people acquire objects from across social divisions to create new cultural identities. In particular, it is a feature of subcultures such as, for example, the punk movement. Here, objects that possess one meaning (or no meaning) in the dominant culture are acquired and given a new, often subversive meaning. For example, the safety pin became a form of decoration in punk culture.

Philosophy In his book The Savage Mind (1962, English translation 1966), French anthropologist Claude Lévi-Strauss used the word 'bricolage to describe any spontaneous action, further extending this to include the characteristic patterns of mythological thought. The reasoning here being that, since mythological thought is all generated by human imagination, it is based on personal experience, and so the images and entities generated through 'mythological thought' rise from pre-existing things in the imaginer's mind.[2] Jacques Derrida extends this notion to any discourse. "If one calls bricolage the necessity of borrowing one's concept from the text of a heritage which is more or less coherent or ruined, it must be said that every discourse is bricoleur." [3]

Gilles Deleuze and Félix Guattari, in their 1972 book Anti-Oedipus, identify bricolage as the characteristic mode of production of the schizophrenic producer.[4] Bricolage 17

Biology In biology the biologist François Jacob uses the term bricolage to describe the apparently cobbled-together character of much biological structure (cf. kludge), and views it as a consequence of the evolutionary history of the organism.[5]

Education In the discussion of constructionism, Seymour Papert discusses two styles of solving problems. Contrary to the analytical style of solving problems he describes bricolage as a way to learn and solve problems by trying, testing, playing around. Joe L. Kincheloe has used the term bricolage in educational research to denote the use of multiperspectival research methods. In Kincheloe's conception of the research bricolage, diverse theoretical traditions are employed in a broader critical theoretical/critical pedagogical context to lay the foundation for a transformative mode of multimethodological inquiry. Using these multiple frameworks and methodologies researchers are empowered to produce more rigorous and praxiological insights into socio-political and educational phenomena. Kincheloe theorizes a critical multilogical epistemology and critical connected ontology to ground the research bricolage. These philosophical notions provide the research bricolage with a sophisticated understanding of the complexity of knowledge production and the interrelated complexity of both researcher positionality and phenomena in the world. Such complexity demands a more rigorous mode of research that is capable of dealing with the complications of socio-educational experience. Such a critical form of rigor avoids the reductionism of many monological, mimetic research orientations (see Kincheloe, 2001, 2005; Kincheloe & Berry, 2004).

Popular culture

Fashion In his essay "Subculture: The Meaning of Style", Dick Hebdige discusses how an individual can be identified as a bricoleur when they "appropriated another range of commodities by placing them in a symbolic ensemble which served to erase or subvert their original straight meanings".[6] The fashion industry uses bricolage-like styles by incorporating items typically utilized for other purposes. For example, candy wrappers are woven together to produce a purse [7]. The movie Zoolander parodies this interesting concept with Mugatu's Derelicte, a line of clothing made from trash.

Television MacGyver is a television series in which the protagonist is the paragon of a bricoleur,[8] creating solutions for the problem to be solved out of immediately available found objects. The A-Team is another example of bricoleur, with the team often finding themselves in situation which required creating, mainly weapons, out of any objects available. The Wombles, a children's program based on creatures living in Wimbledon Common, is also a fine example of bricoleur. In the theme song composed by Mike Batt, the lyrics include "making good use of the things that they find, things that the everyday folk leave behind". Bricolage 18

Information technology

Information systems In information systems, bricolage is used by Claudio Ciborra to describe the way in which strategic information systems (SIS) can be built in order to maintain successful competitive advantage over a longer period of time than standard SIS. By valuing tinkering and allowing SIS to evolve from the bottom-up, rather than implementing it from the top-down, the firm will end up with something that is deeply rooted in the organisational culture that is specific to that firm and is much less easily imitated.[9] There is also a content management system called Bricolage.

Internet In her book Life on the Screen (1995), Sherry Turkle discusses the concept of bricolage as it applies to problem solving in code projects and workspace productivity. She advocates the "bricoleur style" of programming as a valid and underexamined alternative to what she describes as the conventional structured "planner" approach. In this style of coding, the programmer works without an exhaustive preliminary specification, opting instead for a step-by-step growth and re-evaluation process. In her essay Epistemological Pluralism [10], Turkle writes: "The bricoleur resembles the painter who stands back between brushstrokes, looks at the canvas, and only after this contemplation, decides what to do next."

Business

Organization and management Karl Weick identifies the following requirements for successful bricolage in organizations.[11] • intimate knowledge of resources • careful observation and listening • trusting one's ideas • self-correcting structures, with feedback

See also • Collage • Do it yourself • Syncretic

External links • Bricolage Wiki [12]

References [1] Shuker Popular Music: Key Concepts 1988 [2] Claude Lévi-Strauss, La Pensée sauvage (Paris, 1962). English translation as The Savage Mind (Chicago, 1966). ISBN 0-226-47484-4. See

also (http:/ / tesugen. com/ archives/ 03/ 08/ bricolage) (http:/ / varenne. tc. columbia. edu/ bib/ info/ levstcld066savamind. html)

[3] Jacques Derrida, "Structure, Sign, and Play in the Discourse of the Human Sciences" (http:/ / hydra. humanities. uci. edu/ derrida/ sign-play. html) [4] Gilles Deleuze and Félix Guattari, Anti-Oedipus: Capitalism and Schizophrenia. Trans. Robert Hurley, Mark Seem, and Helen R. Lane. Continuum edition. London: Continuum, 2004 (1972). p.7-8. [5] Molino, Jean (2000). "Toward an Evolutionary Theory of Music and Language", The Origins of Music. Cambridge, Mass: A Bradford Book,

The MIT Press. ISBN 0-262-23206-5. (p.169). See also "Bicoid, nanos, and bricolage" (http:/ / pharyngula. org/ index/ weblog/ comments/ Bricolage 19

bicoid_nanos_and_bricolage/ ) by PZ Myers. [6] "Subculture: The Meaning of Style". Dick Hebdige. Cultural Studies: An Anthology. Ed. Michael Ryan. 2008. Pg. 592

[7] http:/ / www. ecoist. com/ pc/ catalog/ UL%20(01)_md. jpg

[8] Ian Bogost, Comparative Video Game Criticism (http:/ / gac. sagepub. com/ cgi/ content/ abstract/ 1/ 1/ 41), Games and Culture, Vol. 1, No. 1, 41-46 (2006). [9] Ciborra, Claudio (1992). "From Thinking to Tinkering: The Grassroots of Strategic Information Systems", The Information Society 8, 297-309

[10] http:/ / www. papert. org/ articles/ EpistemologicalPluralism. html [11] Karl Weick, "Organizational Redesign as Improvisation", reprinted in Making Sense of the Organization

[12] http:/ / wiki. bricolage. cc

Categorization

Categorization is the process in which ideas and objects are recognized, differentiated and understood. Categorization implies that objects are grouped into categories, usually for some specific purpose. Ideally, a category illuminates a relationship between the subjects and objects of knowledge. Categorization is fundamental in language, prediction, inference, decision making and in all kinds of environmental interaction. There are many categorization theories and techniques. In a broader historical view, however, three general approaches to categorization may be identified: • Classical categorization • Conceptual clustering • Prototype theory

The classical view Classical categorization comes to us first from Plato, who, in his Statesman dialogue, introduces the approach of grouping objects based on their similar properties. This approach was further explored and systematized by Aristotle in his Categories treatise, where he analyzes the differences between classes and objects. Aristotle also applied intensively the classical categorization scheme in his approach to the classification of living beings (which uses the technique of applying successive narrowing questions such as "Is it an animal or vegetable?", "How many feet does it have?", "Does it have fur or feathers?", "Can it fly?"...), establishing this way the basis for natural taxonomy. The classical Aristotelian view claims that categories are discrete entities characterized by a set of properties which are shared by their members. In analytic philosophy, these properties are assumed to establish the conditions which are both necessary and sufficient conditions to capture meaning. According to the classical view, categories should be clearly defined, mutually exclusive and collectively exhaustive. This way, any entity of the given classification universe belongs unequivocally to one, and only one, of the proposed categories.

Conceptual clustering Conceptual clustering is a modern variation of the classical approach, and derives from attempts to explain how knowledge is represented. In this approach, classes (clusters or entities) are generated by first formulating their conceptual descriptions and then classifying the entities according to the descriptions. Conceptual clustering developed mainly during the 1980s, as a machine paradigm for unsupervised learning. It is distinguished from ordinary data clustering by generating a concept description for each generated category. Categorization tasks in which category labels are provided to the learner for certain objects are referred to as supervised classification, supervised learning, or concept learning. Categorization tasks in which no labels are supplied are referred to as unsupervised classification, unsupervised learning, or data clustering. The task of Categorization 20

supervised classification involves extracting information from the labeled examples that allows accurate prediction of class labels of future examples. This may involve the abstraction of a rule or concept relating observed object features to category labels, or it may not involve abstraction (e.g., exemplar models). The task of clustering involves recognizing inherent structure in a data set and grouping objects together by similarity into classes. It is thus a process of generating a classification structure. Conceptual clustering is closely related to fuzzy set theory, in which objects may belong to one or more groups, in varying degrees of fitness.

Prototype Theory Since the research by Eleanor Rosch and George Lakoff in the 1970s, categorization can also be viewed as the process of grouping things based on prototypes - the idea of necessary and sufficient conditions is almost never met in categories of naturally occurring things. It has also been suggested that categorization based on prototypes is the basis for human development, and that this learning relies on learning about the world via embodiment. A cognitive approach accepts that natural categories are graded (they tend to be fuzzy at their boundaries) and inconsistent in the status of their constituent members. Systems of categories are not objectively "out there" in the world but are rooted in people's experience. Conceptual categories are not identical for different cultures, or indeed, for every individual in the same culture. Categories form part of a hierarchical structure when applied to such subjects as taxonomy in biological classification: higher level: life-form level, middle level: generic or genus level, and lower level: the species level. These can be distinguished by certain traits that put an item in its distinctive category. But even these can be arbitrary and are subject to revision. Categories at the middle level are perceptually and conceptually the more salient. The generic level of a category tends to elicit the most responses and richest images and seems to be the psychologically basic level. Typical taxonomies in zoology for example exhibit categorization at the embodied level, with similarities leading to formulation of "higher" categories, and differences leading to differentiation within categories.

Miscategorisation Miscategorization can be a logical fallacy in which diverse and dissimilar objects, concepts, entities, etc. are grouped together based upon illogical common denominators, or common denominators that virtually any concept, object or entity have in common. A common way miscategorization occurs is through an over-categorization of concepts, objects or entities, and then miscategorization based upon overly-similar variables that virtually all things have in common.

See also • Category learning • Semantics • Symbol grounding • Library classification • Multi-label classification • Family resemblance • Socrates • Taxonomy • Ontology • Information architecture Categorization 21

External links • To Cognize is to Categorize: Cognition is Categorization [1] • Categories and Induction [2]

References

[1] http:/ / eprints. ecs. soton. ac. uk/ 11725/

[2] http:/ / www. javedabsar. com/ public/ pmwiki. php?n=Main. CognitivePsychology

Computational creativity

Computational creativity (also known as artificial creativity, mechanical creativity or creative computation) is a multidisciplinary endeavour that is located at the intersection of the fields of artificial intelligence, cognitive psychology, philosophy, and the arts. The goal of computational creativity is to model, simulate or replicate creativity using a computer, to achieve one of several ends: • to construct a program or computer capable of human-level creativity • to better understand human creativity and to formulate an algorithmic perspective on creative behavior in humans • to design programs that can enhance human creativity without necessarily being creative themselves The field of computational creativity concerns itself with theoretical and practical issues in the study of creativity. Theoretical work on the nature and proper definition of creativity is performed in parallel with practical work on the implementation of systems that exhibit creativity, with one strand of work informing the other.

Theoretical issues As measured by the amount of activity in the field (e.g., publications, conferences and workshops), computational creativity is a growing area of research. But the field is still hampered by a number of fundamental problems: • Creativity is very difficult, perhaps even impossible, to define in objective terms. • Creativity takes many forms in human activity, some eminent (meaning "recognized" or "ingenious", e.g., Einstein's creativity; sometimes referred to as "Creativity" with a capital C) and some mundane. • Creativity can mean different things in different contexts: Is it a state of mind, a talent or ability, or a process? Does it describe a person, an activity or an end-product? Can collaborative work in which exceptional products emerge from simple interactions be considered creative? These are problems that complicate the study of creativity in general, but certain problems attach themselves specifically to computational creativity: • Can creativity be hard-wired? In existing systems to which creativity is attributed, is the creativity that of the system or that of the system's programmer or designer? • How do we evaluate computational creativity? What counts as creativity in a computational system? Are natural language generation systems creative? Are machine translation systems creative? What distinguishes research in computational creativity from research in artificial intelligence generally? • If eminent creativity is about rule-breaking or the disavowal of convention, how is it possible for an algorithmic system to be creative? In essence, this is a variant of the Ada Lovelace objection to machine intelligence, as recapitulated by modern theorists such as Teresa Amabile:[1] If a machine can do only what it was programmed to do, how can its behavior ever be called creative? Computational creativity 22

Defining creativity in computational terms Since no single perspective or definition seems to offer a complete picture of creativity, the AI researchers Newell, Shaw and Simon [2] developed the combination of novelty and usefulness into the corner-stone of a multi-pronged view of creativity, one that uses the following four criteria to categorize a given answer or solution as creative: 1. The answer is novel and useful (either for the individual or for society) 2. The answer demands that we reject ideas we had previously accepted 3. The answer results from intense motivation and persistence 4. The answer comes from clarifying a problem that was originally vague Notice how these criteria touch on many of the stereotypical themes that are typically associated with creativity: newness and value (1), transformation and revolution (2), passion and drive (3), vision and insight (4). These four criteria also combine elements of the producer-perspective and the product-perspective described earlier: criterion (1) characterizes the two most important qualities of a creative product, while criteria (2) – (4) characterize the attitude and actions of the producer of such a product. A given product may satisfy all or none of these criteria, but we should expect products that exhibit all four to be widely perceived as creative, while products that exhibit just some of these criteria will be judged with greater subjectivity and variation. Though no criterion is likely to be either necessary or sufficient, criterion (1) is perhaps the most common hallmark of creativity and thus serves to anchor the others. From a computational perspective, then, one can consider (1) to be a must-have feature, and (2) – (4) as desirable extras. Newell and Simon[3] [4] are best known for their contribution to the search-in-a-state-space paradigm of AI, sometimes caricatured as Good Old Fashioned AI (GOFAI), and it is interesting to consider how the GOFAI paradigm can incorporate these criteria. From a search perspective, criterion (1) characterizes the goal or end-state of a computational search, criterion (4) characterizes the starting state from which the search is launched, criterion (3) characterizes the scale of the search, suggesting that many dead-ends are likely to be encountered, while criterion (2) suggests that well-worn pathways through the search space are best avoided if a creative end-state is to be reached.

Key ideas Some high-level and philosophical themes recur throughout the field of computational creativity.

P-creativity and H-creativity Margaret Boden[5] [6] refers to creativity that is novel merely to the agent that produces it as "P-creativity" (or "psychological creativity"), and refers to creativity that is recognized as novel by society at large as "H-creativity" (or "historical creativity").

Exploratory and transformational creativity Boden also distinguishes between the creativity that arises from an exploration within an established conceptual space, and the creativity that arises from a deliberate transformation or transcendence of this space. She labels the former as "exploratory creativity" and the latter as "transformational creativity", seeing the latter as a form of creativity far more radical, challenging, and rarer than the former. Following Newell and Simon’s criteria, we can see that both forms of creativity should produce results that are appreciably novel and useful (criterion 1), but exploratory creativity is more likely to arise from a thorough and persistent search of a well-understood space (criterion 3) while transformational creativity should involve the rejection of some of the constraints that define this space (criterion 2) or some of the assumptions that define the problem itself (criterion 4). Boden’s insights have guided work in computational creativity at a very general level, providing more an inspirational touchstone for development work than a technical framework of algorithmic substance. However, Boden’s insights are the subject of formalization, most notably in the work by Geraint Wiggins[7] . Computational creativity 23

Generation and evaluation The criterion that creative products should be novel and useful means that creative computational systems are typically structured into two phases, generation and evaluation. In the first phase, novel (to the system itself, thus P-Creative) constructs are generated; unoriginal constructs that are already known to the system are filtered at this stage. This body of potentially creative constructs are then evaluated, to determine which are meaningful and useful and which are not. This two-phase structure conforms to the Geneplore model of Finke, Ward and Smith[8] , which is a psychological model of creative generation based on empirical observation of human creativity.

Combinatorial creativity A great deal, perhaps all, of human creativity can be understood as a novel combination of pre-existing ideas or objects. Common strategies for combinatorial creativity include: • placing a familiar object in an unfamiliar setting (e.g., Marcel Duchamp's Fountain) or an unfamiliar object in a familiar setting (e.g., a fish-out-of-water story such as The Beverly Hillbillies) • Blending two superficially different objects or genres (e.g., a sci-fi story set in the Wild West, with robot cowboys, as in Westworld, or the reverse, as in Firefly; Jewish haiku poems, etc.) • Comparing a familiar object to a superficially unrelated and semantically distant concept (e.g., "Makeup is the Western burka"; "A zoo is a gallery with living exhibits") • Adding a new and unexpected feature to an existing concept (e.g., adding a scalpel to a Swiss Army knife; adding a camera to a mobile phone) • Compressing two incongruous scenarios into the same narrative to get a joke (e.g., the Emo Philips joke “Women are always using me to advance their careers. Damned anthropologists!”) • Using an iconic image from one domain in a domain for an unrelated or incongruous idea or product (e.g., using the Marlboro Man image to sell cars, or to advertise the dangers of smoking-related impotence). The combinatorial perspective allows us to model creativity as a search process through the space of possible combinations. The combinations can arise from composition or concatenation of different representations, or through a rule-based or stochastic transformation of initial and intermediate representations. Genetic algorithms and neural networks can be used to generate blended or crossover representations that capture a combination of different inputs.

Bisociation Arthur Koestler proposes a very general model of creative combination in his 1964 book The Act of Creation,[9] claiming that scientific discovery, art and humour are all linked by a common mechanism called "bisociation". Koestler lacked a formal, computational vocabulary for describing bisociation, which he defined as a reconciliation of two orthogonal matrices of thought (conceptual structures, mental spaces).

Conceptual blending Mark Turner and Gilles Fauconnier [10] [11] propose a model called Conceptual Integration Networks that elaborates upon the ideas of Koestler by synthesizing ideas from Cognitive Linguistic research into mental spaces and conceptual metaphors. Their basic model defines an integration network as four connected spaces: • A first input space (contains one conceptual structure or mental space) • A second input space (to be blended with the first input) • A generic space of stock conventions and image-schemas that allow the input spaces to be understood from an integrated perspective • A blend space in which a selected projection of elements from both input spaces are combined; inferences arising from this combination also reside here, sometimes leading to emergent structures that conflict with the inputs. Fauconnier and Turner describe a collection of optimality principles that are claimed to guide the construction of a well-formed integration network. In essence, they see blending as a compression mechanism in which two or more Computational creativity 24

input structures are compressed into a single blend structure. This compression operates on the level of conceptual relations. For example, a series of similarity relations between the input spaces can be compressed into a single identity relationship in the blend. Blending theory is an elaborate framework that provides a rich terminology for describing the products of creative thinking, from metaphors to jokes to neologisms to adverts. It is most typically applied retrospectively, to describe how a blended conceptual structure could have arisen from a particular pair of input structures. These conceptual structures are often good examples of human creativity, but blending theory is not a theory of creativity, nor – despite its authors’ claims – does it describe a mechanism for creativity. The theory lacks an explanation for how a creative individual chooses the input spaces that should be blended to generate a desired result. Nonetheless, some computational success has been achieved with the blending model by extending pre-existing computational models of analogical mapping that are compatible by virtue of their emphasis on connected semantic structures[12] . More recently, Francisco Câmara Pereira[13] presented an implementation of blending theory that employs ideas both from GOFAI and from genetic algorithms to realize some aspects of blending theory in a practical form; his example domains range from the linguistic to the visual, and the latter most notably includes the creation of mythical monsters by combining 3-D graphical models.

Linguistic creativity Language provides continuous opportunity for creativity, evident in the generation of novel sentences, phrasings, puns, neologisms, rhymes, allusions, sarcasm, irony, similes, metaphors, analogies, witticisms, and jokes. Native speakers of morphologically rich languages (including all Slavic languages) frequently create new word-forms that are easily understood, although they will never find their way to the dictionary. The area of natural language generation has been well studied, but these creative aspects of everyday language have yet to be incorporated with any robustness or scale.

Story generation Substantial work has been conducted in this area of linguistic creation since the 1970s, with the development of James Meehan's TALE-SPIN [14] system. TALE-SPIN viewed stories as narrative descriptions of a problem-solving effort, and created stories by first establishing a goal for the story’s characters so that their search for a solution could be tracked and recorded. The MINSTREL[15] system represents a complex elaboration of this basis approach, distinguishing a range of character-level goals in the story from a range of author-level goals for the story. Systems like Bringsjord's BRUTUS[16] elaborate these ideas further to create stories with complex inter-personal themes like betrayal. Nonetheless, MINSTREL explicitly models the creative process with a set of Transform Recall Adapt Methods (TRAMs) to create novel scenes from old. The MEXICA[17] model of Rafael Pérez y Pérez and Mike Sharples is more explicitly interested in the creative process of storytelling, and implements a version of the engagement-reflection cognitive model of creative writing.

Metaphor and simile Example of a metaphor: "She was an ape." Example of a simile: "Felt like a tiger-fur blanket." The computational study of these phenomena has mainly focused on interpretation as a knowledge-based process. Computationalists such as Yorick Wilks, James Martin,[18] Dan Fass, John Barnden,[19] and Mark Lee have developed knowledge-based approaches to the processing of metaphors, either at a linguistic level or a logical level. Tony Veale and Yanfen Hao have developed a system, called Sardonicus, that acquires a comprehensive database of explicit similes from the web; these similes are then tagged as bona-fide (e.g., "as hard as steel") or ironic (e.g., "as hairy as a bowling ball", "as pleasant as a root canal"); similes of either type can be retrieved on demand for any given adjective. They use these similes as the basis of an on-line metaphor generation system called Aristotle[20] that can suggest lexical metaphors for a given descriptive goal (e.g., Computational creativity 25

to describe a supermodel as skinny, the source terms “pencil”, “whip”, “whippet”, “rope”, “stick-insect” and “snake” are suggested).

Analogy The process of analogical reasoning has been studied from both a mapping and a retrieval perspective, the latter being key to the generation of novel analogies. The dominant school of research, as advanced by Dedre Gentner. views analogy as a structure-preserving process; this view has been implemented in the structure mapping engine or SME[21] , the MAC/FAC retrieval engine (Many Are Called, Few Are Chosen), ACME (Analogical Constraint Mapping Engine) and ARCS (Analogical Retrieval Constraint System). Other mapping-based approaches include Sapper[22] , which situates the mapping process in a semantic-network model of memory. Analogy is a very active sub-area of creative computation and creative cognition; active figures in this sub-area include Douglas Hofstadter, Paul Thagard, and Keith Holyoak. Also worthy of note here is Peter Turney and Michael Littman's machine learning approach to the solving of SAT-style analogy problems; their approach achieves a score that compares well with average scores achieved by humans on these tests.

Joke generation Humour is an especially knowledge-hungry process, and the most successful joke-generation systems to date have focussed on pun-generation, as exemplified by the work of Kim Binsted and Graeme Ritchie.[23] This work includes the JAPE system, which can generate a wide range of puns that are consistently evaluated as novel and humorous by young children. An improved version of JAPE has been developed in the guise of the STANDUP system, which has been experimentally deployed as a means of enhancing linguistic interaction with children with communication disabilities. Some limited progress has been made in generating humour that involves other aspects of natural language, such as the deliberate misunderstanding of pronominal reference (in the work of Hans Wim Tinholt and Anton Nijholt), as well as in the generation of humorous acronyms in the HAHAcronym system[24] of Oliviero Stock and Carlo Strapparava.

Neologisms The blending of multiple word forms is a dominant force for new word creation in language; these new words are commonly called "blends" or "portmanteau words" (after Lewis Carroll). Tony Veale has developed a system called ZeitGeist[25] that harvests neological headwords from Wikipedia and interprets them relative to their local context in Wikipedia and relative to specific word senses in WordNet. ZeitGeist has been extended to generate neologisms of its own; the approach combines elements from an inventory of word parts that are harvested from WordNet, and simultaneously determines likely glosses for these new words (e.g., "food traveller" for "gastronaut" and "time traveller" for "chrononaut"). It then uses Web search to determine which glosses are meaningful and which neologisms have not been used before; this search identifies the subset of generated words that are both novel ("H-creative") and useful. Neurolinguistic inspirations have been used to analyze the process of novel word creation in the brain[26] , understand neurocognitive processes responsible for intuition, insight, imagination and creativity[27] and to create a server that invents novel names for products, based on their description[28] . Computational creativity 26

Poetry More than iron, more than lead, more than gold I need electricity. I need it more than I need lamb or pork or lettuce or cucumber. I need it for my dreams. Racter, from The Policeman's Beard Is Half Constructed Like jokes, poems involve a complex interaction of different constraints, and no general-purpose poem generator adequately combines the meaning, phrasing, structure and rhyme aspects of poetry. Nonetheless, Pablo Gervás[29] has developed a noteworthy system called ASPERA that employs a case-based reasoning (CBR) approach to generating poetic formulations of a given input text via a composition of poetic fragments that are retrieved from a case-base of existing poems. Each poem fragment in the ASPERA case-base is annotated with a prose string that expresses the meaning of the fragment, and this prose string is used as the retrieval key for each fragment. Metrical rules are then used to combine these fragments into a well-formed poetic structure. Example software projects include: • Racter • Flowerewolf [30] automatic poetry generator And poetry collections include: • The Policeman's Beard Is Half Constructed [31]

Musical creativity Computational creativity in the music domain has focussed both on the generation of musical scores for use by human musicians, and on the generation of music for performance by computers. The domain of generation has included classical music (with software that generates music in the style of Mozart and Bach) and jazz. Most notably, David Cope[32] has written a software system called "Experiments in Musical Intelligence" (or "EMI") that is capable of analyzing and generalizing from existing music by a human composer to generate novel musical compositions in the same style. EMI's output is convincing enough to persuade human listeners that its music is human-generated to a high level of competence[33] . Creativity research in jazz has focussed on the process of improvisation and the cognitive demands that this places on a musical agent: reasoning about time, remembering and conceptualizing what has already been played, and planning ahead for what might be played next. The robot Shimon, developed by Gil Weinberg of Georgia Tech, has demonstrated jazz improvisation.[34]

Visual and artistic creativity Computational creativity in the generation of visual art has had some notable successes in the creation of both abstract art and representational art. The most famous program in this domain is Harold Cohen's AARON,[35] which has been continuously developed and augmented since 1973. Though formulaic, Aaron exhibits a range of outputs, generating black-and-white drawings or colour paintings that incorporate human figures (such as dancers), potted plants, rocks, and other elements of background imagery. These images are of a sufficiently high quality to be displayed in reputable galleries. Other software artists of note include the NEvAr system (for "Neuro-Evolutionary Art") of Penousal Machado.[36] NEvAr uses a genetic algorithm to derive a mathematical function that is then used to generate a coloured three-dimensional surface. A human user is allowed to select the best pictures after each phase of the genetic algorithm, and these preferences are used to guide successive phases, thereby pushing NEvAr’s search into pockets of the search space that are considered most appealing to the user. The Painting Fool, developed by Simon Colton originated as a system for overpainting digital images of a given scene in a choice of different painting styles, colour palettes and brush types. Given its dependence on an input Computational creativity 27

source image to work with, the earliest iterations of the Painting Fool raised as questions about the extent of, or lack of, creativity in a computational art system. Nonetheless, in more recent work, The Painting Fool has been extended to create novel images, much as AARON does, from its own limited imagination. Images in this vein include cityscapes and forests, which are generated by a process of constraint satisfaction from some basic scenarios provided by the user (e.g., these scenarios allow the system to infer that objects closer to the viewing plane should be larger and more color-saturated, while those further away should be less saturated and appear smaller). Artistically, the images now created by the Painting Fool appear on a par with those created by Aaron, though the extensible mechanisms employed by the former (constraint satisfaction, etc.) may well allow it to develop into a more elaborate and sophisticated painter.

Events The First International Conference on Computational Creativity was held in January 2010 at the University of Coimbra, Lisbon, Portugal. Previously, the community of computational creativity has held a dedicated workshop, the International Joint Workshop on Computational Creativity, every year since 1999. Usually held as part of a larger conference event, this workshop series is now autonomous. Previous events in this series include: • IJWCC 2003, Acapulco, Mexico, as part of IJCAI'2003 • IJWCC 2004, Madrid, Spain, as part of ECCBR'2004 • IJWCC 2005, Edinburgh, UK, as part of IJCAI'2005 • IJWCC 2006, Riva del Garda, Italy, as part of ECAI'2006 • IJWCC 2007, London, UK, a stand-alone event • IJWCC 2008, Madrid, Spain, a stand-alone event The steering committee for these events comprises the following researchers: • Amilcar Cardoso (University of Coimbra, Portugal) • Simon Colton (Imperial College London, UK) • Pablo Gervás (Universidad Complutense de Madrid, Spain) • Francisco C Pereira (University of Coimbra, Portugal) • Tony Veale (University College Dublin, Ireland) • Geraint A. Wiggins (Goldsmiths, University of London, UK)

Publication forums In addition to the proceedings of these workshops, the computational creativity community has thus far produced two special journal issues dedicated to the topic: • Journal of Knowledge-Based Systems, volume 9, issue 7, November 2006 • New Generation Computing, volume 24, issue 3, 2006

See also • Algorithmic composition • Algorithmic art • Artificial Architecture • Computer-generated music • Computer-generated mathematics • Computer art • Digital morphogenesis • Generative systems • Musikalisches Würfelspiel (Musical dice game) Computational creativity 28

• Digital poetry • Procedural generation

External links Further reading

[37] • An Overview of Artificial Creativity on Think Artificial • Gero, J. S. and Sosa, R. "Artificial Creativity in [38] [40] • Cohen, H., "the further exploits of AARON, Painter" , SEHR, volume 4, Communities of Design Agents" , 2006 [41] issue 2: Constructions of the Mind, 1995 • LaDuke, B. "Knowledge Machine" [39] • Artificial Creativity Blog

Applications and examples

[42] [49] • ArchiKluge • generative art by Bogdan Soban [43] [50] • draw-something • CLAC - Software for Logical Composition [44] [51] • Glot-Bot v2 • The SWALE project [45] [42] • picbreeder • jMapper - Java Library for Analogy/Metaphor Generation [46] [52] • The Painting Fool • Aristotle - online metaphor generation and browsing system [47] • Mambo invents novel words [48] • Transhypnagogia - computer hallucinations

Institutions and individuals

[53] • Margaret Boden [54] • Neurocognitive Computational Creativity, including Mambo server, Wlodek Duch lab [55] • The Creative Systems Area of the AI Group/CISUC [56] • notnot Creative Systems [57] • Stephen L. Thaler, Ph.D.

References [1] Amabile, Teresa (1983), The social psychology of creativity, New York, NY: Springer-Verlag [2] Newell, Allen, Shaw, J. G., and Simon, Herbert A. (1963), The process of creative thinking, H. E. Gruber, G. Terrell and M. Wertheimer (Eds.), Contemporary Approaches to Creative Thinking, pp 63 – 119. New York: Atherton [3] Newell, Allen, Simon, Herbert A. (1972), Human Problem Solving, Englewood Cliffs, NJ: Prentice Hall. [4] Newell, Allen, Simon, Herbert A. (1963), GPS, A Program that Simulates Human Though, E. A. Feigenbaum and J. Feldman (eds.), R. Oldenbourg KG [5] Boden, Margaret (1990), The Creative Mind: Myths and Mechanisms, London: Weidenfeld and Nicholson [6] Boden, Margaret (1999), Computational models of creativity., Handbook of Creativity, pp 351–373 [7] Wiggins, Geraint (2006), A Preliminary Framework for Description, Analysis and Comparison of Creative Systems, Journal of Knowledge Based Systems 19(7), pp. 449-458 [8] Finke, R., Ward, T., and Smith, S. (1992), Creative cognition: Theory, research and applications, Cambridge: MIT press. [9] Koestler, Arthur (1964), The Act of Creation, Macmillan [10] Fauconnier, Gilles, Turner, Mark (2007), The Way We Think, Basic Books [11] Fauconnier, Gilles, Turner, Mark (2007), Conceptual Integration Networks, Cognitive Science, 22(2) pp 133–187 [12] Veale, Tony, O’Donoghue, Diarmuid (2007), Computation and Blending, Cognitive Linguistics, 11(3-4), special issue on Conceptual Blending

[13] Pereira, Francisco Câmara (2006), Creativity and Artificial Intelligence: A Conceptual Blending Approach (http:/ / eden. dei. uc. pt/

~camara/ AICreativity), Applications of Cognitive Linguistics. Amsterdam: Mouton de Gruyter, [14] Meehan, James (1981), TALE-SPIN, Shank, R. C. and Riesbeck, C. K., (eds.), Inside Computer Understanding: Five Programs plus Miniatures. Hillsdale, NJ: Lawrence Erlbaum Associates [15] Turner, S.R. (1994), The Creative Process: A Computer Model of Storytelling, Hillsdale, NJ: Lawrence Erlbaum Associates [16] Bringsjord, S., Ferrucci, D. A. (2000), Artificial Intelligence and Literary Creativity. Inside the Mind of BRUTUS, a Storytelling Machine., Hillsdale NJ: Lawrence Erlbaum Associates Computational creativity 29

[17] Pérez y Pérez, Rafael, Sharples, Mike (2001), MEXICA: A computer model of a cognitive account of creative writing, Journal of Experimental and Theoretical Artificial Intelligence, 13, pp 119-139 [18] Martin, James (1990), A Computational Model of Metaphor Interpretation, Academic Press [19] Barnden, John (1992), Belief in Metaphor: Taking Commonsense Psychology Seriously, Computational Intelligence 8, pp 520-552 [20] Veale, Tony, Hao, Yanfen (2007), Comprehending and Generating Apt Metaphors: A Web-driven, Case-based Approach to Figurative Language, Proceedings of AAAI 2007, the 22nd AAAI Conference on Artificial Intelligence. Vancouver, Canada

[21] Falkenhainer, Brian, Forbus, Ken and Gentner, Dedre (1989), The structure-mapping engine: Algorithm and examples (http:/ / www. qrg.

northwestern. edu/ papers/ Files/ smeff2(searchable). pdf), Artificial Intelligence, 20(41) pp 1–63, [22] Veale, Tony, O’Donoghue, Diarmuid (2007), Computation and Blending, Cognitive Linguistics, 11(3-4), special issue on Conceptual Blending [23] Binsted, K., Pain, H., and Ritchie, G. (1997), Children's evaluation of computer-generated punning riddles, Pragmatics and Cognition, 5(2), pp 309–358 [24] Stock, Oliviero, Strapparava, Carlo (2003), HAHAcronym: Humorous agents for humorous acronyms, Humor: International Journal of Humor Research, 16(3) pp 297–314 [25] Veale, Tony (2006), Tracking the Lexical Zeitgeist with Wikipedia and WordNet, Proceedings of ECAI’2006, the 17th European Conference on Artificial Intelligence [26] Duch, Wlodzislaw (2007), Creativity and the Brain, In: A Handbook of Creativity for Teachers. Ed. Ai-Girl Tan, World Scientific Publishing, Singapore, pp 507–530 [27] Duch, Wlodzislaw (2007), Intuition, Insight, Imagination and Creativity, IEEE Computational Intelligence Magazine, 2(3) pp 40–52 [28] Pilichowski Maciej, Duch Wlodzislaw (2007), Experiments with computational creativity, Neural Information Processing – Letters and Reviews, 11(4-6) pp 123-133 [29] Gervás, Pablo (2001), An expert system for the composition of formal Spanish poetry, Journal of Knowledge-Based Systems 14(3-4) pp 181–188

[30] http:/ / nodebox. net/ code/ index. php/ Flowerewolf

[31] http:/ / www. ubu. com/ historical/ racter/ index. html [32] Cope, David (2006), Computer Models of Musical Creativity, Cambridge, MA: MIT Press

[33] Triumph of the Cyborg Composer (http:/ / www. miller-mccune. com/ culture-society/ triumph-of-the-cyborg-composer-8507/ )

[34] http:/ / www. npr. org/ templates/ story/ story. php?storyId=121763193 [35] McCorduck, Pamela (1991), Aaron's Code., W.H. Freeman & Co., Ltd. [36] Romero, Juan, Machado, Penousal (eds.) (2008), The Art of Artificial Evolution: A Handbook on Evolutionary Art and Music, Natural Computing Series. Berlin: Springer Verlag

[37] http:/ / www. thinkartificial. org/ artificial-creativity

[38] http:/ / www. stanford. edu/ group/ SHR/ 4-2/ text/ cohen. html

[39] http:/ / www. acblog. net/

[40] http:/ / www. arch. usyd. edu. au/ ~john/ publications/ 2002/ 02SosaGeroCAADRIA. pdf

[41] http:/ / www. anti-knowledge. com/ book/ 00_Title. htm

[42] http:/ / armyofclerks. net/ ArchiKluge/ index. htm

[43] http:/ / draw-something. robmyers. org/

[44] http:/ / www. ocf. berkeley. edu/ ~jkunken/ glot-bot/

[45] http:/ / picbreeder. org

[46] http:/ / www. thepaintingfool. com/

[47] http:/ / www-users. mat. uni. torun. pl/ ~macias/ mambo/

[48] http:/ / www. archive. org/ details/ Transhypnagogia-ComputerGeneratedForms

[49] http:/ / www. soban-art. com/

[50] http:/ / www. 1stleft. com/ clac/ English/ index. htm

[51] http:/ / www. cs. indiana. edu/ ~leake/ projects/ swale/

[52] http:/ / afflatus. ucd. ie/ aristotle/

[53] http:/ / www. sussex. ac. uk/ informatics/ profile276. html

[54] http:/ / www. is. umk. pl/ projects/ cre. html

[55] http:/ / eden. dei. uc. pt/ ~amilcar/ CreativeSystems/

[56] http:/ / www. xs4all. nl/ ~notnot

[57] http:/ / www. imagination-engines. com/ thaler. htm Data mining 30 Data mining

Data mining is the process of extracting patterns from data. Data mining is becoming an increasingly important tool to transform this data into information. It is commonly used in a wide range of profiling practices, such as marketing, surveillance, fraud detection and scientific discovery. Data mining can be used to uncover patterns in data but is often carried out only on samples of data. The mining process will be ineffective if the samples are not a good representation of the larger body of data. Data mining cannot discover patterns that may be present in the larger body of data if those patterns are not present in the sample being "mined". Inability to find patterns may become a cause for some disputes between customers and service providers. Therefore data mining is not foolproof but may be useful if sufficiently representative data samples are collected. The discovery of a particular pattern in a particular set of data does not necessarily mean that a pattern is found elsewhere in the larger data from which that sample was drawn. An important part of the process is the verification and validation of patterns on other samples of data. The related terms data dredging, data fishing and data snooping refer to the use of data mining techniques to sample sizes that are (or may be) too small for statistical inferences to be made about the validity of any patterns discovered (see also data-snooping bias). Data dredging may, however, be used to develop new hypotheses, which must then be validated with sufficiently large sample sets.

