A A ARTISTS’ ARTICLE - R L T I F Modeling the Emergence E of Complexity: Complex Systems, the Origin of Life and Interactive A B S T R A C T
On-Line Art The origin of this paper lies in the fundamental question of how complexity arose in the course of evolution and how one might construct an artistic Christa Sommerer and Laurent Mignonneau interactive system to model and simulate this emergence of complexity. Relying on the idea that interaction and communica- tion between entities of a system drive the emergence of structures that are more com- he Internet seems especially suited to inter- connected web of people who can plex than the mere parts of that T system, the authors propose to actions and transformations of data. Internet users can be con- transmit visual and written infor- apply principles of complex sidered entities or particles who transmit information (e.g. mation over the Internet. As the in- system theory to the creation of written texts or images). As these data or entities are transferred formation is transported from VERBARIUM, an interactive, from location to location they could, in principle, change in location to location, it would be computer-generated and audience-participatory artwork status and value. One could imagine a system that could in- transformed, creating an intercon- on the Internet, and to test crease its internal complexity as more and more users interact nected, open-ended system featur- whether complexity can emerge with its information. Just like a genetic string or “meme” as de- ing phase transitions toward more within this system. scribed by Susan Blackmore and Richard Dawkins [1], these complex structures. Before investi- strings of information would change and mutate as they were gating how our prototype system transmitted by the users; they eventually could create an in- was built, we present a short summary of the theories that terconnected system that, similar to the models presented by ground this research proposal. Stuart Kauffman [2], features a phase transition toward more complex structures. Based on these considerations, we propose in VERBARIUM a prototype system for modeling a complex sys- tem for the Internet; we also introduce its construction prin- Fig. 1. Screenshot of the VERBARIUM web site at the Cartier Founda- ciples and translation mechanisms and analyze how the data it tion in Paris, 1999. (© Christa Sommerer and Laurent Mignonneau)
CONCEPTUAL OBJECTIVE The aim of the research presented here is to construct an Internet-based interactive artwork that applies and tests prin- ciples of complex-system and origin-of-life theories to the cre- ation of a computer-generated and audience-participatory networked system on the Internet. Complex systems theory is a eld of research that studies simple subsystems as they in- crease in complexity. Such increases in complexity can take place as phase transitions, when particles in a network switch one another on or off to catalyze or inhibit one another’s pro- duction. There are various denitions and qualities that char- acterize complex systems, and this paper proposes to test whether some of these principles can be applied to an inter-
Christa Sommerer (artist), ATR Media Information Science Laboratories, 2–2 Hikaridai, Seika-cho, Soraku-gun, 6190288 Kyoto, Japan; Institute of Advanced Media Arts and Sciences, 3–95 Ryoke-cho, Ogaki-shi, Gifu 503–0014, Japan. E-mail:
Laurent Mignonneau (artist), ATR Media Information Science Laboratories, 2–2 Hikaridai, Seika-cho, Soraku-gun, 6190288 Kyoto, Japan; Institute of Advanced Media Arts and Sciences, 3–95 Ryoke-cho, Ogaki-shi, Gifu 503–0014, Japan. E-mail:
Originally presented at the Seventh International Conference on Articial Life (A-Life VII), 1–6 August 2000, Portland, OR, U.S.A. First published in M.A. Bedau, J.S. McCaskill, N.H. Packard and S. Rasmussen, eds., Articial Life VII: Proceedings of the Seventh Interna- tional Conference (Cambridge, MA: MIT Press, 2000). Reprinted by permission.
© MIT Press LEONARDO, Vol. 35, No. 2, pp. 161–169, 2002 161 A A - R L T various patterns of behaviors, evolved; of life was presented in 1986 by Walter I and how with these developments, the Gilbert [17]. F environment and the ecological systems E Although the “ RNA world” model changed [11]. seems very convincing, the question of Speculation on how life on Earth where RNA came from in the rst place might have originated has a long history , remains open. Leslie Orgel [18], Chris- perhaps as long as the history of hu- tian Böhler [19] and P.E. Nielsen [20] manity. The widely accepted hypothesis found that a peptide nucleic acid, called that life originated from chemical PNA, could be a precursor form of RNA, processes derives largely from the 1924 because it can act to transcribe its de- work of Russian biochemist Alexander I. tailed genetic information directly to Oparin (translated to English in 1938) RNA; therefore, PNA could have initi- [12]. In the 1930s, Oparin and J.B.S. Hal- ated the RNA world. Another scientist, dane suggested that life on Earth could Hendrik Tiedemann, suggests that the have emerged from an early atmosphere nucleotide bases and sugars needed in lled with such gases as methane, am- RNA could have been built from hydro- monia, hydrogen and water vapor [13]. gen cyanide and formaldehyde , both Oparin and Haldane called this early at- available in the early atmosphere of the mosphere the primordial soup. Accord- Earth. Fig. 2. An example of VERBARIUM’s growth ing to their primordial soup theory, life Completely opposed to the “ RNA structures. would have originated in the sea as reac- world” theories on the origin of life is the tions of these chemical gases were trig- dual-origin theory of A.G. Cairns-Smith ORIGIN OF LIFE THEORIES gered by the energy of lightning, [21]. According to Cairns-Smith, the ultraviolet radiation, volcanic heat and starting point in the early crystallization The search for “laws of form” that explain natural radioactivity. of life was not “high-tech” carbon but the patterns of order and complexity seen In the early 1950s, Stanley Miller [14] “low-tech” silicon, a component of clay. in nature has intrigued researchers and of the University of Chicago’s chemistry In this theory, clay has the capacity to philosophers since the Age of Enlighten- department simulated such a primordial grow and reassemble itself by exchang- ment. These researchers have included atmosphere and was able to synthesize ing its ion components through muta- such famous scholars as William Bateson signicant amounts of amino acids, the tion and mechanical imperfectio ns. [3], Richard Owen [4], Hans Driesch [5], main components of all life-forms, from More recent proponents of the mineral D’Arcy Wentworth Thompson [6] and methane, ammonia, water vapor and hy- and early molecular-based theories on Conrad Waddington [7]. Their quest drogen. This experiment gave credence the molecular evolution of metabolism could generally be subsumed under the to the belief that the chemical building subscribe to the “iron-sulphur world” the- term Rational Morphology, a counterpart blocks of life could have been created by ory of Günter Wächtershä user [22], the to the functionalistic approach of the Nat- natural physical processes in the pri - “thioester world” theory of Christian De ural Theology promoted by Charles Dar- mordial environment. Modern propo- Duve [23] and the “inorganic pyrophos- win [8] and Neo-Dar winist Richard nents of the primordial soup theory now phate world” or “PPi world” theor y of Dawkins [9]. While Natural Theology think that the rst living things were ran- Baltscheffsky. Wächtershä user proposes considers form mainly a function of nat- dom replicators that assembled them- a model wherein the early evolution of ural selection and adaptation, Rational selves from components oating around life as a process begins with chemical ne- Morphologists emphasize the creative in the primordial soup. Based on exper - cessity and winds up in genetic exchange. principle of emergence that accounts for iments by Sol Spiegelman [15], who was Somewhat related to the question of the order of structures found in nature. able to create self-replicating RNA strings how life occurred in the rst place, The quest for the laws of form is closely in an environment lled with a primitive whether the rst stages of life were meta- linked to the question of the emergence “seed” virus and a constant supply of bolic or genetic, is the question of how of life. The discussion on how life replicase enzymes, Manfred Eigen went to draw the line between life and non-life. emerged has a long history and basically a step further by omitting the initial While Gilbert, Eigen, Böhler , Nielsen and involves two opposing views: the Aris- “seed” virus. Eigen succeeded in showing Orgel agree that the RNA world is a rst totelian and the Platonic. These two views that self-replicating RNA strands could stage of life, Wächtershä user and others of the natural world have dominated sci- assemble themselves from replicase en- believe that rather primitive entities on ence over the past two millennia, as de- zymes alone. In Eigen’s theory of the ori- mineral surfaces can also be called alive, scribed by Roger Lewin [10]. Herrick gin of life, RNA molecules can evolve although he calls them “two-dimensional Baltscheffsky notes that self-replicating patterns and nally de- life.” On the other hand, John Maynard fundamental to a deeper understanding velop a primitive genetic code. As the Smith and Eörg Szathmár y [24] stress of complex biological functions are ideas molecules specify and take on different that a living organism needs to possess at about how life originated and evolved. functions, complex and cooperative in- minimum a reproduction mechanism, They include questions about how the rst compounds, essential to life, ap- teractions take place: Eigen calls these in- and T. Gánti [25] proposes as a minimum peared on Earth; how the rst replicat- teractions “hypercycles.” Mutation and requirement for a living organism that it ing molecules came into being; how RNA competition among these hyper cycles - possess three essential subsystems: a ge- and DNA were formed; how prokaryotes nally create prototypes of modern cells, netic system, a unit that synthesizes the and the earliest eukar yotes emerged; and the earlier chemical evolution is components, and a membrane. how different species, with traits like sus- ceptibility, sentience, perception, cogni- eventually replaced by biological evolu- Another major issue in understanding tion, and self-consciousness, and with tion [16]. A similar theory on the origin life’s origin is to determine the origin of