Background Humans have been "manually" extracting patterns from data for centuries, but the increasing volume of data in modern times has called for more automated approaches. Early methods of identifying patterns in data include Bayes' theorem (1700s) and regression analysis (1800s). The proliferation, ubiquity and increasing power of computer technology has increased data collection and storage. As data sets have grown in size and complexity, direct hands-on data analysis has increasingly been augmented with indirect, automatic data processing. This has been aided by other discoveries in computer science, such as neural networks, clustering, genetic algorithms (1950s), decision trees (1960s) and support vector machines (1980s). Data mining is the process of applying these methods to data with the intention of uncovering hidden patterns.[1] It has been used for many years by businesses, scientists and governments to sift through volumes of data such as airline passenger trip records, census data and supermarket scanner data to produce market research reports. (Note, however, that reporting is not always considered to be data mining.) A primary reason for using data mining is to assist in the analysis of collections of observations of behaviour. Such data are vulnerable to collinearity because of unknown interrelations. An unavoidable fact of data mining is that the (sub-)set(s) of data being analysed may not be representative of the whole domain, and therefore may not contain examples of certain critical relationships and behaviours that exist across other parts of the domain. To address this sort of issue, the analysis may be augmented using experiment-based and other approaches, such as Choice Modelling for human-generated data. In these situations, inherent correlations can be either controlled for, or removed altogether, during the construction of the experimental design. There have been some efforts to define standards for data mining, for example the 1999 European Cross Industry Standard Process for Data Mining (CRISP-DM 1.0) and the 2004 Java Data Mining standard (JDM 1.0). These are evolving standards; later versions of these standards are under development. Independent of these standardization efforts, freely available open-source software systems like the R Project, Weka, KNIME, RapidMiner and others have become an informal standard for defining data-mining processes. Notably, all these systems are able to import and export models in PMML (Predictive Model Markup Language) which provides a standard way to represent data mining models so that these can be shared between different statistical applications[2] . PMML is an XML-based language developed by the Data Mining Group (DMG)[3] , an independent group composed of many data mining Data mining 31

companies. PMML version 4.0 was released in June 2009.[3] [4] [5]

Research and evolution In addition to industry driven demand for standards and interoperability, professional and academic activity have also made considerable contributions to the evolution and rigour of the methods and models; an article published in a 2008 issue of the International Journal of Information Technology and Decision Making summarises the results of a literature survey which traces and analyzes this evolution.[6] The premier professional body in the field is the Association for Computing Machinery's Special Interest Group on Knowledge discovery and Data Mining (SIGKDD). Since 1989 they have hosted an annual international conference and published its proceedings,[7] and since 1999 have published a biannual academic journal titled "SIGKDD Explorations".[8] Other Computer Science conferences on data mining include: • DMIN - International Conference on Data Mining;[9] • DMKD - Research Issues on Data Mining and Knowledge Discovery; • ECML-PKDD - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases; • ICDM - IEEE International Conference on Data Mining;[10] • MLDM - Machine Learning and Data Mining in Pattern Recognition; • SDM - SIAM International Conference on Data Mining • EDM - International Conference on Educational Data Mining

Process

Pre-processing Before data mining algorithms can be used, a target data set must be assembled. As data mining can only uncover patterns already present in the data, the target dataset must be large enough to contain these patterns while remaining concise enough to be mined in an acceptable timeframe. A common source for data is a datamart or data warehouse. Pre-process is essential to analyse the multivariate datasets before clustering or data mining. The target set is then cleaned. Cleaning removes the observations with noise and missing data. The clean data is reduced into feature vectors, one vector per observation. A feature vector is a summarised version of the raw data observation. For example, a black and white image of a face which is 100px by 100px would contain 10,000 bits of raw data. This might be turned into a feature vector by locating the eyes and mouth in the image. Doing so would reduce the data for each vector from 10,000 bits to three codes for the locations, dramatically reducing the size of the dataset to be mined, and hence reducing the processing effort. The feature(s) selected will depend on what the objective(s) is/are; obviously, selecting the "right" feature(s) is fundamental to successful data mining. The feature vectors are divided into two sets, the "training set" and the "test set". The training set is used to "train" the data mining algorithm(s), while the test set is used to verify the accuracy of any patterns found. Data mining 32

Data mining Data mining commonly involves four classes of tasks:[11] • Clustering - is the task of discovering groups and structures in the data that are in some way or another "similar", without using known structures in the data. • Classification - is the task of generalizing known structure to apply to new data. For example, an email program might attempt to classify an email as legitimate or spam. Common algorithms include decision tree learning, nearest neighbor, naive Bayesian classification and neural networks. • Regression - Attempts to find a function which models the data with the least error. • Association rule learning - Searches for relationships between variables. For example a supermarket might gather data on customer purchasing habits. Using association rule learning, the supermarket can determine which products are frequently bought together and use this information for marketing purposes. This is sometimes referred to as market basket analysis. See also structured data analysis.

Results validation The final step of knowledge discovery from data is to verify the patterns produced by the data mining algorithms occur in the wider data set. Not all patterns found by the data mining algorithms are necessarily valid. It is common for the data mining algorithms to find patterns in the training set which are not present in the general data set, this is called overfitting. To overcome this, the evaluation uses a test set of data which the data mining algorithm was not trained on. The learnt patterns are applied to this test set and the resulting output is compared to the desired output. For example, a data mining algorithm trying to distinguish spam from legitimate emails would be trained on a training set of sample emails. Once trained, the learnt patterns would be applied to the test set of emails which it had not been trained on, the accuracy of these patterns can then be measured from how many emails they correctly classify. A number of statistical methods may be used to evaluate the algorithm such as ROC curves. If the learnt patterns do not meet the desired standards, then it is necessary to reevaluate and change the preprocessing and data mining. If the learnt patterns do meet the desired standards then the final step is to interpret the learnt patterns and turn them into knowledge.

Notable uses

Games Since the early 1960s, with the availability of oracles for certain combinatorial games, also called tablebases (e.g. for 3x3-chess) with any beginning configuration, small-board dots-and-boxes, small-board-hex, and certain endgames in chess, dots-and-boxes, and hex; a new area for data mining has been opened up. This is the extraction of human-usable strategies from these oracles. Current pattern recognition approaches do not seem to fully have the required high level of abstraction in order to be applied successfully. Instead, extensive experimentation with the tablebases, combined with an intensive study of tablebase-answers to well designed problems and with knowledge of prior art, i.e. pre-tablebase knowledge, is used to yield insightful patterns. Berlekamp in dots-and-boxes etc. and John Nunn in chess endgames are notable examples of researchers doing this work, though they were not and are not involved in tablebase generation. Data mining 33

Business Data mining in customer relationship management applications can contribute significantly to the bottom line. Rather than randomly contacting a prospect or customer through a call center or sending mail, a company can concentrate its efforts on prospects that are predicted to have a high likelihood of responding to an offer. More sophisticated methods may be used to optimise resources across campaigns so that one may predict which channel and which offer an individual is most likely to respond to — across all potential offers. Additionally, sophisticated applications could be used to automate the mailing. Once the results from data mining (potential prospect/customer and channel/offer) are determined, this "sophisticated application" can either automatically send an e-mail or regular mail. Finally, in cases where many people will take an action without an offer, uplift modeling can be used to determine which people will have the greatest increase in responding if given an offer. Data clustering can also be used to automatically discover the segments or groups within a customer data set. Businesses employing data mining may see a return on investment, but also they recognise that the number of predictive models can quickly become very large. Rather than one model to predict how many customers will churn, a business could build a separate model for each region and customer type. Then instead of sending an offer to all people that are likely to churn, it may only want to send offers to customers that will likely take an offer. And finally, it may also want to determine which customers are going to be profitable over a window of time and only send the offers to those that are likely to be profitable. In order to maintain this quantity of models, they need to manage model versions and move to automated data mining. Data mining can also be helpful to human-resources departments in identifying the characteristics of their most successful employees. Information obtained, such as universities attended by highly successful employees, can help HR focus recruiting efforts accordingly. Additionally, Strategic Enterprise Management applications help a company translate corporate-level goals, such as profit and margin share targets, into operational decisions, such as production plans and workforce levels.[12] Another example of data mining, often called the market basket analysis, relates to its use in retail sales. If a clothing store records the purchases of customers, a data-mining system could identify those customers who favour silk shirts over cotton ones. Although some explanations of relationships may be difficult, taking advantage of it is easier. The example deals with association rules within transaction-based data. Not all data are transaction based and logical or inexact rules may also be present within a database. In a manufacturing application, an inexact rule may state that 73% of products which have a specific defect or problem will develop a secondary problem within the next six months. Market basket analysis has also been used to identify the purchase patterns of the Alpha consumer. Alpha Consumers are people that play a key roles in connecting with the concept behind a product, then adopting that product, and finally validating it for the rest of society. Analyzing the data collected on these type of users has allowed companies to predict future buying trends and forecast supply demands. Data Mining is a highly effective tool in the catalog marketing industry. Catalogers have a rich history of customer transactions on millions of customers dating back several years. Data mining tools can identify patterns among customers and help identify the most likely customers to respond to upcoming mailing campaigns. Related to an integrated-circuit production line, an example of data mining is described in the paper "Mining IC Test Data to Optimize VLSI Testing."[13] In this paper the application of data mining and decision analysis to the problem of die-level functional test is described. Experiments mentioned in this paper demonstrate the ability of applying a system of mining historical die-test data to create a probabilistic model of patterns of die failure which are then utilised to decide in real time which die to test next and when to stop testing. This system has been shown, based on experiments with historical test data, to have the potential to improve profits on mature IC products. Data mining 34

Science and engineering In recent years, data mining has been widely used in area of science and engineering, such as bioinformatics, genetics, medicine, education and electrical power engineering. In the area of study on human genetics, an important goal is to understand the mapping relationship between the inter-individual variation in human DNA sequences and variability in disease susceptibility. In lay terms, it is to find out how the changes in an individual's DNA sequence affect the risk of developing common diseases such as cancer. This is very important to help improve the diagnosis, prevention and treatment of the diseases. The data mining technique that is used to perform this task is known as multifactor dimensionality reduction.[14] In the area of electrical power engineering, data mining techniques have been widely used for condition monitoring of high voltage electrical equipment. The purpose of condition monitoring is to obtain valuable information on the insulation's health status of the equipment. Data clustering such as self-organizing map (SOM) has been applied on the vibration monitoring and analysis of transformer on-load tap-changers(OLTCS). Using vibration monitoring, it can be observed that each tap change operation generates a signal that contains information about the condition of the tap changer contacts and the drive mechanisms. Obviously, different tap positions will generate different signals. However, there was considerable variability amongst normal condition signals for the exact same tap position. SOM has been applied to detect abnormal conditions and to estimate the nature of the abnormalities.[15] Data mining techniques have also been applied for dissolved gas analysis (DGA) on power transformers. DGA, as a diagnostics for power transformer, has been available for many years. Data mining techniques such as SOM has been applied to analyse data and to determine trends which are not obvious to the standard DGA ratio techniques such as Duval Triangle.[15] A fourth area of application for data mining in science/engineering is within educational research, where data mining has been used to study the factors leading students to choose to engage in behaviors which reduce their learning[16] and to understand the factors influencing university student retention.[17] A similar example of the social application of data mining is its use in expertise finding systems, whereby descriptors of human expertise are extracted, normalised and classified so as to facilitate the finding of experts, particularly in scientific and technical fields. In this way, data mining can facilitate Institutional memory. Other examples of applying data mining technique applications are biomedical data facilitated by domain ontologies,[18] mining clinical trial data,[19] traffic analysis using SOM,[20] et cetera. In adverse drug reaction surveillance, the Uppsala Monitoring Centre has, since 1998, used data mining methods to routinely screen for reporting patterns indicative of emerging drug safety issues in the WHO global database of 4.6 million suspected adverse drug reaction incidents.[21] Recently, similar methodology has been developed to mine large collections of electronic health records for temporal patterns associating drug prescriptions to medical diagnoses.[22]

Spatial data mining Spatial data mining is the application of data mining techniques to spatial data. Spatial data mining follows along the same functions in data mining, with the end objective to find patterns in geography. So far, data mining and Geographic Information Systems (GIS) have existed as two separate technologies, each with its own methods, traditions and approaches to visualization and data analysis. Particularly, most contemporary GIS have only very basic spatial analysis functionality. The immense explosion in geographically referenced data occasioned by developments in IT, digital mapping, remote sensing, and the global diffusion of GIS emphasises the importance of developing data driven inductive approaches to geographical analysis and modeling. Data mining, which is the partially automated search for hidden patterns in large databases, offers great potential benefits for applied GIS-based decision-making. Recently, the task of integrating these two technologies has become critical, especially as various public and private sector organisations possessing huge databases with thematic and Data mining 35

geographically referenced data begin to realise the huge potential of the information hidden there. Among those organisations are: • offices requiring analysis or dissemination of geo-referenced statistical data • public health services searching for explanations of disease clusters • environmental agencies assessing the impact of changing land-use patterns on climate change • geo-marketing companies doing customer segmentation based on spatial location.

Challenges Geospatial data repositories tend to be very large. Moreover, existing GIS datasets are often splintered into feature and attribute components, that are conventionally archived in hybrid data management systems. Algorithmic requirements differ substantially for relational (attribute) data management and for topological (feature) data management [23] . Related to this is the range and diversity of geographic data formats, that also presents unique challenges. The digital geographic data revolution is creating new types of data formats beyond the traditional "vector" and "raster" formats. Geographic data repositories increasingly include ill-structured data such as imagery and geo-referenced multi-media [24] . There are several critical research challenges in geographic knowledge discovery and data mining. Miller and Han [25] offer the following list of emerging research topics in the field: • Developing and supporting geographic data warehouses - Spatial properties are often reduced to simple aspatial attributes in mainstream data warehouses. Creating an integrated GDW requires solving issues in spatial and temporal data interoperability, including differences in semantics, referencing systems, geometry, accuracy and position. • Better spatio-temporal representations in geographic knowledge discovery - Current geographic knowledge discovery (GKD) techniques generally use very simple representations of geographic objects and spatial relationships. Geographic data mining techniques should recognise more complex geographic objects (lines and polygons) and relationships (non-Euclidean distances, direction, connectivity and interaction through attributed geographic space such as terrain). Time needs to be more fully integrated into these geographic representations and relationships. • Geographic knowledge discovery using diverse data types - GKD techniques should be developed that can handle diverse data types beyond the traditional raster and vector models, including imagery and geo-referenced multimedia, as well as dynamic data types (video streams, animation).

Surveillance Previous data mining to stop terrorist programs under the U.S. government include the Total Information Awareness (TIA) program, Secure Flight (formerly known as Computer-Assisted Passenger Prescreening System (CAPPS II)), Analysis, Dissemination, Visualization, Insight, Semantic Enhancement (ADVISE[26] ), and the Multistate Anti-Terrorism Information Exchange (MATRIX).[27] These programs have been discontinued due to controversy over whether they violate the US Constitution's 4th amendment, although many programs that were formed under them continue to be funded by different organisations, or under different names.[28] Two plausible data mining techniques in the context of combating terrorism include "pattern mining" and "subject-based data mining". Data mining 36

Pattern mining "Pattern mining" is a data mining technique that involves finding existing patterns in data. In this context patterns often means association rules. The original motivation for searching association rules came from the desire to analyze supermarket transaction data, that is, to examine customer behaviour in terms of the purchased products. For example, an association rule "beer ⇒ crisps (80%)" states that four out of five customers that bought beer also bought crisps. In the context of pattern mining as a tool to identify terrorist activity, the National Research Council provides the following definition: "Pattern-based data mining looks for patterns (including anomalous data patterns) that might be associated with terrorist activity — these patterns might be regarded as small signals in a large ocean of noise."[29] [30] [31] Pattern Mining includes new areas such a Music Information Retrieval (MIR) where patterns seen both in the temporal and non temporal domains are imported to classical knowledge discovery search techniques.

Subject-based data mining "Subject-based data mining" is a data mining technique involving the search for associations between individuals in data. In the context of combatting terrorism, the National Research Council provides the following definition: "Subject-based data mining uses an initiating individual or other datum that is considered, based on other information, to be of high interest, and the goal is to determine what other persons or financial transactions or movements, etc., are related to that initiating datum."[30]

Privacy concerns and ethics Some people believe that data mining itself is ethically neutral.[32] However, the ways in which data mining can be used can raise questions regarding privacy, legality, and ethics.[33] In particular, data mining government or commercial data sets for national security or law enforcement purposes, such as in the Total Information Awareness Program or in ADVISE, has raised privacy concerns.[34] [35] Data mining requires data preparation which can uncover information or patterns which may compromise confidentiality and privacy obligations. A common way for this to occur is through data aggregation. Data aggregation is when the data are accrued, possibly from various sources, and put together so that they can be analyzed.[36] This is not data mining per se, but a result of the preparation of data before and for the purposes of the analysis. The threat to an individual's privacy comes into play when the data, once compiled, cause the data miner, or anyone who has access to the newly-compiled data set, to be able to identify specific individuals, especially when originally the data were anonymous. It is recommended that an individual is made aware of the following before data are collected: • the purpose of the data collection and any data mining projects, • how the data will be used, • who will be able to mine the data and use them, • the security surrounding access to the data, and in addition, • how collected data can be updated.[36] In the United States, privacy concerns have been somewhat addressed by their congress via the passage of regulatory controls such as the Health Insurance Portability and Accountability Act (HIPAA). The HIPAA requires individuals to be given "informed consent" regarding any information that they provide and its intended future uses by the facility receiving that information. According to an article in Biotech Business Week, “In practice, HIPAA may not offer any greater protection than the longstanding regulations in the research arena, says the AAHC. More importantly, the rule's goal of protection through informed consent is undermined by the complexity of consent forms that are required of patients and participants, which approach a level of incomprehensibility to average individuals.” [37] This underscores the necessity for data anonymity in data aggregation practices. Data mining 37

One may additionally modify the data so that they are anonymous, so that individuals may not be readily identified.[36] However, even de-identified data sets can contain enough information to identify individuals, as occurred when journalists were able to find several individuals based on a set of search histories that were inadvertently released by AOL.[38]

Marketplace surveys Several researchers and organizations have conducted reviews of data mining tools and surveys of data miners. These identify some of the strengths and weaknesses of the software packages. They also provide an overview of the behaviors, preferences and views of data miners. Some of these reports include: • Forrester Research 2010 Predictive Analytics and Data Mining Solutions report.[39] • Annual Rexer Analytics Data Miner Surveys.[40] [41] [42] • Gartner 2008 "Magic Quadrant" report.[43] • Robert Nisbet's 2006 Three Part Series of articles "Data Mining Tools: Which One is Best For CRM?"[44] • Haughton et al.'s 2003 Review of Data Mining Software Packages in The American Statistician.[45]

Groups and associations • SIGKDD, the ACM Special Interest Group on Knowledge Discovery and Data Mining.

See also

Applications • Data Mining in Agriculture • Surveillance / Mass surveillance • National Security Agency • Quantitative structure-activity relationship • Customer analytics • Police-enforced ANPR in the UK • Stellar wind (code name)

Methods • Association rule learning • Cluster analysis • Structured data analysis (statistics) • Java Data Mining • Data analysis • Predictive analytics • Knowledge discovery Data mining 38

Miscellaneous • Data mining agent • Data warehouse • PMML Data mining is about analysing data; for information about extracting information out of data, see: • Information extraction • Named entity recognition • Profiling • Profiling practices

Further reading • Bhagat, Phiroz Pattern Recognition in Industry, Elsevier, ISBN 0-08-044538-1. • Cabena, Peter, Pablo Hadjnian, Rolf Stadler, Jaap Verhees and Alessandro Zanasi (1997) Discovering Data Mining: From Concept to Implementation, Prentice Hall, ISBN 0137439806. • Dummer, Stephen W., False Positives And Secure Flight Using Dataveillance When Viewed Through The Ever Increasing Likelihood Of Identity Theft, 11 J. of Tech. Law & Pol’y 259 (2006). • Dummer, Stephen W., Comment: Secure Flight and Dataveillance, A New Type Of Civil Liberties Erosion: Stripping Your Rights When You Don’t Even Know It, 75 MISS. L.J. 583 (2005). • Feldman, Ronen and James Sanger The Text Mining Handbook, Cambridge University Press, ISBN 9780521836579. • Guo, Yike and Robert Grossman, editors (1999) High Performance Data Mining: Scaling Algorithms, Applications and Systems, Kluwer Academic Publishers. • Hastie, Trevor, Robert Tibshirani and Jerome Friedman (2001). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer, ISBN 0387952845. • Hornick, Mark F., Erik Marcade and Sunil Venkayala Java Data Mining: Strategy, Standard, and Practice: A Practical Guide for Architecture, Design, And Implementation (Broché). • Bing Liu (2007). Web Data Mining: Exploring Hyperlinks, Contents and Usage Data. Springer, ISBN 3540378812. • Mierswa, Ingo, Michael Wurst, Ralf Klinkenberg, Martin Scholz and Timm Euler (2006) YALE: Rapid Prototyping for Complex Data Mining Tasks, in Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-06). • Mucherino, Antonio and Papajoirgji, Petraq and Pardalos, Panos, 'Data Mining in Agriculture', Springer, 2009. Author web page on the book [46] Springer [47] • Nisbet, Robert, John Elder, Gary Miner, 'Handbook of Statistical Analysis & Data Mining Applications, Academic Press/Elsevier, ISBN: 9780123747655 (2009) • Poncelet, Pascal, Florent Masseglia and Maguelonne Teisseire, editors (October 2007) Data Mining Patterns: New Methods and Applications, Information Science Reference, ISBN 978-1599041629. • Pang-Ning Tan, Michael Steinbach and Vipin Kumar, Introduction to Data Mining (2005), ISBN 0-321-32136-7 • Sergios Theodoridis, Konstantinos Koutroumbas (2009) "Pattern Recognition" , 4th Edition, Academic Press, ISBN 978-1-59749-272-0. • Wang, X.Z.; Medasani, S.; Marhoon, F; Al-Bazzaz, H. (2004) Multidimensional visualisation of principal component scores for process historical data analysis, Industrial & Engineering Chemistry Research, 43(22), pp. 7036–7048. • Wang, X.Z. (1999) Data mining and knowledge discovery for process monitoring and control. Springer, London. • Weiss and Indurkhya Predictive Data Mining, Morgan Kaufmann. Data mining 39

• Witten, Ian and Eibe Frank (2000) Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations, ISBN 1-55860-552-5. (See also Free Weka software.)

External links • ACM SIGKDD [48], the professional association for Knowledge Discovery and Data Mining • Data Mining Software [49] at the Open Directory Project

References [1] Kantardzic, Mehmed (2003). Data Mining: Concepts, Models, Methods, and Algorithms. John Wiley & Sons. ISBN 0471228524. OCLC 50055336. [2] Alex Guazzelli, Wen-Ching Lin, Tridivesh Jena. PMML in Action: Unleashing the Power of Open Standards for Data Mining and Predictive

Analytics. (http:/ / www. amazon. com/ PMML-Action-Unleashing-Standards-Predictive/ dp/ 1452858268/ ref=ntt_at_ep_dpi_1) CreateSpace, 2010

[3] The Data Mining Group (DMG). (http:/ / www. dmg. org/ ) The DMG is an independent, vendor led group which develops data mining standards, such as the Predictive Model Markup Language (PMML).

[4] PMML Project Page (http:/ / sourceforge. net/ projects/ pmml)

[5] Alex Guazzelli, Michael Zeller, Wen-Ching Lin, Graham Williams. PMML: An Open Standard for Sharing Models. (http:/ / journal.

r-project. org/ 2009-1/ RJournal_2009-1_Guazzelli+ et+ al. pdf) The R Journal, vol 1/1, May 2009. [6] Y. Peng, G. Kou, Y. Shi, Z. Chen (2008). "A Descriptive Framework for the Field of Data Mining and Knowledge Discovery". International Journal of Information Technology and Decision Making, Volume 7, Issue 4 7: 639 – 682. doi:10.1142/S0219622008003204.

[7] Proceedings (http:/ / www. kdd. org/ conferences. php), International Conferences on Knowledge Discovery and Data Mining, ACM, New York.

[8] SIGKDD Explorations (http:/ / www. kdd. org/ explorations/ about. php), ACM, New York.

[9] International Conference on Data Mining: 5th (2009) (http:/ / www. dmin--2009. com/ ); 4th (2008) (http:/ / www. dmin-2008. com/ ); 3rd

(2007) (http:/ / www. dmin-2007. com/ ); 2nd (2006) (http:/ / www. dmin-2006. com/ ); 1st (2005) (http:/ / www. informatik. uni-trier. de/

~ley/ db/ conf/ dmin/ dmin2005. html)

[10] IEEE International Conference on Data Mining (http:/ / www. informatik. uni-trier. de/ ~ley/ db/ conf/ icdm/ index. html): ICDM09 (http:/ /

www. cs. umbc. edu/ ICDM09/ ), Miami, FL; ICDM08 (http:/ / icdm08. isti. cnr. it/ ), Pisa (Italy); ICDM07 (http:/ / www. ist. unomaha. edu/

icdm2007/ ), Omaha, NE; ICDM06 (http:/ / www. comp. hkbu. edu. hk/ iwi06/ icdm/ ), Hong Kong; ICDM05 (http:/ / www. cacs. ull. edu/

~icdm05/ ), Houston, TX; ICDM04 (http:/ / icdm04. cs. uni-dortmund. de/ ), Brighton (UK); ICDM03 (http:/ / www. cs. uvm. edu/ ~xwu/

icdm-03. html), Melbourne, FL; ICDM02 (http:/ / kis. maebashi-it. ac. jp/ icdm02/ ), Maebashi City (Japan); ICDM01 (http:/ / www. cs. uvm.

edu/ ~xwu/ icdm-01. html), San Jose, CA. [11] Fayyad, Usama; Gregory Piatetsky-Shapiro, and Padhraic Smyth (1996). "From Data Mining to Knowledge Discovery in Databases" (http:/

/ www. kdnuggets. com/ gpspubs/ aimag-kdd-overview-1996-Fayyad. pdf). . Retrieved 2008-12-17. [12] Ellen Monk, Bret Wagner (2006). Concepts in Enterprise Resource Planning, Second Edition. Thomson Course Technology, Boston, MA. ISBN 0-619-21663-8. OCLC 224465825.

[13] Tony Fountain, Thomas Dietterich & Bill Sudyka (2000) Mining IC Test Data to Optimize VLSI Testing (http:/ / web. engr. oregonstate.

edu/ ~tgd/ publications/ kdd2000-dlft. pdf), in Proceedings of the Sixth ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. (pp. 18-25). ACM Press. [14] Xingquan Zhu, Ian Davidson (2007). Knowledge Discovery and Data Mining: Challenges and Realities. Hershey, New Your. pp. 18. ISBN 978-159904252-7. [15] A.J. McGrail, E. Gulski et al.. "Data Mining Techniques to Asses the Condition of High Voltage Electrical Plant". CIGRE WG 15.11 of Study Committee 15. [16] R. Baker. "Is Gaming the System State-or-Trait? Educational Data Mining Through the Multi-Contextual Application of a Validated Behavioral Model". Workshop on Data Mining for User Modeling 2007. [17] J.F. Superby, J-P. Vandamme, N. Meskens. "Determination of factors influencing the achievement of the first-year university students using data mining methods". Workshop on Educational Data Mining 2006. [18] Xingquan Zhu, Ian Davidson (2007). Knowledge Discovery and Data Mining: Challenges and Realities. Hershey, New York. pp. 163–189. ISBN 978-159904252-7. [19] ibid. pp. 31–48. [20] Yudong Chen, Yi Zhang, Jianming Hu, Xiang Li. "Traffic Data Analysis Using Kernel PCA and Self-Organizing Map". Intelligent Vehicles Symposium, 2006 IEEE. [21] Bate A, Lindquist M, Edwards IR, Olsson S, Orre R, Lansner A, De Freitas RM. A Bayesian neural network method for adverse drug reaction signal generation. Eur J Clin Pharmacol. 1998 Jun;54(4):315-21. [22] Norén GN, Bate A, Hopstadius J, Star K, Edwards IR. Temporal Pattern Discovery for Trends and Transient Effects: Its Application to Patient Records. Proceedings of the Fourteenth International Conference on Knowledge Discovery and Data Mining SIGKDD 2008, pages Data mining 40

963-971. Las Vegas NV, 2008. [23] Healey, R., 1991, Database Management Systems. In Maguire, D., Goodchild, M.F., and Rhind, D., (eds.), Geographic Information Systems: Principles and Applications (London: Longman). [24] Câmara, A. S. and Raper, J., (eds.), 1999, Spatial Multimedia and Virtual Reality, (London: Taylor and Francis). [25] Miller, H. and Han, J., (eds.), 2001, Geographic Data Mining and Knowledge Discovery, (London: Taylor & Francis). [26] Government Accountability Office, Data Mining: Early Attention to Privacy in Developing a Key DHS Program Could Reduce Risks, GAO-07-293, Washington, D.C.: February 2007.

[27] Secure Flight Program report (http:/ / www. msnbc. msn. com/ id/ 20604775/ ), MSNBC.

[28] "Total/Terrorism Information Awareness (TIA): Is It Truly Dead?" (http:/ / w2. eff. org/ Privacy/ TIA/ 20031003_comments. php). Electronic Frontier Foundation (official website). 2003. . Retrieved 2009-03-15. [29] R. Agrawal et al., Fast discovery of association rules, in Advances in knowledge discovery and data mining pp. 307-328, MIT Press, 1996. [30] National Research Council, Protecting Individual Privacy in the Struggle Against Terrorists: A Framework for Program Assessment, Washington, DC: National Academies Press, 2008. [31] Stephen Haag et al. (2006). Management Information Systems for the information age. Toronto: McGraw-Hill Ryerson. pp. 28. ISBN 0-07-095569-7. OCLC 63194770.

[32] William Seltzer. The Promise and Pitfalls of Data Mining: Ethical Issues (http:/ / www. amstat. org/ committees/ ethics/ linksdir/

Jsm2005Seltzer. pdf). .

[33] Chip Pitts (March 15, 2007). "The End of Illegal Domestic Spying? Don't Count on It" (http:/ / www. washingtonspectator. com/ articles/

20070315surveillance_1. cfm). Washington Spectator. .

[34] K.A. Taipale (December 15, 2003). "Data Mining and Domestic Security: Connecting the Dots to Make Sense of Data" (http:/ / www. stlr.

org/ cite. cgi?volume=5& article=2). Columbia Science and Technology Law Review 5 (2). SSRN 546782 (http:/ / ssrn. com/ abstract=546782) / OCLC 45263753. .

[35] John Resig, Ankur Teredesai (2004). "A Framework for Mining Instant Messaging Services" (http:/ / citeseer. ist. psu. edu/

resig04framework. html). In Proceedings of the 2004 SIAM DM Conference. .

[36] Think Before You Dig: Privacy Implications of Data Mining & Aggregation (http:/ / www. nascio. org/ publications/ documents/

NASCIO-dataMining. pdf), NASCIO Research Brief, September 2004. [37] Biotech Business Week Editors. (June 30, 2008). BIOMEDICINE; HIPAA Privacy Rule Impedes Biomedical Research. Biotech Business Week. Retrieved 17 Nov 2009 from LexisNexis Academic.

[38] AOL search data identified individuals (http:/ / www. securityfocus. com/ brief/ 277), SecurityFocus, August 2006.

[39] James Kobielus (1 July 2008) The Forrester Wave™: Predictive Analytics and Data Mining Solutions, Q1 2010 (http:/ / www. forrester.

com/ rb/ Research/ wave& trade;_predictive_analytics_and_data_mining_solutions,/ q/ id/ 56077/ t/ 2), Forrester Research.

[40] Karl Rexer, Heather Allen, & Paul Gearan (2009) 2009 Data Miner Survey Summary (http:/ / www. rexeranalytics. com/

Data-Miner-Survey-Results-2009. html), presented at SPSS Directions Conference, Oct. 2009.

[41] Karl Rexer, Paul Gearan, & Heather Allen (2008) 2008 Data Miner Survey Summary (http:/ / www. rexeranalytics. com/

Data-Miner-Survey-Results-2008. html), presented at SPSS Directions Conference, Oct. 2008, and Oracle BIWA Summit, Nov. 2008.

[42] Karl Rexer, Paul Gearan, & Heather Allen (2007) 2007 Data Miner Survey Summary (http:/ / www. rexeranalytics. com/

Data-Miner-Survey-Results. html), presented at SPSS Directions Conference, Oct. 2007, and Oracle BIWA Summit, Oct. 2007.

[43] Gareth Herschel (1 July 2008) Magic Quadrant for Customer Data-Mining Applications (http:/ / mediaproducts. gartner. com/ reprints/ sas/

vol5/ article3/ article3. html), Gartner Inc.

[44] Robert Nisbet (2006) Data Mining Tools: Which One is Best for CRM? Part 1 (http:/ / www. information-management. com/ specialreports/

20060124/ 1046025-1. html), Information Management Special Reports, January 2006. [45] Dominique Haughton, Joel Deichmann, Abdolreza Eshghi, Selin Sayek, Nicholas Teebagy, & Heikki Topi (2003) A Review of Software

Packages for Data Mining (http:/ / www. jstor. org/ pss/ 30037299), The American Statistician, Vol. 57, No. 4, pp. 290-309.

[46] http:/ / www. antoniomucherino. it/ en/ book. php

[47] http:/ / www. springer. com/ math/ applications/ book/ 978-0-387-88614-5

[48] http:/ / www. sigkdd. org

[49] http:/ / www. dmoz. org/ Computers/ Software/ Databases/ Data_Mining/ / Deskilling 41 Deskilling

Deskilling is the process by which skilled labor within an industry or economy is eliminated by the introduction of technologies operated by semiskilled or unskilled workers. This results in cost savings due to lower investment in human capital, and reduces barriers to entry, weakening the bargaining power of the human capital. It is criticized for decreasing quality, demeaning labor (rendering work mechanical, rather than thoughtful and making workers automatons rather than artisans), and undermining community.

Examples Examples of deprofessionalization can be found across many professions, and include: • CNC machine tools replacing machinists • assembly line workers replacing artisans and craftsmen • super-automatic espresso machines replacing skilled baristas • pharmacists • social workers • nurses • librarians

Impact Work is fragmented, and individuals lose the integrated skills and comprehensive knowledge of the crafts persons.[1] In an application to the arts, Benjamin Buchloh defines deskilling as "a concept of considerable importance in describing numerous artistic endeavors throughout the twentieth century with relative precision. All of these are linked in their persistent effort to eliminate artisanal competence and other forms of manual virtuosity from the horizon of both artist competence and aesthetic valuation."

Related Related to the topic of deskilling is deprofessionalization and labor-saving devices. See also the Luddite fallacy.

Further reading • Stephen Wood (December 1981). Degradation of Work: Skill, Deskilling and the Braverman Debate. HarperCollins. ISBN 0091454018. • Hal Foster, Rosalind Krauss, Yve-Alain Bois, and Benjamin H. D. Buchloh (March 2005). Art Since 1900: Modernism, Antimodernism, Postmodernism. Thames & Hudson. ISBN 0500238189. • Beatrice Edwards. "Deskilling AND Downsizing: Some Thoughts About The Future Of Technical Education" [2]. Retrieved 2007-04-08. • Sociology Department, Langara College [3] • Sociology Department, McMaster University [4] • Technology, Capitalism and Anarchism [5] Deskilling 42

See also • Automation • Unionization • Craft guild • Division of Labor

References

[1] "Online Dictionary of the Social Sciences" (http:/ / bitbucket. icaap. org/ dict. pl?term=DESKILLING). . Retrieved 2007-04-08.

[2] http:/ / iacd. oas. org/ La%20Educa%20123-125/ edw. htm

[3] http:/ / www. langara. bc. ca/ sociology/ Deskilling. html

[4] http:/ / socserv2. mcmaster. ca/ soc/ courses/ soc4jj3/ stuweb/ pbl_3/ skills. htm

[5] http:/ / flag. blackened. net/ blackflag/ 219/ 219techn. htm

Digital morphogenesis

Digital morphogenesis is a process of shape development (or morphogenesis[1] ) enabled by computation. While this concept is applicable in many areas, the term "digital morphogenesis" is used primarily in architecture. In architecture, digital morphogenesis is a group of methods that employ digital media for form-making and adaptation rather than for representation, often in an aspiration to express or respond to contextual processes.[2] [3] [4] [5] "In this inclusive understanding, digital morphogenesis in architecture bears a largely analogous or metaphoric relationship to the processes of morphogenesis in nature, sharing with it the reliance on gradual development but not necessarily adopting or referring to the actual mechanisms of growth or adaptation. Recent discourse on digital morphogenesis in architecture links it to a number of concepts including emergence, self-organization and form-finding."[6]

Bibliography • Burry, Jane, et al. (2005). 'Dynamical Structural Modeling: A Collaborative Design Exploration', International Journal of Architectural Computing, 3, 1, pp. 27-42 • De Landa, Manuel (1997). A Thousand Years of Nonlinear History (New York: Zone Books) • Feuerstein, Günther (2002). Biomorphic Architecture: Human and Animal Forms in Architecture (Stuttgart; London: Axel Menges) • Frazer, John H. (1995). An Evolutionary Architecture, Themes VII (London: Architectural Association) [7] • Hensel, Michael and Achim Menges (2008). 'Designing Morpho-Ecologies: Versatility and Vicissitude of Heterogeneous Space', Architectural Design, 78, 2, pp. 102-111 • Hensel, Michael, Achim Menges, and Michael Weinstock, eds (2004). Emergence: Morphogenetic Design Strategies, Architectural Design (London: Wiley) • Hensel, Michael and Achim Menges (2006). 'Material and Digital Design Synthesis', Architectural Design, 76, 2, pp. 88-95 • Hensel, Michael and Achim Menges (2006). 'Differentiation and Performance: Multi-Performance Architectures and Modulated Environments', Architectural Design, 76, 2, pp. 60-69 • Hingston, Philip F., Luigi C. Barone, and Zbigniew Michalewicz, eds (2008). Design by Evolution: Advances in Evolutionary Design (Berlin; London: Springer) • Kolarevic, Branko (2000). 'Digital Morphogenesis and Computational Architectures', in Proceedings of the 4th Conference of Congreso Iberoamericano de Grafica Digital, SIGRADI 2000 - Construindo (n)o Espaço Digital (Constructing the Digital Space), Rio de Janeiro (Brazil) 25–28 September 2000, ed. by José Ripper Kós, Andréa Pessoa Borde and Diana Rodriguez Barros, pp. 98-103 [8] Digital morphogenesis 43

• Leach, Neil (2009). 'Digital Morphogenesis', Architectural Design, 79, 1, pp. 32-37 • Lynn, Greg (1999). Animate Form (New York: Princeton Architectural Press) • Lynn, Greg (1998). Folds, Bodies & Blobs: Collected Essays (Bruxelles: La Lettre volée) • Menges, Achim (2007). 'Computational Morphogenesis: Integral Form Generation and Materialization Processes', in Proceedigns of Em‘body’ing Virtual Architecture: The Third International Conference of the Arab Society for Computer Aided Architectural Design (ASCAAD 2007), 28–30 November 2007, Alexandria, Egypt, ed. by Ahmad Okeil, Aghlab Al-Attili and Zaki Mallasi, pp. 725-744 • Menges, Achim (2006). 'Polymorphism', Architectural Design, 76, 2, pp. 78-87 • Ottchen, Cynthia (2009). 'The Future of Information Modelling and the End of Theory: Less is Limited, More is Different', Architectural Design, 79, 2, pp. 22-27 • Prusinkiewicz, Przemyslaw, and Aristid Lindenmayer (2004). The Algorithmic Beauty of Plants (New York: Springer-Verlag) • Roudavski, Stanislav (2009). 'Towards Morphogenesis in Architecture', International Journal of Architectural Computing, 7, 3, pp. 345-374 [9] • Sabin, Jenny E. and Peter Lloyd Jones (2008). 'Nonlinear Systems Biology and Design: Surface Design', in Proceedings of the 28th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA), Silicon + Skin: Biological Processes and Computation, Minneapolis 16-19 October 2008, ed. by Andrew Kudless, Neri Oxman and Marc Swackhamer, pp. 54-65 • Sevaldson, Birger (2005). Developing Digital Design Techniques: Investigations on Creative Design Computing (PhD, Oslo School of Architecture) • Sevaldson, Birger (2000). 'Dynamic Generative Diagrams', in Promise and Reality: State of the Art versus State of Practice in Computing for the Design and Planning Process. 18th eCAADe Conference Proceedings, ed. by Dirk Donath (Weimar: Bauhaus Universität), pp. 273-276 • Steadman, Philip (2008). The Evolution of Designs: Biological Analogy in Architecture and the Applied Arts (New York: Routledge) • Tierney, Therese (2007). Abstract Space: Beneath the Media Surface (Oxon: Taylor & Francis), p. 116 • Weinstock, Michael (2006). 'Self-Organisation and the Structural Dynamics of Plants', Architectural Design, 76, 2, pp. 26-33 • Weinstock, Michael (2006). 'Self-Organisation and Material Constructions', Architectural Design, 76, 2, pp. 34-41

External links • Architectural Association studio on Morphogenesis [10] • The 28th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA), Silicon + Skin: Biological Processes and Computation [11][12][13]

See also • Bionics • Bioinspiration & Biomimetics • Biomimicry • Blobitecture • Digital architecture • Digital art • Evolutionary art • Evolutionary computation • Generative art Digital morphogenesis 44

• Organic architecture

References [1] The original usage was in the field of biology. The usage in geology is also well established, cf. geomorphology. [2] Kolarevic, Branko (2000). 'Digital Morphogenesis and Computational Architectures', in Proceedigns of the 4th Confernece of Congreso Iberoamericano de Grafica Digital, SIGRADI 2000 - Construindo (n)o Espaço Digital (Constructing the Digital Space), Rio de Janeiro

(Brazil) 25–28 September 2000, ed. by José Ripper Kós, Andréa Pessoa Borde and Diana Rodriguez Barros, pp. 98-103 (http:/ / cumincad.

scix. net/ data/ works/ att/ 4077. content. pdf) [3] Kolarevic, Branko and Ali Malkawi, eds (2005). Performative Architecture: Beyond Instrumentality (New York; London: Spon Press), p. 195 [4] Leach, Neil (2009). 'Digital Morphogenesis', Architectural Design, 79, 1, pp. 32-37 [5] Roudavski, Stanislav (2009). 'Towards Morphogenesis in Architecture', International Journal of Architectural Computing, 7, 3, pp. 345-374,

p. 348 (http:/ / repository. unimelb. edu. au/ 10187/ 5444) [6] Roudavski, Stanislav (2009), pp. 348, 349

[7] http:/ / www. aaschool. ac. uk/ publications/ ea/ intro. html

[8] http:/ / cumincad. scix. net/ data/ works/ att/ 4077. content. pdf

[9] http:/ / repository. unimelb. edu. au/ 10187/ 5444

[10] http:/ / www. morphogenesis. org/ about_us. php

[11] http:/ / www. acadia. org/ acadia2008/

[12] http:/ / www. acadia. org/ ?g=proceedings

[13] http:/ / cumincad. scix. net/ cgi-bin/ works/ BrowseTree?field=series& separator=:& recurse=0& order=AZ& value=ACADIA

Heuristic

Heuristic (pronounced /hjʉˈrɪstɨk/, from the Greek "Εὑρίσκω" for "find" or "discover") is an adjective for experience-based techniques that help in problem solving, learning and discovery. Archimedes is said to have shouted "Heureka" (later converted to "Eureka") after discovering the principle of displacement in his bath. A heuristic method is used to come to a solution rapidly that is hoped to be close to the best possible answer, or 'optimal solution'. A heuristic is a "rule of thumb", an educated guess, an intuitive judgment or simply common sense. A heuristic is a general way of solving a problem. Heuristics as a noun is another name for heuristic methods. In more precise terms, heuristics stand for strategies using readily accessible, though loosely applicable, information to control problem solving in human beings and machines.[1]

Example It may be argued that the most fundamental heuristic is trial and error, which can be used in everything from matching bolts to bicycles to finding the values of variables in algebra problems. Here are a few other commonly used heuristics, from Polya's 1945 book, How to Solve It:[2] • If you are having difficulty understanding a problem, try drawing a picture. • If you can't find a solution, try assuming that you have a solution and seeing what you can derive from that ("working backward"). • If the problem is abstract, try examining a concrete example. • Try solving a more general problem first (the "inventor's paradox": the more ambitious plan may have more chances of success). Heuristic 45

Psychology In psychology, heuristics are simple, efficient rules, hard-coded by evolutionary processes or learned, which have been proposed to explain how people make decisions, come to judgments, and solve problems, typically when facing complex problems or incomplete information. These rules work well under most circumstances, but in certain cases lead to systematic errors or cognitive biases. Although much of the work of discovering heuristics in human decision-makers was done by Amos Tversky and Daniel Kahneman[3] , the concept has been originally introduced by Nobel laureate Herbert Simon. Gerd Gigerenzer focuses on how heuristics can be used to make judgments that are in principle accurate, rather than producing cognitive biases – heuristics that are "fast and frugal".[4] In 2002, Daniel Kahneman and Shane Frederick proposed that cognitive heuristics work by a process called attribute substitution which happens without conscious awareness.[5] According to this theory, when somebody makes a judgment (of a target attribute) which is computationally complex, a rather easier calculated heuristic attribute is substituted. In effect, a cognitively difficult problem is dealt with by answering a rather simpler problem, without being aware of this happening.[5] This theory explains cases where judgments fail to show regression toward the mean.[6]

Theorized psychological heuristics

Well known • Anchoring and adjustment • Availability heuristic • Representativeness heuristic • Naïve diversification • Escalation of commitment

Less well known

• Affect heuristic • Gaze heuristic • Similarity heuristic • Contagion heuristic • Peak-end rule • Simulation heuristic • Effort heuristic • Recognition • Social proof • Familiarity heuristic heuristic • Take-the-best heuristic • Fluency heuristic • Scarcity heuristic

Philosophy In philosophy, especially in Continental European philosophy, the adjective "heuristic" (or the designation "heuristic device") is used when an entity X exists to enable understanding of, or knowledge concerning, some other entity Y. A good example is a model which, as it is never identical with what it models, is a heuristic device to enable understanding of what it models. Stories, metaphors, etc., can also be termed heuristic in that sense. A classic example is the notion of utopia as described in Plato's best-known work, The Republic. This means that the "ideal city" as depicted in The Republic is not given as something to be pursued, or to present an orientation-point for development; rather, it shows how things would have to be connected, and how one thing would lead to another (often with highly problematic results), if one would opt for certain principles and carry them through rigorously. "Heuristic" is also often commonly used as a noun to describe a rule-of-thumb, procedure, or method.[7] Philosophers of science have emphasized the importance of heuristics in creative thought and constructing scientific theories.[8] (See the logic of discovery, and philosophers such as Imre Lakatos,[9] Lindley Darden, and others.) Heuristic 46

Law In legal theory, especially in the theory of law and economics, heuristics are used in the law when case-by-case analysis would be impractical, insofar as "practicality" is defined by the interests of a governing body.[10] For instance, in many states in the United States the legal drinking age is 21, because it is argued that people need to be mature enough to make decisions involving the risks of alcohol consumption. However, assuming people mature at different rates, the specific age of 21 would be too late for some and too early for others. In this case, the somewhat arbitrary deadline is used because it is impossible or impractical to tell whether one individual is mature enough that society can trust them with that kind of responsibility. Some proposed changes, however, have included the completion of an alcohol education course rather than the attainment of 21 years of age as the criterion for legal alcohol possession. This would situate youth alcohol policy more on a case-by-case model and less on a heuristic one, since the completion of such a course would presumably be voluntary and not uniform across the population. The same reasoning applies to patent law. Patents are justified on the grounds that inventors need to be protected in order to have incentive to invent. It is therefore argued that, in society's best interest, inventors should be issued with a temporary government-granted monopoly on their product, so that they can recoup their investment costs and make economic profit for a limited period of time. In the United States the length of this temporary monopoly is 20 years from the date the application for patent was filed, though the monopoly does not actually begin until the application has matured into a patent. However, like the drinking-age problem above, the specific length of time would need to be different for every product in order to be efficient; a 20-year term is used because it is difficult to tell what the number should be for any individual patent. More recently, some, including University of North Dakota law professor Eric E. Johnson, have argued that patents in different kinds of industries – such as software patents – should be protected for different lengths of time.[11]

Computer science In computer science, a heuristic is a technique designed to solve a problem that ignores whether the solution can be proven to be correct, but which usually produces a good solution or solves a simpler problem that contains or intersects with the solution of the more complex problem. Most real-time, and even some on-demand, anti-virus scanners use heuristic signatures to look for specific attributes and characteristics for detecting viruses and other forms of malware. Heuristics are intended to gain computational performance or conceptual simplicity, potentially at the cost of accuracy or precision. In their Turing Award acceptance speech, Herbert Simon and Allen Newell discuss the Heuristic Search Hypothesis: a physical symbol system will repeatedly generate and modify known symbol structures until the created structure matches the solution structure. That is, each successive iteration depends upon the step before it, thus the heuristic search learns what avenues to pursue and which ones to disregard by measuring how close the current iteration is to the solution. Therefore, some possibilities will never be generated as they are measured to be less likely to complete the solution. A heuristic method can accomplish its task by using search trees. However, instead of generating all possible solution branches, a heuristic selects branches more likely to produce outcomes than other branches. It is selective at each decision point; picking branches that are more likely to produce solutions. [12] Heuristic 47

Human-computer interaction In human-computer interaction, heuristic evaluation is a usability-testing technique devised by expert usability consultants. In heuristic evaluation, the user interface is reviewed by experts and its compliance to usability heuristics (broadly stated characteristics of a good user interface, based on prior experience) is assessed, and any violating aspects are recorded.

Heuristic Considerations in the Design of Software Applications A well-designed user interface enables users to intuitively navigate complex systems, without difficulty. It guides the user when necessary using tooltips, help buttons, invitations to chat with support, etc., providing help when needed. This is not always an easy process though. Software developers and the targeted end-users alike each disregard heuristics at their own peril. End users often need to increase their understanding of the basic framework that a project entails (so that their expectations are realistic), and developers often need to push to learn more about their target audience (so that their learning styles can be judged somewhat). Business rules crucial to the organization are often so obvious to the end-user that they are not conveyed to the developer, who may lack domain knowledge in the particular field of endeavor the application is meant to serve. A proper Software Requirement Specification (SRS) models the heuristics of how a user will process the information being rendered on-screen. An SRS is ideally shared with the end-user well before the actual Software Design Specification (SDS) is written and the application is developed, so that the user's feedback about their experience can be used to adapt the design of the application. This saves much time in the Software Development Life Cycle (SDLC). Unless heuristics are considered adequately enough, the project will likely suffer many implementation problems and setbacks.

Engineering In engineering, a heuristic is an experience-based method that can be used as an aid to solve process design problems, varying from size of equipment to operating conditions. By using heuristics, time can be reduced when solving problems. There are several methods which are available to engineers. These include Failure mode and effects analysis and Fault tree analysis. The former relies on a group of qualified engineers to evaluate problems, rank them in order of importance and then recommend solutions. The methods of forensic engineering are an important source of information for investigating problems, especially by elimination of unlikely causes and using the weakest link principle. Because heuristics are fallible, it is important to understand their limitations. They are intended to be used as aids in order to make quick estimates and preliminary process designs.

Pitfalls of heuristics Heuristic algorithms are often employed because they may be seen to "work" without having been mathematically proven to meet a given set of requirements. One common pitfall in implementing a heuristic method to meet a requirement comes when the engineer or designer fails to realize that the current data set does not necessarily represent future system states. While the existing data can be pored over and an algorithm can be devised to successfully handle the current data, it is imperative to ensure that the heuristic method employed is capable of handling future data sets. This means that the engineer or designer must fully understand the rules that generate the data and develop the algorithm to meet those requirements and not just address the current data sets. Statistical analysis should be conducted when employing heuristics to estimate the probability of incorrect outcomes. Heuristic 48

If one seeks to use a heuristic as a means of solving a search or knapsack problem, then one must be careful to make sure that the heuristic function which one is choosing to use is an admissible heuristic. Given a heuristic function labeled as: h(v , v ) which is meant to approximate the true optimal distance d∗(v , v ) to the goal node v in a directed graph G i g i i g containing n total nodes or vertexes labeled v , v , ... , v . 0 1 n "Admissible" means that h(v , v ) ≤ d∗(v , v ) for ALL (v , v ) where {i, g} ∈ [0, 1, ... , n]. i g i g i g If a heuristic is not admissible, it might never find the goal, by ending up in a dead end of graph G or by skipping back and forth between two nodes (v , v ) where {i, j} ≠ g. i j

See also • Algorithm • Behavioral economics • Daniel Kahneman • Failure mode and effects analysis • Problem solving • Teachable moment • List of cognitive biases

Further reading • How To Solve It: Modern Heuristics, Zbigniew Michalewicz and David B. Fogel, Springer Verlag, 2000. ISBN 3-540-66061-5 • Russell, Stuart J.; Norvig, Peter (2003), Artificial Intelligence: A Modern Approach [13] (2nd ed.), Upper Saddle River, New Jersey: Prentice Hall, ISBN 0-13-790395-2 • The Problem of Thinking Too Much [14], 2002–12–11, Persi Diaconis

External links • The Heuristic Wiki [15] • “Discovering Assumptions” [16] by Paul Niquette

References [1] Pearl, Judea (1983). Heuristics: Intelligent Search Strategies for Computer Problem Solving. New York, Addison-Wesley, p. vii. [2] Polya, George (1945) How To Solve It: A New Aspect of Mathematical Method, Princeton, NJ: Princeton University Press. ISBN 0-691-02356-5 ISBN 0-691-08097-6 [3] Daniel Kahneman, Amos Tversky and Paul Slovic, eds. (1982) Judgment under Uncertainty: Heuristics & Biases. Cambridge, UK, Cambridge University Press ISBN 0-521-28414-7 [4] Gerd Gigerenzer, Peter M. Todd, and the ABC Research Group (1999). Simple Heuristics That Make Us Smart. Oxford, UK, Oxford University Press. ISBN 0-19-514381-7 [5] Kahneman, Daniel; Shane Frederick (2002). "Representativeness Revisited: Attribute Substitution in Intuitive Judgment". in Thomas Gilovich, Dale Griffin, Daniel Kahneman. Heuristics and Biases: The Psychology of Intuitive Judgment. Cambridge: Cambridge University Press. pp. 49–81. ISBN 9780521796798. OCLC 47364085. [6] Kahneman, Daniel (December 2003). "Maps of Bounded Rationality: Psychology for Behavioral Economics". American Economic Review (American Economic Association) 93 (5): 1449–1475. doi:10.1257/000282803322655392. ISSN 0002-8282.

[7] K. M. Jaszczolt (2006). "Defaults in Semantics and Pragmatics" (http:/ / plato. stanford. edu/ entries/ defaults-semantics-pragmatics/ ), The Stanford Encyclopedia of Philosophy, ISSN 1095-5054

[8] Roman Frigg and Stephan Hartmann (2006). "Models in Science" (http:/ / plato. stanford. edu/ entries/ models-science/ ), The Stanford Encyclopedia of Philosophy, ISSN 1095-5054

[9] Olga Kiss (2006). "Heuristic, Methodology or Logic of Discovery? Lakatos on Patterns of Thinking" (http:/ / www. mitpressjournals. org/

doi/ pdf/ 10. 1162/ posc. 2006. 14. 3. 302), Perspectives on Science, vol. 14, no. 3, pp. 302-317, ISSN 1063-6145 Heuristic 49

[10] Gerd Gigerenzer and Christoph Engel, eds. (2007). Heuristics and the Law, Cambridge, The MIT Press, ISBN 978-0-262-07275-5

[11] Eric E. Johnson (2006). "Calibrating Patent Lifetimes" (http:/ / www. eejlaw. com/ writings/ Johnson_Calibrating_Patent_Lifetimes. pdf), Santa Clara Computer & High Technology Law Journal, vol. 22, p. 269-314 [12] Newell, A. & Simon, H. A. (1976). Computer science as empirical inquiry: symbols and search. Comm. Of the ACM. 19, 113-126.

[13] http:/ / aima. cs. berkeley. edu/

[14] http:/ / www-stat. stanford. edu/ ~cgates/ PERSI/ papers/ thinking. pdf

[15] http:/ / greenlightwiki. com/ heuristic

[16] http:/ / niquette. com/ books/ sophmag/ heurist. htm

Hidden curriculum

Hidden curriculum, in the most general terms, is “some of the outcomes or by-products of schools or of non-school settings, particularly those states which are learned but not openly intended.”[1] However, a variety of definitions have been developed based on the broad range of perspectives of those who study this phenomenon. Any setting, including traditionally recreational and social activities, may teach unintended lessons since it is tied not necessarily to schools but rather to learning experiences.[2] But most often, hidden curriculum refers to various types of knowledge gained in primary and secondary school settings, usually with a negative connotation referring to inequalities suffered as a result of its presence. This attitude stems from the commitment of the school system of the United States to promote democracy and ensure equal intellectual development, goals that are hindered by these intangible lessons [3] . In this context, hidden curriculum is said to reinforce existing social inequalities by educating students in various matters and behaviors according to their class and social status. In the same way that there is an unequal distribution of cultural capital in this society, there is a corresponding distribution of knowledge amongst its students.[4] The hidden curriculum can also refer to the transmission of norms, values, and beliefs conveyed in both the formal educational content and the social interactions within these schools.[5] Hidden curriculum is difficult to explicitly define because it varies among its students and their experiences and because is it constantly changing as the knowledge and beliefs of a society evolve. The concept that the hidden curriculum expresses is the idea that schools do more than simply transmit knowledge, as laid down in the official curricula. Behind it lies criticism of the social implications, political underpinnings, and cultural outcomes of modern educative activities. While early examinations were concerned with identifying the anti-democratic nature of schooling, later studies have taken various tones, including those concerned with socialism, capitalism, and anarchism in education.

Educational history Early workers in the field of education were influenced by the notion that the preservation of the social privileges, interests, and knowledge of one group within the population was worth the exploitation of less powerful groups.[6] Over time this theory has become less blatant, yet its underlying tones remain a contributing factor to the issue of the hidden curriculum. Several educational theories have been developed to help give meaning and structure to the hidden curriculum and to illustrate the role that schools play in socialization. Three of these theories, as cited by Henry Giroux and Anthony Penna, are a structural-functional view of schooling, a phenomenological view related to the “new” sociology of education, and a radical critical view corresponding to the neo-Marxist analysis of the theory and practice of education. The structural-functional view focuses on how norms and values are conveyed within schools and how their necessities for the functioning of society become indisputably accepted. The phenomenological view suggests that meaning is created through situational encounters and interactions, and it implies that knowledge is somewhat objective. The radical critical view recognizes the relationship between economic and cultural reproduction and stresses the relationships among the theory, ideology, and social practice of learning. Although the first two theories have contributed to the analysis of the hidden curriculum, the radical critical view of schooling provides the most Hidden curriculum 50

insight.[7] Most importantly it acknowledges the perpetuated economic and social aspects of education that are clearly illustrated by the hidden curriculum. It also illustrates the significance of abstract characteristics like theory and ideology that help define this phenomenon.

Sources Various aspects of learning contribute to the success of the hidden curriculum, including practices, procedures, rules, relationships, and structures.[8] Many school-specific sources, some of which may be included in these aspects of learning, give rise to important elements of the hidden curriculum. These sources may include, but are not limited to, the social structures of the classroom, the teacher’s exercise of authority, rules governing the relationship between teachers and students, standard learning activities, the teacher’s use of language, textbooks, audio-visual aids, furnishings, architecture, disciplinary measures, timetables, tracking systems, and curricular priorities.[9] Variations among these sources promote the disparities found when comparing the hidden curricula corresponding to various class and social statuses. While the actual material that students absorb through the hidden curriculum is of utmost importance, the personnel who convey it elicit special investigation. This particularly applies to the social and moral lessons conveyed by the hidden curriculum, for the moral characteristics and ideologies of teachers and other authority figures are translated into their lessons, albeit not necessarily with intention.[10] Yet these unintended learning experiences can result from interactions with not only instructors, but also with peers. Like interactions with authority figures, interactions amongst peers can promote moral and social ideals. But they can also foster the exchange of information and are thus important sources of knowledge that contribute to the success of the hidden curriculum.

Function Although the hidden curriculum conveys a great deal of knowledge to its students, the inequality promoted through its disparities among classes and social statuses often invokes a negative connotation. For example, Pierre Bourdieu asserts that education-related capital must be accessible to promote academic achievement. The effectiveness of schools becomes limited when these forms of capital are unequally distributed.[11] Since the hidden curriculum is considered to be a form of education-related capital, it promotes this ineffectiveness of schools as a result of its unequal distribution. As a means of social control, the hidden curriculum promotes the acceptance of a social destiny without promoting rational and reflective consideration.[12] According to Elizabeth Vallance, the functions of hidden curriculum include “the inculcation of values, political socialization, training in obedience and docility, the perpetuation of traditional class structure-functions that may be characterized generally as social control.”[13] Hidden curriculum can also be associated with the reinforcement of social inequality, as evidenced by the development of different relationships to capital based on the types of work and work-related activities assigned to students varying by social class.[14]

Higher education and tracking While studies on the hidden curriculum mostly focus on fundamental primary and secondary education, higher education also feels the effects of this latent knowledge. For example, gender biases become present in specific fields of study; the quality of and experiences associated with prior education become more significant; and class, gender, and race become more evident at higher levels of education.[15] One additional aspect of hidden curriculum that plays a major part in the development of students and their fates is tracking. This method of imposing educational and career paths upon students at young ages relies on various factors such as class and status to reinforce socioeconomic differences. Children tend to be placed on tracks guiding them towards socioeconomic occupations similar to that of their parents, without real considerations for their strengths and weaknesses. As students advance through the educational system, they follow along their tracks by completing the Hidden curriculum 51

predetermined courses.[16] This is one of the main factors limiting social mobility in America today.

Literary references John Dewey explored the hidden curriculum of education in his early 20th century works, particularly his classic, Democracy and Education. Dewey saw patterns evolving and trends developing in public schools which lent themselves to his pro-democratic perspectives. His work was quickly rebutted by educational theorist George Counts, whose 1929 book, Dare the School Build a New Social Order challenged the presumptive nature of Dewey's works. Where Dewey (and other child development theorists including Jean Piaget, Erik Erikson and Maria Montessori) hypothesized a singular path through which all young people travelled in order to become adults, Counts recognized the reactive, adaptive, and multifaceted nature of learning. This nature caused many educators to slant their perspectives, practices, and assessments of student performance in particular directions which affected their students drastically. Counts' examinations were expanded on by Charles Beard, and later, Myles Horton as he created what became the Highlander Folk School in Tennessee. The phrase "hidden curriculum" was reportedly coined by Philip W. Jackson (Life In Classrooms, 1968). He argued that we need to understand "education" as a socialization process. Shortly after Jackson's coinage, MIT's Benson Snyder published The Hidden Curriculum, which addresses the question of why students—even or especially the most gifted—turn away from education. Snyder advocates the thesis that much of campus conflict and students' personal anxiety is caused by a mass of unstated academic and social norms, which thwart the students' ability to develop independently or think creatively. The hidden curriculum has been further explored by a number of educators. Starting with Pedagogy of the Oppressed, published in 1972, through the late 1990s, Brazilian educator Paulo Freire explored various effects of presumptive teaching on students, schools, and society as a whole. Freire's explorations were in sync with those of John Holt and Ivan Illich, each of whom were quickly identified as radical educators. More recent definitions were given by Meighan ("A Sociology of Educating", 1981): The hidden curriculum is taught by the school, not by any teacher...something is coming across to the pupils which may never be spoken in the English lesson or prayed about in assembly. They are picking-up an approach to living and an attitude to learning. and Michael Haralambos ("Sociology: Themes and Perspectives", 1991): The hidden curriculum consists of those things pupils learn through the experience of attending school rather than the stated educational objectives of such institutions. Recently a variety of authors, including Neil Postman, Henry Giroux, bell hooks, and Jonathan Kozol have examined the effects of hidden curriculum. One increasingly popular proponent, John Taylor Gatto, radically criticizes compulsory education in his book Dumbing Us Down: The Hidden Curriculum of Compulsory Schooling (1992).

See also • Cultural capital • Curriculum studies • Critical pedagogy • Dumbing Us Down • Tacit knowledge • The Hidden Curriculum (book) • Youth voice in education • Educational Inequality Hidden curriculum 52

References [1] Martin, Jane. “What Should We Do with a Hidden Curriculum When We Find One?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 122–139. [2] Martin, Jane. “What Should We Do with a Hidden Curriculum When We Find One?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 122–139. [3] Cornbleth, Catherine. “Beyond Hidden Curriculum?” Journal of Curriculum Studies. 16.1(1984): 29–36. [4] Apple, Michael and Nancy King. “What Do Schools Teach?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 82–99. [5] Giroux, Henry and Anthony Penna. “Social Education in the Classroom: The Dynamics of the Hidden Curriculum.” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 100–121. [6] Apple, Michael and Nancy King. “What Do Schools Teach?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 82–99. [7] Giroux, Henry and Anthony Penna. “Social Education in the Classroom: The Dynamics of the Hidden Curriculum.” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 100–121. [8] Martin, Jane. “What Should We Do with a Hidden Curriculum When We Find One?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 122–139. [9] Martin, Jane. “What Should We Do with a Hidden Curriculum When We Find One?” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 122–139. [10] Kohlberg, Lawrence. “The Moral Atmosphere of the School.” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 61–81. [11] Gordon, Edmumd W., Beatrice L. Bridglall, and Aundra Saa Meroe. Preface. Supplemental Education: The Hidden Curriculum of High Academic Achievement. By Gordon, Edmumd W., Beatrice L. Bridglall, and Aundra Saa Meroe. Lanham, Maryland: Rowman & Littlefield Publishers, Inc., 2005. ix–x. [12] Greene, Maxine. Introduction. The Hidden Curriculum and Moral Education. By Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 1–5. [13] Vallance, Elizabeth. “Hiding the Hidden Curriculum: An Interpretation of the Language of Justification in Nineteenth-Century Educational Reform.” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 9–27. [14] Anyon, Jean. “Social Class and the Hidden Curriculum of Work.” The Hidden Curriculum and Moral Education. Ed. Giroux, Henry and David Purpel. Berkeley, California: McCutchan Publishing Corporation, 1983. 143–167. [15] Margolis, Eric, Michael Soldatenko, Sandra Acker, and Marina Gair. “Peekaboo: Hiding and Outing the Curriculum.” The Hidden Curriculum in Higher Education. Ed. Margolis, Eric. New York: Routledge, 2001. [16] Rosenbaum, James E. The Hidden Curriculum of High School Tracking. New York: John Wiley & Sons, 1976. Information continuum 53 Information continuum

The term Information continuum is used to describe the whole set of all information, in connection with information management. The term may be used in reference to the information or the information infrastructure of a people, a species, a scientific subject or an institution. The Internet is sometimes called an 'Information continuum'.

References • "THE INFORMATION CONTINUUM, Evolution of Social Information Transfer in Monkeys, Apes, and Hominids", BARBARA J. KING, 1994

External links • Monash University - Faculty of Information Technology [1]

References

[1] http:/ / www. sims. monash. edu. au/ subjects/ ims5048

Knowhow

Know-how (or knowhow as it is sometimes written) is practical knowledge of how to get something done, as opposed to “know-what” (facts), “know-why” (science), or “know-who” (networking). Know-how is often tacit knowledge, which means that it is difficult to transfer to another person by means of writing it down or verbalising it. The opposite of tacit knowledge is explicit knowledge. In the context of industrial property (now generally viewed as intellectual property (IP)), know-how is a component in the transfer of technology in national and international environments, co-existing with or separate from other IP rights such as patents, trademarks and copyright and is an economic asset.[1] .

Definition of industrial know-how Know-how can be defined as confidentially held, or better, 'closely-held' information in the form of unpatented inventions, formulae, designs, drawings, procedures and methods, together with accumulated skills and experience in the hands of a licensor firm's professional personnel which could assist a transferee/licensee of the object product in its manufacture and use and bring to it a competitive advantage. It can be further supported with privately-maintained expert knowledge on the operation, maintenance, use/application of the object product and of its sale, usage or disposition. The inherent proprietary value of know-how lies embedded in the legal protection afforded to trade secrets in general law, particularly, 'case law'.[2] Know-how, in short, is "private intellectual property". The 'trade secret law' varies from country to country, unlike the case for patents, trademarks and copyright where there are formal 'conventions' through which subscribing countries grant the same protection to the 'property' as the others; examples of which are the Paris Convention for the Protection of Industrial Property and the World Intellectual Property Organization (WIPO), under United Nations, a supportive organization designed "to encourage creative activity, [and] to promote the protection of intellectual property throughout the world". A trade- secret may be defined as: • it is information Knowhow 54

• it is secret, not absoutely so • there is intent to keep it secret • it has inustrial, financial or trade application • it has economic value For purposes of illustration, the following may be a provision in a license agreement serving to define know-how: Know-how shall mean technical data, formulae, standards, technical information, specifications, processes, methods, code books, raw materials, as well as all information, knowledge, assistance, trade practices and secrets, and improvements thereto, divulged, disclosed, or in any way communicated to the Licensee under this Agreement, unless such information was, at the time of disclosure, or thereafter becomes part of the general knowledge or literature which is generally available for public use from other lawful sources. The burden of proving that any information disclosed hereunder is not confidential information shall rest on the licensee.

Show-how Show-how is a diluted form of know-how as even a walk-through a manufacturing plant provides valuable insights to the client's representatives into how a product is made, assembled or processed. Show-how is also used to demonstrate technique. An enlarged program of show-how is the typical content of Technical Assistance Agreements where the licensor firm, if one is involved, provides a substantial training program to the client's personnel on-site and off-site. (Note: such training does not imply any grant of 'license'.)

Disclosure agreements There are two sets of agreements associated with the transfer of know-how agreement:(a) the disclosure and (b) the non-disclosure agreements which are not separately parts of the principal know-how agreement. The initial need for 'disclosure' arises from the fact that a licensee firm may wish to know what is the specific, unique or general 'content' of the know-how that a licensor firm possesses which promises value to the licensee on entering into contract. Disclosure also aids the potential licensee in selecting among competitive offers, if any. Such disclosures are made by licensors only under non-disclosure or confidentiality agreements in which there are express undertakings that should the ultimate license not materialize, the firm to whom the disclosure is made will not reveal - and equally important - by any manner apply, any part of the disclosed knowledge which is not in the public domain or previously known to the firm receiving the information. Non-disclosure agreements are undertaken by those who receive confidential information from the licensee, relating to licensed know-how, so as to perform their tasks. Among them are the personnel of engineering firms who construct the plant for the licensee or those who are key employees of the licensee who have detailed access to disclosed data etcetera to administer their functions in operating the know-how-based plant. These are also in the nature of confidentiality agreements and carry the definition of know-how, in full or truncated part, on the need-to-know basis. Knowhow 55

General know-how Outside of usage in terms of industrial property, know-how is viewed as procedural knowledge (which term also reveals its nature).

See also • Procedural knowledge

References [1] Manual on Technology Transfer Negotiation, United Nations Industrial Development Organization (A Reference for Policy-makers and Practitioners on Technology Transfer), United Nations Industrial Development Organization, Vienna, Austria (1996) ISBN 92-1-106302-7 [2] Licensing Guide for Developing Countries, World Intellectual Property Organization (WIPO), Geneva, 1977, ISBN 92-805-0395-2

Knowledge representation and reasoning

Knowledge representation and reasoning is an area of artificial intelligence whose fundamental goal is to represent knowledge in a manner that facilitates inferencing (i.e. drawing conclusions) from knowledge. It analyzes how to formally think - how to use a symbol system to represent a domain of discourse (that which can be talked about), along with functions that allow inference (formalized reasoning) about the objects. Generally speaking, some kind of logic is used both to supply formal semantics of how reasoning functions apply to symbols in the domain of discourse, as well as to supply operators such as quantifiers, modal operators, etc. that, along with an interpretation theory, give meaning to the sentences in the logic. When we design a knowledge representation (and a knowledge representation system to interpret sentences in the logic in order to derive inferences from them) we have to make choices across a number of design spaces. The single most important decision to be made, is the expressivity of the KR. The more expressive, the easier and more compact it is to "say something". However, more expressive languages are harder to automatically derive inferences from. An example of a less expressive KR would be propositional logic. An example of a more expressive KR would be autoepistemic temporal modal logic. Less expressive KRs may be both complete and consistent (formally less expressive than set theory). More expressive KRs may be neither complete nor consistent. The key problem is to find a KR and a supporting reasoning system that can make the inferences your application needs within the resource constraints appropriate to the problem at hand. Recent developments in KR have been driven by the Semantic Web, and have included development of XML-based knowledge representation languages and standards, including RDF, RDF Schema, Topic Maps, DARPA Agent Markup Language (DAML), Ontology Inference Layer (OIL), and Web Ontology Language (OWL).

Overview There are representation techniques such as frames, rules, tagging, and semantic networks which have originated from theories of human information processing. Since knowledge is used to achieve intelligent behavior, the fundamental goal of knowledge representation is to represent knowledge in a manner as to facilitate inferencing (i.e. drawing conclusions) from knowledge. Some issues that arise in knowledge representation from an AI perspective are: • How do people represent knowledge? • What is the nature of knowledge? • Should a representation scheme deal with a particular domain or should it be general purpose? • How expressive is a representation scheme or formal language? Knowledge representation and reasoning 56

• Should the scheme be declarative or procedural? There has been very little top-down discussion of the knowledge representation (KR) issues and research in this area is a well aged quillwork. There are well known problems such as "spreading activation" (this is a problem in navigating a network of nodes), "subsumption" (this is concerned with selective inheritance; e.g. an ATV can be thought of as a specialization of a car but it inherits only particular characteristics) and "classification." For example a tomato could be classified both as a fruit and a vegetable. In the field of artificial intelligence, problem solving can be simplified by an appropriate choice of knowledge representation. Representing knowledge in some ways makes certain problems easier to solve. For example, it is easier to divide numbers represented in Hindu-Arabic numerals than numbers represented as Roman numerals.

History of knowledge representation and reasoning In computer science, particularly artificial intelligence, a number of representations have been devised to structure information. KR is most commonly used to refer to representations intended for processing by modern computers, and in particular, for representations consisting of explicit objects (the class of all elephants, or Clyde a certain individual), and of assertions or claims about them ('Clyde is an elephant', or 'all elephants are grey'). Representing knowledge in such explicit form enables computers to draw conclusions from knowledge already stored ('Clyde is grey'). Many KR methods were tried in the 1970s and early 1980s, such as heuristic question-answering, neural networks, theorem proving, and expert systems, with varying success. Medical diagnosis (e.g., Mycin) was a major application area, as were games such as chess. In the 1980s formal computer knowledge representation languages and systems arose. Major projects attempted to encode wide bodies of general knowledge; for example the "Cyc" project (still ongoing) went through a large encyclopedia, encoding not the information itself, but the information a reader would need in order to understand the encyclopedia: naive physics; notions of time, causality, motivation; commonplace objects and classes of objects. Through such work, the difficulty of KR came to be better appreciated. In computational linguistics, meanwhile, much larger databases of language information were being built, and these, along with great increases in computer speed and capacity, made deeper KR more feasible. Several programming languages have been developed that are oriented to KR. Prolog developed in 1972,[1] but popularized much later, represents propositions and basic logic, and can derive conclusions from known premises. KL-ONE (1980s) is more specifically aimed at knowledge representation itself. In 1995, the Dublin Core standard of metadata was conceived. In the electronic document world, languages were being developed to represent the structure of documents, such as SGML (from which HTML descended) and later XML. These facilitated information retrieval and data mining efforts, which have in recent years begun to relate to knowledge representation. Development of the Semantic Web, has included development of XML-based knowledge representation languages and standards, including RDF, RDF Schema, Topic Maps, DARPA Agent Markup Language (DAML), Ontology Inference Layer (OIL), and Web Ontology Language (OWL). Knowledge representation and reasoning 57

Topics in Knowledge representation and reasoning

Language and notation Some people think it would be best to represent knowledge in the same way that it is represented in the human mind, or to represent knowledge in the form of human language. Psycholinguistics is investigating how the human mind stores and manipulates language. Other branches of cognitive science examine how human memory stores sounds, sights, smells, emotions, procedures, and abstract ideas. Science has not yet completely described the internal mechanisms of the brain to the point where they can simply be replicated by computer programmers. Various artificial languages and notations have been proposed for representing knowledge. They are typically based on logic and mathematics, and have easily parsed grammars to ease machine processing. They usually fall into the broad domain of ontologies.

Ontology languages After CycL, a number of ontology languages have been developed. Most are declarative languages, and are either frame languages, or are based on first-order logic. Most of these languages only define an upper ontology with generic concepts, whereas the domain concepts are not part of the language definition. Gellish English is an example of an ontological language that includes a full engineering English Dictionary.

Links and structures While hyperlinks have come into widespread use, the closely related semantic link is not yet widely used. The mathematical table has been used since Babylonian times. More recently, these tables have been used to represent the outcomes of logic operations, such as truth tables, which were used to study and model Boolean logic, for example. Spreadsheets are yet another tabular representation of knowledge. Other knowledge representations are trees, by means of which the connections among fundamental concepts and derivative concepts can be shown. Visual representations are relatively new in the field of knowledge management but give the user a way to visualise how one thought or idea is connected to other ideas enabling the possibility of moving from one thought to another in order to locate required information. The approach is not without its competitors.[2]

Notation The recent fashion in knowledge representation languages is to use XML as the low-level syntax. This tends to make the output of these KR languages easy for machines to parse, at the expense of human readability and often space-efficiency. First-order predicate calculus is commonly used as a mathematical basis for these systems, to avoid excessive complexity. However, even simple systems based on this simple logic can be used to represent data that is well beyond the processing capability of current computer systems: see computability for reasons. Examples of notations: • DATR is an example for representing lexical knowledge • RDF is a simple notation for representing relationships between and among objects Knowledge representation and reasoning 58

Storage and manipulation One problem in knowledge representation is how to store and manipulate knowledge in an information system in a formal way so that it may be used by mechanisms to accomplish a given task. Examples of applications are expert systems, machine translation systems, computer-aided maintenance systems and information retrieval systems (including database front-ends). Semantic networks may be used to represent knowledge. Each node represents a concept and arcs are used to define relations between the concepts.The Conceptual graph model is probably the oldest model still alive. One of the most expressive and comprehensively described knowledge representation paradigms along the lines of semantic networks is MultiNet (an acronym for Multilayered Extended Semantic Networks). From the 1960s, the knowledge frame or just frame has been used. Each frame has its own name and a set of attributes, or slots which contain values; for instance, the frame for house might contain a color slot, number of floors slot, etc. Using frames for expert systems is an application of object-oriented programming, with inheritance of features described by the "is-a" link. However, there has been no small amount of inconsistency in the usage of the "is-a" link: Ronald J. Brachman wrote a paper titled "What IS-A is and isn't", wherein 29 different semantics were found in projects whose knowledge representation schemes involved an "is-a" link. Other links include the "has-part" link. Frame structures are well-suited for the representation of schematic knowledge and stereotypical cognitive patterns. The elements of such schematic patterns are weighted unequally, attributing higher weights to the more typical elements of a schema [3]. A pattern is activated by certain expectations: If a person sees a big bird, he or she will classify it rather as a sea eagle than a golden eagle, assuming that his or her "sea-scheme" is currently activated and his "land-scheme" is not. Frame representations are object-centered in the same sense as semantic networks are: All the facts and properties connected with a concept are located in one place - there is no need for costly search processes in the database. A behavioral script is a type of frame that describes what happens temporally; the usual example given is that of describing going to a restaurant. The steps include waiting to be seated, receiving a menu, ordering, etc. The different solutions can be arranged in a so-called semantic spectrum with respect to their semantic expressivity.

Further reading • Ronald J. Brachman; What IS-A is and isn't. An Analysis of Taxonomic Links in Semantic Networks; IEEE Computer, 16 (10); October 1983 [4] • Ronald J. Brachman, Hector J. Levesque Knowledge Representation and Reasoning, Morgan Kaufmann, 2004 ISBN 978-1-55860-932-7 • Ronald J. Brachman, Hector J. Levesque (eds) Readings in Knowledge Representation, Morgan Kaufmann, 1985, ISBN 0-934613-01-X • Chein, M., Mugnier, M.-L. (2009),Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs, Springer, 2009,ISBN: 978-1-84800-285-2 [5]. • Randall Davis, Howard Shrobe, and Peter Szolovits; What Is a Knowledge Representation? AI Magazine, 14(1):17-33,1993 [6] • Ronald Fagin, Joseph Y. Halpern, Yoram Moses, Moshe Y. Vardi Reasoning About Knowledge, MIT Press, 1995, ISBN 0-262-06162-7 • Jean-Luc Hainaut, Jean-Marc Hick, Vincent Englebert, Jean Henrard, Didier Roland: Understanding Implementations of IS-A Relations. ER 1996: 42-57 [7] • Hermann Helbig: Knowledge Representation and the Semantics of Natural Language, Springer, Berlin, Heidelberg, New York 2006 • Arthur B. Markman: Knowledge Representation Lawrence Erlbaum Associates, 1998 Knowledge representation and reasoning 59

• John F. Sowa: Knowledge Representation: Logical, Philosophical, and Computational Foundations. Brooks/Cole: New York, 2000 • Adrian Walker, Michael McCord, John F. Sowa, and Walter G. Wilson: Knowledge Systems and Prolog, Second Edition, Addison-Wesley, 1990

External links • What is a Knowledge Representation? [8] by Randall Davis and others • Introduction to Knowledge Modeling [9] by Pejman Makhfi • Introduction to Description Logics course [10] by Enrico Franconi, Faculty of Computer Science, Free University of Bolzano, Italy • DATR Lexical knowledge representation language [11] • Loom Project Home Page [12] • Description Logic in Practice: A CLASSIC Application [13] • The Rule Markup Initiative [14] • Schemas [3] • Nelements KOS [15] - a generic 3d knowledge representation system

References

[1] Timeline: A Brief History of Artificial Intelligence (http:/ / www. aaai. org/ AITopics/ pmwiki/ pmwiki. php/ AITopics/ BriefHistory), AAAI

[2] Other visual search tools are built by Convera Corporation (http:/ / www. convera. com/ ), Entopia, Inc. (http:/ / www. kmconnection. com/

pguide/ KSP2000348. htm), EPeople Inc. (http:/ / www. epeople. com/ home. shtml), and Inxight Software Inc (http:/ / www. inxight. com/ ).

[3] http:/ / moodle. ed. uiuc. edu/ wiked/ index. php/ Schemas

[4] http:/ / citeseer. nj. nec. com/ context/ 177306/ 0

[5] http:/ / www. lirmm. fr/ gbkrbook/

[6] http:/ / citeseer. ist. psu. edu/ davis93what. html

[7] http:/ / www. informatik. uni-trier. de/ ~ley/ db/ conf/ er/ HainautHEHR96. html

[8] http:/ / medg. lcs. mit. edu/ ftp/ psz/ k-rep. html

[9] http:/ / www. makhfi. com/ KCM_intro. htm

[10] http:/ / www. inf. unibz. it/ ~franconi/ dl/ course/

[11] http:/ / www. ccl. kuleuven. ac. be/ LKR/ html/ datr. html

[12] http:/ / www. isi. edu/ isd/ LOOM/ LOOM-HOME. html

[13] http:/ / www. research. att. com/ sw/ tools/ classic/ tm/ ijcai-95-with-scenario. html

[14] http:/ / www. dfki. uni-kl. de/ ruleml/

[15] http:/ / nelements. org Lateral thinking 60 Lateral thinking

Lateral thinking is a term coined by Edward de Bono in the book New Think: The Use of Lateral Thinking published in 1967; it refers to solving problems through an indirect and creative approach. Lateral thinking is about reasoning that is not immediately obvious and about ideas that may not be obtainable by using only traditional step-by-step logic.