162 Sommerer and Mignonneau, Modeling the Emergence of Complexity A A - R human societies, industrial rms, com- L T Example word: This peting technologies, etc. All of them are I T => rseed(84) => {0.36784, 0.553688, 0.100701,...} F aggregates of matter, energy and infor- E (actual values for the update parameters) mation that display the following char- h => rseed(104) => {0.52244, 0.67612, 0.90101,...} acteristics. They: # 0.52244 * 10 => get integer 5 => 5 different couple to each other functions are called within design function table learn, adapt and organize mutate and evolve # 0.67612 * 50 => get integer 33 => function 33 increase in diversity within design function table will be updated by value 0.36784 react to their neighbors and to ex- from 1. value of rseed(84) ternal control explore their options # 0.90101 * 50 => get integer 45 => function 45 within design function table will be updated by value 0.553688 replicate from 2. value rseed(84) organize a hierarchy of higher-order ...... until 5. value structures. To nd a common principle behind the organizational forces in natural sys- Fig. 3. An example of assignment between random functions and design functions. tems is a complex task, and it seems as if the genetic translation apparatus and the times on planets within the radio range there are as many theories as there are genetic code as described by Francis of Earth” [36]. theorists. Some of the numerous theories Crick in 1968 [26], Crick et al. in 1976 on complex systems are briey encapsu- [27] and Carl Woese [28]. Clas Blomberg lated in Appendix A (valuable informa- [29] has claimed that the only way to get COMPLEX SYSTEM THEORY tion on the various approaches and a stable translation mechanism is a feed- Closely related to the question of how life denitions of complex system theory are back between the code and the proteins on earth originated is the question of taken from Edmonds [38]). that were synthesized by the mechanisms how complexity arises. Complex system they controlled. Furthermore, Maynard theory has only emerged as a eld of re- Smith and Szathmáry suggest that the re- search in the past decade. It approaches PROPERTIESOF COMPLEX lations between amino acids and nucleic the question of how life on Earth could SYSTEMS acid sequences were established before have appeared by searching for inherent Intrinsically linked to dening complexity the translation apparatus, serving as an structures in living systems and trying to is the search for properties of complex sys- improved catalyst in the RNA world. dene common patterns within these tems. Various scholars have undertaken It would exceed the scope of this paper structures. It studies how parts of a system the task of dening these properties. to describe all the other theories on the give rise to the collective behaviors of the Again, as for the denitions of complexity origin of life in detail; some of them, how- system and how the system interacts with (see Appendix A), there is no commonly ever, should be mentioned briey here. its environment. Social systems formed (in agreed upon “list” of properties that are These include the “membrane rst” the- part) out of people, brains formed out of thought to completely describe it. Some of ory of Harold Morowitz [30] and the “self- neurons, molecules formed out of atoms the commonly mentioned features of com- replicating peptide” theor y of D.H. Lee and weather formed out of air currents plex systems are: et al. [31]. Theories that life was rst in- are all examples of complex systems. The troduced by meteorites from other plan- eld of complex systems cuts across all tra- Variety ets or stars include the “radiopanspermia” ditional disciplines of science, as well as A complex system is likely to exhibit a theory of Fred Hoyle and Chandra those of engineering, management, and great variety in its behavior and proper- Wickramasinghe [32] and Carl Chyba’s medicine. It focuses on certain questions ties. Thus variety is an indication of com- “handedness of the solar system” theor y about parts, wholes and relationships. plexity (though not always, as sometimes and its in uence on the origin of life These questions are relevant to all tradi- a very complex system is necessary to [33], as well as the “chirality” theories of tional elds. There are three interrelated maintain equilibrium). Variety can be Yoshihisa Inoue [34]. approaches to the modern study of com- measured by the simple counting of John Casti notes in his book Paradigms plex systems: (1) studying how interac- types, the spread of numerical values or Regained that when it comes to dening tions give rise to patterns of behavior; (2) the simple presence of sudden changes. what it means to be alive, there are as understanding the ways to describe com- many answers as there are biologists [35]. plex systems; and (3) studying the process Dependency While the numerous theories about the of formation of complex systems through Francis Heylighen [39] suggests that a origin of life suggest that scientists today pattern formation and evolution [37]. system’s complexity increases when the are still in the dark about the details of Although there is no exact denition variety (distinction) and dependency life’s beginnings and have not been able of what a complex system is, there is now (connection) of parts or aspects increase to create it from scratch, Richard an understanding that, when a set of in at least one of many possible dimen- Dawkins argues that this is rather to be evolving autonomous particles or agents sions, including the three ordinary spa- expected: “If the spontaneous origin of interact, the resulting global system dis- tial dimensions as well as the dimensions life turned out to be a probable enough plays emergent collective properties, evo- of geometrical structure, spatial scale, event to have occurred during a few man- lution and critical behavior having time or dynamics, or temporal or dy- decades in which chemists have done universal characteristics. These agents or namical scale. In order to show that com- their experiments, then life should have particles may be complex molecules, plexity has increased overall, it sufces to arisen many times on Earth and many cells, living organisms, animal groups, show that all things being equal, variety
Sommerer and Mignonneau, Modeling the Emergence of Complexity 163 A A - R L T Edmonds notes that the de nition of I complexity as midpoint between order F E and disorder depends on the level of rep- resentation: what seems complex in one representation may seem ordered or dis- ordered in a representation on a differ- ent scale.