Methods Critical thinking is primarily concerned with judging the true value of statements and seeking errors. Lateral thinking is more concerned with the movement value of statements and ideas. A person would use lateral thinking when they want to move from one known idea to creating new ideas. Edward de Bono defines four types of thinking tools: • Idea generating tools that are designed to break current thinking patterns—routine patterns, the status quo • Focus tools that are designed to broaden where to search for new ideas • Harvest tools that are designed to ensure more value is received from idea generating output • Treatment tools that are designed to consider real-world constraints, resources, and support[1] Random Entry Idea Generating Tool: Choose an object at random, or a noun from a dictionary, and associate that with the area you are thinking about. For example imagine you are thinking about how to improve a web site. Choosing an object at random from an office you might see a fax machine. A fax machine transmits images over the phone to paper. Fax machines are becoming rare. People send faxes directly to phone numbers. Perhaps this could be a new way to embed the web site's content in emails and other sites. Provocation Idea Generating Tool: choose to use any of the provocation techniques—wishful thinking, exaggeration, reversal, escape, or arising. Create a list of provocations and then use the most outlandish ones to move your thinking forward to new ideas. Challenge Idea Generating Tool: A tool which is designed to ask the question "Why?" in a non-threatening way: why something exists, why it is done the way it is. The result is a very clear understanding of "Why?" which naturally leads to fresh new ideas. The goal is to be able to challenge anything at all, not just items which are problems. For example you could challenge the handles on coffee cups. The reason for the handle seems to be that the cup is often too hot to hold directly. Perhaps coffee cups could be made with insulated finger grips, or there could be separate coffee cup holders similar to beer holders. Concept Fan Idea Generating Tool: Ideas carry out concepts. This tool systematically expands the range and number of concepts in order to end up with a very broad range of ideas to consider. Disproving: Based on the idea that the majority is always wrong (Henrik Ibsen, Galbraith), take anything that is obvious and generally accepted as "goes without saying", question it, take an opposite view, and try to convincingly disprove it. The other focus, harvesting and treatment tools deal with the output of the generated ideas and the ways to use them. Lateral thinking 61

Lateral thinking and problem solving Problem Solving: When something creates a problem, the performance or the status quo of the situation drops. Problem solving deals with finding out what caused the problem and then figuring out ways to fix the problem. The objective is to get the situation to where it should be. For example, a production line has an established run rate of 1000 items per hour. Suddenly, the run rate drops to 800 items per hour. Ideas as to why this happened and solutions to repair the production line must be thought of. Creative Problem Solving: Using creativity, one must solve a problem in an indirect and unconventional manner. For example, if a production line produced 1000 books per hour, creative problem solving could find ways to produce more books per hour, use the production line, or reduce the cost to run the production line. Creative Problem Identification: Many of the greatest non-technological innovations are identified while realizing an improved process or design in everyday objects and tasks either by accidental chance or by studying and documenting real world experience.

See also • Derailment (thought disorder) • Lateral thinking puzzles, also referred as situation puzzles • Oblique Strategies • Provocative operation • Serendipity • Thinking outside the box • Inductive reasoning • Deductive reasoning

Further reading • De Bono, Edward (1970). Lateral thinking: creativity step by step [2]. Harper & Row. pp. 300. ISBN 0-14-021978-1. • De Bono, Edward (1972). Po: Beyond Yes and No. Penguin Books. ISBN 0-14-021715-0. • De Bono, Edward (1992). Serious creativity: using the power of lateral thinking to create new ideas [3]. HarperBusiness. pp. 338. ISBN 0-88730-635-7. • Sloane, Paul (1994). Test your Lateral Thinking IQ [4]. Sterling Publishing. pp. 96. ISBN 0-8069-0684-7. • The Leader's Guide to Lateral Thinking Skills, Paul Sloane, (Kogan Page, 2006), ISBN 0-7494-4797-4

References [1] Lateral Thinking: The Power of Provocation manual: Published in 2006 by de Bono Thinking Systems

[2] http:/ / books. google. com/ books?id=H-ROAAAAMAAJ

[3] http:/ / books. google. com/ books?id=NbB9AAAAMAAJ

[4] http:/ / books. google. com/ books?id=0op9AAAAMAAJ Linnaean taxonomy 62 Linnaean taxonomy

Linnaean taxonomy is either 1. the particular classification (taxonomy) of Linnaeus, as set forth in his Systema Naturae (1735) and subsequent works. In the taxonomy of Linnaeus there are three kingdoms, divided into classes, and they, in turn, into orders, genera (singular: genus), and species (singular: species), with an additional rank lower than species. 2. a term for rank-based classification of organisms, in general. That is, taxonomy in the traditional sense of the word: rank-based scientific classification, This term is especially used as opposed to cladistic systematics, which groups organisms into clades. It is attributed to Linnaeus, although he neither invented the concept of ranked classification (it goes back to Aristotle) nor gave it its present form. In fact, it does not have an exact present form, as "Linnaean taxonomy" as such does not really exist: it is a collective (abstracting) term for what actually are Title page of Systema Naturae, Leiden, 1735 several separate fields, which use similar approaches.

the same applies to "Linnaean name": depending on the context this may either be a formal name given by Linnaeus (personally), such as Giraffa camelopardalis Linnaeus, 1758, or a formal name in the accepted nomenclature (as opposed to a modernistic clade name).

The taxonomy of Linnaeus In his Imperium Naturae, Linnaeus established three kingdoms, namely Regnum Animale, Regnum Vegetabile and Regnum Lapideum. This approach, the Animal, Vegetable and Mineral Kingdoms, survives today in the popular mind, notably in the form of the parlour game question: "Is it animal, vegetable or mineral?". The work of Linnaeus had a huge impact on science; it was indispensable as a foundation for biological nomenclature, now regulated by the Nomenclature Codes. Two of his works, the first edition of the Species Plantarum (1753) for plants and the tenth edition of the Systema Naturae (1758) are accepted among the starting points of nomenclature; his binomials (names for species) and his generic names take priority over those of others. However, the impact he had on science was not because of the value of his taxonomy. His taxonomy was not particularly notable, or even a step backward compared to his contemporaries. Linnaean taxonomy 63

For animals

Only in the Animal Kingdom is the higher taxonomy of Linnaeus still more or less recognizable and some of these names are still in use, but usually not quite for the same groups as used by Linnaeus. He divided the Animal Kingdom into six classes, in the tenth edition, of 1758, these were: • Classis 1. MAMMALIA • Classis 2. AVES • Classis 3. AMPHIBIA • Classis 4. PISCES • Classis 5. INSECTA The 1735 classification of animals • Classis 6. VERMES • Classis 7. REPTILA

For plants His orders and classes of plants, according to his Systema Sexuale, were never intended to represent natural groups (as opposed to his ordines naturales in his Philosophia Botanica) but only for use in identification. They were used in that sense well into the nineteenth century. Linnaean taxonomy 64

The Linnaean classes for plants, in the Sexual System, were: • Classis 1. MONANDRIA • Classis 2. DIANDRIA • Classis 3. TRIANDRIA • Classis 4. TETRANDRIA • Classis 5. PENTANDRIA • Classis 6. HEXANDRIA • Classis 7. HEPTANDRIA • Classis 8. OCTANDRIA • Classis 9. ENNEANDRIA • Classis 10. DECANDRIA • Classis 11. DODECANDRIA • Classis 12. ICOSANDRIA • Classis 13. POLYANDRIA • Classis 14. DIDYNAMIA • Classis 15. TETRADYNAMIA • Classis 16. MONADELPHIA • Classis 17. DIADELPHIA • Classis 18. POLYADELPHIA • Classis 19. SYNGENESIA • Classis 20. GYNANDRIA

• Classis 21. MONOECIA Key to the Sexual System (from the 10th, 1758, edition of the • Classis 22. DIOECIA Systema Naturae) • Classis 23. POLYGAMIA

• Classis 24. CRYPTOGAMIA

For minerals His taxonomy of minerals has dropped long since from use. In the tenth edition, 1758, of the Systema Naturae, the Linnaean classes were: • Classis 1. PETRÆ • Classis 2. MINERÆ • Classis 3. FOSSILIA • Classis 4. VITAMENTRA

Rank-based scientific classification This rank-based method of classifying living organisms was originally popularized by (and much later named for) Linnaeus, although it has changed considerably since his time. The greatest innovation of Linnaeus, and still the most important aspect of this system, is the general use of binomial nomenclature, the combination of a genus name and a second term, which together uniquely identify each species of organism. For example, the human species is uniquely identified by the name Homo sapiens. No other species of organism can have this same binomen (the technical term for a binomial in the case of animals). Prior to Linnaean taxonomy, animals were classified according to their mode of movement. A strength of Linnaean taxonomy is that it can be used to organize the different kinds of living organisms, simply and practically. Every species can be given a unique (and hopefully stable) name, as compared with common names Linnaean taxonomy 65

that are often neither unique nor consistent from place to place and language to language. This uniqueness and stability are, of course, a result of the acceptance by working systematists (biologists specializing in taxonomy), not merely of the binomial names themselves, but of the rules governing the use of these names, which are laid down in formal Nomenclature Codes. Species can be placed in a ranked hierarchy, starting with either domains or kingdoms. Domains are divided into kingdoms. Kingdoms are divided into phyla (singular: phylum) — for animals; the term division, used for plants and fungi, is equivalent to the rank of phylum (and the current International Code of Botanical Nomenclature allows the use of either term). Phyla (or divisions) are divided into classes, and they, in turn, into orders, families, genera (singular: genus), and species (singular: species). There are ranks below species: in zoology, subspecies (but see form or morph); in botany, variety (varietas) and form (forma), etc. Groups of organisms at any of these ranks are called taxa (singular: taxon) or taxonomic groups. The Linnaean system has proven robust and it remains the only extant working classification system at present that enjoys universal scientific acceptance. However, although the number of ranks is unlimited, in practice any classification becomes more cumbersome the more ranks are added. Among the later subdivisions that have arisen are such entities as phyla, families, and tribes, as well as any number of ranks with prefixes (superfamilies, subfamilies, etc). The use of newer taxonomic tools such as cladistics and phylogenetic nomenclature has led to a different way of looking at evolution (expressed in many, nested clades) and this sometimes leads to a desire for more ranks.

The alternative Over time, the understanding of the relationships between living things has changed. Linnaeus could only base his scheme on the structural similarities of the different organisms. The greatest change was the widespread acceptance of evolution as the mechanism of biological diversity and species formation, following the 1859 publication of Charles Darwin's On the Origin of Species. It then became generally understood that classifications ought to reflect the phylogeny of organisms, the descent by evolution. In cladistics, originating in the work of Willi Hennig, 1950 onwards, each taxon is grouped so as to include the common ancestor of the group's members (and thus to avoid polyphyly). Such taxa may be either monophyletic (including all descendants) such as genus Homo, or paraphyletic (excluding some descendants), such as genus Australopithecus. Originally, Linnaeus established three kingdoms in his scheme, namely for Plants, Animals and an additional group for minerals, which has long since been abandoned. Since then, various life forms have been moved into three new kingdoms: Monera, for prokaryotes (i.e., bacteria); Protista, for protozoans and most algae; and Fungi. This five kingdom scheme is still far from the phylogenetic ideal and has largely been supplanted in modern taxonomic work by a division into three domains: Bacteria and Archaea, which contain the prokaryotes, and Eukaryota, comprising the remaining forms. These arrangements should not be seen as definitive. They are based on the genomes of the organisms; as knowledge on this increases, so will classifications change. Representing presumptive evolutionary relationships, especially given the wide acceptance of cladistic methodology and numerous molecular phylogenies that have challenged long-accepted classifications, within the framework of Linnaean taxonomy is sometimes seen as problematic. Therefore, some systematists have proposed a PhyloCode to replace it. Linnaean taxonomy 66

See also • Evolutionary tree — a way to express insights into evolutionary relationships • History of plant systematics • Zoology mnemonic for a list of mnemonic sentences used to help people remember the list of Linnaean ranks.

Further reading • Dawkins, Richard. 2004. The Ancestor's Tale: A Pilgrimage to the Dawn of Life. Boston: Houghton Mifflin. ISBN 0618005838 • Ereshefsky, Marc. 2000. The Poverty of the Linnaean Hierarchy: A Philosophical Study of Biological Taxonomy. Cambridge: Cambridge University Press. • Gould, Stephen Jay. 1989. Wonderful Life: The Burgess Shale and the Nature of History. W. W. Norton & Co. ISBN 0-393-02705-8 • Pavord, Anna. The Naming of Names: The Search for Order in the World of Plants. Bloomsbury. ISBN 0-747-57052-0

External links • Wikispecies [1] • International Code of Botanical Nomenclature [2] (Saint Louis Code), Electronic version • ICZN website [3], for zoological nomenclature • Text of the ICZN [4], Electronic version • ZooBank: The World Register of Animal Names [5] • International Committee on Systematics of Prokaryotes [6] for bacteria • International Code of Zoological Nomenclature. 4th Edition. By the International Union of Biological Sciences [4] • ICTVdB website [7], for virus nomenclature by the International Union of Microbiological Societies • Tree of Life [8] • European Species Names in Linnaean, Czech, English, German and French [9]

References

[1] http:/ / species. wikipedia. org

[2] http:/ / www. bgbm. org/ iapt/ nomenclature/ code/ SaintLouis/ 0000St. Luistitle. htm

[3] http:/ / www. iczn. org/

[4] http:/ / www. iczn. org/ iczn/ index. jsp

[5] http:/ / www. zoobank. org

[6] http:/ / www. the-icsp. org/

[7] http:/ / www. ncbi. nlm. nih. gov/ ICTVdb/

[8] http:/ / tolweb. org

[9] http:/ / www. finitesite. com/ dandelion/ Linnaeus. HTML List of uniform tilings 67 List of uniform tilings

This table shows the 11 convex uniform tilings (regular and semiregular) of the Euclidean plane, and their dual tilings. There are three regular, and eight semiregular, tilings in the plane. The semiregular tilings form new tilings from their duals, each made from one type of irregular face. Uniform tilings are listed by their vertex configuration, the sequence of faces that exist on each vertex. For example 4.8.8 means one square and two octagons on a vertex. These 11 uniform tilings have 32 different uniform colorings. A uniform coloring allows identical sided polygons at a vertex to be colored differently, while still maintaining vertex-uniformity and transformational congruence between vertices. (Note: Some of the tiling images shown below are not color uniform) In addition to the 11 convex uniform tilings, there are also 14 nonconvex tilings, using star polygons, and reverse orientation vertex configurations. Dual tilings are listed by their face configuration, the number of faces at each vertex of a face. For example V4.8.8 means isosceles triangle tiles with one corner with 4 triangles, and two corners containing 8 triangles. In the 1987 book, Tilings and Patterns, Branko Grünbaum calls the vertex uniform tilings Archimedean in parallel to the Archimedean solids, and the dual tilings Laves tilings in honor of crystalographer Fritz Laves. John Conway calls the duals Catalan tilings, in parallel to the Catalan solid polyhedra.

Convex uniform tilings of the Euclidean plane

The [4,4] group family

Uniform tilings Vertex figure Dual uniform tilings (Platonic and Archimedean) Wythoff symbol(s) (called Laves or Catalan tilings) Symmetry group

self-dual (quadrille) Square tiling (quadrille) 4.4.4.4 (or 44) 4 | 2 4 p4m

List of uniform tilings 68

Tetrakis square tiling (kisquadrille) Truncated square tiling (truncated 4.8.8 quadrille) 2 | 4 4 4 4 2 | p4m

Cairo pentagonal tiling (4-fold pentille) Snub square tiling (snub quadrille) 3.3.4.3.4 | 4 4 2 p4g, p4, and pg

The [6,3] group family

Platonic and Archimedean tilings Vertex figure Dual Laves tilings Wythoff symbol(s) Symmetry group

6.6.6 (or 63) 3 | 6 2 Triangular tiling (deltile) 2 6 | 3 3 3 3 | Hexagonal tiling (hextille) p6m

List of uniform tilings 69

3.6.3.6 (or (3.6)2) 2 | 6 3 Rhombille tiling (rhombille) 3 3 | 3 p6m and p3m1 Trihexagonal tiling (hexadeltille)

3.12.12 2 3 | Triakis triangular tiling (kisdeltile) p6m

Truncated hexagonal tiling (truncated hextille)

3.3.3.3.3.3 (or 36) 6 | 3 2 Hexagonal tiling (hextile) 3 | 3 3 | 3 3 3 Triangular tiling (deltile) p6m and p3m1

3.4.6.4 3 | 6 2 Deltoidal trihexagonal tiling (tetrille) p6m

Rhombitrihexagonal tiling (rhombihexadeltille) List of uniform tilings 70

4.6.12 or *632 Bisected hexagonal tiling 2 6 3 | (kisrhombille) p6m Truncated trihexagonal tiling (truncated hexadeltille)

3.3.3.3.6 | 6 3 2 Floret pentagonal tiling (6-fold pentille) p6

Snub hexagonal tiling (snub hexatille)

Non-Wythoffian uniform tiling

Platonic and Archimedean tilings Vertex figure Dual Laves tilings Wythoff symbol(s) Symmetry group

3.3.3.4.4 2 | 2 (2 2) cmm Prismatic pentagonal tiling (iso(4-)pentille) Elongated triangular tiling (isosnub quadrille) none

See also • Uniform tiling • Convex uniform honeycomb - The 28 uniform 3-dimensional tessellations, a parallel construction to the convex uniform Euclidean plane tilings. • Uniform tilings in hyperbolic plane

References • Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. W. H. Freeman and Company. ISBN 0-7167-1193-1. • H.S.M. Coxeter, M.S. Longuet-Higgins, J.C.P. Miller, Uniform polyhedra, Phil. Trans. 1954, 246 A, 401-50. List of uniform tilings 71

• Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 2-3 Circle packings, plane tessellations, and networks, p 34-40) • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1] (Chapter 19, Archimedean tilings, table 19.1, Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table)

External links • Weisstein, Eric W., "Uniform tessellation [2]" from MathWorld. • Uniform Tessellations on the Euclid plane [3] • Tessellations of the Plane [4] • David Bailey's World of Tessellations [5] • k-uniform tilings [6] • n-uniform tilings [7]

References

[1] http:/ / www. akpeters. com/ product. asp?ProdCode=2205

[2] http:/ / mathworld. wolfram. com/ UniformTessellation. html

[3] http:/ / www2u. biglobe. ne. jp/ ~hsaka/ mandara/ ue2

[4] http:/ / www. orchidpalms. com/ polyhedra/ tessellations/ tessel. htm

[5] http:/ / www. tess-elation. co. uk/ index. htm

[6] http:/ / www. uwgb. edu/ dutchs/ symmetry/ uniftil. htm

[7] http:/ / probabilitysports. com/ tilings. html

Machine learning

Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to evolve behaviors based on empirical data, such as from sensor data or databases. A major focus of machine learning research is to automatically learn to recognize complex patterns and make intelligent decisions based on data; the difficulty lies in the fact that the set of all possible behaviors given all possible inputs is too complex to describe generally in programming languages, so that in effect programs must automatically describe programs. Artificial intelligence is a closely related field, as are probability theory and statistics, data mining, pattern recognition, adaptive control, and theoretical computer science.

Definition A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.[1]

Human interaction Some machine learning systems attempt to eliminate the need for human intuition in data analysis, while others adopt a collaborative approach between human and machine. Human intuition cannot, however, be entirely eliminated, since the system's designer must specify how the data is to be represented and what mechanisms will be used to search for a characterization of the data. Machine learning 72

Algorithm types Machine learning algorithms are organized into a taxonomy, based on the desired outcome of the algorithm. • Supervised learning generates a function that maps inputs to desired outputs. For example, in a classification problem, the learner approximates a function mapping a vector into classes by looking at input-output examples of the function. • Unsupervised learning models a set of inputs, like clustering. • Semi-supervised learning combines both labeled and unlabeled examples to generate an appropriate function or classifier. • Reinforcement learning learns how to act given an observation of the world. Every action has some impact in the environment, and the environment provides feedback in the form of rewards that guides the learning algorithm. • Transduction tries to predict new outputs based on training inputs, training outputs, and test inputs. • Learning to learn learns its own inductive bias based on previous experience.

Theory The computational analysis of machine learning algorithms and their performance is a branch of theoretical computer science known as computational learning theory. Because training sets are finite and the future is uncertain, learning theory usually does not yield absolute guaranties of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. In addition to performance bounds, computational learning theorists study the time complexity and feasibility of learning. In computational learning theory, a computation is considered feasible if it can be done in polynomial time. There are two kinds of time complexity results. Positive results show that a certain class of functions can be learned in polynomial time. Negative results show that certain classes cannot be learned in polynomial time. There are many similarities between Machine Learning theory and Statistics, although they use different terms.

Approaches

Decision tree learning Decision tree learning uses a decision tree as a predictive model which maps observations about an item to conclusions about the item's target value.

Association rule learning Association rule learning is a method for discovering interesting relations between variables in large databases.

Artificial neural networks An artificial neural network (ANN), usually called "neural network" (NN), is a mathematical model or computational model that tries to simulate the structure and/or functional aspects of biological neural networks. It consists of an interconnected group of artificial neurons and processes information using a connectionist approach to computation. Modern neural networks are non-linear statistical data modeling tools. They are usually used to model complex relationships between inputs and outputs or to find patterns in data. Machine learning 73

Genetic programming Genetic programming (GP) is an evolutionary algorithm-based methodology inspired by biological evolution to find computer programs that perform a user-defined task. It is a specialization of genetic algorithms (GA) where each individual is a computer program. It is a machine learning technique used to optimize a population of computer programs according to a fitness landscape determined by a program's ability to perform a given computational task.

Inductive logic programming Inductive logic programming (ILP) is an approach to rule learning uses logic programming as a uniform representation for examples, background knowledge, and hypotheses. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.

Support vector machines Support vector machines (SVMs) are a set of related supervised learning methods used for classification and regression. Given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other.

Clustering Cluster analysis or clustering is the assignment of a set of observations into subsets (called clusters) so that observations in the same cluster are similar in some sense. Clustering is a method of unsupervised learning, and a common technique for statistical data analysis.

Bayesian networks A Bayesian network, belief network or directed acyclic graphical model is a probabilistic graphical model that represents a set of random variables and their conditional independencies via a directed acyclic graph (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms exist that perform inference and learning.

Reinforcement learning Reinforcement learning is concerned with how an agent ought to take actions in an environment so as to maximize some notion of long-term reward. Reinforcement learning algorithms attempt to find a policy that maps states of the world to the actions the agent ought to take in those states. Reinforcement learning differs from the supervised learning problem in that correct input/output pairs are never presented, nor sub-optimal actions explicitly corrected.

Applications Applications for machine learning include machine perception, computer vision, natural language processing, syntactic pattern recognition, search engines, medical diagnosis, bioinformatics, brain-machine interfaces and cheminformatics, detecting credit card fraud, stock market analysis, classifying DNA sequences, speech and handwriting recognition, object recognition in computer vision, game playing, software engineering, adaptive websites, robot locomotion, and structural health monitoring. Machine learning 74

Software RapidMiner and Weka are software suites containing a variety of machine learning algorithms.

Journals and conferences • Machine Learning (journal) • Journal of Machine Learning Research • International Conference on Machine Learning (ICML) (conference) • Neural Information Processing Systems (NIPS) (conference) • List of upcoming Machine Learning Conferences [2] (conference)

See also

• Computational intelligence • Multi-label classification • Data mining • Pattern recognition • Explanation-based learning • Predictive analytics • Important publications in machine learning

Further reading • Sergios Theodoridis, Konstantinos Koutroumbas (2009) "Pattern Recognition" , 4th Edition, Academic Press, ISBN 978-1-59749-272-0. • Ethem Alpaydın (2004) Introduction to Machine Learning (Adaptive Computation and Machine Learning), MIT Press, ISBN 0262012111 • Christopher M. Bishop (2006) Pattern Recognition and Machine Learning, Springer ISBN 0-387-31073-8. • Bing Liu (2007), Web Data Mining: Exploring Hyperlinks, Contents and Usage Data [3]. Springer, ISBN 3540378812 • Toby Segaran, Programming Collective Intelligence, O'Reilly ISBN 0-596-52932-5 • Ray Solomonoff, "An Inductive Inference Machine [4]" A privately circulated report from the 1956 Dartmouth Summer Research Conference on AI. • Ray Solomonoff, An Inductive Inference Machine, IRE Convention Record, Section on Information Theory, Part 2, pp., 56-62, 1957. • Ryszard S. Michalski, Jaime G. Carbonell, Tom M. Mitchell (1983), Machine Learning: An Artificial Intelligence Approach, Tioga Publishing Company, ISBN 0-935382-05-4. • Ryszard S. Michalski, Jaime G. Carbonell, Tom M. Mitchell (1986), Machine Learning: An Artificial Intelligence Approach, Volume II, Morgan Kaufmann, ISBN 0-934613-00-1. • Yves Kodratoff, Ryszard S. Michalski (1990), Machine Learning: An Artificial Intelligence Approach, Volume III, Morgan Kaufmann, ISBN 1-55860-119-8. • Ryszard S. Michalski, George Tecuci (1994), Machine Learning: A Multistrategy Approach, Volume IV, Morgan Kaufmann, ISBN 1-55860-251-8. • Bhagat, P. M. (2005). Pattern Recognition in Industry, Elsevier. ISBN 0-08-044538-1. • Bishop, C. M. (1995). Neural Networks for Pattern Recognition, Oxford University Press. ISBN 0-19-853864-2. • Richard O. Duda, Peter E. Hart, David G. Stork (2001) Pattern classification (2nd edition), Wiley, New York, ISBN 0-471-05669-3. • Huang T.-M., Kecman V., Kopriva I. (2006), Kernel Based Algorithms for Mining Huge Data Sets, Supervised, Semi-supervised, and Unsupervised Learning [5], Springer-Verlag, Berlin, Heidelberg, 260 pp. 96 illus., Hardcover, ISBN 3-540-31681-7. Machine learning 75

• KECMAN Vojislav (2001), Learning and Soft Computing, Support Vector Machines, Neural Networks and Fuzzy Logic Models [6], The MIT Press, Cambridge, MA, 608 pp., 268 illus., ISBN 0-262-11255-8. • MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms [7], Cambridge University Press. ISBN 0-521-64298-1. • Mitchell, T. (1997). Machine Learning, McGraw Hill. ISBN 0-07-042807-7. • Ian H. Witten and Eibe Frank Data Mining: Practical machine learning tools and techniques Morgan Kaufmann ISBN 0-12-088407-0. • Sholom Weiss and Casimir Kulikowski (1991). Computer Systems That Learn, Morgan Kaufmann. ISBN 1-55860-065-5. • Mierswa, Ingo and Wurst, Michael and Klinkenberg, Ralf and Scholz, Martin and Euler, Timm: YALE: Rapid Prototyping for Complex Data Mining Tasks, in Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-06), 2006. • Trevor Hastie, Robert Tibshirani and Jerome Friedman (2001). The Elements of Statistical Learning [8], Springer. ISBN 0387952845. • Vladimir Vapnik (1998). Statistical Learning Theory. Wiley-Interscience, ISBN 0471030031.

External links • Ruby implementations of several machine learning algorithms [9] • Andrew Ng's Stanford lectures and course materials [10] • The Encyclopedia of Computational Intelligence [11] • International Machine Learning Society [12] • Kmining List of machine learning, data mining and KDD scientific conferences [13] • Machine Learning Open Source Software [14] • Machine Learning Video Lectures [15] • Open Source Artificial Learning Software [16] • The Computational Intelligence and Machine Learning Virtual Community [17] • R Machine Learning Task View [18] • Machine Learning Links and Resources [19]

References [1] Tom M. Mitchell (1997) Machine Learning p.2

[2] http:/ / sites. google. com/ site/ fawadsyed/ upcoming-conferences

[3] http:/ / www. cs. uic. edu/ ~liub/ WebMiningBook. html

[4] http:/ / world. std. com/ ~rjs/ indinf56. pdf

[5] http:/ / learning-from-data. com

[6] http:/ / support-vector. ws

[7] http:/ / www. inference. phy. cam. ac. uk/ mackay/ itila/

[8] http:/ / www-stat. stanford. edu/ ~tibs/ ElemStatLearn/

[9] http:/ / ai4r. rubyforge. org

[10] http:/ / see. stanford. edu/ see/ courseinfo. aspx?coll=348ca38a-3a6d-4052-937d-cb017338d7b1

[11] http:/ / scholarpedia. org/ article/ Encyclopedia_of_Computational_Intelligence

[12] http:/ / machinelearning. org/

[13] http:/ / kmining. com/ info_conferences. html

[14] http:/ / mloss. org/ about/

[15] http:/ / videolectures. net/ Top/ Computer_Science/ Machine_Learning/

[16] http:/ / salproject. codeplex. com

[17] http:/ / cimlcommunity. org/

[18] http:/ / cran. r-project. org/ web/ views/ MachineLearning. html

[19] http:/ / www. reddit. com/ r/ MachineLearning/ Mathematical morphology 76 Mathematical morphology

Mathematical morphology (MM) is a theory and technique for the analysis and processing of geometrical structures, based on set theory, lattice theory, topology, and random functions. MM is most commonly applied to digital images, but it can be employed as well on graphs, surface meshes, solids, and many other spatial structures. Topological and geometrical continuous-space concepts such as size, shape, convexity, connectivity, and geodesic distance, can be characterized by MM on both continuous and discrete spaces. MM is also the foundation of morphological image processing, which consists of a set of operators that transform images according to the above characterizations.

MM was originally developed for binary images, and was later extended to grayscale functions and images. The subsequent

generalization to complete lattices is widely accepted today as MM's A shape (in blue) and its morphological dilation theoretical foundation. (in green) and erosion (in yellow) by a diamond-shape structuring element. History

Mathematical Morphology was born in 1964 from the collaborative work of Georges Matheron and Jean Serra, at the École des Mines de Paris, France. Matheron supervised the PhD thesis of Serra, devoted to the quantification of mineral characteristics from thin cross sections, and this work resulted in a novel practical approach, as well as theoretical advancements in integral geometry and topology. In 1968, the Centre de Morphologie Mathématique was founded by the École des Mines de Paris in Fontainebleau, France, lead by Matheron and Serra. During the rest of the 1960's and most of the 1970's, MM dealt essentially with binary images, treated as sets, and generated a large number of binary operators and techniques: Hit-or-miss transform, dilation, erosion, opening, closing, granulometry, thinning, skeletonization, ultimate erosion, conditional bisector, and others. A random approach was also developed, based on novel image models. Most of the work in that period was developed in Fontainebleau. From mid-1970's to mid-1980's, MM was generalized to grayscale functions and images as well. Besides extending the main concepts (such as dilation, erosion, etc...) to functions, this generalization yielded new operators, such as morphological gradients, top-hat transform and the Watershed (MM's main segmentation approach). In the 1980's and 1990's, MM gained a wider recognition, as research centers in several countries began to adopt and investigate the method. MM started to be applied to a large number of imaging problems and applications. In 1986, Jean Serra further generalized MM, this time to a theoretical framework based on complete lattices. This generalization brought flexibility to the theory, enabling its application to a much larger number of structures, including color images, video, graphs, meshes, etc... At the same time, Matheron and Serra also formulated a theory for morphological filtering, based on the new lattice framework. The 1990's and 2000's also saw further theoretical advancements, including the concepts of connections and levelings. In 1993, the first International Symposium on Mathematical Morphology (ISMM) took place in Barcelona, Spain. Since then, ISMMs are organized every 2-3 years, each time in a different part of the world: Fontainebleau, France Mathematical morphology 77

(1994); Atlanta, USA (1996); Amsterdam, Netherlands (1998); Palo Alto, CA, USA (2000); Sydney, Australia (2002); Paris, France (2004); Rio de Janeiro, Brazil (2007); and Groningen, Netherlands (2009).

References • "Introduction" by Pierre Soille, in (Serra et al. (Eds.) 1994), pgs. 1-4. • "Appendix A: The 'Centre de Morphologie Mathématique', an overview" by Jean Serra, in (Serra et al. (Eds.) 1994), pgs. 369-374. • "Foreword" in (Ronse et al. (Eds.) 2005)

Binary morphology In binary morphology, an image is viewed as a subset of an Euclidean space or the integer grid , for some dimension d.

Structuring element The basic idea in binary morphology is to probe an image with a simple, pre-defined shape, drawing conclusions on how this shape fits or misses the shapes in the image. This simple "probe" is called structuring element, and is itself a binary image (i.e., a subset of the space or grid). Here are some examples of widely used structuring elements (denoted by B): • Let ; B is an open disk of radius r, centered at the origin. • Let ; B is a 3x3 square, that is, B={(-1,-1), (-1,0), (-1,1), (0,-1), (0,0), (0,1), (1,-1), (1,0), (1,1)}. • Let ; B is the "cross" given by: B={(-1,0), (0,-1), (0,0), (0,1), (1,0)}.

Basic operators The basic operations are shift-invariant (translation invariant) operators strongly related to Minkowski addition. Let E be a Euclidean space or an integer grid, and A a binary image in E.

Erosion

The erosion of the binary image A by the structuring element B is defined by:

The erosion of the dark-blue square by a disk, resulting in the light-blue square.

, where B is the translation of B by the vector z, i.e., , . z Mathematical morphology 78

When the structuring element B has a center (e.g., B is a disk or a square), and this center is located on the origin of E, then the erosion of A by B can be understood as the locus of points reached by the center of B when B moves inside A. For example, the erosion of a square of side 10, centered at the origin, by a disc of radius 2, also centered at the origin, is a square of side 6 centered at the origin.

The erosion of A by B is also given by the expression: .

Example application: Assume we have received a fax of a dark photocopy. Everything looks like it was written with a pen that is bleeding. Erosion process will allow thicker lines to get skinny and detect the hole inside the letter "o".

Dilation

The dilation of A by the structuring element B is defined by:

The dilation of the dark-blue square by a disk, resulting in the light-blue square with rounded corners.

.

The dilation is commutative, also given by: .

If B has a center on the origin, as before, then the dilation of A by B can be understood as the locus of the points covered by B when the center of B moves inside A. In the above example, the dilation of the square of side 10 by the disk of radius 2 is a square of side 14, with rounded corners, centered at the origin. The radius of the rounded corners is 2. The dilation can also be obtained by: , where Bs denotes the symmetric of B, that is, . Example application: Dilation is the opposite of the erosion. Figures that are very lightly drawn get thick when "dilated". Easiest way to describe it is to imagine the same fax/text is written with a thicker pen. Mathematical morphology 79

Opening

The opening of A by B is obtained by the erosion of A by B, followed by dilation of the resulting image by B:

The opening of the dark-blue square by a disk, resulting in the light-blue square with round corners.

.

The opening is also given by , which means that it is the locus of translations of the structuring

element B inside the image A. In the case of the square of radius 10, and a disc of radius 2 as the structuring element, the opening is a square of radius 10 with rounded corners, where the corner radius is 2. Example application: Let's assume someone has written a note on a non-soaking paper that writing looks like it is growing tiny hairy roots all over. Opening essentially removes the outer tiny "hairline" leaks and restores the text. The side effect is that it rounds off things. The sharp edges start to disappear.

Closing

The closing of A by B is obtained by the dilation of A by B, followed by erosion of the resulting structure by B:

The closing of the dark-blue shape (union of two squares) by a disk, resulting in the union of the dark-blue shape and the light-blue areas.

. The closing can also be obtained by , where Xc denotes the complement of X relative to E (that is, ). The above means that the closing is the complement of the locus of translations of the symmetric of the structuring element outside the image A. Mathematical morphology 80

Properties of the basic operators Here are some properties of the basic binary morphological operators (dilation, erosion, opening and closing): • They are translation invariant. • They are increasing, that is, if , then , and , etc. • The dilation is commutative. • If the origin of E belongs to the structuring element B, then . • The dilation is associative, i.e., . Moreover, the erosion satisfies . • Erosion and dilation satisfy the duality . • Opening and closing satisfy the duality . • The dilation is distributive over set union • The erosion is distributive over set intersection • The dilation is a pseudo-inverse of the erosion, and vice-versa, in the following sense: if and only if . • Opening and closing are idempotent. • Opening is anti-extensive, i.e., , whereas the closing is extensive, i.e., .

Other operators and tools • Hit-or-miss transform • Morphological skeleton • Filtering by reconstruction • Ultimate erosions and conditional bisectors • Granulometry • Geodesic distance functions

Grayscale morphology In grayscale morphology, images are functions mapping a Euclidean space or grid E into , where is the set of reals, is an element larger than any real number, and is an element smaller than any real number. Grayscale structuring elements are also functions of the same format, called "structuring functions". Denoting an image by f(x) and the structuring function by b(x), the grayscale dilation of f by b is given by

, where "sup" denotes the supremum. Similarly, the erosion of f by b is given by

, where "inf" denotes the infimum. Just like in binary morphology, the opening and closing are given respectively by , and . Mathematical morphology 81

Flat structuring functions It is common to use flat structuring elements in morphological applications. Flat structuring functions are functions b(x) in the form

,

where . In this case, the dilation and erosion are greatly simplified, and given respectively by

, and

. In the bounded, discrete case (E is a grid and B is bounded), the supremum and infimum operators can be replaced by the maximum and minimum. Thus, dilation and erosion are particular cases of order statistics filters, with dilation returning the maximum value within a moving window (the symmetric of the structuring function support B), and the erosion returning the minimum value within the moving window B. In the case of flat structuring element, the morphological operators depend only on the relative ordering of pixel values, regardless their numerical values, and therefore are especially suited to the processing of binary images and grayscale images whose light transfer function is not known.

Other operators and tools • Morphological Gradients • Top-hat transform • Watershed (algorithm) By combining these operators one can obtain algorithms for many image processing tasks, such as feature detection, image segmentation, image sharpening, image filtering, and classification.

Mathematical morphology on complete lattices Complete lattices are partially ordered sets, where every subset has an infimum and a supremum. In particular, it contains a least element and a greatest element (also denoted "universe").

Adjunctions (Dilation and Erosion) Let be a complete lattice, with infimum and minimum symbolized by and , respectively. Its universe and least element are symbolized by U and , respectively. Moreover, let be a collection of elements from L. A dilation is any operator that distributes over the supremum, and preserves the least element. I.e.:

• ,

• . An erosion is any operator that distributes over the infimum, and preserves the universe. I.e.:

• ,

• . Dilations and erosions form Galois connections. That is, for all dilation there is one and only one erosion that satisfies Mathematical morphology 82

for all . Similarly, for all erosion there is one and only one dilation satisfying the above connection. Furthermore, if two operators satisfy the connection, then must be a dilation, and an erosion. Pairs of erosions and dilations satisfying the above connection are called "adjunctions", and the erosion is said to be the adjoint erosion of the dilation, and vice-versa.

Opening and Closing For all adjunction , the morphological opening and morphological closing are defined as follows: , and . The morphological opening and closing are particular cases of algebraic opening (or simply opening) and algebraic closing (or simply closing). Algebraic openings are operators in L that are idempotent, increasing, and anti-extensive. Algebraic closings are operators in L that are idempotent, increasing, and extensive.

Particular cases Binary morphology is a particular case of lattice morphology, where L is the power set of E (Euclidean space or grid), that is, L is the set of all subsets of E, and is the set inclusion. In this case, the infimum is set intersection, and the supremum is set union. Similarly, grayscale morphology is another particular case, where L is the set of functions mapping E into , and , , and , are the point-wise order, supremum, and infimum, respectively. That is, is f and g are functions in L, then if and only if ; the infimum is given by ; and the supremum is given by .

References • Image Analysis and Mathematical Morphology by Jean Serra, ISBN 0126372403 (1982) • Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances by Jean Serra, ISBN 0-12-637241-1 (1988) • An Introduction to Morphological Image Processing by Edward R. Dougherty, ISBN 0-8194-0845-X (1992) • Morphological Image Analysis; Principles and Applications by Pierre Soille, ISBN 3540-65671-5 (1999), 2nd edition (2003) • Mathematical Morphology and its Application to Signal Processing, J. Serra and Ph. Salembier (Eds.), proceedings of the 1st international symposium on mathematical morphology (ISMM'93), ISBN 84-7653-271-7 (1993) • Mathematical Morphology and Its Applications to Image Processing, J. Serra and P. Soille (Eds.), proceedings of the 2nd international symposium on mathematical morphology (ISMM'93), ISBN 0-7923-3093-5 (1994) • Mathematical Morphology and its Applications to Image and Signal Processing, Henk J.A.M. Heijmans and Jos B.T.M. Roerdink (Eds.), proceedings of the 4th international symposium on mathematical morphology (ISMM'98), ISBN 0-7923-5133-9 (1998) • Mathematical Morphology: 40 Years On, Christian Ronse, Laurent Najman, and Etienne Decencière (Eds.), ISBN 1-4020-3442-3 (2005) • Mathematical Morphology and its Applications to Signal and Image Processing, Gerald J.F. Banon, Junior Barrera, Ulisses M. Braga-Neto (Eds.), proceedings of the 8th international symposium on mathematical morphology (ISMM'07), ISBN 978-85-17-00032-4 (2007) Mathematical morphology 83

External links • Online course on mathematical morphology [1], by Jean Serra (in English, French, and Spanish) • Center of Mathematical Morphology [2], Paris School of Mines • History of Mathematical Morphology [3], by Georges Matheron and Jean Serra • Morphology Digest, a newsletter on mathematical morphology [4], by Pierre Soille • Lectures on Image Processing: A collection of 18 lectures in pdf format from Vanderbilt University. Lectures 16-18 are on Mathematical Morphology [5], by Alan Peters • Mathematical Morphology; from Computer Vision lectures [6], by Robyn Owens • Free SIMD Optimized Image processing library [7] • Java applet demonstration [8] • FILTERS : a free open source image processing library [9] • Fast morphological erosions, dilations, openings, and closings [10]

References

[1] http:/ / cmm. ensmp. fr/ ~serra/ cours/ index. htm

[2] http:/ / cmm. ensmp. fr/ index_eng. html

[3] http:/ / cmm. ensmp. fr/ ~serra/ pdf/ birth_of_mm. pdf

[4] http:/ / mdigest. jrc. ec. europa. eu

[5] http:/ / www. archive. org/ details/ Lectures_on_Image_Processing

[6] http:/ / homepages. inf. ed. ac. uk/ rbf/ CVonline/ LOCAL_COPIES/ OWENS/ LECT3/ node3. html

[7] http:/ / fulguro. sourceforge. net

[8] http:/ / www. cs. bris. ac. uk/ ~majid/ mengine/ morph. html

[9] http:/ / filters. sourceforge. net/

[10] http:/ / www. ulg. ac. be/ telecom/ research/ libmorphoDoc/ index. html

Mental model

A mental model is an explanation of someone's thought process about how something works in the real world. It is a representation of the surrounding world, the relationships between its various parts and a person's intuitive perception about their own acts and their consequences. Our mental models help shape our behaviour and define our approach to solving problems (akin to a personal algorithm) and carrying out tasks.

Overview A mental model is a kind of internal symbol or representation of external reality, hypothesized to play a major role in cognition, reasoning and decision-making. Kenneth Craik suggested in 1943 that the mind constructs "small-scale models" of reality that it uses to anticipate events. One example is provided in the following description from Richard Feynman: I had a scheme, which I still use today when somebody is explaining something that I'm trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they're all excited. As they're telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball) – disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn't true for my hairy green ball thing, so I say, 'False!' Jay Wright Forrester defined general mental models as: Mental model 84

"The image of the world around us, which we carry in our head, is just a model. Nobody in his head imagines all the world, government or country. He has only selected concepts, and relationships between them, and uses those to represent the real system." In psychology, the term "mental models" is sometimes used to refer to mental representations or mental simulation generally. At other times it is used to refer to mental models and reasoning and to the mental model theory of reasoning developed by Philip Johnson-Laird and Ruth M.J. Byrne.

History The term is believed to have originated with Kenneth Craik in his 1943 book The Nature of Explanation. Georges-Henri Luquet in Le dessin enfantin (Children's Drawings), published in 1927 by Alcan, Paris, argued that children construct internal models, a view that influenced, among others, Jean Piaget. Philip Johnson-Laird published Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness in 1983. In the same year, Dedre Gentner and Albert Stevens edited a collection of chapters in a book also titled Mental Models.[1] The first line of their book explains the idea further: "One function of this chapter is to belabor the obvious; people's views of the world, of themselves, of their own capabilities, and of the tasks that they are asked to perform, or topics they are asked to learn, depend heavily on the conceptualizations that they bring to the task." (See Mental Models (Gentner-Stevens book).) Since then there has been much discussion and use of the idea in human-computer interaction and usability by researchers including Donald Norman and Steve Krug in his book Don't Make Me Think. Walter Kintsch and Teun A. van Dijk, using the term situation model (in their book Strategies of Discourse Comprehension, 1983), showed the relevance of mental models for the production and comprehension of discourse.

Mental models and reasoning One view of human reasoning is that it depends on mental models. On this view mental models can be constructed from perception, imagination, or the comprehension of discourse (Johnson-Laird, 1983). Such mental models are akin to architects' models or to physicists' diagrams in that their structure is analogous to the structure of the situation that they represent, unlike, say, the structure of logical forms used in formal rule theories of reasoning. In this respect they are a little like pictures in the "picture" theory of language described by Ludwig Wittgenstein in 1922. Philip Johnson-Laird and Ruth M.J. Byrne developed a theory of mental models which makes the assumption that reasoning depends, not on logical form, but on mental models (Johnson-Laird and Byrne, 1991).

Principles of mental models Mental models are based on a small set of fundamental assumptions, which distinguish them from other proposed representations in the psychology of reasoning (Byrne and Johnson-Laird, 2009). Each mental model represents a possibility. A mental model represents one possibility, capturing what is common to all the different ways in which the possibility may occur (Johnson-Laird and Byrne, 2002). Mental models are iconic, i.e., each part of a model corresponds to each part of what it represents (Johnson-Laird, 2006). Mental models are based on a principle of truth: they represent only those situations that are possible, and each model of a possibility represents only what is true in that possibility according to the proposition. Mental models can represent what is false, temporarily assumed to be true, e.g., in the case of counterfactual conditionals and counterfactual thinking (Byrne, 2005). Mental model 85

Reasoning with mental models People infer that a conclusion is valid if it holds in all the possibilities. Procedures for reasoning with mental models rely on counterexamples to refute invalid inferences; they establish validity by ensuring that a conclusion holds over all the models of the premises. Reasoners focus on a subset of the possible models of multiple-model problems—often just a single model. The ease with which reasoners can make deductions is affected by many factors, including age and working memory (Barrouillet, et al, 2000). They reject a conclusion if they find a counterexample, i.e., a possibility in which the premises hold, but the conclusion does not (Schroyens, et al. 2003; Verschueren, et al., 2005).

Criticisms Scientific debate continues about whether human reasoning is based on mental models, formal rules of inference (e.g., O'Brien, 2009), domain-specific rules of inference (e.g., Cheng & Holyoak, 2008; Cosmides, 2005), or probabilities (e.g., Oaksford and Chater, 2007). Many empirical comparisons of the different theories have been carried out (e.g., Oberauer, 2006).

Mental models in system dynamics

Characteristics A mental model is generally: • founded on hardly qualifiable, impugnable, obscure, or incomplete facts • flexible – is considerably variable in positive as well as in negative sense • effects as information filter – causes selective perception, perception of us only selected parts of information • compared with the complexities surrounding the world is very limited and even when the model is extensive and in accordance with a certain reality in the derivation of logical consequences of it we are very limited. We must take into account such restrictions on working memory—i.e. well-known rule on the maximum number of elements that we are suddenly able to remember, gestaltismus or failure of the principles of logic, etc. • source of information, which can not find anywhere else are available at any time and can be used, if other routes are possible, which is linked with the fact that it is not always clearly understood by the other and the process of interpretation can be interpreted in different ways[2] [3] [4] Mental models are fundamental to understanding organizational learning. Mental models are "deeply held images of thinking and acting."[5] Mental models are so basic to our understanding of the world that we are hardly conscious of them.

Expression of mental models Three basic forms are used[2] : • Polygons – whose vertices sharing the edge represent related items. • Causal loop diagrams – displaying tendency and a direction of information connections and the resulting causality • Flow diagram – a more appropriate way to express a dynamic system

Mental model in relation to the system dynamics and systemic thinking The simplification of reality, you create so that we were able to find a sense of reality, seeking to overcome systemic thinking and system dynamics. These two disciplines help us to construct a better coordinated with the reality of mental models and simulate it accurately. They increase the probability that the consequences of how we will decide and act in accordance with Mental model 86

how we plan to.[2] • System dynamics – extending our mental models through the creation of explicit models, which are clear, easily communicating and can be compared with each other. • Systemic thinking – seeking the means to improve the mental models and thereby improve the quality of dynamic decisions that are based on mental models

Single and double-loop learning After analyzing the basic characteristics, it is necessary to bring the process of change mental models, or the process of learning. Learning is a back-loop process and feedback can be illustrated as:

Single-loop learning Our mental models affect the way we work with the information and determine the final decision. The decision itself changes, but the mental models remain the same. It is the predominant method of learning, because it is very convenient. One established mental model is fixed, so the next decision is very fast.

Double-loop learning Is used when it is necessary to change the mental model on which our decision depends. Unlike single loops, this model includes a shift in understanding—from simple and static to broader and more dynamic—such as taking into account the changes in the surroundings and the need for expression changes in mental models.[3]

Process of learning

Feedback process Single-loop learning Double-loop learning

Language to express the system of thought For a description of the structure is used in general to understand the universal graphic symbols, which can describe the structure of generating behavior of any system in time. If individual elements correctly defined, it is possible for a computer in a software model to simulate and interpret the results (e.g. in the form of graphs).

See also • Internal model • Cognitive psychology • Cognitive map • Educational psychology • abstract model • Neuro-Linguistic Programming • Knowledge representation • System Dynamics Mental model 87

• Conceptual Model • OODA Loop - Boyd's notion of "Orientation" corresponds with that of one’s Mental Model of the exterior world.

References

[1] Mental models (http:/ / www. lauradove. info/ reports/ mental models. htm) Report at www.lauradove.info.

[2] Šusta, Marek. "Několik slov o systémové dynamice a systémovém myšlení" (http:/ / proverbs. cz/ media/ art/ SM_ST. pdf) (in Czech) (PDF). Proverbs, a.s.. pp. 3–9. . Retrieved 2009-01-15. [3] Mildeova, S., Vojtko V. (2003) (in Czech). Systémová dynamika. Prague: Oeconomica. pp. 19–24. ISBN 80-245-0626-2.

[4] Ford, David N., Sterman, John D.. "Expert Knowledge Elicitation to Improve Mental and Formal Models" (http:/ / web. mit. edu/ jsterman/

www/ ford_sterman_elicit_1. pdf) (PDF). Cambridge, Massachusetts, USA - Massachusetts Institute of Technology. pp. 18–23. . Retrieved 11.1.2009. [5] "LEADING FOR A CHANGE", Ralph Jacobson, 2000, Chapter 5, Page102 • Barrouillet, P. et al. (2000). Conditional reasoning by mental models: chronometric and developmental evidence. Cognit. 75, 237-266. • Byrne, R.M.J. (2005). The Rational Imagination: How People Create Counterfactual Alternatives to Reality. Cambridge MA: MIT Press. • Byrne, R.M.J. & Johnson-Laird, P.N. (2009). 'If' and the problems of conditional reasoning. Trends in Cognitive Sciences. 13, 282-287 • Cheng, P.C. and Holyoak, K.J. (2008) Pragmatic reasoning schemas. In Reasoning: studies of human inference and its foundations (Adler, J.E. and Rips, L.J., eds), pp. 827–842, Cambridge University Press • Cosmides, L. et al. (2005) Detecting cheaters. Trends in Cognitive Sciences. 9,505–506 • Oberauer K. (2006) Reasoning with conditionals: A test of formal models of four theories. Cognit. Psychol. 53:238–283. • O’Brien, D. (2009). Human reasoning requires a mental logic. Behav. Brain Sci. 32, 96–97 • Oaksford, M. and Chater, N. (2007) Bayesian Rationality. Oxford University Press • Johnson-Laird, P.N. (1983). Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness. Cambridge: Cambridge University Press. • Johnson-Laird, P.N. (2006) How We Reason. Oxford University Press • Johnson-Laird, P.N. and Byrne, R.M.J. (2002) Conditionals: a theory of meaning, inference, and pragmatics. Psychol. Rev. 109, 646–678 • Schroyens, W. et al. (2003). In search of counterexamples: Deductive rationality in human reasoning. Quart. J. Exp. Psychol. 56(A), 1129–1145. • Verschueren, N. et al. (2005). Everyday conditional reasoning: A working memory-dependent tradeoff between counterexample and likelihood use. Mem. Cognit. 33, 107-119.

Further reading • Georges-Henri Luquet (2001). Children's Drawings. Free Association Books. ISBN 1-85343-516-3 • G. Robles-De-La-Torre & R. Sekuler (2004). " Numerically Estimating Internal Models of Dynamic Virtual

Objects (http:/ / www. roblesdelatorre. com/ gabriel/ GR-RS-Estimating-Internal-Models. pdf)". In: ACM Transactions on Applied Perception 1(2), pp. 102–117.

• John D. Sterman, A Skeptic’s Guide to Computer Models, Massachusetts Institute of Technology (http:/ / sysdyn.

clexchange. org/ sdep/ Roadmaps/ RM9/ D-4101-1. pdf)

• P.N.Johnson-Laird, The History of Mental Models (http:/ / weblamp. princeton. edu/ ~psych/ psychology/

research/ johnson_laird/ pdfs/ 2005HistoryMentalModels. pdf)

• P.N.Johnson-Laird, Mental Models, Deductive Reasoning, and the Brain (http:/ / cogsci. bme. hu/ ~babarczy/

Orak/ BMEpostgrad/ semantics/ 2005spring/ Johnson-Lairdmental_models. pdf) Mental model 88

External links

• Mental Models and Usability (http:/ / www. lauradove. info/ reports/ mental models. htm)

• Mental Models and Reasoning Laboratory (http:/ / www. princeton. edu/ ~mentmod)

• What's Your Idea of a Mental Model? (http:/ / www. boxesandarrows. com/ view/ whats_your_idea_of_a_mental_model_)

• Systems Analysis, Modelling and Prediction Group, University of Oxford (http:/ / www. eng. ox. ac. uk/ samp/ )

• System Dynamics Society (http:/ / www. systemdynamics. org/ )

Montessori sensorial materials

Montessori Sensorial Materials are materials used in the Montessori classroom that help the child develop his or her 5 senses. The materials are designed to help the child refine tactile, visual, auditory, olfactory, and gustatory senses. This is the next level of difficulty after those of practical life. This article is designed to explain several of the Montessori Sensorial materials used in the classroom environment. Sensorial Materials, like many other materials in the Montessori classroom, have what is called a "control of error." This means that the child will work with the material, but will have a way for them to check their own work rather than seeking out the teacher. This is done to help promote independence on the part of the child.

The Cylinder Blocks There are 4 cylinder blocks. The purpose of the cylinder blocks are to provide various size dimensions so the child can distinguish between large and small, tall and short, thick and thin, or a combination of the two. The cylinder blocks are wooden blocks that contain 10 cylinders of various dimensions that can be removed by a knobbed handle. In order to remove the cylinders, the child tends to naturally use a 3 finger pincher grip used on pencils. There are several activities that can be done with the cylinder blocks. The main activity involves removing the cylinders from the block and replacing them. The control of error comes when the child is unable to replace a cylinder. The mistake is apparent and the child is unable to return it to the shelf uncompleted.

The Pink Tower The pink tower work has 10 pink cubes. The smallest cube is 1 cubic centimeter and the largest cube is 1000 cubic centimeters (each side is 10 cm in length). The work is designed to provide the child with a concept of "big" and "small." The child starts with the largest cube and puts the 2nd largest cube on top of it. The work continues until all 10 cubes are stacked on top of each other. The control of error is visual. The child sees the cubes are in the wrong order. If the cubes are stacked on the corner, the smallest cube may be used to place on each level. The ledge of each level will be 1cm wide and the child will be able to see if the small cube fits on each ledge. Montessori sensorial materials 89

The Broad Stair The broad stair is designed to teach the concepts of "thick" and "thin." The broad stairs are 10 sets of wooden prisms with a natural or brown stain finish. Each stair is 20 cm in length and varies in thickness from 1 square cm to 10 square cm. When the broad stairs are put together from thickest to thinnest, the material makes stairs going down. As an extension, the broad stairs are often used with the pink tower to allow the child to make many designs.

The Pink Tower and the Broad Stairs are shown here together in an extension activity. The child can make a variety of designs limited only by his or her imagination and the constraints of the material.

The Red Rods The red rods are 10 red rods with equal diameter. They vary only in length. The smallest is 10 cm long and the largest is one meter long. Each rod is 1 square inch thick. By holding the ends of the rods with two hands, the material is designed to give the child a sense of long and short in a very concrete manner.

The Colored Cylinders Also called the knobless cylinders, these are cylinders of the exact same size and dimensions as the cylinder blocks mentioned above. There are 4 boxes of cylinders: • Yellow cylinders that vary in height and width. The shortest cylinder is the thinnest and the tallest cylinder is the thickest. • Red cylinders that are the same height, but vary in width. • Blue cylinders that have the same width, but vary in height. • Green cylinders that vary in height and width. The shortest cylinder is the thickest and the tallest cylinder is the thinnest. The child can do a variety of exercises with these materials, including matching them with the cylinder blocks, stacking them on top of each other to form a tower, and arranging them in size or different patterns. When the yellow, red, and green cylinders are placed on top of each other, they all are the same height. [1] Montessori sensorial materials 90

Colored Cylinders laid out in a design. The green, yellow, and red cylinders are Here, the knobless cylinders are used with the stacked on top of each other. cylinders from the cylinder block.

The Binomial Cube The binomial cube is a cube that has the following pieces: 1 red cube, 3 black and red prisms. 3 black and blue prisms, and 1 blue cube. A box with 8 prisms represent the elements of or: The pieces are stored in a box with two hinged opening sides. The color pattern of the cube is painted all around the outside of the box (except the bottom). The material is not designed as a math material until the elementary years of Montessori Education. In the Primary levels (ages 3-6), it is used as a sensorial material.

The Binomial Cube Montessori sensorial materials 91

The Trinomial Cube The trinomial cube is similar to the binomial cube, but has the following pieces: 1 red cube and 6 black and red prisms (varying in size) 1 blue cube and 6 black and blue prisms (varying in size) 1 yellow cube and 6 black and yellow prisms (varying in size) 6 black prisms (same size) This is used similar to the binomial cube, but is a physical representation of the math formula:

Other materials There are many Montessori materials that deal with the Sensorial area and more are being investigated and developed by teachers. Other popular Montessori Sensorial materials include: • Monomial Cube: A cube similar to the binomial and trinomial cube. The child has a sensorial experience of the power of multiplying by 2 and developing that into a cube. • Geometric Cabinet: Several different shapes are inset into wood and placed in drawers. The child distinguishes the different shapes, learns their names, and learns how to discriminate from the shapes. • The Constructive Triangles: Different triangles are put together to form various shapes. Shapes made with the triangles include the parallelogram, hexagon, rhombus, and trapezoid. • Color Tablets: Boxes with tablets inside. The sides are usually made of wood or plastic. The middle is painted wood or plastic. The only difference with these are the colors in the middle. There are 3 color boxes. The first has the 3 basic colors of red, blue, and yellow. The 2nd has 12 different colors. The third box has 9 colors, but in different grades from light to dark. • The Geometric Solids: 10 Geometric 3-dimensional shapes made from wood and usually painted blue. The shapes are: • Sphere • Cone • Ovoid • Ellipsoid • Triangle Based Pyramid • Square Based Pyramid • Cube • Cylinder • Rectangular Prism • Triangular Prism • The Mystery Bag contains various object that the child feels and sorts without looking into the bag. The object is removed after the child has decided how to sort it and a visual check is done. (Though this may also be done blindfolded to add to the experience). • Rough And Smooth Boards: Sandpaper is glued onto a smooth wood board. Various grading of sandpaper are used later as an extension of this activity to help the child discriminate between them. • Fabric Box: Different fabric materials are used that the child must feel and match. A blindfold is usually used so the child cannot see the materials. • Thermic Bottles: Different temperature water is added to metal bottles. The child lines them up from "hottest" to "coldest." • Baric Tablets: Wooden tablets of various weight to help the child discriminate between weight. Montessori sensorial materials 92

• The Sound Cylinders: 2 boxes, each containing 6 cylinders. One set has a red top and the other a blue top. When shaken, each cylinder of the same color gives off a different sound. The sound from the red cylinder is matched with the same exact sound from the blue cylinder. • The Bells: 26 bells are used in the Montessori classroom to enable the child to develop a strong sense of musical tones.

The Color Tablets: Box 3 The Geometric Solids The Montessori Bells

See also • Froebel Gifts • Unit block • Alphabet Nursery Blocks (ABC-Blocks) • Waldorf doll

References

[1] http:/ / flickr. com/ photos/ 27682674@N02/ 2582293141/ Packing problem 93 Packing problem

Packing problems are a class of optimization problems in recreational mathematics which involve attempting to pack objects together (often inside a container), as densely as possible. Many of these problems can be related to real life storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a packing problem, you are given: • 'containers' (usually a single two- or three-dimensional convex region, or an infinite space) • 'goods' (usually a single type of shape), some or all of which must be packed into this container Usually the packing must be without overlaps between goods and other goods or the container walls. The aim is to find the configuration with the maximal density. In some variants the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimised.

Packing infinite space Many of these problems, when the container size is increased in all directions, become equivalent to the problem of packing objects as densely as possible in infinite Euclidean space. This problem is relevant to a number of scientific disciplines, and has received significant attention. The Kepler conjecture postulated an optimal solution for packing spheres hundreds of years before it was proven correct by Thomas Callister Hales. Many other shapes have received attention, including ellipsoids, tetrahedra, icosahedra, and unequal-sphere dimers.

Hexagonal packing of circles

These problems are mathematically distinct from the ideas in the circle packing theorem. The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere. Circles (and their counterparts in other dimensions) can never be packed with 100% efficiency in dimensions larger than one (in a one dimensional universe, circles merely consist of two points). That is, there will always be unused space if you are only packing circles. The most efficient way of packing circles, hexagonal packing produces approximately 90% efficiency. [1]

Packing in 3-dimensional containers The hexagonal packing of circles on a 2-dimensional Euclidean plane.

Spheres into a Euclidean ball The problem of finding the smallest ball such that disjoint open unit balls may be packed inside it has a simple and complete answer in -dimensional Euclidean space if , and in an infinite dimensional Hilbert space with no restrictions. It is worth describing in detail here, to give a flavor of the general problem. In this case, a configuration of pairwise tangent unit balls is available. Place the centers at the vertices of a regular dimensional simplex with edge 2; this is easily realized starting from an orthonormal basis. A small computation shows that the distance of each vertex from the barycenter is . Moreover, any other point of Packing problem 94

the space necessarily has a larger distance from at least one of the vertices. In terms of inclusions of balls, the open unit balls centered at are included in a ball of radius , which is minimal for this configuration.

To show that this configuration is optimal, let be the centers of disjoint open unit balls contained in a ball of radius centered at a point . Consider the map from the finite set into taking in the corresponding for each . Since for all , this map is 1-Lipschitz and by the Kirszbraun theorem it extends to a 1-Lipschitz map that is globally defined; in particular, there exists a point such that for all one has , so that also . This shows that there are disjoint unit open balls in a ball of radius if and only if . Notice that in an infinite dimensional Hilbert space this implies that there are infinitely many disjoint open unit balls inside a ball of radius if and only if . For instance, the unit balls centered at , where is an orthonormal basis, are disjoint and included in a ball of radius centered at the origin. Moreover, for , the maximum number of disjoint open unit balls inside a ball of radius r is .

Spheres in a cuboid Determine the number of spherical objects of given diameter d can be packed into a cuboid of size a × b × c.

Packing in 2-dimensional containers

Packing circles

Circles in circle Some of the more non-trivial circle packing problems are packing unit circles into the smallest possible larger circle. Minimum solutions:

Number of circles Circle radius

1 1

2 2

3 2.154...

4 2.414...

5 2.701...

6 3

7 3

8

3.304... 9 3.613...

10 3.813...

11 3.923...

12 4.029...

13 4.236...

14 4.328... Packing problem 95

15 4.521...

16 4.615...

17 4.792...

18 4.863...

19 4.863...

20 5.122...

Circles in square

Pack n unit circles into the smallest possible square. This is closely related to spreading points in a unit square with the objective of finding the greatest minimal separation, d , between points[2] . To convert n between these two formulations of the problem, the square side for unit circles will be L=2+2/d . n Optimal solutions have been proven for n≤30.[3]

Circles in isosceles right triangle

Pack n unit circles into the smallest possible isosceles right triangle (lengths shown are length of leg) Minimum solutions: The optimal packing of 15 circles in a square.

Number of circles Length

1 3.414...

2 4.828...

3 5.414...

4 6.242...

5 7.146...

6

7.414... 7 8.181...

8 8.692...

9 9.071...

10 9.414...

11 10.059...

12 10.422...

13 10.798...

14 11.141...

15 11.414... Packing problem 96

Circles in equilateral triangle Pack n unit circles into the smallest possible equilateral triangle (lengths shown are side length). Minimum solutions:

Number of circles Length

1 3.464...

2 5.464...

3 5.464...

4

6.928... 5

7.464... 6 7.464...

7 8.928...

8 9.293...

9 9.464...

10 9.464...

11 10.730...

12 10.928...

13 11.406...

14 11.464...

15 11.464...

Circles in regular hexagon Pack n unit circles into the smallest possible regular hexagon (lengths shown are side length). Minimum solutions: Packing problem 97

Number of circles Length

1 1.154...

2 2.154...

3 2.309...

4 2.666...

5 2.999...

6 3.154...

7 3.154...

8 3.709...

9 4.011...

10 4.119...

11 4.309...

12 4.309...

13 4.618...

14 4.666...

15 4.961...

Packing squares

Squares in square A problem is the square packing problem, where one must determine how many squares of side 1 you can pack into a square of side a. Obviously, if a is an integer, the answer is a2, but the precise, or even asymptotic, amount of wasted space for a a non-integer is open. Proven minimum solutions:[4]

Number of squares Square size

1 1

2 2

3 2

4 2

5

2.707 (2 + 2 −1/2) 6 3

7

3 8 3 Packing problem 98

9 3

10

3.707 (3 + 2 −1/2)

Other results: • If you can pack n2 − 2 squares in a square of side a, then a ≥ n.[5] • The naive approach (side matches side) leaves wasted space of less than 2a + 1.[4] • The wasted space is asymptotically o(a7/11).[6] • The wasted space is not asymptotically o(a1/2).[7] • 11 unit squares cannot be packed in a square of side less than .[8]

Squares in circle Pack n squares in the smallest possible circle. Minimum solutions:

Number of squares Circle radius

1 0.707...

2 1.118...

3 1.288...

4 1.414...

5 1.581...

6 1.688...

7 1.802...

8 1.978...

9 2.077...

10 2.121...

11 2.215...

12 2.236... Packing problem 99

Packing rectangles

Identical rectangles in a rectangle The problem of packing multiple instances of a single rectangle of size (l,w), allowing for 90o rotation, in a bigger rectangle of size (L,W) has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230)[9] .

Related fields In tiling or tesselation problems, there are to be no gaps, nor overlaps. Many of the puzzles of this type involve packing rectangles or polyominoes into a larger rectangle or other square-like shape. There are significant theorems on tiling rectangles (and cuboids) in rectangles (cuboids) with no gaps or overlaps: Klarner's theorem: An a × b rectangle can be packed with 1 × n strips iff n | a or n | b.[10] de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) The study of polyomino tilings largely concerns two classes of problems: to tile a rectangle with congruent tiles, and to pack one of each n-omino into a rectangle. A classic puzzle of the second kind is to arrange all twelve pentominoes into rectangles sized 3×20, 4×15, 5×12 or 6×10.

See also • Set packing • Bin packing problem • Slothouber-Graatsma puzzle • Conway puzzle • Tetris • Covering problem • Knapsack problem • Tetrahedron packing • Cutting stock problem • Kissing number problem

References • Weisstein, Eric W., "Klarner's Theorem [11]" from MathWorld. • Weisstein, Eric W., "de Bruijn's Theorem [12]" from MathWorld.

External links Many puzzle books as well as mathematical journals contain articles on packing problems. • Links to various MathWorld articles on packing [13] • MathWorld notes on packing squares. [14] • Erich's Packing Center [15] • "Box Packing" [16] by Ed Pegg, Jr., the Wolfram Demonstrations Project, 2007. Packing problem 100

References

[1] http:/ / mathworld. wolfram. com/ CirclePacking. html [2] Croft, Hallard T.; Falconer, Kenneth J.; Guy, Richard K. (1991). Unsolved Problems in Geometry. New York: Springer-Verlag. pp. 108–110. ISBN 0-387-97506-3.

[3] Eckard Specht (20 May 2010). "The best known packings of equal circles in a square" (http:/ / hydra. nat. uni-magdeburg. de/ packing/ csq/

csq. html). . Retrieved 25 May 2010.

[4] Erich Friedman, "Packing unit squares in squares: a survey and new results" (http:/ / www. combinatorics. org/ Surveys/ ds7. html), The Electronic Journal of Combinatorics DS7 (2005).

[5] M. Kearney and P. Shiu, "Efficient packing of unit squares in a square" (http:/ / www. combinatorics. org/ Volume_9/ Abstracts/ v9i1r14. html), The Electronic Journal of Combinatorics 9:1 #R14 (2002).

[6] P. Erdős and R. L. Graham, "On packing squares with equal squares" (http:/ / www. math. ucsd. edu/ ~sbutler/ ron/ 75_06_squares. pdf), Journal of Combinatorial Theory, Series A 19 (1975), pp. 119–123. [7] K. F. Roth and R. C. Vaughan, "Inefficiency in packing squares with unit squares", Journal of Combinatorial Theory, Series A 24 (1978), pp. 170-186.

[8] W. Stromquist, "Packing 10 or 11 unit squares in a square" (http:/ / www. combinatorics. org/ Volume_10/ Abstracts/ v10i1r8. html), The Electronic Journal of Combinatorics 10 #R8 (2003). [9] E G Birgin, R D Lobato, R Morabito, "An effective recursive partitioning approach for the packing of identical rectangles in a rectangle", Journal of the Operational Research Society, 2010, 61, pp. 306-320.

[10] Wagon, Stan (August-September 1987). "Fourteen Proofs of a Result About Tiling a Rectangle" (http:/ / mathdl. maa. org/ images/

upload_library/ 22/ Ford/ Wagon601-617. pdf). The American Mathematical Monthly 94 (7): 601–617. . Retrieved 6 Jan 2010.

[11] http:/ / mathworld. wolfram. com/ KlarnersTheorem. html

[12] http:/ / mathworld. wolfram. com/ deBruijnsTheorem. html

[13] http:/ / mathworld. wolfram. com/ Packing. html

[14] http:/ / mathworld. wolfram. com/ SquarePacking. html

[15] http:/ / www. stetson. edu/ ~efriedma/ packing. html

[16] http:/ / demonstrations. wolfram. com/ BoxPacking/

Prior knowledge for pattern recognition

Pattern recognition is a very active field of research intimately bound to machine learning. Also known as classification or statistical classification, pattern recognition aims at building a classifier that can determine the class of an input pattern. This procedure, known as training, corresponds to learning an unknown decision function based only on a set of input-output pairs that form the training data (or training set). Nonetheless, in real world applications such as character recognition, a certain amount of information on the problem is usually known beforehand. The incorporation of this prior knowledge into the training is the key element that will allow an increase of performance in many applications.

Definition Prior knowledge [1] refers to all information about the problem available in addition to the training data. However, in this most general form, determining a model from a finite set of samples without prior knowledge is an ill-posed problem, in the sense that a unique model may not exist. Many classifiers incorporate the general smoothness assumption that a test pattern similar to one of the training samples tends to be assigned to the same class. The importance of prior knowledge in machine learning is suggested by its role in search and optimization. Loosely, the no free lunch theorem states that all search algorithms have the same average performance over all problems, and thus implies that to gain in performance on a certain application one must use a specialized algorithm that includes some prior knowledge about the problem. The different types of prior knowledge encountered in pattern recognition are now regrouped under two main categories: class-invariance and knowledge on the data. Prior knowledge for pattern recognition 101

Class-invariance A very common type of prior knowledge in pattern recognition is the invariance of the class (or the output of the classifier) to a transformation of the input pattern. This type of knowledge is referred to as transformation-invariance. The mostly used transformations used in image recognition are: • translation; • rotation; • skewing; • scaling. Incorporating the invariance to a transformation parametrized in into a classifier of output for an input pattern corresponds to enforce the equality

Local invariance can also be considered for a transformation centered at , so that , by the constraint

It must be noted that in these Equations can be either the decision function of the classifier or its real-valued output. Another approach is to consider the class-invariance with respect to a "domain of the input space" instead of a transformation. In this case, the problem becomes finding so that

where is the membership class of the region of the input space. A different type of class-invariance found in pattern recognition is the permutation-invariance, i.e. invariance of the class to a permutation of elements in a structured input. A typical application of this type of prior knowledge is a classifier invariant to permutations of rows in matrix inputs.

Knowledge on the data Other forms of prior knowledge than class-invariance concern the data more specifically and are thus of particular interest for real-world applications. The three particular cases that most often occur when gathering data are: • Unlabeled samples are available with supposed class-memberships; • Imbalance of the training set due to a high proportion of samples of a class; • Quality of the data may vary from a sample to another. Prior knowledge on these can enhance the quality of the recognition if included in the learning. Moreover, not taking into account the poor quality of some data or a large imbalance between the classes can mislead the decision of a classifier. Prior knowledge for pattern recognition 102

References • E. Krupka and N. Tishby, "Incorporating Prior Knowledge on Features into Learning", Eleventh International Conference on Artificial Intelligence and Statistics (AISTATS 07)

References [1] B. Scholkopf and A. Smola, "Learning with Kernels", MIT Press 2002.

Quasi-empirical method

Quasi-empirical methods are applied in science and in mathematics. The term "empirical methods" refers to experiment, disclosure of apparatus for reproduction of experiments, and other ways in which science is validated by scientists. Empirical methods are studied extensively in the philosophy of science but cannot be used directly in fields whose hypotheses are not invalidated by real experiment (mathematics, theology, ideology). In these fields, the prefix 'quasi' came to denote methods that are "almost" or "socially approximate" an ideal of truly empirical methods. It is unnecessary to find all counterexamples to a theory; all that is required to disprove a theory logically is one counterexample. The converse does not prove a theory; Bayesian inference simply makes a theory more likely, by weight of evidence. One can argue that no science is capable of finding all counter-examples to a theory, therefore, no science is strictly empirical, it's all quasi-empirical. But usually, the term "quasi-empirical" refers to the means of choosing problems to focus on (or ignore), selecting prior work on which to build an argument or proof, notations for informal claims, peer review and acceptance, and incentives to discover, ignore, or correct errors. These are common to both science and mathematics, and do not include experimental method. Albert Einstein's discovery of the general relativity theory relied upon thought experiments and mathematics. Empirical methods only became relevant when confirmation was sought. Furthermore, some empirical confirmation was found only some time after the general acceptance of the theory. Thought experiments are almost standard procedure in philosophy, where a conjecture is tested out in the imagination for possible effects on experience; when these are thought to be implausible, unlikely to occur, or not actually occurring, then the conjecture may be either rejected or amended. Logical positivism was a perhaps extreme version of this practice, though this claim is open to debate. Post-20th-century philosophy of mathematics is mostly concerned with quasi-empirical methods especially as reflected in actual mathematical practice of working mathematicians.

See also • quasi-empiricism in mathematics • empirical methods • philosophy of science • philosophy of mathematics • mathematical practice Semantic similarity 103 Semantic similarity

Semantic similarity is a concept whereby a set of documents or terms within term lists are assigned a metric based on the likeness of their meaning / semantic content. According to some opinions the concept of semantic similarity is different from semantic relatedness because semantic relatedness includes concepts as antonymy and meronymy, while similarity doesn't. However, much of the literature uses these terms interchangeably, along with terms like semantic distance. In essence, semantic similarity, semantic distance, and semantic relatedness all mean, "How much does term A have to do with term B?" The answer to this question, as given by the many automatic measures of semantic similarity/relatedness [1], is usually a number between -1 and 1, or between 0 and 1. 1 signifies extremely high similarity/relatedness, and 0 signifies little-to-none. An intuitive way of displaying terms according to their semantic similarity is by grouping together closer related terms and spacing more distantly related ones wider apart. This is common - if sometime subconscious - practice for mind maps and concept maps. Concretely, this can be achieved for instance by defining a topological similarity, by using ontologies to define a distance between words (a naive metric for terms arranged as nodes in a directed acyclic graph like a hierarchy would be the minimal distance—in separating edges—between the two term nodes), or using statistical means such as a vector space model to correlate words and textual contexts from a suitable text corpus (co-occurrence). Semantic similarity measures have been recently applied and developed in biomedical ontologies, namely, the Gene Ontology. They are mainly used to compare genes and proteins based on the similarity of their functions rather than on their sequence similarity. [2] These comparisons can be done using some tools freely available on the web: • ProteInOn [3] can be used to find interacting proteins, find assigned GO terms and calculate the functional semantic similarity of proteins and to get the information content and calculate the functional semantic similarity of GO terms. • FuSSiMeG [4] provides a functional similarity measure between two proteins using the semantic similarity between the GO terms annotated with the proteins. • CESSM [5] provides a tool for the automated evaluation of GO-based semantic similarity measures. Besides applications in bioinformatics, similarity is also applied to find similar geographic features or feature types. For instance the SIM-DL similarity server [6] can be used to compute similarities between concepts stored in geographic feature type ontologies.

See also • Terminology extraction • Semantic relatedness • Coherence (linguistics) • Analogy • Semantic differential Semantic similarity 104

External links • List of related literature [7] • WordNet::Similarity [8] (using WordNet as an ontology) • WordNet Explorer [9] (interactive graphic WordNet database editor) • Similarity-based Learning Methods for the Semantic Web [10] (C. d'Amato, PhD Thesis) • Survey on Semantic Similarity Measures [11] (C. d'Amato, S. Staab, N. Fanizzi, EKAW 2008, Springer-Verlag)

References

[1] http:/ / cwl-projects. cogsci. rpi. edu/ msr/

[2] Pesquita C, Faria D, Falcão AO, Lord P, Couto FM (2009). "Semantic Similarity in Biomedical Ontologies" (http:/ / www. ploscompbiol.

org/ article/ info:doi/ 10. 1371/ journal. pcbi. 1000443). PLoS Computational Biology 5 (7): e1000443. doi:10.1371/journal.pcbi.1000443. PMID 19649320. PMC 2712090. .

[3] http:/ / xldb. fc. ul. pt/ biotools/ proteinon/

[4] http:/ / xldb. fc. ul. pt/ biotools/ rebil/ ssm/

[5] http:/ / xldb. fc. ul. pt/ biotools/ cessm/

[6] http:/ / sim-dl. sourceforge. net/

[7] http:/ / www. similarity-blog. de/ ?page_id=3

[8] http:/ / www. d. umn. edu/ ~tpederse/ similarity. html

[9] http:/ / wordventure. eti. pg. gda. pl/ WordnetTG. html

[10] http:/ / www. di. uniba. it/ ~cdamato/ PhDThesis_dAmato. pdf

[11] http:/ / portal. acm. org/ citation. cfm?id=1434078

Serendipity

Serendipity is a propensity for making fortuitous discoveries while looking for something unrelated. The word has been voted as one of the ten English words that were hardest to translate in June 2004 by a British translation company.[1] However, due to its sociological use, the word has been imported into many other languages.[2]

Etymology

The word derives from a fairy tale called The Three Princes of Serendip, where Serendip is the Arabic name for Sri Lanka.[3] The word was coined by Horace Walpole in 1754 in a letter he wrote to a friend. The letter read, "It was once when I read a silly fairy tale, called The Three Princes of Serendip: as their highnesses traveled, they were always making discoveries, by accidents and sagacity, of things The intended subject of the photograph was a which they were not in quest of: for instance, one of them perched Black-crowned Night Heron; the discovered that a camel blind of the right eye had traveled the photographer discovered later that the image serendipitously included a Pileated Woodpecker. same road lately, because the grass was eaten only on the left side, where it was worse than on the right—now do you understand serendipity? One of the most remarkable instances of this accidental sagacity (for you must observe that no discovery of a thing you are looking for, comes under this description) was of my Lord Shaftsbury, who happening to dine at Lord Chancellor Clarendon's, found out the marriage of the Duke of York and Mrs. Hyde, by the respect with which her mother treated her at table."[4] Serendipity 105

Role in science and technology One aspect of Walpole's original definition of serendipity that is often missed in modern discussions of the word is the "sagacity" of being able to link together apparently innocuous facts to come to a valuable conclusion. Thus, while some scientists and inventors are reluctant about reporting accidental discoveries, others openly admit its role; in fact serendipity is a major component of scientific discoveries and inventions. According to M.K. Stoskopf[5] "it should be recognized that serendipitous discoveries are of significant value in the advancement of science and often present the foundation for important intellectual leaps of understanding". The amount of benefit contributed by serendipitous discoveries varies extensively among the several scientific disciplines. Pharmacology and chemistry are probably the fields where serendipity is more common. Most authors who have studied scientific serendipity both in a historical, as well as in an epistemological point of view, agree that a prepared and open mind is required on the part of the scientist or inventor to detect the importance of information revealed accidentally. This is the reason why most of the related accidental discoveries occur in the field of specialization of the scientist. About this, Albert Hofmann, the Swiss chemist who discovered LSD properties by unintentionally ingesting it at his lab, wrote It is true that my discovery of LSD was a chance discovery, but it was the outcome of planned experiments and these experiments took place in the framework of systematic pharmaceutical, chemical research. It could better be described as serendipity. The French scientist Louis Pasteur also famously said: "In the fields of observation chance favors only the prepared mind."[6] This is often rendered as "Chance favors the prepared mind." William Shakespeare expressed the same sentiment 250 years earlier in act 4 of his play Henry V: "All things are ready if our minds be so." History, of course, does not record accidental exposures of information which could have resulted in a new discovery, and we are justified in suspecting that they are many. There are several examples of this, however, and prejudice of preformed concepts is probably the largest obstacle. See for example [7] for a case where this happened (the rejection of an accidental discovery in the field of self-stimulation of the limbic system in humans).

Role in economics M. E. Graebner describes serendipitous value in the context of the acquisition of a business as "windfalls that were not anticipated by the buyer prior to the deal": i.e., unexpected advantages or benefits incurred due to positive synergy effects of the merger. Ikujiro Nonaka (1991,p. 94 November-December issue of HBR) points out that the serendipitous quality of innovation is highly recognized by managers and links the success of Japanese enterprises to their ability to create knowledge not by processing information but rather by "tapping the tacit and often highly subjective insights, intuitions, and hunches of individual employees and making those insights available for testing and use by the company as a whole".

Examples in science and technology

Chemistry • The German chemist Friedrich August Kekulé von Stradonitz having a reverie of Ourobouros, a snake forming a circle, leading to his solution of the closed chemical structure of cyclic compounds, such as benzene. • Lysergic Acid Diethylamide (or LSD) by Albert Hofmann, who found this potent hallucinogen while trying to find medically useful derivatives in ergot, a fungus growing on wheat. • Gelignite by Alfred Nobel, when he accidentally mixed collodium (gun cotton) with nitroglycerin • Polymethylene by Hans von Pechmann, who prepared it by accident in 1898 while heating diazomethane • Low density polyethylene by Eric Fawcett and Reginald Gibson at the ICI works in Northwich, England. It was the first industrially practical polyethylene synthesis and was discovered (again by accident) in 1933 Serendipity 106

• Silly Putty by James Wright, on the way to solving another problem: finding a rubber substitute for the United States during World War II. • Chemical synthesis of urea, by Friedrich Woehler. He was attempting to produce ammonium cyanate by mixing potassium cyanate and ammonium chloride and got urea, the first organic chemical to be synthesised, often called the 'Last Nail' of the coffin of the Élan vital Theory • Pittacal, the first synthetic dyestuff, by Carl Ludwig Reichenbach. The dark blue dye appeared on wooden posts painted with creosote to drive away dogs who urinated on them. • Mauve, the first aniline dye, by William Henry Perkin. At the age of 18, he was attempting to create artificial quinine. An unexpected residue caught his eye, which turned out to be the first aniline dye—specifically, mauveine, sometimes called aniline purple. • Racemization, by Louis Pasteur. While investigating the properties of sodium ammonium tartrate he was able to separate for the first time the two optical isomers of the salt. His luck was twofold: it is the only racemate salt to have this property, and the room temperature that day was slightly below the point of separation. • Teflon, by Roy J. Plunkett, who was trying to develop a new gas for refrigeration and got a slick substance instead, which was used first for lubrication of machine parts • Cyanoacrylate-based Superglue (a.k.a. Krazy Glue) was accidentally twice discovered by Dr. Harry Coover, first when he was developing a clear plastic for gunsights and later, when he was trying to develop a heat-resistant polymer for jet canopies. • Scotchgard moisture repellant, used to protect fabrics and leather, was discovered accidentally in 1953 by Patsy Sherman. One of the compounds she was investigating as a rubber material that wouldn't deteriorate when in contact with aircraft fuel spilled onto a tennis shoe and would not wash out; she then considered the spill as a protectant against spills. • Cellophane, a thin, transparent sheet made of regenerated cellulose, was developed in 1908 by Swiss chemist Jacques Brandenberger, as a material for covering stain-proof tablecloth. • The chemical element helium. British chemist William Ramsay isolated helium while looking for argon but, after separating nitrogen and oxygen from the gas liberated by sulfuric acid, noticed a bright-yellow spectral line that matched the D3 line observed in the spectrum of the Sun. • The chemical element Iodine was discovered by Bernard Courtois in 1811, when he was trying to remove residues with strong acid from the bottom of his saltpeter production plant which used seaweed ashes as a prime material. • Polycarbonates, a kind of clear hard plastic • The synthetic polymer celluloid was discovered by British chemist and metallurgist Alexander Parkes in 1856, after observing that a solid residue remained after evaporation of the solvent from photographic collodion. Celluloid can be described as the first plastic used for making solid objects (the first ones being billiard balls, substituting for expensive ivory). • Rayon, the first synthetic silk, was discovered by French chemist Hilaire de Chardonnet, an assistant to Louis Pasteur. He spilled a bottle of collodion and found later that he could draw thin strands from the evaporated viscous liquid. • The possibility of synthesizing indigo, a natural dye extracted from a plant with the same name, was discovered by a chemist named Sapper who was heating coal tar when he accidentally broke a thermometer whose mercury content acted as a catalyst to produce phthalic anhydride, which could readily be converted into indigo. • The dye monastral blue was discovered in 1928 in Scotland, when chemist A.G. Dandridge heated a mixture of chemicals at high temperature in a sealed iron container. The iron of the container reacted with the mixture, producing some pigments called phthalocyanines. By substituting copper for iron he produced an even better pigment called 'monastral blue', which became the basis for many new coloring materials for paints, lacquers and printing inks. • Acesulfame, an artificial sweetener, was discovered accidentally in 1967 by Karl Claus at Hoechst AG. Serendipity 107

• Another sweetener, cyclamate, was discovered by graduate student Michael Sveda, when he smoked a cigarette accidentally contaminated with a compound he had recently synthesized. • Aspartame (NutraSweet) was accidentally ingested by G.D. Searle & Company chemist James M. Schlatter, who was trying to develop a test for an anti-ulcer drug. • Saccharin was accidentally discovered during research on coal tar derivatives. • Saran (plastic) was discovered when Ralph Wiley had trouble washing beakers used in development of a dry cleaning product. It was soon used to make plastic wrap. • A new blue pigment with almost perfect properties was discovered accidentally by scientists at Oregon State University after heating manganese oxide.[8]

Pharmacology • Penicillin by Alexander Fleming. He failed to disinfect cultures of bacteria when leaving for his vacations, only to find them contaminated with Penicillium molds, which killed the bacteria. However, he had previously done extensive research into antibacterial substances. • The psychedelic effects of LSD by Albert Hofmann. A chemist, he unintentionally absorbed a small amount of it upon investigating its properties, and had the first acid trip in history, while cycling to his home in Switzerland; this is commemorated among LSD users annually as Bicycle Day. • 5-fluorouracil's therapeutic action on actinic keratosis, was initially investigated for its anti-cancer actions • Minoxidil's action on baldness; originally it was an oral agent for treating hypertension. It was observed that bald patients treated with it grew hair too. • Viagra (sildenafil citrate), an anti-impotence drug. It was initially studied for use in hypertension and angina pectoris. Phase I clinical trials under the direction of Ian Osterloh suggested that the drug had little effect on angina, but that it could induce marked penile erections. • Retin-A anti-wrinkle action. It was a vitamin A derivative first used for treating acne. The accidental result in some older people was a reduction of wrinkles on the face • The libido-enhancing effect of l-dopa, a drug used for treating Parkinson's disease. Older patients in a sanatorium had their long-lost interest in sex suddenly revived. • The first anti-psychotic drug, chlorpromazine, was discovered by French pharmacologist Henri Laborit. He wanted to add an anti-histaminic to a pharmacological combination to prevent surgical shock and noticed that patients treated with it were unusually calm before the operation. • The anti-cancer drug cisplatin was discovered by Barnett Rosenberg. He wanted to explore what he thought was an inhibitory effect of an electric field on the growth of bacteria. It was rather due to an electrolysis product of the platinum electrode he was using. • The anesthetic nitrous oxide (laughing gas). Initially well known for inducing altered behavior (hilarity), its properties were discovered when British chemist Humphry Davy tested the gas on himself and some of his friends, and soon realised that nitrous oxide considerably dulled the sensation of pain, even if the inhaler was still semi-conscious. • Mustine – a derivative of mustard gas (a chemical weapon), used for the treatment of some forms of cancer. In 1943, physicians noted that the white cell counts of US soldiers, accidentally exposed when a cache of mustard gas shells were bombed in Bari, Italy, decreased, and mustard gas was investigated as a therapy for Hodgkin's lymphoma. • Prontosil, an antibiotic of the sulfa group was an azo dye. German chemists at Bayer had the wrong idea that selective chemical stains of bacteria would show specific antibacterial activity. Prontosil had it, but in fact it was due to another substance metabolised from it in the body, sulfanilimide. Serendipity 108

Medicine and Biology • Bioelectricity, by Luigi Galvani. He was dissecting a frog at a table where he had been conducting experiments with static electricity. His assistant touched an exposed sciatic nerve of the frog with a metal scalpel which had picked up a charge, provoking a muscle contraction. • Neural control of blood vessels, by Claude Bernard • Anaphylaxis, by Charles Richet. When he tried to reuse dogs that had previously shown allergic reactions to sea anemone toxin, the reactions developed much faster and were more severe the second time. • The role of the pancreas in glucose metabolism, by Oskar Minkowski. Dogs that had their pancreas removed for an unrelated physiological investigation urinated profusely; the urine also attracted flies, signaling its high glucose content. • Coronary catheterization was discovered as a method when a cardiologist at the Cleveland Clinic accidentally injected radiocontrast into the coronary artery instead of the left ventricle. • The mydriatic effects of belladonna extracts, by Friedrich Ferdinand Runge • Interferon, an antiviral factor, was discovered accidentally by two Japanese virologists, Yasu-ichi Nagano and Yasuhiko Kojima while trying to develop an improved vaccine for smallpox. • The hormone melatonin was discovered in 1917 when it was shown that extract of bovine pineal glands lightened frog skin. In 1958 its chemical structure was defined by Aaron B. Lerner and in the mid-70s it was demonstrated that also in humans the production of melatonin exhibits and influences a circadian rhythm.

Physics and Astronomy • The, quite possibly apocryphal, story of Archimedes' prototypical cry of Eureka when he realised in the bathtub that a body's displacement water allowed him to measure the weight-to-volume ratio of any irregularly shaped body, such as a gold crown. • Isaac Newton's famed apple falling from a tree, supposedly leading to his musings about the nature of gravitation. • Discovery of the planet Uranus by William Herschel. Herschel was looking for comets, and initially identified Uranus as a comet until he noticed the circularity of its orbit and its distance and suggested that it was a planet, the first one discovered since antiquity. • Infrared radiation, again by William Herschel, while investigating the temperature differences between different colors of visible light by dispersing sunlight into a spectrum using a glass prism. He put thermometers into the different visible colors where he expected a temperature increase, and one as a control to measure the ambient temperature in the dark region beyond the red end of the spectrum. The thermometer beyond the red unexpectedly showed a higher temperature than the others, showing that there was non-visible radiation beyond the red end of the visible spectrum. • The thermoelectric effect was discovered accidentally by Estonian physicist Thomas Seebeck in 1821, who found that a voltage developed between the two ends of a metal bar when it was submitted to a difference of temperature. • Electromagnetism, by Hans Christian Ørsted. While he was setting up his materials for a lecture, he noticed a compass needle deflecting from magnetic north when the electric current from the battery he was using was switched on and off. • Radioactivity, by Henri Becquerel. While trying to investigate phosphorescent materials using photographic plates, he stumbled upon uranium. • X rays, by Wilhelm Roentgen. Interested in investigating cathodic ray tubes, he noted that some fluorescent papers in his lab were illuminated at a distance although his apparatus had an opaque cover • S. N. Bose discovered Bose-Einstein statistics when a mathematical error surprisingly explained anomalous data. • The first demonstration of wave–particle duality during the Davisson–Germer experiment at Bell Labs after a leak in the vacuum system and attempts to recover from it unknowingly altered the crystal structure of the nickel target and led to the accidental experimental confirmation of the de Broglie hypothesis. Davisson went on to share Serendipity 109

the 1937 Nobel Prize in Physics for the discovery. • Cosmic Microwave Background Radiation, by Arno A. Penzias and Robert Woodrow Wilson. What they thought was excess thermal noise in their antenna at Bell Labs was due to the CMBR. • Cosmic gamma-ray bursts were discovered in the late 1960s by the US Vela satellites, which were built to detect nuclear tests in the Soviet Union • The rings of Uranus were discovered by astronomers James L. Elliot, Edward W. Dunham, and Douglas J. Mink on March 10, 1977. They planned to use the occultation of the star SAO 158687 by Uranus to study the planet's atmosphere, but found that the star disappeared briefly from view five times both before and after it was eclipsed by the planet. They deduced that a system of narrow rings was present.[9] • Pluto's moon Charon was discovered by US astronomer James Christy in 1978. He was going to discard what he thought was a defective photographic plate of Pluto, when his Star Scan machine broke down. While it was being repaired he had time to study the plate again and discovered others in the archives with the same "defect" (a bulge in the planet's image which was actually a large moon). • High-temperature superconductivity was discovered serendipitously by physicists Johannes Georg Bednorz and Karl Alexander Müller, ironically when they were searching for a material that would be a perfect electrical insulator (nonconducting). They won the 1987 Nobel Prize in Physics. • Metallic hydrogen was found accidentally in March 1996 by a group of scientists at Lawrence Livermore National Laboratory, after a 60-year search. • A new method to create black silicon was developed in the lab of Eric Mazur.

Inventions • Discovery of the principle behind inkjet printers by a Canon engineer. After putting his hot soldering iron by accident on his pen, ink was ejected from the pen's point a few moments later. • Vulcanization of rubber, by Charles Goodyear. He accidentally left a piece of rubber mixture with sulfur on a hot plate, and produced vulcanized rubber • Safety glass, by French scientist Edouard Benedictus. In 1903 he accidentally knocked a glass flask to the floor and observed that the broken pieces were held together by a liquid plastic that had evaporated and formed a thin film inside the flask. • Corn flakes and wheat flakes (Wheaties) were accidentally discovered by the Kelloggs brothers in 1898, when they left cooked wheat unattended for a day and tried to roll the mass, obtaining a flaky material instead of a sheet. • The microwave oven was invented by Percy Spencer while testing a magnetron for radar sets at Raytheon, he noticed that a peanut candy bar in his pocket had melted when exposed to radar waves. • Pyroceramic (used to make Corningware, among other things) was invented by S. Donald Stookey, a chemist working for the Corning company, who noticed crystallization in an improperly cooled batch of tinted glass. • The Slinky was invented by US Navy engineer Richard T. James after he accidentally knocked a torsion spring off his work table and observed its unique motion. • Arthur Fry happened to attend a 3M college's seminar on a new "low-tack" adhesive and, wanting to anchor his bookmarks in his hymnal at church, went on to invent Post-It Notes. Serendipity 110

• Chocolate chip cookies were invented by Ruth Wakefield when she attempted to make chocolate drop cookies. She did not have the required chocolate so she broke up a candy bar and placed the chunks into the cookie mix. These chunks later morphed into what is now known as chocolate chip cookies.

Examples in exploration

Stories of accidental discovery in exploration abound, of course, The chocolate chip cookie was invented through because the aim of exploration is to find new things and places. The serendipity principle of serendipity applies here, however, when the explorer had one aim in mind and found another unexpectedly. In addition, discoveries have been made by people simply attempting to reach a known destination but who departed from the customary or intended route for a variety of reasons. Some classical cases were discoveries of the Americas by explorers with other aims.

• The first European to see the coast of North America was reputedly Bjarni Herjólfsson, who was blown off course by a storm in 985 or 986 while trying to reach Greenland. • Christopher Columbus was looking for a new way to India in 1492 and wound up landing in The Americas. Native Americans were therefore called Indians. • Although the first European to see and step on South America was Christopher Columbus in Northeast Venezuela in 1498, Brazil was also discovered by accident, first by Spaniard Vicente Pinzon in 1499, who was only trying to explore the West Indies previously discovered by him and Columbus, and stumbled upon the Northeast of Brazil, in the region now known as Cabo de Santo Agostinho, in the state of Pernambuco. He also discovered the Amazon and Oiapoque rivers. • Pedro Álvares Cabral, a Portuguese admiral, who was sailing with his fleet to India via the South African route discovered by Vasco da Gama, headed southwest to avoid the calms off the coast of the Gulf of Guinea, and so encountered the coast of Brazil in 1500.

Uses of serendipity Serendipity is used as a sociological method in Anselm L. Strauss' and Barney G. Glaser's Grounded Theory, building on ideas by sociologist Robert K. Merton, who in Social Theory and Social Structure (1949) referred to the "serendipity pattern" as the fairly common experience of observing an unanticipated, anomalous and strategic datum which becomes the occasion for developing a new theory or for extending an existing theory. Robert K. Merton also coauthored (with Elinor Barber) The Travels and Adventures of Serendipity (Princeton: Princeton University Press, 2003), which traces the origins and uses of the word "serendipity" since it was coined. The book is "a study in sociological semantics and the sociology of science", as the subtitle of the book declares. It further develops the idea of serendipity as scientific "method" (as juxtaposed with purposeful discovery by experiment or retrospective prophecy). Serendipity 111

Related terms William Boyd coined the term zemblanity to mean somewhat the opposite of serendipity: "making unhappy, unlucky and expected discoveries occurring by design".[10] It derives from Novaya Zemlya (or Nova Zembla), a cold, barren land with many features opposite to the lush Sri Lanka (Serendip). On this island Willem Barents and his crew were stranded while searching for a new route to the east. Bahramdipity is derived directly from Bahram Gur as characterized in the "The Three Princes of Serendip". It describes the suppression of serendipitous discoveries or research results by powerful individuals.[11]

Bibliography • Theodore G. Remer, Ed.: Serendipity and the Three Princes, from the Peregrinaggio of 1557, Edited, with an Introduction and Notes, by Theodore G. Remer, Preface by W.S. Lewis. University of Oklahoma Press, 1965. LCC 65-10112 • Robert K. Merton, Elinor Barber: The Travels and Adventures of Serendipity: A Study in Sociological Semantics and the Sociology of Science. Princeton University Press, 2004. ISBN 0-691-11754-3. (Manuscript written 1958). • Patrick J. Hannan: Serendipity, Luck and Wisdom in Research. iUniverse, 2006. ISBN 0-595-36551-5 • Royston M. Roberts: Serendipity: Accidental Discoveries in Science. Wiley, 1989. ISBN 0-471-60203-5 • Pek Van Andel: "Anatomy of the unsought finding : serendipity: origin, history, domains, traditions, appearances, patterns and programmability." British Journal for the Philosophy of Science, 1994, 45(2), 631–648.

See also • Coincidence • Insight • Lateral thinking • Synchronicity

References [1] "Words hardest to translate: Encyclopedia II – Words hardest to translate – The list by Today Translations." Global Oneness – The meeting place for Cultural Creatives – Articles, News, Community, Forums, Travel & Events and much more. 21 Apr. 2009 . [2] For example: Portuguese serendipicidade or serendipidade; French sérendipicité or sérendipité but also heureux hasard, "fortunate chance";

Italian serendipità ( Italian Dictionary Hoepli, cfr. (http:/ / dizionari. hoepli. it/ Dizionario_Italiano/ parola/ serendipita. aspx?idD=1&

Query=serendipità & lettera=S); Dutch serendipiteit; German Serendipität; Japanese serendipiti (セレンディピティ); Swedish, Danish and Norwegian serendipitet; Romanian serendipitate; Spanish serendipia, Polish: Serendypność; Finnish serendipiteetti

[3] Serendip @ Dictionary.Reference.com (http:/ / dictionary. reference. com/ browse/ Serendip) and Serendipity @ Dictionary.Reference.com

(http:/ / dictionary. reference. com/ browse/ serendipity) [4] As given by W. S. Lewis, ed., Horace Walpole's Correspondence, Yale edition, in the book by Theodore G. Remer, ed.: Serendipity and the Three Princes, from the Peregrinaggio of 1557, Edited, with an Introduction and Notes, by Theodore G. Remer, Preface by W.S. Lewis. University of Oklahoma Press, 1965. LCC 65-10112

[5] http:/ / www. ncbi. nlm. nih. gov/ entrez/ query. fcgi?db=pubmed& cmd=Retrieve& dopt=AbstractPlus& list_uids=16179740& query_hl=2& itool=pubmed_DocSum [6] Original French, as at Louis Pasteur: Dans les champs de l'observation le hasard ne favorise que les esprits préparés.

[7] http:/ / www. ncbi. nlm. nih. gov/ entrez/ query. fcgi?db=pubmed& cmd=Retrieve& dopt=AbstractPlus& list_uids=16608738& query_hl=4& itool=pubmed_docsum

[8] "Accidental Discovery Produces Durable New Blue Pigment for Multiple Applications" (http:/ / www. sciencedaily. com/ releases/ 2009/ 11/

091116143621. htm). Sciencedaily.com. 2009-11-19. . Retrieved 2010-05-31.

[9] Elliot, J.L.; Dunham, E. and Mink, D. (1977). "The rings of Uranus" (http:/ / www. nature. com/ nature/ journal/ v267/ n5609/ abs/ 267328a0. html). Nature 267: 328–330. doi:10.1038/267328a0. . [10] Boyd, William. Armadillo, Chapter 12, Knopf, New York, 1998. ISBN 0-375-40223-3

[11] (a) Sommer, Toby J. "'Bahramdipity' and Scientific Research", The Scientist, 1999, 13(3), 13. (http:/ / www. the-scientist. com/ yr1999/ feb/

opin_990201. html) Serendipity 112

(b) Sommer, Toby J. "Bahramdipity and Nulltiple Scientific Discoveries," Science and Engineering Ethicss, 2001, 7(1), 77–104. (http:/ /

www. uow. edu. au/ arts/ sts/ bmartin/ dissent/ documents/ Sommer. pdf) • "The view from Serendip", by Arthur C. Clarke, Random House, 1977. • "Momentum and Serendipity: how acquired leaders create value in the integration of technology firms", by Melissa E. Graebner, McCombs School of Business, University of Texas at Austin, Austin, Texas, U.S.A. 2004.

External links

• Polymers & Serendipity: Case Studies (http:/ / www. thebakken. org/ education/ SciMathMN/

polymers-serendipity/ polymer1. htm) – rayon, nylon, and more examples in chemistry

• Social Serendipity (http:/ / reality. media. mit. edu/ serendipity. php) – MIT Media Lab project using mobile phones for social matchmaking

• The Three Princes of Serendip (http:/ / livingheritage. org/ three_princes. htm) – one version of the story.

• Serendip (http:/ / serendip. brynmawr. edu) – a website continually evolving using the principles of serendipity

• Serendipity and the Internet (http:/ / news. bbc. co. uk/ 1/ hi/ technology/ 5018998. stm) from Bill Thompson at the BBC

• Accidental discoveries (http:/ / www. pbs. org/ wgbh/ nova/ cancer/ discoveries. html). PBS

• Serendipity of Science (http:/ / www. simonsingh. net/ Serendipity. html) – a BBC Radio 4 series by Simon Singh

• Top Ten: Accidental discoveries (http:/ / web. archive. org/ web/ 20071011073747/ http:/ / exn. ca/ stories/ 2004/

04/ 19/ 51. asp). Discovery Channel Explore your World.

• ACM Paper on Creating serendipitous encounters in a geographically distributed community (http:/ / portal. acm.

org/ citation. cfm?id=1178745. 1178756).

• Serendipitous Information Retrieval : An Academic Research Publication by Elaine G. Toms (http:/ / www.

ercim. org/ publication/ ws-proceedings/ DelNoe01/ 3_Toms. pdf)

• Programming for Serendipity - AAAI Technical Report FS-02-01 (http:/ / papers. ssrn. com/ sol3/ papers. cfm?abstract_id=1385402)

• The Serendipity Equations (http:/ / papers. ssrn. com/ sol3/ papers. cfm?abstract_id=1380082)

• Psychology today's main article about serendipity (http:/ / www. psychologytoday. com/ magazine/ archive/ 2010/ 05) Similarity (geometry) 113 Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. More precisely, one is congruent to the result of a uniform scaling (enlarging or shrinking) of the other. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. One can be obtained from the other by uniformly "stretching" the same amount on all directions, possibly with additional rotation and reflection, i.e., both have the same shape, or one has the same shape as the mirror image of the other. For example, all circles are similar to each other, Shapes shown in the same color are similar all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, nor are hyperbolas all similar to each other. If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar.

This article assumes that a scaling, enlargement or stretch can have a scale factor of 1, so that all congruent shapes are also similar, but some school text books specifically exclude congruent triangles from their definition of similar triangles by insisting that the sizes must be different to qualify as similar.

Similar triangles To understand the concept of similarity of triangles, one must think of two different concepts. On the one hand there is the concept of shape and on the other hand there is the concept of scale. If you were to draw a map, you would probably try to preserve the shape of what you are mapping, while you would make your picture at a unit rate that is in proportion to the original size or value. In particular, similar triangles are triangles that have the same shape and are up to scale of one another. For a triangle, the shape is determined by its angles, so the statement that two triangles have the same shape simply means that there is a correspondence between angles that preserve their measures. Formally speaking, we say that two triangles and are similar if either of the following conditions holds: 1. Corresponding sides have lengths in the same ratio:

i.e. . This is equivalent to saying that one triangle is an enlargement of the other.

2. is equal in measure to , and is equal in measure to . This also implies that is equal in measure to . When two triangles and are similar, we write

The 'is similar to' symbol can also be expressed as three vertical lines: lll This idea extends to similar polygons with more sides. Given any two similar polygons, corresponding sides are proportional. However, proportionality of corresponding sides is not sufficient to prove similarity for polygons Similarity (geometry) 114

beyond triangles (otherwise, for example, all rhombi would be similar). Corresponding angles must also be equal in measure.

Angle/side similarities The following three criteria are sufficient to prove that a pair of triangles are similar. In summary, they state that if triangles have the same shape then they are to scale (AA criterion), and that if they are to scale then they have the same shape (SSS). Another extra criterion, SAS, will also be explained below. • AA: if two triangles have two corresponding pairs of angles with the same measure then they are similar. Sometimes this criterion is also referred to as AAA because two angles of equal measure implies equality of the third. This criterion means that if a triangle is copied to preserve the shape, then the copy is to scale. • SSS: If the ratio of corresponding sides of two triangles does not depend on the sides chosen, then the triangles are similar. This means that if any triangle copied to scale is also copied in shape. • SAS: if two sides are taken in a triangle, that are proportional to two corresponding sides in another triangle, and the angles included between these sides have the same measure, then the triangles are similar. This means that to enlarge a triangle, it is sufficient to copy one angle, and scale just the two sides that form the angle. See also: Congruence (geometry), Solution of triangles

Similar curves Several other types curves are similar, with all examples of that type being similar to each other. These include: • Parabola • Catenary • Graphs of the logarithm function for different bases • Logarithmic spiral

Similarity in Euclidean space One of the meanings of the terms similarity and similarity transformation (also called dilation) of a Euclidean space is a function f from the space into itself that multiplies all distances by the same positive scalar r, so that for any two points x and y we have

where "d(x,y)" is the Euclidean distance from x to y. Two sets are called similar if one is the image of the other under such a similarity. A special case is a homothetic transformation or central similarity: it neither involves rotation nor taking the mirror image. A similarity is a composition of a homothety and an isometry. Therefore, in general Euclidean spaces every similarity is an affine transformation, because the Euclidean group E(n) is a subgroup of the affine group. Viewing the complex plane as a 2-dimensional space over the reals, the 2D similarity transformations expressed in terms of the complex plane are and , and all affine transformations are of the form (a, b, and c complex). Similarity (geometry) 115

Similarity in general metric spaces

In a general metric space (X, d), an exact similitude is a function f from the metric space X into itself that multiplies all distances by the same positive scalar r, called f's contraction factor, so that for any two points x and y we have

Sierpinski triangle. A space having self-similarity dimension ln 3 / ln 2 = log 3, 2 which is approximately 1.58. (from Hausdorff dimension.)

Weaker versions of similarity would for instance have f be a bi-Lipschitz function and the scalar r a limit

This weaker version applies when the metric is an effective resistance on a topologically self-similar set. A self-similar subset of a metric space (X, d) is a set K for which there exists a finite set of similitudes with contraction factors such that K is the unique compact subset of X for which

These self-similar sets have a self-similar measure with dimension D given by the formula

which is often (but not always) equal to the set's Hausdorff dimension and packing dimension. If the overlaps between the are "small", we have the following simple formula for the measure: Similarity (geometry) 116

Topology In topology, a metric space can be constructed by defining a similarity instead of a distance. The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity: the closer the points, the lesser the distance). The definition of the similarity can vary among authors, depending on which properties are desired. The basic common properties are 1. Positive defined: 2. Majored by the similarity of one element on itself (auto-similarity): and

More properties can be invoked, such as reflectivity ( ) or finiteness ( ). The upper value is often set at 1 (creating a possibility for a probabilistic interpretation of the similitude).

Self-similarity Self-similarity means that a pattern is non-trivially similar to itself, e.g., the set {.., 0.5, 0.75, 1, 1.5, 2, 3, 4, 6, 8, 12, ..}. When this set is plotted on a logarithmic scale it has translational symmetry.

See also • Congruence (geometry) • Hamming distance (string or sequence similarity) • inversive geometry • Jaccard index • Proportionality • Semantic similarity • Similarity search • Similarity space on Numerical taxonomy • Homoeoid (shell of concentric, similar ellipsoids)

External links • Animated demonstration of similar triangles [1]

References

[1] http:/ / www. mathopenref. com/ similartriangles. html Simulacrum 117 Simulacrum

Simulacrum (plural: -cra), from the Latin simulacrum which means "likeness, similarity",[1] is first recorded in the English language in the late 16th century, used to describe a representation of another thing, such as a statue or a painting, especially of a god; by the late 19th century, it had gathered a secondary association of inferiority: an image without the substance or qualities of the original.[2] Philosopher Fredric Jameson offers photorealism as an example of artistic simulacrum, where a painting is created by copying a photograph that is itself a copy of the real.[3] Other art forms that play with simulacra include Trompe l'oeil,[4] Pop Art, Italian neorealism and the French New Wave.[5]

Simulacrum in philosophy The simulacrum has long been of interest to philosophers. In his Sophist, Plato speaks of two kinds of image-making. The first is a faithful reproduction, attempted to copy precisely the original. The second is distorted intentionally in order to make the copy appear correct to viewers. He gives an example of Greek statuary, which was crafted larger on top than on bottom so that viewers from the ground would see it correctly. If they could view it in scale, they would realize it was malformed. This example from visual arts serves as a metaphor for philosophical arts and the tendency of some philosophers to distort truth in such a way that it appeared accurate unless viewed from the proper angle.[6] Nietzsche addresses the concept of simulacrum (but does not use the term) in The Twilight of the Idols, suggesting that most philosophers, by ignoring the reliable input of their senses and resorting to the constructs of language and reason, arrive at a distorted copy of reality.[7] Modern French social theorist Jean Baudrillard argues that a simulacrum is not a copy of the real, but becomes truth in its own right: the hyperreal. Where Plato saw two steps of reproduction — faithful and intentionally distorted (simulacrum) — Baudrillard sees four: (1) basic reflection of reality, (2) perversion of reality; (3) pretence of reality (where there is no model); and (4) simulacrum, which “bears no relation to any reality whatsoever.” Baudrillard uses the concept of god as an example of simulacrum.[8] In Baudrillard’s concept, like Nietzsche’s, simulacra are perceived as negative, but another modern philosopher who addressed the topic, Gilles Deleuze, takes a different view, seeing simulacra as the avenue by which accepted ideals or “privileged position” could be “challenged and overturned.”[9] Deleuze defines simulacra as "those systems in which different relates to different by means of difference itself. What is essential is that we find in these systems no prior identity, no internal resemblance."[10]

Simulacrum in literature, film, and television Simulacra often make appearances in speculative fiction. Examples of simulacra in the sense of artificial or supernaturally created life forms include Ovid’s ivory statue from Metamorphoses, the medieval golem of Jewish folklore, Mary Shelley’s creature from Frankenstein, Carlo Collodi’s Pinocchio, Karel Čapek's RUR (Rossum's Universal Robots [he was credited as the person who coined the term robot]), and Fritz Lang's Metropolis, with "Maria," the robotrix, Stanislaw Lem's Solaris and the synthetic life in Philip K. Dick’s Do Androids Dream of Electric Sheep?. Another Philip K. Dick novel pertinently entitled The Simulacra centres on a fraudulent government led by a presidential simulacrum (more specifically, an android); another work of his called We can build you also revolves around this concept and features simulacra. Simulacra of worlds or environments may also appear: author Michael Crichton visited this theme several times, in Westworld and in Jurassic Park; other examples include the elaborately staged worlds of The Truman Show; The Matrix; Synecdoche, New York; Equilibrium; and in Tales from the Darkside in the episode Bigalow's Last Smoke. Some stories focus on simulacra as objects. One example would be Oscar Wilde’s The Picture of Dorian Gray. The term also appears in Vladimir Nabokov's Lolita. Simulacrum 118

Simulacrum and recreation Recreational simulacra include reenactments of historical events or replicas of landmarks, such as Colonial Williamsburg and the Eiffel Tower, and constructions of fictional or cultural ideas, such as Fantasyland at Disney’s Magic Kingdom. The various Disney parks have by some philosophers been regarded as the ultimate recreational simulacra, with Baudrillard noting that Walt Disney World Resort is a copy of a copy, “a simulacrum to the second power.”[11] In 1975, Italian author Umberto Eco expressed his belief that at Disney’s parks, “we not only enjoy a perfect imitation, we also enjoy the conviction that imitation has reached its apex and afterwards reality will always be inferior to it."[12] This is for some an ongoing concern. Examining the impact of Disney’s simulacrum of national parks, Disney's Wilderness Lodge, environmentalist Jennifer Cypher and anthropologist Eric Higgs expressed worry that “the boundary between artificiality and reality will become so thin that the artificial will become the centre of moral value.”[13] Eco also refers to commentary on watching sports as sports to the power of three, or sports cubed. First, there are the players who participate in the sport, the real; then the onlookers merely witnessing it; then, the commentary itself on the act of witnessing the sport. Visual artist Paul McCarthy has created entire installations based upon Pirates of the Caribbean, and theme park simulacra, with videos playing inside the installation itself.

Simulacra in caricature An interesting example of simulacra is caricature. Where an artist draws a line drawing that closely approximates the facial features of a real person, the sketch cannot be easily identified by a random observer; the sketch could just as easily be a resemblance of any person, rather than the particular subject. However, a caricaturist will exaggerate prominent facial features far beyond their actuality, and a viewer will pick up on these features and be able to identify the subject, even though the caricature bears far less actual resemblance to the subject.

Simulacra in iconography Beer (1999: p.11) employs the term 'simulacrum' to denote the formation of a sign or iconographic image whether iconic or aniconic in the landscape or greater field of Thanka Art and Tantric Buddhist iconography. For example, an iconographic representation of a cloud formation sheltering a deity in a thanka or covering the auspice of a sacred mountain in the natural environment may be discerned as a simulacrum of an 'auspicious canopy' (Sanskrit: Chhatra) of the Ashtamangala.[14] Perceptions of religious imagery in natural phenomena approaches a cultural universal and may be proffered as evidence of the natural creative spiritual engagement of the experienced environment endemic to the human psychology.

Word usage

The latinised plural simulacra is interchangeable with the anglicised version simulacrums. http:/ / www.

merriam-webster. com/ dictionary/ simulacrum

See also • Jean Baudrillard • Body double • Doppelgänger • Gilles Deleuze • Look-alike • Pareidolia • Pastiche • Simulated reality • Songlines Simulacrum 119

• Thoughtform

External links • "Two Essays: Simulacra and Science Fiction; Ballard’s Crash" [15] Baudrillard, Jean • "The Simulacrum's Revenge," sec 3.2 of Flatline Constructs: Gothic and Cybernetic-Theory Fiction [16] Fisher, Mark

References

[1] "Word of the Day Archive: Thursday May 1, 2003" dictionary.com http:/ / dictionary. reference. com/ wordoftheday/ archive/ 2003/ 05/ 01. html retrieved May 2, 2007 [2] "simulacrum" The New Shorter Oxford English Dictionary 1993

[3] Massumi, Brian. "Realer than Real: The Simulacrum According to Deleuze and Guattari." http:/ / www. anu. edu. au/ hrc/ first_and_last/

works/ realer. htm retrieved May 2, 2007

[4] Baudrillard, Jean. "XI. Holograms." Simulacra and Simulations. transl. Sheila Faria Glaser. http:/ / www. egs. edu/ faculty/ jean-baudrillard/

articles/ simulacra-and-simulations-xi-holograms/ retrieved May 5, 2010

[5] Massumi, Brian. "Realer than Real: The Simulacrum According to Deleuze and Guattari." http:/ / www. anu. edu. au/ hrc/ first_and_last/

works/ realer. htm retrieved May 2, 2007

[6] Plato. The Sophist. transl. Benjamin Jowett. http:/ / philosophy. eserver. org/ plato/ sophist. txt retrieved May 2, 2007

[7] Nietzsche, “Reason in Philosophy.” Twilight of the Idols. transl. Walter Kaufmann and R.J. Hollingdale. 1888. http:/ / www. handprint. com/

SC/ NIE/ GotDamer. html#sect3 retrieved May 2, 2007

[8] Baudrillard, Jean. excerpt Simulacra and Simulations. http:/ / www. stanford. edu/ dept/ HPS/ Baudrillard/ Baudrillard_Simulacra. html retrieved May 2, 2007. [9] Deleuze, Gilles. Difference and Repetition. transl. Paul Patton. Columbia University Press: Columbia, 1968, p. 69. [10] p.299.

[11] Baudrillard, Jean. "Disneyworld Company." transl. Francois Debrix. Liberation. March 4, 1996. http:/ / www. egs. edu/ faculty/

jean-baudrillard/ articles/ disneyworld-company/ retrieved May 5, 2010.

[12] Eco, Umberto. "The City of Robots" Travels in Hyperreality. Reproduced in relevant portion at http:/ / www. acsu. buffalo. edu/ ~breslin/

eco_robots. html retrieved May 2, 2007

[13] Cypher, Jennifer and Eric Higgs. “Colonizing the Imagination: Disney’s Wilderness Lodge.” http:/ / www. ethics. ubc. ca/ papers/ invited/

cypher-higgs. html retrieved May 2, 2007 [14] Beer, Robert (1999). The Encyclopedia of Tibetan Symbols and Motifs, (Hardcover). Shambhala Publications. ISBN 157062416X, ISBN 978-1570624162, p.11

[15] http:/ / www. depauw. edu/ sfs/ backissues/ 55/ baudrillard55art. htm

[16] http:/ / www. cinestatic. com/ trans-mat/ Fisher/ FC3s2. htm Squaring the square 120 Squaring the square

Squaring the square is the problem of tiling an integral square using only other integral squares. (An integral square is a square whose sides have integer length.) The name was coined in a humorous analogy with squaring the circle. Squaring the square is an easy task unless additional conditions are set. The most studied restriction is that the squaring be perfect, meaning that the sizes of the smaller squares are all different. A related problem is squaring the plane, which can be done even with the restriction that each natural number occurs exactly once as a size of a square in the tiling.

Perfect squared squares

A "perfect" squared square is a square such that each of the smaller squares has a different size. It is first recorded as being studied by R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte, at Cambridge University. They transformed the square tiling into an equivalent electrical circuit — they called it "Smith diagram" — by considering the squares as resistors that connected to their neighbors at their top and bottom edges, and Smith diagram of a rectangle then applied Kirchhoff's circuit laws and circuit decomposition techniques to that circuit.

The first perfect squared square was found by Roland Sprague in 1939. If we take such a tiling and enlarge it so that the formerly smallest tile now has the size of the square S we started out from, then we see that we obtain from this a tiling of the plane with integral squares, each having a different size. Martin Gardner has published an extensive [1] article written by W. T. Tutte about the early history of squaring the square.

Simple squared squares

A "simple" squared square is one where no subset of the squares forms a rectangle or square, otherwise it is "compound". The smallest simple perfect squared square was discovered by A. J. W. Duijvestijn using a computer search. His tiling uses 21 squares, and has been proved to be minimal. The smallest perfect compound squared square was discovered by T.H. Willcocks in 1946 and has 24 squares; however, it was not until 1982 that Duijvestijn, Pasquale Joseph Federico and P. Leeuw mathematically proved it to be the lowest-order example.[2]

The smallest simple squared square forms the logo of the Trinity

Mathematical Society. Lowest-order perfect squared square Squaring the square 121

Mrs. Perkins's quilt When the constraint of all the squares being different sizes is relaxed, a squared square such that the side lengths of the smaller squares do not have a common divisor larger than 1 is called a "Mrs. Perkins's quilt". In other words, the greatest common divisor of all the smaller side lengths should be 1. The Mrs. Perkins's quilt problem is to find a Mrs. Perkins's quilt with the fewest pieces for a given n × n square.

Squaring the plane In 1975, Solomon Golomb raised the question whether the whole plane can be tiled by squares whose sizes are all natural numbers without repetitions, which he called the heterogeneous tiling conjecture. This problem was later publicized by Martin Gardner in his Scientific American column and appeared in several books, but it defied solution for over 30 years. In Tilings and Patterns, published in 1987, Branko Grünbaum and G. C. Shephard stated that in all perfect integral tilings of the plane known at that time, the sizes of the squares grew exponentially. Recently, James Henle and Frederick Henle proved that this, in fact, can be done. Their proof is constructive and proceeds by "puffing up" an ell-shaped region formed by two side-by-side and horizontally flush squares of different sizes to a perfect tiling of a larger rectangular region, then adjoining the square of the smallest size not yet used to get another, larger ell-shaped region. The squares added during the puffing up procedure have sizes that have not yet appeared in the construction and the procedure is set up so that the resulting rectangular regions are expanding in all four directions, which leads to a tiling of the whole plane.

Cubing the cube Cubing the cube is the analogue in three dimensions of squaring the square: that is, given a cube C, the problem of dividing it into finitely many smaller cubes, no two congruent. Unlike the case of squaring the square, a hard but solvable problem, cubing the cube is impossible. This can be shown by a relatively simple argument. Consider a hypothetical cubed cube. The bottom face of this cube is a squared square; lift off the rest of the cube, so you have a square region of the plane covered with a collection of cubes Consider the smallest cube in this collection, with side c (call it S). Since the smallest square of a squared square cannot be on its edge, its neighbours will all tower over it, meaning that there isn't space to put a cube of side larger than c on top of it. Since the construction is a cubed cube, you're not allowed to use a cube of side equal to c; so only smaller cubes may stand upon S. This means that the top face of S must be a squared square, and the argument continues by infinite descent. Thus it is not possible to dissect a cube into finitely many smaller cubes of different sizes. Similarly, it is impossible to hypercube a hypercube, because each cell of the hypercube would need to be a cubed cube, and so on into the higher dimensions.

References • C. J. Bouwkamp and A. J. W. Duijvestijn, Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25, Eindhoven Univ. Technology, Dept. of Math., Report 92-WSK-03, Nov. 1992. • C. J. Bouwkamp and A. J. W. Duijvestijn, Album of Simple Perfect Squared Squares of order 26, Eindhoven University of Technology, Faculty of Mathematics and Computing Science, EUT Report 94-WSK-02, December 1994. • Brooks, R. L.; Smith, C. A. B.; Stone, A. H.; and Tutte, W. T. The Dissection of Rectangles into Squares, Duke Math. J. 7, 312–340, 1940 Squaring the square 122

• Martin Gardner, "Squaring the square," in The 2nd Scientific American Book of Mathematical Puzzles and Diversions. • Frederick V. Henle and James M. Henle, "Squaring the plane" [3], American Mathematical Monthly, 115, January 2008, 3–12

External links • Perfect squared squares:

• http:/ / www. squaring. net/

• http:/ / www. maa. org/ editorial/ mathgames/ mathgames_12_01_03. html

• http:/ / www. math. uwaterloo. ca/ navigation/ ideas/ articles/ honsberger2/ index. shtml

• http:/ / www. math. niu. edu/ ~rusin/ known-math/ 98/ square_dissect

• http:/ / www. stat. ualberta. ca/ people/ schmu/ preprints/ sq. pdf • Nowhere-neat squared squares:

• http:/ / karl. kiwi. gen. nz/ prosqtre. html • Mrs. Perkins's quilt: • Mrs. Perkins's Quilt [4] on MathWorld

References

[1] http:/ / www. squaring. net/ history_theory/ brooks_smith_stone_tutte_II. html

[2] "Compound Perfect Squares", By A. J. W. Duijvestijn, P. J. Federico, and P. Leeuw, Published in American Mathematical Monthly (http:/ /

www. maa. org/ pubs/ monthly. html) Volume 89 (1982) pp 15-32

[3] http:/ / maven. smith. edu/ ~jhenle/ stp/ stp. pdf

[4] http:/ / mathworld. wolfram. com/ MrsPerkinssQuilt. html Structural information theory 123 Structural information theory

Structural information theory (SIT) is a theory about human perception and, in particular, about perceptual organization, that is, about the way the human visual system organizes a raw visual stimulus into objects and object parts. SIT was initiated, in the 1960s, by Emanuel Leeuwenberg[1] [2] [3] and has been developed further by Hans Buffart, Peter van der Helm [4], and Rob van Lier [5]. It has been applied to a wide range of research topics, mostly in visual form perception but also in, for instance, visual ergonomics, data visualization, and music perception. SIT began as a quantitative model of visual pattern classification. Nowadays, it also includes quantitative models of symmetry perception and amodal completion, and it is theoretically founded in formalizations of visual regularity and viewpoint dependency. SIT has been argued[6] to be the best defined and most successful extension of Gestalt ideas. It is the only Gestalt approach providing a formal calculus that generates plausible perceptual interpretations.

The simplicity principle Although visual stimuli are fundamentally multi-interpretable, the human visual system usually has a clear preference for only one interpretation. To explain this preference, SIT introduced a formal coding model starting from the assumption that the perceptually preferred interpretation of a stimulus is the one with the simplest code. A simplest code is a code with minimum information load, that is, a code that enables a reconstruction of the stimulus using a minimum number of descriptive parameters. Such a code is obtained by capturing a maximum amount of visual regularity and yields a hierarchical organization of the stimulus in terms of wholes and parts. The assumption that the visual system prefers simplest interpretations is called the simplicity principle.[7] Historically, the simplicity principle is an information-theoretical descendant of the Gestalt law of Prägnanz,[8] which was based on the natural tendency of physical systems to settle into stable minimum-energy states. Furthermore, just as the later-proposed minimum description length principle in algorithmic information theory (AIT), it can be seen as a formalization of Occam's Razor in which the best hypothesis for a given set of data is the one that leads to the largest compression of the data.

Structural versus algorithmic information theory Since the 1960s, SIT (in psychology) and AIT (in computer science) evolved independently as viable alternatives for Shannon's classical information theory which had been developed in communication theory.[9] In Shannon's approach, things are assigned codes with lengths based on their probability in terms frequencies of occurrence (as, e.g., in the Morse code). In many domains, including perception, such probabilities are hardly quantifiable if at all, however. Both SIT and AIT circumvent this problem by turning to descriptive complexities of individual things. Although SIT and AIT share many starting points and objectives, there are also several relevant differences: • First, SIT makes the perceptually relevant distinction between structural and metrical information, whereas AIT does not; • Second, SIT encodes for a restricted set of perceptually relevant kinds of regularities, whereas AIT encodes for any imaginable regularity; • Third, in SIT, the relevant outcome of an encoding is a hierarchical organization, whereas in AIT, it is a complexity value. Structural information theory 124

Simplicity versus likelihood In visual perception research, the simplicity principle contrasts with the Helmholtzian likelihood principle,[10] which assumes that the preferred interpretation of a stimulus is the one with the highest probability of being correct in this world. As shown within a Bayesian framework using AIT findings,[11] the simplicity principle would imply that perceptual interpretations are fairly veridical (i.e., truthful) in many worlds rather than, as assumed by the likelihood principle, highly veridical in only one world. In other words, whereas the likelihood principle suggests that the visual system is a special-purpose system (i.e., dedicated to one world), the simplicity principle suggests that it is a general-purpose system (i.e., suited in many worlds). Crucial to the latter finding is the distinction between, and integration of, viewpoint-independent and viewpoint-dependent factors in vision, as proposed in SIT's empirically successful model of amodal completion.[12] In the Bayesian framework, these factors correspond to prior probabilities and conditional probabilities, respectively. In SIT's model, however, both factors are quantified in terms of complexities, that is, complexities of objects and spatial relationships, respectively. This approach is consistent with neuroscientific ideas about the distinction and interaction between the ventral ("what") and dorsal ("where") streams in the brain.[13]

SIT versus connectionism and dynamic systems theory On the one hand, a representational theory like SIT seems opposite to dynamic systems theory (DST). On the other hand, connectionism can be seen as something in between, that is, it flirts with DST when it comes to the usage of differential equations and it flirts with theories like SIT when it comes to the representation of information. In fact, the analyses provided by SIT, connectionism, and DST, correspond to what Marr called the computational, the algorithmic, and the implementational levels of description, respectively. According to Marr, such analyses are complementary rather than opposite. What SIT, connectionism, and DST have in common is that they describe nonlinear system behavior, that is, a minor change in the input may yield a major change in the output. Their complementarity expresses itself in that they focus on different aspects: • First, DST focuses primarily on how the state of a physical system as a whole (in this case, the brain) develops over time, whereas both SIT and connectionism focus primarily on what a system does in terms of information processing; according to both SIT and connectionism, this information processing (which, in this case, can be said to constitute cognition) thrives on interactions between bits of information. • Second, regarding these interactions between bits of information, connectionism focuses primarily on the nature of concrete interaction mechanisms (assuming existing bits of information suited for any input), whereas SIT focuses primarily on the nature of the (assumed to be transient, i.e., input-dependent) bits of information involved and on the nature of the outcome of the interaction between them (modelling the interaction itself in a more abstract way).

Modelling principles In SIT, candidate interpretations of a stimulus are represented by symbol strings, in which identical symbols refer to identical perceptual primitives (e.g., blobs or edges). Every substring of such a string represents a spatially contiguous part of an interpretation, so that the entire string can be read as a reconstruction recipe for the interpretation and, thereby, for the stimulus. These strings then are encoded (i.e., they are searched for visual regularities) to find the interpretation with the simplest code. In SIT's formal coding model, this encoding is modelled by way of symbol manipulation. In psychology, this has led to critical statements of the sort of "SIT assumes that the brain performs symbol manipulation". Such statements, however, fall in the same category as statements such as "physics assumes that nature applies formulas such as Einstein's E=mc2 or Newton's F=ma" and "DST models assume that dynamic systems apply differential equations". Structural information theory 125

That is, these statements ignore that the very concept of formalization means that things are represented by symbols and that relationships between these things are captured by formulas or, in the case of SIT, by simplest codes.

Visual regularity To obtain simplest codes, SIT applies coding rules that capture the kinds of regularity called iteration, symmetry, and alternation. These have been shown[14] to be the only regularities that satisfy the formal accessibility criteria of • (a) being so-called holographic regularities that • (b) allow for so-called hierarchically transparent codes. A crucial difference with respect to the traditional, so-called transformational, formalization of visual regularity is that, holographically, mirror symmetry is composed of many relationships between symmetry pairs rather than one relationship between symmetry halfs. Whereas the transformational characterization may be better suited for object recognition, the holographic characterization seems more consistent with the build up of mental representations in object perception. The perceptual relevance of the criteria of holography and transparency has been verified in the so-called holographic approach to visual regularity.[15] This approach provides an empirically successful model of the detectability of single and combined visual regularities, whether or not perturbed by noise. Furthermore, the transparent holographic regularities have been shown to lend themselves for transparallel processing which means that, in the process of selecting a simplest code from among all possible codes, O(2N) codes can be taken into account as if only one code of length N were concerned.[16] This supports the computational tractability of simplest codes and, thereby, the feasibility of the simplicity principle in perceptual organization.

References [1] Leeuwenberg, E. L. J. (1968). Structural information of visual patterns: an efficient coding system in perception. The Hague: Mouton. [2] Leeuwenberg, E. L. J. (1969). Quantitative specification of information in sequential patterns. Psychological Review, 76, 216-220. [3] Leeuwenberg, E. L. J. (1971). A perceptual coding language for visual and auditory patterns. American Journal of Psychology, 84, 307-349.

[4] http:/ / www. nici. ru. nl/ ~peterh

[5] http:/ / www. nici. kun. nl/ ~robvl [6] Palmer, S. E. (1999). Vision science: Photons to phenomenology. Cambridge, MA: MIT Press. [7] Hochberg, J. E., & McAlister, E. (1953). A quantitative approach to figural "goodness". Journal of Experimental Psychology, 46, 361-364. [8] Koffka, K. (1935). Principles of gestalt psychology. London: Routledge & Kegan Paul. [9] Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379-423, 623-656. [10] von Helmholtz, H. L. F. (1962). Treatise on Physiological Optics (J. P. C. Southall, Trans.). New York: Dover. (Original work published 1909) [11] van der Helm, P. A. (2000). Simplicity versus likelihood in visual perception: From surprisals to precisals. Psychological Bulletin, 126, 770-800. [12] van Lier, R. J., van der Helm, P. A., & Leeuwenberg, E. L. J. (1994). Integrating global and local aspects of visual occlusion. Perception, 23, 883-903. [13] Ungerleider, L. G., & Mishkin, M. (1982). Two cortical visual systems. In D. J. Ingle, M. A. Goodale, & R. J. W. Mansfield (Eds.), Analysis of Visual Behavior (pp. 549--586). Cambridge, MA: MIT Press. [14] van der Helm, P. A., & Leeuwenberg, E. L. J. (1991). Accessibility, a criterion for regularity and hierarchy in visual pattern codes. Journal of Mathematical Psychology, 35, 151-213. [15] van der Helm, P. A., & Leeuwenberg, E. L. J. (1996). Goodness of visual regularities: A nontransformational approach. Psychological Review, 103, 429-456. [16] van der Helm, P. A. (2004). Transparallel processing by hyperstrings. Proceedings of the National Academy of Sciences USA, 101 (30)}, 10862-10867. Task analysis 126 Task analysis

Task analysis is the analysis of how a task is accomplished, including a detailed description of both manual and mental activities, task and element durations, task frequency, task allocation, task complexity, environmental conditions, necessary clothing and equipment, and any other unique factors involved in or required for one or more people to perform a given task. Task analysis emerged from research in applied behavior analysis and still has considerable research in that area. Information from a task analysis can then be used for many purposes, such as personnel selection and training, tool or equipment design, procedure design (e.g., design of checklists or decision support systems) and automation.

Applications of Task analysis The term "task" is often used interchangeably with activity or process. Task analysis often results in a hierarchical representation of what steps it takes to perform a task for which there is a goal and for which there is some lowest-level "action" that is performed. Task analysis is often performed by human factors professionals. Task analysis may be of manual tasks, such as bricklaying, and be analyzed as time and motion studies using concepts from industrial engineering. Cognitive task analysis is applied to modern work environments such as supervisory control where little physical work occurs, but the tasks are more related to situation assessment, decision making, and response planning and execution. Task analysis is also used in education. It is a model that is applied to classroom tasks to discover which curriculum components are well matched to the capabilities of students with learning disabilities and which task modification might be necessary. It discovers which tasks a person hasn't mastered, and the information processing demands of tasks that are easy or problematic. In behavior modification, it is a breakdown of a complex behavioral sequence into steps. This often serves as the basis for Chaining.

Task analysis versus Work domain analysis If task analysis is likened to a set of instructions on how to navigate from point A to point B, then work domain analysis (WDA) is like having a map of the terrain that includes Point A and Point B. WDA is broader and focuses on the environmental constraints and opportunities for behavior, as in Gibsonian ecological psychology and ecological interface design.

Task analysis and documentation Since the 1980s, a major change in technical documentation has been to emphasize the tasks performed with a system rather than documenting the system itself.[1] In software documentation particularly, long printed technical manuals that exhaustively describe every function of the software are being replaced by online help organized into tasks. This is part of the new emphasis on usability and user-centered design rather than system/software/product design. This task orientation in technical documentation began with publishing guidelines issued by IBM in the late 1980s. Later IBM studies led to John Carroll's theory of minimalism in the 1990s. With the development of XML as a markup language suitable for both print and online documentation (replacing SGML with its focus on print), IBM developed the Darwin Information Typing Architecture XML standard in 2000. Now an OASIS standard, DITA has a strong emphasis on task analysis. Its three basic information types are Task, Concept, and Reference. Tasks are analyzed into steps, with a main goal of identifying steps that are reusable in multiple tasks. Task analysis 127

See also • Business process mapping and business process modeling • Cognitive ergonomics • Job analysis • Workflow • Human reliability • Programmed instruction • Direct Instruction • Applied Behavior Analysis

Further reading • Crandall, B., Klein, G., and Hoffman, R. (2006). Working minds: A practitioner's guide to cognitive task analysis. MIT Press. • Kirwan, B. and Ainsworth, L. (Eds.) (1992). A guide to task analysis. Taylor and Francis. • Hackos, JoAnn T. and Redish, Janice C. (1998). User and Task Analysis for Interface Design. Wiley. • Brockmann, R. John (1986). Writing Better Computer User Documentation - From Paper to Online. Wiley-Interscience. • Carroll, John M. (1990). The Nurnberg Funnel - Designing Minimalist Instruction for Practical Computer Skill. MIT.

External links • Task analysis [2] • Cognitive Performance Group of FL [3] • Conduct Task Analysis (Usability.gov) [4] • Task Analysis (User Experience Design resources) [5]

References [1] (Hackos and Redish, 1998)

[2] http:/ / maxweber. hunter. cuny. edu/ pub/ eres/ EDSPC715_MCINTYRE/ TaskAnalysis. html

[3] http:/ / cognitiveperformancegroup. com/

[4] http:/ / www. usability. gov/ analyze/ analysis. html

[5] http:/ / deyalexander. com. au/ resources/ uxd/ task-analysis. html Techne 128 Techne

Techne, or techné, as distinguished from episteme, is etymologically derived from the Greek word τέχνη (Ancient Greek: [tékʰnɛː], Modern Greek [ˈtexni] Wikipedia:Media helpFile:Ell-Techni.ogg) which is often translated as craftsmanship, craft, or art. It is the rational method involved in producing an object or accomplishing a goal or objective. The means of this method is through art. Techne resembles episteme in the implication of knowledge of principles, although techne differs in that its intent is making or doing, as opposed to "disinterested understanding." As one observer has argued, techne "was not concerned with the necessity and eternal a priori truths of the cosmos, nor with the a posteriori contingencies and exigencies of ethics and politics. [...] Moreover, this was a kind of knowledge associated with people who were bound to necessity. That is, techne was chiefly operative in the domestic sphere, in farming and slavery, and not in the free realm of the Greek polis."[1] Aristotle saw it as representative of the imperfection of human imitation of nature. For the ancient Greeks, it signified all the Mechanical Arts including medicine and music. The English aphorism, ‘gentlemen don’t work with their hands,’ is said to have originated in ancient Greece in relation to their cynical view on the arts. Due to this view, it was only fitted for the lower class while the upper class practiced the Liberal Arts of ‘free’ men (Dorter 1973). Socrates also compliments techne only when it was used in the context of episteme. Episteme sometimes means knowing how to do something in a craft-like way. The craft-like knowledge is called a ‘technê.' It is most useful when the knowledge is practically applied, rather than theoretically or aesthetically applied. For the ancient Greeks, when techne appears as art, it is most often viewed negatively, whereas when used as a craft it is viewed positively: because a craft is the practical application of an art, rather than art as an end in itself. In The Republic, written by Plato, the knowledge of forms "is the indispensable basis for the philosophers' craft of ruling in the city" (Stanford 2003). Techne is often used in philosophical discourse to distinguish from art (or poiesis). This use of the word also occurs in The Digital Humanities to differentiate between linear narrative presentation of knowledge and dynamic presentation of knowledge, wherein techne represents the former and poiesis represents the latter.

See also • Episteme • Phronesis

External links • Epistêmê and Technê from the Stanford Encyclopedia of Philosophy [2] • Dictionary of Philosophy [3] • Kenneth Dorter "The Ion: Plato’s Characterization of Art" [4] Techne 129

Additional References Dunne, Joseph. Back to the Rough Ground: 'Phronesis' and 'Techne' in Modern Philosophy and in Aristotle. Notre Dame, Indiana: University of Notre Dame Press, 1997. (ISBN 978-0-2680-0689-1)

References [1] Young, Damon A. (Apr 2009). "BOWING TO YOUR ENEMIES: COURTESY, BUDŌ, AND JAPAN.". Philosophy East & West 59 (2): 188–215.

[2] http:/ / plato. stanford. edu/ entries/ episteme-techne

[3] http:/ / www. ditext. com/ runes/ t. html

[4] http:/ / www. compilerpress. atfreeweb. com/ Anno%20Dorter%20Platos%20Characterization%20of%20Art%20JAAC%201973. htm

Tessellation

A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.

In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics.[1] The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations,

often made of glazed clay. A tessellation of pavement

Wallpaper groups

Tilings with translational symmetry can be categorized by wallpaper group, of which 17 exist. All seventeen of these patterns are known to exist in the Alhambra palace in Granada, Spain. Of the three regular tilings two are in the category p6m and one is in p4m. Tessellation 130

A Honeycomb is an example of a tessellated natural structure

Tessellations and color

When discussing a tiling that is displayed in colors, to avoid ambiguity one needs to specify whether the colors are part of the tiling or just part of its illustration. See also symmetry. The four color theorem states that for every tessellation of a normal Euclidean plane, with a set of four available colors, each tile can be

colored in one color such that no tiles of equal color meet at a curve of If this parallelogram pattern is colored before positive length. Note that the coloring guaranteed by the four-color tiling it over a plane, seven colors are required to theorem will not in general respect the symmetries of the tessellation. ensure each complete parallelogram has a consistent color that is distinct from that of To produce a coloring which does, as many as seven colors may be adjacent areas. (This tiling can be compared to needed, as in the picture at right. the surface of a torus.) Tiling before coloring, only four colors are needed. Tessellations with quadrilaterals

Copies of an arbitrary quadrilateral can form a tessellation with 2-fold rotational centers at the midpoints of all sides, and translational symmetry whose basis vectors are the diagonal of the quadrilateral or, equivalently, one of these and the sum or difference of the two. For an asymmetric quadrilateral this tiling belongs to wallpaper group p2. As fundamental domain we have the quadrilateral. Equivalently, we can construct a parallelogram subtended by a minimal set of translation vectors, starting from a rotational center. We can divide this by one diagonal, and take one half (a triangle) as fundamental domain. Such a triangle has the same area as the quadrilateral and can be constructed from it by cutting and pasting. Tessellation 131

Regular and semi-regular tessellations

A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semiregular tessellation uses a variety of regular polygons; there are eight of these. The arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation is even less regular: the only requirement is that adjacent tiles only share full sides, i.e. no tile shares a partial side with any other tile. Other types of tessellations exist, depending on types of figures and types of pattern. There are regular versus irregular, periodic versus Hexagonal tessellation of a floor aperiodic, symmetric versus asymmetric, and fractal tessellations, as well as other classifications.

Penrose tilings using two different polygons are the most famous example of tessellations that create aperiodic patterns. They belong to a general class of aperiodic tilings that can be constructed out of self-replicating sets of polygons by using recursion. A monohedral tiling is a tessellation in which all tiles are congruent. Spiral monohedral tilings include the Voderberg tiling discovered by Hans Voderberg in 1936, whose unit tile is a nonconvex enneagon; and the Hirschhorn tiling discovered by Michael Hirschhorn in the 1970s, whose unit tile is an irregular pentagon.

Self-dual tessellations Tilings and honeycombs can also be self-dual. All n-dimensional hypercubic honeycombs with Schlafli symbols {4,3n−2,4}, are self-dual. Tessellation 132

Tessellations and computer models

In the subject of computer graphics, tessellation techniques are often used to manage datasets of polygons and divide them into suitable structures for rendering. Normally, at least for real-time rendering, the data is tessellated into triangles, which is sometimes referred to as triangulation. Tessellation is a staple feature of DirectX 11 and OpenGL.[2] [3]

In computer-aided design the constructed design is represented by a boundary representation topological model, where analytical 3D surfaces and curves, limited to faces and edges constitute a continuous boundary of a 3D body. Arbitrary 3D bodies are often too complicated to analyze directly. So they are approximated (tessellated) with a mesh of small, easy-to-analyze pieces of 3D volume — usually either A tessellation of a disk used to solve a finite irregular tetrahedrons, or irregular hexahedrons. The mesh is used for element problem. finite element analysis.

Mesh of a surface is usually generated per individual faces and edges (approximated to polylines) so that original limit vertices are included into mesh. To ensure approximation of the original surface suits needs of the further processing 3 basic parameters are usually defined for the surface mesh generator: • Maximum allowed distance between planar approximation polygon and the surface (aka "sag"). This parameter ensures that mesh is similar enough to the original analytical surface (or the polyline is similar to the original curve). • Maximum allowed size of the approximation polygon (for triangulations it can be maximum allowed length of triangle sides). This parameter ensures enough detail for further analysis. These rectangular bricks are connected in a tessellation which, considered as an edge-to-edge • Maximum allowed angle between two adjacent approximation tiling, is topologically identical to a hexagonal polygons (on the same face). This parameter ensures that even very tiling; each hexagon is flattened into a rectangle small humps or hollows that can have significant effect to analysis whose long edges are divided in two by the will not disappear in mesh. neighboring bricks. Algorithm generating mesh is driven by the parameters (example: CATIA V5 tessellation library). Some computer analyses require adaptive mesh. Mesh is being locally enhanced (using stronger parameters) in areas where it is needed during the analysis. Some geodesic domes are designed by tessellating the sphere with triangles that are as close to equilateral triangles as possible.

Tessellations in nature

Basaltic lava flows often display columnar jointing as a result of contraction forces causing cracks as the lava cools. The extensive crack networks that develop often produce hexagonal columns of lava. One example of such an array of columns is the Giant's Causeway in Northern Ireland. Tessellation 133

The Tessellated pavement in Tasmania is a rare sedimentary rock formation where the rock has fractured into rectangular blocks.

This basketweave tiling is topologically identical to the Cairo pentagonal tiling, with one side of each rectangle counted as two edges, divided by a vertex on the two neighboring rectangles.

Number of sides of a polygon versus number of sides at a vertex For an infinite tiling, let be the average number of sides of a polygon, and the average number of sides meeting at a vertex. Then . For example, we have the combinations , for the tilings in the article Tilings of regular polygons. A continuation of a side in a straight line beyond a vertex is counted as a separate side. For example, the bricks in the picture are considered hexagons, and we have combination (6, 3). Similarly, for the basketweave tiling often found on bathroom floors, we have . For a tiling which repeats itself, one can take the averages over the repeating part. In the general case the averages are taken as the limits for a region expanding to the whole plane. In cases like an infinite row of tiles, or tiles getting smaller and smaller outwardly, the outside is not negligible and should also be counted as a tile while taking the limit. In extreme cases the limits may not exist, or depend on how the region is expanded to infinity. For finite tessellations and polyhedra we have

where is the number of faces and the number of vertices, and is the Euler characteristic (for the plane and for a polyhedron without holes: 2), and, again, in the plane the outside counts as a face. The formula follows observing that the number of sides of a face, summed over all faces, gives twice the total number of sides in the entire tessellation, which can be expressed in terms of the number of faces and the number of vertices. Similarly the number of sides at a vertex, summed over all vertices, also gives twice the total number of sides. From the two results the formula readily follows. In most cases the number of sides of a face is the same as the number of vertices of a face, and the number of sides meeting at a vertex is the same as the number of faces meeting at a vertex. However, in a case like two square faces touching at a corner, the number of sides of the outer face is 8, so if the number of vertices is counted the common corner has to be counted twice. Similarly the number of sides meeting at that corner is 4, so if the number of faces at that corner is counted the face meeting the corner twice has to be counted twice. A tile with a hole, filled with one or more other tiles, is not permissible, because the network of all sides inside and outside is disconnected. However it is allowed with a cut so that the tile with the hole touches itself. For counting the number of sides of this tile, the cut should be counted twice. Tessellation 134

For the Platonic solids we get round numbers, because we take the average over equal numbers: for we get 1, 2, and 3. From the formula for a finite polyhedron we see that in the case that while expanding to an infinite polyhedron the number of holes (each contributing −2 to the Euler characteristic) grows proportionally with the number of faces and the number of vertices, the limit of is larger than 4. For example, consider one layer of cubes, extending in two directions, with one of every 2 × 2 cubes removed. This has combination (4, 5), with , corresponding to having 10 faces and 8 vertices per hole. Note that the result does not depend on the edges being line segments and the faces being parts of planes: mathematical rigor to deal with pathological cases aside, they can also be curves and curved surfaces.

Tessellations of other spaces

M.C.Escher, Circle Limit III A torus can be tiled by a repeating matrix of (1959) An example tessellation of the surface of a sphere by a isogonal quadrilaterals. truncated icosidodecahedron.

As well as tessellating the 2-dimensional Euclidean plane, it is also possible to tessellate other n-dimensional spaces by filling them with n-dimensional polytopes. Tessellations of other spaces are often referred to as honeycombs. Examples of tessellations of other spaces include: • Tessellations of n-dimensional Euclidean space. For example, filling 3-dimensional Euclidean space with cubes to create a cubic honeycomb. • Tessellations of n-dimensional elliptic space, either the n-sphere (spherical tiling, spherical polyhedron) or n-dimensional real projective space (elliptic tiling, projective polyhedron). For example, projecting the edges of a regular dodecahedron onto its circumsphere creates a tessellation of the 2-dimensional sphere with regular spherical pentagons, while taking the quotient by the antipodal map yields the hemi-dodecahedron, a tiling of the projective plane. • Tessellations of n-dimensional hyperbolic space. For example, M. C. Escher's Circle Limit III depicts a tessellation of the hyperbolic plane using the Poincaré disk model with congruent fish-like shapes. The hyperbolic plane admits a tessellation with regular p-gons meeting in q's whenever ; Circle Limit III may be understood as a tiling of octagons meeting in threes, with all sides replaced with jagged lines and each octagon then cut into four fish. See (Magnus 1974) for further non-Euclidean examples. There are also abstract polyhedra which do not correspond to a tessellation of a manifold because they are not locally spherical (locally Euclidean, like a manifold), such as the 11-cell and the 57-cell. These can be seen as tilings of more general spaces. Tessellation 135

See also • Convex uniform honeycomb - The 28 uniform 3-dimensional tessellations, a parallel construction to this plane set • Coxeter groups - algebraeic groups that can be used to find tesselations • Girih tiles • Honeycomb (geometry) • Jig-saw puzzle • List of regular polytopes • List of uniform tilings • Mathematics and fiber arts • Mosaic • Nikolas Schiller - Artist using tessellations of aerial photographs • Penrose tilings • Pinwheel tiling • Polyiamond - tilings with equilateral triangles • Polyomino • Quilting • Self-replication • Tile • Tiling puzzle • Tiling, Aperiodic • Tilings of regular polygons • Trianglepoint - needlepoint with polyiamonds (equilateral triangles) • Triangulation • Uniform tessellation • Uniform tiling • Uniform tilings in hyperbolic plane • Voronoi tessellation • Wallpaper group - seventeen types of two-dimensional repetitive patterns • Wang tiles

References • Grunbaum, Branko and G. C. Shephard. Tilings and Patterns. New York: W. H. Freeman & Co., 1987. ISBN 0-7167-1193-1. • Coxeter, H.S.M.. Regular Polytopes, Section IV : Tessellations and Honeycombs. Dover, 1973. ISBN 0-486-61480-8. • Magnus, Wilhelm (1974), Noneuclidean tesselations and their groups, Academic Press, ISBN 978-0-12465450-1 Tessellation 136

External links • Interactive Girih Tiles - Tessellation [4] • K-12 Tessellation Lesson [5] • Tilings Encyclopedia [6] - Reference for Substitution Tilings • Math Forum Tessellation Tutorials [7] - make your own • Mathematical Art of M. C. Escher [8] - tessellations in art • The 14 Different Types of Convex Pentagons that Tile the Plane [9] • Tiling Plane & Fancy [10] at Southern Polytechnic State University • Grotesque Geometry, Andrew Crompton [11] • Tessellations.org - many examples and do it yourself tutorials from the artistic, not mathematical, point of view [12]

• Tessellation.info A database with over 500 tessellations categorized by artist and depicted subjects [13] • Tiles and Tessellations [14] • Semiregular pattern [15] - This pattern can describe a collapsing cylinder • Hyperbolic Tessellations [16], David E. Joyce, Clark University • Some Special Radial and Spiral Tilings [17]

References

[1] tessellate (http:/ / m-w. com/ dictionary/ tessellate), Merriam-Webster Online

[2] http:/ / msdn. microsoft. com/ en-us/ library/ ff476340%28v=VS. 85%29. aspx

[3] http:/ / www. opengl. org/ registry/ doc/ glspec40. core. 20100311. pdf

[4] http:/ / www. geopersia. com/

[5] http:/ / www. coolmath4kids. com/ tesspag1. html

[6] http:/ / tilings. math. uni-bielefeld. de/

[7] http:/ / mathforum. org/ sum95/ suzanne/ tess. intro. html

[8] http:/ / www. mathacademy. com/ pr/ minitext/ escher/ index. asp

[9] http:/ / www. mathpuzzle. com/ tilepent. html

[10] http:/ / www. spsu. edu/ math/ tile/

[11] http:/ / www. cromp. com/ tess

[12] http:/ / tessellations. org

[13] http:/ / tessellation. info

[14] http:/ / www. eschertile. com/ kids/ math-art. htm

[15] http:/ / easyweb. easynet. co. uk/ ~iany/ patterns/ semiregular_2tri1squ1tri1squ. htm

[16] http:/ / aleph0. clarku. edu/ ~djoyce/ poincare/ poincare. html

[17] http:/ / www. uwgb. edu/ dutchs/ symmetry/ radspir1. htm Totem 137 Totem

A totem is any supposed entity that watches over or assists a group of people, such as a family, clan, or tribe.[1] Totems support larger groups than the individual person. In kinship and descent, if the apical ancestor of a clan is nonhuman, it is called a totem. Normally this belief is accompanied by a totemic myth. Although the term is of Ojibwe origin in North America, totemistic beliefs are not limited to Native Americans. Similar totem-like beliefs have been historically present in societies throughout much of the world, including Africa, Asia, Australia, Eastern Europe, Western Europe, and the Arctic polar region. In modern times, some single individuals, not otherwise involved in the practice of a tribal religion, have chosen to adopt a personal spirit animal helper, which has special meaning to them, and may refer to this as a totem. This non-traditional usage of the term is prevalent in the New Age movement, and the mythopoetic men's movement.

Totemism

Totemism (derived from the root -oode- in the Ojibwe language, which referred to something kinship-related, c.f. odoodem, "his totem") is a religious belief that is frequently associated with shamanistic religions. The totem is usually an animal or other natural figure that spiritually represents a group of related people such as a clan.

Totemism was a key element of study in the development of 19th and early 20th century theories of religion, especially for thinkers such as Émile Durkheim, who concentrated their study on primitive societies (which was an acceptable description at the time). Personal Totem of Mohegan Chief Tantaquidgeon, commemorated on a plaque at Drawing on the identification of social Norwich, Connecticut. group with spiritual totem in Australian aboriginal tribes, Durkheim theorized that all human religious expression was intrinsically founded in the relationship to a group.

In his essay "Le Totemisme aujourdhui" (Totemism Today), the anthropologist Claude Lévi-Strauss argued that human cognition, which is based on analogical thought, is independent of social context. From this, he excludes mathematical thought, which operates primarily through logic. Totems are chosen arbitrarily for the sole purpose of making the physical world a comprehensive and coherent classificatory system. Lévi-Strauss argues that the use of physical analogies is not an indication of a more primitive mental capacity. It is rather, a more efficient way to cope with this particular no mode of life in which abstractions are rare, and in which the physical environment is in direct friction with the society. He also holds that scientific explanation entails the discovery of an "arrangement"; moreover, since "the science of the concrete" is a classificatory system enabling individuals to classify the world in a rational fashion, it is neither more nor less a science than any other in the western world. It is important to recognise that in this text, Lévi-Strauss manifests the egalitarian nature of his work. Lévi-Strauss diverts the theme of anthropology toward the understanding of human cognition. Totem 138

Lévi-Strauss looked at the ideas of Firth and Fortes, Durkheim, Malinowski, and Evans-Pritchard to reach his conclusions. Firth and Fortes argued that totemism was based on physical or psychological similarities between the clan and the totemic animal. Malinowski proposed that it was based on empirical interest or that the totem was 'good to eat.' In other words, there was rational interest in preserving the species. Finally Evans-Pritchard argued that the reason for totems was Cultural flag of the Kanak community, showing a flèche metaphoric. His work with the Nuer led him to believe that faîtière - a spear-like wooden totem monument placed atop Kanak traditional dwellings. totems are a symbolic representation of the group. Lévi-Strauss considered Evan-Pritchard's work the correct explanation.

North American totem poles

The mis-named totem poles of the Pacific Northwest of North America are, in fact, not totemic in nature, rather they are heraldic in nature. They feature many different designs (bears, birds, frogs, people, and various supernatural beings and aquatic creatures) that function as crests of families or chiefs. They recount stories owned by those families or chiefs, and/or commemorate special occasions.

Possibly totemic culture in ancient China

The Sanxingdui Culture in southern China, dating back more than 5000 years, possibly placed bronze and gold heads on totems. Chinese transliterates totem as tuteng (圖騰). Sanxingdui bronze masks and heads (radiocarbon dated circa 1200BCE) appear to have been mounted on wooden poles. Some scholars have suggested that totemic culture spread from ancient Asian populations to the rest of the world. Others conclude that totemism arose separately in numerous cultures; totemic cultures in North America are estimated to have been more than 10,000 years old.

Korean JangSeung

A Jangseung or village guardian is a Korean totem pole usually made of wood. Jangseungs were traditionally placed at the edges of villages to mark for village boundaries and frighten away demons or welcome people in. They were also worshipped as village tutelary deities. JangSeungs were usually carved in the images of Janguns (equivalent to Admirals or Generals) and their wives. Many JangSeungs are also depicted laughing but in a frightening way. Many of the villages felt that the frightening laughter A totem pole in Thunderbird Park, of the JangSeungs would frighten away the demons because the JangSeungs have no fear. Victoria, British Columbia Totem 139

Totem beads in the Himalayan region In the Himalayan region as well as on the whole Tibetan plateau area and adjacent areas, certain beaded jewelry is believed to have totemistic capabilities. Tibetans in particular give much importance to heirloom beads such as dzi beads. Though dzi beads were not produced in ancient Tibet, but by an unknown culture, most ancient dzi beads are owned by Tibetans. Different protective qualities depend on design, number of eyes, damage, color, shine, etc.

The ancient Polish rodnidze The rodnidze known among the pre-Christian ancestors of the Poles is considered to have been roughly similar to the totem as mentioned above. In historical times, scholars considered that the animals and birds represented on the coats-of-arms of various Polish aristocratic clans may have been remnants of such totems (see Ślepowron coat of arms, Korwin coat of arms, possible remnants of a raven-rodnidze).

See also • Animal worship • Animism • Anishinaabe clan system • Aumakua • Axis Mundi • Charge (heraldry) • Devak, a type of family totem in Maratha culture • Moiety • Jangseung • Tamga, an abstract seal or device used by Eurasian nomadic peoples • Totem and Taboo by Sigmund Freud • Nature worship

External links • Celtic Totem Animals Discussion Group - Help us find ancient totem references & meanings. [2] • Totem Animals: Finding Your Animal Totem, Totemic Artwork [3] • Totem Spirit Animals: Discovering Animal Totems, Dictionaries, Feathers [4] • Historical Wonders of Sanxingdui [5] • Welcome to Sanxingdui [6] (with history of excavation) • Totems in Zimbabwe [7]

References

[1] Merriam-Webster Online Dictionary (http:/ / www. webster. com/ dictionary/ totem) and Webster's New World College Dictionary, Fourth Edition

[2] http:/ / celticnetwork. ning. com/ group/ celticsymbolmeanings/ forum/ topics/ totem-animals

[3] http:/ / foxloft. com/ symbolism

[4] http:/ / www. starstuffs. com/ animal_totems/

[5] http:/ / www. china. org. cn/ e-sanxingdui/

[6] http:/ / www. sanxingdui. com/

[7] http:/ / zimbabwe. poetryinternational. org/ cwolk/ view/ 20894/ Trial and error 140 Trial and error

Trial and error, or trial by error or try an error, is a general method of problem solving, fixing things, or for obtaining knowledge. "Learning doesn't happen from failure itself but rather from analyzing the failure, making a change, and then trying again."[1] In the field of computer science, the method is called generate and test. In elementary algebra, when solving equations, it is "guess and check". This approach can be seen as one of the two basic approaches to problem solving and is contrasted with an approach using insight and theory.

Methodology This approach is more successful with simple problems and in games, and is often resorted to when no apparent rule applies. This does not mean that the approach need be careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that may result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area.

Simplest applications Ashby (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem; and they have very different efficiencies: Suppose there are 1000 on/off switches which have to be set to a particular combination by random-based testing, each test to take one second. [This is also discussed in Traill (1978/2006, section C1.2]. The strategies are: • the perfectionist all-or-nothing method, with no attempt at holding partial successes. This would be expected to take more than 10^301 seconds, [i.e. 2^1000 seconds, or 3·5×(10^291) centuries!]; • a serial-test of switches, holding on to the partial successes (assuming that these are manifest) would take 500 seconds; while • a parallel-but-individual testing of all switches simultaneously would take only one second. Note the tacit assumption here that no intelligence or insight is brought to bear on the problem. However, the existence of different available strategies allows us to consider a separate ("superior") domain of processing — a "meta-level" above the mechanics of switch handling — where the various available strategies can be randomly chosen. Once again this is "trial and error", but of a different type. This leads us to:

Trial-and-error Hierarchies Ashby's book develops this "meta-level" idea, and extends it into a whole recursive sequence of levels, successively above each other in a systematic hierarchy. On this basis he argues that human intelligence emerges from such organization: relying heavily on trial-and-error (at least initially at each new stage), but emerging with what we would call "intelligence" at the end of it all. Thus presumably the topmost level of the hierarchy (at any stage) will still depend on simple trial-and-error. Traill (1978/2006) suggests that this Ashby-hierarchy probably coincides with Piaget's well-known theory of developmental stages. [This work also discusses Ashby's 1000-switch example; see §C1.2]. After all, it is part of Piagetian doctrine that children learn by first actively doing in a more-or-less random way, and then hopefully learn from the consequences — which all has a certain resemblance to Ashby's random "trial-and-error". Trial and error 141

The basic strategy in many fields? Traill (2008, espec. Table "S" on p.31) follows Jerne and Popper in seeing this strategy as probably underlying all knowledge-gathering systems — at least in their initial phase. Four such systems are identified: • Darwinian evolution which "educates" the DNA of the species! • The brain of the individual (just discussed); • The "brain" of society-as-such (including the publicly-held body of science); and • The immune system.

An ambiguity: Can we have "intention" during a "trial" In the Ashby-and-Cybernetics tradition, the word "trial" usually implies random-or-arbitrary, without any deliberate choice. However amongst non-cyberneticians, "trial" will often imply a deliberate subjective act by some adult human agent; (e.g. in a court-room, or laboratory). So that has sometimes led to confusion. Of course the situation becomes even more confusing if one accepts Ashby's hierarchical explanation of intelligence, and its implied ability to be deliberate and to creatively design — all based ultimately on non-deliberate actions! The lesson here seems to be that one must simply be careful to clarify the meaning of one's own words, and indeed the words of others. [Incidentally it seems that consciousness is not an essential ingredient for intelligence as discussed above.]

Features Trial and error has a number of features: • solution-oriented: trial and error makes no attempt to discover why a solution works, merely that it is a solution. • problem-specific: trial and error makes no attempt to generalise a solution to other problems. • non-optimal: trial and error is generally an attempt to find a solution, not all solutions, and not the best solution. • needs little knowledge: trials and error can proceed where there is little or no knowledge of the subject. It is possible to use trial and error to find all solutions or the best solution, when a testably finite number of possible solutions exist. To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a condition for the possibility of finding a best solution. (Also, when only one solution can exist, as in assembling a jigsaw puzzle, then any solution found is the only solution and so is necessarily the best.)

Examples Trial and error has traditionally been the main method of finding new drugs, such as antibiotics. Chemists simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect. (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of "What chemical will work well as an antibiotic?" the problem in the sophisticated approach is "Which, if any, of the chemicals in this narrow range will work well as an antibiotic?") The method is used widely in many disciplines, such as polymer technology to find new polymer types or families. The scientific method can be regarded as containing an element of trial and error in its formulation and testing of hypotheses. Also compare genetic algorithms, simulated annealing and reinforcement learning - all varieties for search which apply the basic idea of trial and error. Trial and error 142

Biological evolution is also a form of trial and error. Random mutations and sexual genetic variations can be viewed as trials and poor reproductive fitness, or lack of improved fitness, as the error. Thus after a long time 'knowledge' of well-adapted genomes accumulates simply by virtue of them being able to reproduce. Bogosort, a conceptual sorting algorithm (that is extremely inefficient and impractical), can be viewed as a trial and error approach to sorting a list. However, typical simple examples of bogosort do not track which orders of the list have been tried and may try the same order any number of times, which violates one of the basic principles of trial and error. Trial and error is actually more efficient and practical than bogosort; unlike bogosort, it is guaranteed to halt in finite time on a finite list, and might even be a reasonable way to sort extremely short lists under some conditions.

Issues with trial and error Trial and error is usually a last resort for a particular problem, as there are a number of problems with it. For one, trial and error is tedious and monotonous. Also, it is very time-consuming; chemical engineers must sift through millions of various potential chemicals before they find one that works. Fortunately, computers are best suited for trial and error; they do not succumb to the boredom that humans do, and can potentially do thousands of trial-and-error segments in the blink of an eye.

References • Ashby, W. R. (1960: Second Edition). Design for a Brain. Chapman & Hall: London. • Traill, R.R. (1978/2006). Molecular explanation for intelligence…, Brunel University Thesis, HDL.handle.net [2] • Traill, R.R. (2008). Thinking by Molecule, Synapse, or both? — From Piaget’s Schema, to the Selecting/Editing of ncRNA. Ondwelle: Melbourne. Ondwelle.com [3] — or French version Ondwelle.com. [4]

See also • Brute force attack • Brute-force search • Empiricism

References

[1] Coding Horror: Fail Early, Fail Often (http:/ / www. codinghorror. com/ blog/ archives/ 000576. html)

[2] http:/ / hdl. handle. net/ 2438/ 729

[3] http:/ / www. ondwelle. com/ OSM02. pdf

[4] http:/ / www. ondwelle. com/ FrSM02. pdf Unknown unknown 143 Unknown unknown

In epistemology and decision theory, the term unknown unknown refers to circumstances or outcomes that were not conceived of by an observer at a given point in time. The meaning of the term becomes more clear when it is contrasted with the known unknown, which refers to circumstances or outcomes that are known to be possible, but it is unknown whether or not they will be realized. The term is used in project planning and decision analysis to explain that any model of the future can only be informed by information that is currently available to the observer and, as such, faces substantial limitations and unknown risk.

Usage

There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we now “know we don’t know. But there are also unknown unknowns. These are things we do not know we don’t know. ” —United States Secretary of Defense Donald Rumsfeld

The "there are known knowns..." statement was made at a press briefing given by former US Defense Secretary Donald Rumsfeld on February 12, 2002.[1] Mr Rumsfeld's statement relating to the absence of evidence linking the government of Iraq with the supply of weapons of mass destruction to terrorist groups was criticised as an abuse of language, but defended as reflecting a profound, almost philosophical truth. Rumsfeld's defenders have included Canadian columnist Mark Steyn, who called it 'in fact a brilliant distillation of quite a complex matter',[2] and Australian economist and blogger John Quiggin, who wrote that, 'Although the language may be tortured, the basic point is both valid and important ... Having defended Rumsfeld, I’d point out that the considerations he refers to provide the case for being very cautious in going to war.'[3] Italian economists Salvatore Modica and Aldo Rustichini provide an introduction to the economic literature on awareness and unawareness

A subject is certain of something when he knows that thing; he is uncertain when he does not know it, but he knows he does not: he is “consciously uncertain. On the other hand, he is unaware of something when he does not know it, and he does not know he does not know [emphasis added], and so on ad infinitum: he does not perceive, does not have in mind, the object of knowledge. The opposite of unawareness [4] is awareness. ”

Psychoanalytic philosopher Slavoj Žižek extrapolates from these three categories a fourth, the unknown known, that which we don't know or intentionally refuse to acknowledge that we know:[5]

If Rumsfeld thinks that the main dangers in the confrontation with Iraq were the "unknown unknowns," that is, the threats from Saddam “whose nature we cannot even suspect, then the Abu Ghraib scandal shows that the main dangers lie in the "unknown knowns" - the disavowed beliefs, suppositions and obscene practices we pretend not to know about, even though they form the background of our public values. ”

The term was in use within the United States military establishment long before Rumsfeld's quote to the press in 2002. An early use of the term comes from a paper entitled Clausewitz and Modern War Gaming: losing can be better than winning by Raymond B. Furlong, Lieutenant General, USAF (Ret.) in the Air University Review, July-August 1984:

To those things Clausewitz wrote about uncertainty and chance, I would add a few comments on unknown unknowns--those things that a “commander doesn't even know he doesn't know. Participants in a war game would describe an unknown unknown as unfair, beyond the ground rules of the game. But real war does not follow ground rules, and I would urge that games be "unfair" by introducing unknown [6] unknowns. ” Unknown unknown 144

NASA space exploration should largely address a problem class in reliability and risk management stemming primarily from human error, “system risk and multi-objective trade-off analysis, by conducting research into system complexity, risk characterization and modeling, and system reasoning. In general, in every mission we can distinguish risk in three possible ways: a) known-known, b) known-unknown, and c)unknown-unknown. It is probable, almost certain, that space exploration will partially experience similar known or unknown risks [7] embedded in the Apollo missions, Shuttle or Station unless something alters how NASA will perceive and manage safety and reliability. ”

From the same time, conservative lawyer Richard Epstein wrote a well known article in the University of Chicago Law Review about the American labour law doctrine of employment at will (the idea that workers can be fired without warning or reason, unless their contract states terms that are better). In giving some of his reasons in defense of the contract at will, he wrote this.

The contract at will is also a sensible private adaptation to the problem of imperfect information over time. In sharp contrast to the purchase of “standard goods, an inspection of the job before acceptance is far less likely to guarantee its quality thereafter. The future is not clearly known. More important, employees, like employers, know what they do not know. They are not faced with a bolt from the blue, with an "unknown unknown." Rather they face a known unknown for which they can plan. The at-will contract is an essential part of that planning because it allows both sides to take a wait-and-see attitude to their relationship so that new and more accurate choices can be made on the strength of [8] improved information. ”

In a Washington Times interview, the current commander of the United States Northern Command, Admiral James A. Winnefeld Jr., says he is most worried about "the unknown unknowns." [9]

In popular culture Since Rumsfeld's speech, both the full quote and the term "unknown unknowns" have appeared in popular culture.

• The quote is featured in the CD recording, "The Existential Poetry of Donald Rumsfeld" http:/ / www.

stuffedpenguin. com/ index. html • In The Boondocks animated series, the character Gin Rummy, a representation of Donald Rumsfeld, makes several references to unknown unknowns. • The band No Use for a Name used the entire aforementioned quote in their song Fields of Agony (Acoustic) on the record Rock Against Bush, Vol. 2. • In "Lil' George and Lil' Tony Blair", an episode of Lil' Bush, Lil' Rummy makes a reference to the unknown unknowns. • The Joan Jett song "Riddles" features the full unknown unknowns quote. • The title of The Unknown Knowns: A Novel by Jeffrey Rotter is an allusion to the quote, and the full quote appears in the book's inscription. • The title of the House (TV series) episode Known Unknowns is thought to be an allusion to the quote.

See also • Ignoramus et ignorabimus • Ignotum per ignotius • I know that I know nothing • Johari window • List of political catch phrases • Outside Context Problem • Black swan theory Unknown unknown 145

External links • Transcript of Defense Department Briefing, February 12, 2002 [10] • Video of "Unknown unknown" talk on YouTube [11]

References [1] "Defense.gov News Transcript: DoD News Briefing - Secretary Rumsfeld and Gen. Myers, United States Department of Defense

(defense.gov)" (http:/ / www. defense. gov/ transcripts/ transcript. aspx?transcriptid=2636). .

[2] Steyn, Mark (December 9, 2003). "Rummy speaks the truth, not gobbledygook" (http:/ / www. telegraph. co. uk/ comment/ personal-view/

3599959/ Rummy-speaks-the-truth-not-gobbledygook. html). Daily Telegraph. . Retrieved 2008-10-30.

[3] Quiggin, John (February 10, 2004). "In Defense of Rumsfeld" (http:/ / johnquiggin. com/ index. php/ archives/ 2004/ 02/ 10/

in-defense-of-rumsfeld/ ). .

[4] Salvatore Modica; Aldo Rustichini (July 1994). "Awareness and partitional information structures" (http:/ / www. springerlink. com/ content/

l32r06103403mv1v/ ). Theory and Decision 37 (1). .

[5] "What Rumsfeld Doesn't Know That He Knows About Abu Ghraib" (http:/ / www. lacan. com/ zizekrumsfeld. htm). . Retrieved 2009-2-23.

[6] "Air University Review Archive at Air & Space Power Journal" (http:/ / www. airpower. maxwell. af. mil/ airchronicles/ aureview/ 1984/

jul-aug/ furlong. html). . Retrieved 2008-08-14. [7] Maluf DA, Gawdiak YO, Bell DG (3-6 January 2005). "ON SPACE EXPLORATION AND HUMAN ERROR: A paper on reliability and

safety" (http:/ / ntrs. nasa. gov/ archive/ nasa/ casi. ntrs. nasa. gov/ 20060016368_2006006769. pdf) (PDF). . Hilton Waikoloa Village, HI. .

[8] Epstein R (1984). "In defense of the contract at will" (http:/ / jstor. org/ stable/ 1599554). University of Chicago Law Review 51 (4): 947–975. doi:10.2307/1599554. .

[9] "Northcom's new leader boosts focus on Mexico," http:/ / www. washingtontimes. com/ news/ 2010/ jul/ 5/

northcoms-new-leader-boosts-focus-on-mexico/ print/

[10] http:/ / www. defenselink. mil/ transcripts/ transcript. aspx?transcriptid=2636

[11] http:/ / www. youtube. com/ watch?v=_RpSv3HjpEw Article Sources and Contributors 146 Article Sources and Contributors

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Lateral thinking Source: http://en.wikipedia.org/w/index.php?oldid=365255755 Contributors: 1234R6789, 7, Aaron Kauppi, AbsolutDan, Ad.shannon, Adi4094, Ahoerstemeier, Aleksandrit, Alvestrand, Ancheta Wis, Andrew Bronx, AndriuZ, Aumaan, Badly, Balster neb, Barbara Shack, Bart133, Bcjordan, Beast from the Bush, Bobblewik, Bssc, Bushytails, Chancehoney, Charles Matthews, Cirt, ClementSeveillac, Clippership, Conundrumer, Crooked, Cyraan, Czolgolz, DaGizza, Dabomb87, Damian Yerrick, Danelo, DannyStevens, Daveydweeb, David Gerard, Ddon, Dr. Lucifer, Dtobias, Faradayplank, Festinalente, Franis, Fred Bauder, Furrykef, Fxbx, Gerbrant, Gondwanabanana, Grstain, Heroeswithmetaphors, Hunterhogan, IdLoveOne, Ignitis, Inquisitus, Isaacdealey, Itsani07, J.delanoy, JackofOz, Jaschofield, Jedibob5, Jeff3000, Jjzanath, JohannesMarat, John254, Kaihsu, Kbdank71, Kerfuffle53, Kingnosis, KnowledgeHegemonyPart2, Kpjas, KramerNL, Kreb Dragonrider, Kwantada, Letranova, Light current, LuoShengli, Mac Davis, Marskell, Matt Crypto, MattieTK, Mattisse, Maurice Carbonaro, McGeddon, Michael Hardy, Michael hewitt-gleeson, Mridul.26, Mukkakukaku, Mumblingmynah, Mwanner, Nabeth, NeonMerlin, Nerf, Nihiltres, Notheruser, Odikuas, Olathe, Oppthinker, Pakaran, Pcap, Pentasyllabic, Pi, RedAlgorithm, Reinyday, Rich Farmbrough, Rkitko, Ronz, Root4(one), Rumpelstiltskin223, Ryankit, Samsara, Savio sebastian, Shah.bhumir, Shantavira, Signalhead, Siroxo, SpaceFlight89, Spalding, Stelv, Sunils2cool, Suntag, TAPContributor, Tcurwick, The Haunted Angel, UK-Logician-2006, UnitedStatesian, Useight, Vijay.simha7, Visium, Vithos, Vuo, Wayne Miller, Werdna, Which dan, Wikicheng, Wikisculptor, Woohookitty, Xaa, Zagrebo, Zweifel, 267 anonymous edits

Linnaean taxonomy Source: http://en.wikipedia.org/w/index.php?oldid=366794611 Contributors: AdamRaizen, AdamRetchless, AeroSpace, Ahoerstemeier, Andrelevy, Andy Jewell, Anna512, Arc de Ciel, Bejnar, Berton, Bgpaulus, Bmicomp, Brandon, Brya, Bueller 007, Burntsauce, CWY2190, Caltas, Cameronc, Canderson7, CanisRufus, Cantor, Cirbryn, Clicketyclack, Cmforton, Consist, Conversion script, Crazysane, Creidieki, CubicFeet, DGG, Danielkueh, DarkFalls, Davidlchandler, Dcljr, Dittaeva, Dpbsmith, Drur93, Dysmorodrepanis, E Pluribus Anthony redux, Eclecticology, Ecphora, El C, Enchanter, Epbr123, Ericamick, Eugene van der Pijll, Fabartus, FellGleaming, Fir0002, Fred J, Fredrik, FutureNJGov, Gaelen S., Gaia Octavia Agrippa, George100, GerardM, Ginkgo100, Gkasperek, Gnebulon, Gnostrat, Graham87, Grika, Guthrie, Harp, Henrygb, Hephaestos, Huttarl, Idont Havaname, IronGargoyle, IvanLanin, Ixfd64, J. Spencer, JAn Dudík, JCHall, Jamoche, Jeronimo, Jerzy, Jketola, JoJan, Johnluisocasio, Josh Grosse, Josh Parris, Kanenas, Kate, Kintaro, Kmweber, LeaveSleaves, Leptictidium, Lousyd, M1shawhan, MAK, MONGO, MagneticFlux, Mani1, Marshman, Maurreen, Mayumashu, Migozared, MikeKeesey, Mjb, MrDarwin, NickW, Nifky?, Nik42, Obli, OlliffeObscurity, Ornil, Ose, Palefire, Paul Murray, PeepP, Peripitus, Petter Bøckman, Philip Trueman, Pinethicket, Postglock, Ptelea, Radagast83, Ram-Man, Ray.vanlandingham, RexNL, Rgamble, Rich Farmbrough, Rohan Jayasekera, Romanm, Rosarinagazo, Ryguasu, ST47, Salvio giuliano, Schlinkdizzle, Shanoman, Shureg, Skybreaker, Slon02, Snek01, Sophosmoros, Sprited Spheniscidae, Stevertigo, Suidafrikaan, TUF-KAT, Taw, Taxman, TheGrza, Thegaff, Thelmo, Tompw, Triona, Twisted86, Twsx, Ummit, Uyanga, Vlmastra, VolatileChemical, West.andrew.g, Wetman, Williamb, Wwwwolf, Xiahou, Yamamoto Ichiro, Yvwv, ZPM, ZephyrAnycon, ZimZalaBim, 240 anonymous edits

List of uniform tilings Source: http://en.wikipedia.org/w/index.php?oldid=365586812 Contributors: Ambarsande, Charles Matthews, Cholling, Computer97, Crowsnest, Dogears, Everyking, Fibonacci, Giftlite, KSmrq, Maksim-e, Nonenmac, Oleg Alexandrov, Robert Stanforth, Salix alba, Tamfang, Tomruen, Vsmith, ZeroOne, 7 anonymous edits

Machine learning Source: http://en.wikipedia.org/w/index.php?oldid=374620458 Contributors: APH, Aaronbrick, Aceituno, Adiel, Adoniscik, Ahoerstemeier, Ahyeek, AnAj, Arcenciel, Arvindn, Ataulf, BMF81, Baguasquirrel, Beetstra, BenKovitz, BertSeghers, Biochaos, BlaiseFEgan, Boxplot, Bumbulski, Buridan, Businessman332211, Calltech, Celendin, Centrx, Cfallin, ChangChienFu, ChaoticLogic, CharlesGillingham, Chriblo, Chris the speller, Chrisoneall, Clemwang, Clickey, Cmbishop, CommodiCast, Ctacmo, CultureDrone, Cvdwalt, Damienfrancois, Dana2020, Dancter, Darnelr, Dave Runger, DaveWF, DavidCBryant, Debejyo, Defza, Delirium, Denoir, Devantheryv, Dicklyon, Dsilver, Dzkd, Essjay, Evansad, Examtester, Fabiform, FidesLT, Fram, Furrykef, Gareth Jones, Gene s, Genius002, Giftlite, GordonRoss, Grafen, Gtfjbl, Haham hanuka, Helwr, Hike395, Innohead, Intgr, IradBG, J04n, James Kidd, Jbmurray, Jcautilli, Jdizzle123, JimmyShelter, Jmartinezot, Joerg Kurt Wegner, JonHarder, Jrennie, Jrljrl, Jroudh, Jwojt, Jyoshimi, KYN, KellyCoinGuy, Khalid hassani, Kinimod, Kku, KnightRider, Kumioko, Kyhui, Lars Washington, Levin, LokiClock, Lordvolton, MTJM, Masatran, Mdd, Mereda, Michael Hardy, Misterwindupbird, Mneser, Moorejh, Movado73, MrOllie, Mxn, Nesbit, Netalarm, Nk, Nowozin, Pebkac, Penguinbroker, Peterdjones, Pgr94, Piano non troppo, Pintaio, Pmbhagat, Predictor, Proffviktor, Quebec99, QuickUkie, Quintopia, RJASE1, Rajah, Ralf Klinkenberg, Redgecko, RexSurvey, Rjwilmsi, Ronz, Ruud Koot, Ryszard Michalski, Scigrex14, Scorpion451, Seabhcan, Sebastjanmm, Shizhao, Silvonen, Sina2, Soultaco, Srinivasasha, StaticGull, Stephen Turner, Superbacana, Swordsmankirby, Tedickey, Topbanana, Trondtr, Utcursch, VKokielov, Vilapi, Vivohobson, WMod-NS, WhatWasDone, Wht43, Why Not A Duck, Wikinacious, WinterSpw, Wjbean, YrPolishUncle, Yworo, ZeroOne, Иъ Лю Ха, 269 anonymous edits

Mathematical morphology Source: http://en.wikipedia.org/w/index.php?oldid=372682530 Contributors: 16@r, AxelBoldt, CXCV, Charles Matthews, D6, Dai mingjie, Damian Yerrick, DePiep, Erik Garrison, Folajimi, HenningThielemann, Isnow, JaGa, Jorge Stolfi, Kingpin13, Lamoidfl, LeaveSleaves, Linas, LindsayH, Martious, Mbell, Pakaraki, R'n'B, Radagast83, Renatokeshet, Salix alba, Schmloof, Skittleys, Steadysteveo, SteveRwanda, The Firewall, Wprlh, 55 anonymous edits

Mental model Source: http://en.wikipedia.org/w/index.php?oldid=374961139 Contributors: Aapo Laitinen, Aaron Kauppi, Abbasgadhia, Alphax, Arno Matthias, Boldien, Coro, Doczilla, Dr. Lucifer, Ehheh, Fionaangelina, Frisbeeralf, Gamboge, Germandemat, Grayshi, Gregbard, Grutness, Gyan Veda, InBrief, J04n, Jamelan, Kku, LittleHow, Lordparlsey, Lova Falk, Male1979, Mark Fochesato, Mattisse, Mayumi, Mdd, MrOllie, Nectarflowed, Nemolan, No1lakersfan, Open2universe, Pdcook, Protez, RDF-SAS, Retired username, RichardF, Ronz, SamuelTheGhost, SlimVirgin, Spalding, Tamorlan, TeunAvanDijk, The Thing That Should Not Be, Woodswittdealy, Xjent03, 61 anonymous edits

Montessori sensorial materials Source: http://en.wikipedia.org/w/index.php?oldid=374303707 Contributors: BigDunc, CliffC, Fiona lynch, MattThePuppetGuy, Micru, Naveen-sa, Plustgarten, Rjwilmsi, Seberle, T.woelk, 14 anonymous edits

Packing problem Source: http://en.wikipedia.org/w/index.php?oldid=366120346 Contributors: -Ril-, 99of9, Akriasas, Arthur Rubin, Atlantima, BD2412, Bando26, BigrTex, Blotwell, Blueyoshi321, Bryan Derksen, CRGreathouse, Captainj, Charles Matthews, Chuunen Baka, Cngoulimis, DanMS, Dcoetzee, Dmcq, Do262, Dominus, Dysprosia, Etaoin, Falcor84, Gadykozma, Gamma, Giftlite, Gimutsh, Grendelkhan, Jessemerriman, JocK, Karlscherer3, Karol Langner, Kwertii, Leon math, Leonard G., Maksim-e, Michael Hardy, Mikeblas, PMajer, PV=nRT, Paul August, Pleasantville, R'n'B, RMcGuigan, Rettetast, Rolling Man, Samohyl Jan, SharkD, Shreevatsa, Sigma 7, SimonP, Sjakkalle, Slike2, Tamfang, Tea with toast, Timwi, Toon81, Tosha, UdovdM, WAREL, WhiteCrane, Wiki5d, Woohookitty, Ylloh, 54 anonymous edits

Prior knowledge for pattern recognition Source: http://en.wikipedia.org/w/index.php?oldid=367162369 Contributors: Crystallina, Eyal.krupka, J.delanoy, Lauerfab, Melcombe, Protez, ThomHImself, 4 anonymous edits

Quasi-empirical method Source: http://en.wikipedia.org/w/index.php?oldid=275891904 Contributors: Aidje, Dysprosia, Jdclevenger, Jon Awbrey, Mashford, Rfl, Roadrunner, Robofish, Smallman12q, Smelialichu, Taak, TonyClarke, Unionsoap, WhiteC, 4 anonymous edits

Semantic similarity Source: http://en.wikipedia.org/w/index.php?oldid=364276677 Contributors: AKA MBG, Babbage, Cldamat, Dreftymac, Fortdj33, Gabr, Iridescent, Jotomicron, Jvhertum, Kku, Kuru, Michael Hardy, Rama, SRE.K.A.L.24, TerriersFan, Unkx80, Vdannyv, Xicouto, YK Times, 29 anonymous edits

Serendipity Source: http://en.wikipedia.org/w/index.php?oldid=374809402 Contributors: 6birc, Ac rainer, Adam78, AdderUser, Aewold, AlainV, Alansohn, Alberrosidus, Anarchia, AndrewHowse, Anonymous Dissident, ArglebargleIV, ArkinAardvark, Art Carlson, Atlan, Auntof6, AxelBoldt, B9 hummingbird hovering, B9findings, Bastin, Beland, Bigmac31, Bishonen, Black Falcon, Blackknight12, Blacklemon67, Blahm, Blanchardb, BlueBeach, Bob9111, Bobber0001, Bonus Onus, Borgx, Bradley0110, Brendan Moody, Brendan19, Briantw, BrunoAssis, CAN, Canuckguy, CapitalR, Carcharoth, Ceefour, Chairman S., ChicXulub, Chowbok, Chris the speller, Clarityfiend, Coemgenus, Connecto, Conversion script, Cootiequits, CroydThoth, Cyclopia, DS1953, Daibhid C, Dandelions, Darkonc, David Latapie, Deadstar, Diamonddavej, Diberri, Doco, Download, DragonflySixtyseven, Dwelden, El C, Em Mitchell, Enfieldfalls, Enviroboy, Eric-Wester, Falcon8765, Fama Clamosa, Faradayplank, Femmina, Flewis, FructoseFred, Fyyer, Gaius Cornelius, Gasheadsteve, Gaurav, Gegalao, Geniac, Gioto, GirasoleDE, GoDawgs, Graham87, Gregbard, GuidoJJ, Gurch, Harpmj, Hoffmeier, Hordaland, Icairns, Ingolfson, JALockhart, JRinPDX, Ja 62, Janet Davis, Jcampos, Jeff3000, Jelite, Jeltz, Jerzy, Jfdwolff, Article Sources and Contributors 148

Joedeshon, John M Baker, Johnrpenner, Jonasserendipity, Julia Rossi, Juliancolton, K.C. Tang, KF, Kadoo, Kauwika, Kgf0, Khalid hassani, Knulclunk, KoenBinwa, Lambiam, Landak, Largoplazo, Ld100, Leafclover, LedgendGamer, Legare, Lindsay658, Little hamster, Lotje, Louis, Lova Falk, Luk, Luna Santin, Lupin, Lyrl, MackSalmon, Mahanga, Malcolm Farmer, Malcolmxl5, Marcoscramer, Markeilz, MarkkityMark, Marnie57, Mattbr, McLahan, Meetadd, Mild Bill Hiccup, Minesweeper, Mintguy, Mishav, Mormegil, Mousy, Mullising, Murray.booth, Mwanner, Nabeth, Nbarth, Nehwyn, Neksys, Nepaheshgar, Nirvana2013, Njaard, Nonpareility, Nrcprm2026, Numpty999, Oatmeal batman, Olivier, Omphaloscope, Open2universe, OrangeDog, Oxymoron83, PamD, Peak, Pejman47, Peter Delmonte, Peterlewis, Peyre, Pfaoro, Piano non troppo, Pinkadelica, Pixel ;-), Pol098, Printer222, Probios, Quibik, R'n'B, Ragesoss, Rallette, Randywombat, Remco47, Riana, Rich Farmbrough, Ricky81682, Robert Daoust, RockMFR, Rotring, Rsabbatini, Rsubramanian, Russoc4, SLi, Samosa Poderosa, Samtheboy, Saxifrage, Sbfw, Sburke, SchmuckyTheCat, Scott Wilson, Seanwal111111, Serendeva, Shai-kun, Shrisharang, Sietse Snel, Simone, Skunkboy74, Sonyack, Sorenriise, SpuriousQ, SqueakBox, SteinbDJ, Stw, Supertouch, Supreme Deliciousness, T-borg, Take this curve, Tdoublenineone, Tedmund, Tendim, Terrek, Thannan, That Guy, From That Show!, The Ogre, The editor1, TheSensei, Thumperward, Tide rolls, Tillwe, Toby Bartels, Tom harrison, Tomv, Tony Myers, Tony Sidaway, Tonyrex, Toytoy, Tremilux, Twsx, UltraMagnus, Unschool, Vald, VascoAmaral, Vekoler, Vishnava, VolatileChemical, WLU, Wakablogger2, Walkerma, Wayne Miller, West.andrew.g, Wknight94, WolfmanSF, Woohookitty, Yarn Sandwich, Yintan, 百家姓之四, 375 anonymous edits

Similarity (geometry) Source: http://en.wikipedia.org/w/index.php?oldid=374736991 Contributors: 6birc, Agutie, Aleph4, AugPi, AxelBoldt, BenFrantzDale, Bernhard Bauer, Bleakcomb, Bobo192, Bubuka, Calltech, Charles Matthews, ConCompS, Dbenbenn, Dbfirs, Dcljr, Dmcq, Download, Dynaflow, Dysprosia, Erud, Erzbischof, Expedition brilliancy, Foobaz, Fram, Freshacconci, Gandalf61, Gauge, Geekygator, Gene.arboit, Ghazer, Giftlite, Halcyonhazard, HannsEwald, Happenstantially, Henning Makholm, Herbee, Isall, Isnow, J.delanoy, John Reid, Johnkarp, Justinhwang1996, Karlscherer3, Katalaveno, Kku, Krauss, Lambiam, Marino-slo, Mhaitham.shammaa, Michael Hardy, Mild Bill Hiccup, Mpatel, Mr.Prithz, Mr.gondolier, MrOllie, Nassr, NellieBly, Noetica, Patrick, PierreAbbat, PigFlu Oink, Pizza1512, PrestonH, Rama, Rgdboer, RoyBoy, Running, Salgueiro, Salix alba, Se0808, Seberle, Silly rabbit, Slysplace, Snbritishfreak, Spiritia, Splintax, Susfele, Svein Olav Nyberg, Tarquin, Tom harrison, Tom.schramm, Tosha, UsüF, Vegetator, Vrkunkel, WhiteHatLurker, Woohookitty, Wshun, Youmils03, 90 anonymous edits

Simulacrum Source: http://en.wikipedia.org/w/index.php?oldid=373004089 Contributors: 0bvious, 999, Alerante, Alexkon, Altenmann, Alvestrand, Amcbride, Anarchia, Aniche, Artandthought, Audacity, Awakeandalive1, AxelBoldt, B9 hummingbird hovering, Boredzo, Cbradyatinquire, Charles Matthews, Csabo, Culmin, Cyberdrummer, DL5MDA, Dale Arnett, DarwinPeacock, Davodd, Dbachmann, Deltabeignet, DionysosProteus, Dougweller, DreamGuy, Dumbledad, Emdrgreg, EugeneZelenko, Evil Twin Skippy, Forteanajones, Fru1tbat, Gjs238, Grendelkhan, Gtrmp, Gurch, Ikcerog, IsmaelCavazos, J.delanoy, JNW, Jackdavinci, Jade Knight, Jahsonic, JamesMadison, JayFout, Jeltz, Jermerc, JimD, Kai-Hendrik, Karl 6740, Kingturtle, KnowledgeOfSelf, Koavf, Kreachure, Leibniz, Lord davinator, Lordvolton, Magnetic hill, Maprovonsha172, Marina T., Matthew Proctor, Meelar, MementoVivere, Mercmax, Metabolome, Mikeross, Mjpotter, Moonriddengirl, Mscassell, Naddy, Neoist, Nickptar, Nixeagle, Octane, Oni Ookami Alfador, Oxymoron83, Pax:Vobiscum, Piotrus, Psychonaut3000, Qwertyus, R'n'B, RJFJR, Rintrah, Rjwilmsi, Rosser1954, Savidan, Sharnak, Sparkit, Stefanomione, Stemonitis, Strand, Suntree, Susan Davis, Tarotcards, Thaddius, The JPS, TheMathGeek, Thom2002, Totnesmartin, Tozmo, Twp, Tyrenius, Valtron, Wetman, Xenozen, Zen611, 137 anonymous edits

Squaring the square Source: http://en.wikipedia.org/w/index.php?oldid=373484287 Contributors: .:Ajvol:., Arcfrk, Badanedwa, Blotwell, CenturionZ 1, Charles Matthews, Dcljr, Debresser, Euclid 27, Fivemack, Gandalf61, Giftlite, Jinma, Jnestorius, Joseph Myers, Karada, Kinewma, Kingpin13, Linas, Mets501, Mhaitham.shammaa, Michael Hardy, Mjhowell, MrJones, MrOllie, Oleg Alexandrov, Oxymoron83, Rossami, SGBailey, Se anderson, Stevenj, Tarquin, The Anome, Tosha, Wik, WoollyMind, 43 anonymous edits

Structural information theory Source: http://en.wikipedia.org/w/index.php?oldid=266748139 Contributors: AnAj, Bluefloyd1, Doczilla, Fplay, Guaka, Gumum, Kku, Mattisse, Meeples, Michael Hardy, Oliver Pereira, RichardF, Rjwilmsi, Tabletop, Zigger, 2 anonymous edits

Task analysis Source: http://en.wikipedia.org/w/index.php?oldid=374717846 Contributors: Ajlenhoff, Andreas Kaufmann, Andycjp, Appraiser, B, Bobdoyle, Btyner, Dickpenn, J04n, Jeff3000, LeeHunter, Mcfly85, Pmjones, R'n'B, ReverendJuice, Rich Farmbrough, RichardVeryard, Ruidlopes, Spalding, Srippon, Thalvers, Thorkil9, Tklug, Ufubo, Wjwillis, 61 anonymous edits

Techne Source: http://en.wikipedia.org/w/index.php?oldid=356372967 Contributors: Adlerscout, Anarchia, CuteHappyBrute, DBaba, Deucalionite, Doremítzwr, Elijahmeeks, EmilJ, Goldenrowley, Gwythoff, Ironie, Jlg4104, Karada, Knotwork, Kwamikagami, Magarmach, Mauls, Michael Hardy, Miller52, Oddible, Omnipedian, Pablosecca, Pollinosisss, Ragesoss, Rayana fazli, Remuel, Sardanaphalus, Tomisti, Wareh, Xyzzyplugh, 13 anonymous edits

Tessellation Source: http://en.wikipedia.org/w/index.php?oldid=374278876 Contributors: -Ril-, 100110100, 345Kai, ABF, Aaronbrick, Acather96, Adambro, AgentCDE, Aitias, Alansohn, Albedo, Alemily, Alexandroid, Alindsey, Alro, Altenmann, Ambarsande, Amcfreely, Andromedabluesphere440, Andycjp, Andypandy.UK, ArmadilloFromHell, Asav, Ascidian, Atif.t2, Attilios, BeccaNixon09, Ben Standeven, Bhadani, Bjørn som tegner, Blanchardb, Blobglob, Bobianite, Bobo192, BrokenSegue, Bushytails, CALR, Can't sleep, clown will eat me, Canderson7, Capricorn42, Cbuckley, Century0, Cfradut, Chamal N, Charles Matthews, Check mii out channel, Clive42105, Constructive editor, Coolmath, Corpx, Courcelles, Covington, Cullinane, DV8 2XL, DVD R W, DaL33T, Daf, Dark Mage, David Eppstein, David Haslam, David Shay, DavidCary, Delldot, Dfrg.msc, Djinn112, Dk pdx, Dmharvey, Dmitry Brant, Dogears, Dominus, Dreadstar, DreamGuy, Dullums, Dysprosia, EagleFan, Elcbubs115, Eltwarg, Emijrp, Entirety, Epbr123, Evil saltine, Falcor84, Frank Shearar, FruitMonkey, Gandalf61, Geometricarts, Giftlite, Gilliam, Goldenrowley, Grafen, Gregorydavid, Gump Stump, Gurch, Hanzthebest, Hargrimm, Hbent, Hebrides, Heftig, Henning Makholm, Henrygb, Herbee, HexaChord, Hiphopgurl4427, Homestarmy, Hridaylall, Hv, Hydrogen Iodide, Igoldste, Iridescent, Ixfd64, J.delanoy, JSpung, Jaydd, Jeff G., Jitse Niesen, Joan1234, JocK, Joeylawn, JohnBlackburne, Jojhutton, Joseph Myers, Joshua.mccall, Juanscott, Juko, Justicelovespeace, KHenriksson, Karlscherer3, Katalaveno, Katieh5584, Killersakura, Kmspencer, Koven.rm, Kurt Shaped Box, La goutte de pluie, Lilaac, Locos epraix, Lunagron, Maddie!, Madmarigold, Majorly, MarSch, MarcoTolo, Marek69, Martin451, Martybugs, MathsIsFun, Maxamegalon2000, Mccathern, Mdebets, Meekohi, Melsaran, Mhym, Michael Hardy, Mmeeooow, Modernist, Moneymoneymulla, Mschel, Murtasa, Myanw, Mygerardromance, NYKevin, NawlinWiki, Nbarth, Nicholashopkinz, Nlu, Nolamatic, Nonenmac, Obradovic Goran, Oleg Alexandrov, Oxymoron83, Paiev, Patrick, PeR, Petri Krohn, Pharaoh of the Wizards, Philip Trueman, PigFlu Oink, Pingveno, PocketDocket, Possum, Prussianblue, Qst, Quadell, RJASE1, Radagast83, Raven in Orbit, Raven1977, Rawling, RedCoat10, Redmarkviolinist, Richard L. Peterson, Rklawton, Root4(one), Rrburke, Rylee118, SJP, Salix alba, Sam Hocevar, Sandman30s, Sceptre, Seb az86556, Seraphim, Sethnessatwikipedia, Shadowjams, Shirik, Shui9, Sigma 7, Sluzzelin, Snowolf, Spartan-James, Specter01010, Steelpillow, Stickee, Sławomir Biały, Tamfang, Terrillja, The Assassin047, TheOtherJesse, Thumperward, Tiddly Tom, Tomruen, Totalbomb, TravisTX, Trekie8472, Trevorgoodchild, Twastvedt, Ucanlookitup, Uncle Dick, Uthbrian, Votd, Vsmith, Waltpohl, Wetman, WikiLaurent, Willsmith, Windchaser, World, Xanzzibar, Xinit, Yamamoto Ichiro, Yeoldbuddyboy, Yoenit, Zamphuor, 573 anonymous edits

Totem Source: http://en.wikipedia.org/w/index.php?oldid=361907148 Contributors: 1984, Aaronjhill, Adam Bishop, Alansohn, Alerante, Andreas Kaganov, Antaya, ArquiWHAT, Asarelah, B9 hummingbird hovering, Babedacus, Beland, BenFrantzDale, Bestlyriccollection, Blue Milk Mathematician, BrainyBabe, Brenthecht, CJLippert, Capricorn42, Ccacsmss, Changamire, Closedmouth, Clubmarx, Courcelles, Crtrue, CtgPi, DJ Clayworth, Dbachmann, Deathawk, Design, Doceirias, Dogah, Drake Dun, Drivenapart, Eddie Parker, Editor2020, Elfguy, Epbr123, Everyking, Fastfission, FinnWiki, Foxfeather, GLKeeney, Galo1969X, Gatewaycat, Gregmcpherson, Gzdavidwong, Harvest day fool, Hashar, HopperUK, Hyacinth, J S Ayer, J04n, Jaleho, Jaxl, Jay Koh, Jerry, Jimp, Jkhaha123, Joefernandez, Joseph Solis in Australia, Jusdafax, Kaibabsquirrel, Kchishol1970, Keahapana, Kizor, Koavf, Lerna, Lusitana, Mani1, ManicDee, Matebele, MatthewVanitas, Mav, Metanoid, Minghong, Mirv, Miskwito, Mladifilozof, Modernist, Neelix, Neelmack, Neo-Jay, Ohconfucius, OlEnglish, Owen, Parkwells, Party, Pascal.Tesson, PelleSmith, Peterpipper, Picapica, Qtoktok, Radon210, Raso mk, Retodon8, Rich257, Roberta F., Rrburke, SGBailey, SameerKhan, SchfiftyThree, Silsor, Skookum1, Slowking Man, Sluzzelin, SnowFire, Sofeil, Sparkit, SteinbDJ, Sunderland06, TheRedPenOfDoom, Thedjatclubrock, Tjmoel, Tom Harris, True Dog, Trusilver, Twipley, Uanfala, Uly, Unbob, Utcursch, Uyvsdi, Wik, Woohookitty, YUL89YYZ, 144 anonymous edits

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Unknown unknown Source: http://en.wikipedia.org/w/index.php?oldid=373882077 Contributors: 0Bammer, 478jjjz, Agent Smith (The Matrix), Aknorals, Alansohn, Anarchia, Anticipation of a New Lover's Arrival, The, BONKEROO, Blanchardb, Bunnyhop11, Calvados, Camcd93, Card, Chugun, DRosenbach, Dac04, DirkLangeveld, Elitism, Ericdn, Everyking, Falconclaw5000, Flowerkiller1692, GJeffery, Greensburger, Gregbard, Grim Revenant, Grumpyyoungman01, Harryboyles, Headinthedoor, Herda050, Indu Singh, Intgr, Itsmine, Jeff Silvers, JeffUK, John Quiggin, Jusdafax, Lockfoot, MBisanz, Major Bonkers, Mattbuck, Melchoir, Mhym, Michael Hardy, Michael Rogers, Nbarth, Neilernst, Newbyguesses, Onlydeathawaits, Orangerhymes, Qp4, R'n'B, RDBrown, RayAYang, Roygbiv666, Saga City, Sbelknap, Silly rabbit, Skomorokh, Tabletop, Timcapon, Timneu22, Tktktk, Unknownmedia, VBGFscJUn3, Vito corleonne, WAS 4.250, Wavelength, Wikidea, Yobmod, 72 anonymous edits Image Sources, Licenses and Contributors 149 Image Sources, Licenses and Contributors

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