Complexity through Phase Transition Kauffman and other researchers at the Santa Fe Institute for Complex Systems Research call the transition between the areas of simple activity patterns and com- plex activity patterns a phase transition. Kauffman has modeled a hypothetical circuitry of molecules that can switch each other on or off to catalyze or inhibit one of their number’s production. As a consequence of this collective and inter- connected catalysis or closure, more complex molecules are catalyzed, which again function as catalysts for even more complex molecules. Kauffman argues that, given that a critical molecular di- versity of molecules has appeared, life can occur as catalytic closure itself crys- tallizes. The poised state between stabil- ity and exibility is commonly referred to as the “edge of chaos.”
Life at the Edge of Chaos Christopher Langton [45] and Norman Packard, the scientists who coined the term “life at the edge of chaos,” were two of the rst to describe the idea of com- Fig. 4. Screenshot of the VERBARIUM web site, 1999. (© Christa Sommerer and Laurent plex patterns. They discovered that in a Mignonneau) simulation of cellular automata there ex- ists a transitional region that separates and/or connection have increased in at “symmetry breaking,” in that no part or the domains of chaos and order. Cellular least one dimension. aspect of a complex entity can provide automata were invented in the 1950s by sufcient information to actually or sta- John Von Neumann [46]. They form a Irreducibility tistically predict the properties of the complex dynamical system of squares or Irreducibility is a source of complexity. other parts. This again connects to the cells that can change their inner states Randy J. Nelson [40] argues that irre- difculty of modeling associated with from black to white according to the gen- ducibility is a key factor in complex sys- complex systems. eral rules of the system and the states of tems. Similar approaches include the the neighboring cells. When Langton writings of Philip W. Anderson [41], who Complexity as Relative to the and Packard observed the behavior of points out the importance of size to qual- Frame of Reference cellular automata, they found that al- itative behavior, and William Wimsatt Edmonds notes that complexity neces- though cellular automata obey simple [42], who argues that the evolution of sarily depends on the language used to rules of interaction of the type described multiple and overlapping functions will model a system. He argues that effective by Stephen Wolfram [47], they can de- limit reduction in biology. complexity depends on the framework velop complex patterns of activity. As chosen from which to view/model the these complex dynamic patterns develop Ability to Surprise system of study. The criticality of scale in and roam across the entire system, global The ability to surprise is not possessed by the modeling of phenomena has also led structures emerge from local activity very simple and thus well-understood sys- R. Badii and A. Politi [44] to focus their rules, which is typical of complex systems. tems, and consequently has come to be characterization of complexity solely on Langton and Packard’s automata indeed seen as an essential property of complex such hierarchical and scaling effects. show a kind of phase transition between systems [43]. three stages. Langton and Packard hy- Midway between Order and pothesized that the third state, having the Symmetry Breaking Disorder highest level of communication, is also Heylighen argues that complexity can be Complexity is sometimes posited as a the optimal state for adaptation and characterized by a lack of symmetry, or midpoint between order and disorder. change and in fact would provide maxi-
164 Sommerer and Mignonneau, Modeling the Emergence of Complexity A A - R to the VERBARIUM web site, the mes- L T sages are translated by our in-house text- I F to-form editor into various 3D shapes. E These shapes are accumulated into image structures that become more com- plex than the initial input elements. We anticipate that as more users participate, increasingly complex image structures will emerge over time.
VERBARIUM System Overview VERBARIUM is available on-line at the following web page:
Sommerer and Mignonneau, Modeling the Emergence of Complexity 165 A A - R following random numbers rseed(104) (as L T Table 1. VERBARIUM’s design function table. I there are 50 different functions available, F function1 translate ring for certain amount (a) in x E the oats that follow are multiplied by 50 function2 translate ring for certain amount (a) in y to create integers). Figure 3 shows in de- function3 translate ring for certain amount (a) in z tail how the entire assignment of random function4 rotate ring for certain amount (b) in x function5 rotate ring for certain amount (b) in y numbers to design functions operates. As function6 rotate ring for certain amount (b) in z mentioned above, the actual oat values function7 scale ring for certain amount (c) in x for the update parameters come from the function8 scale ring for certain amount (c) in y random seed function of the rst char- function9 scale ring for certain amount (c) in z acter of the word, rseed(84). function10 copy whole segment(s) As explained earlier, the basic module function11 compose a new texture for segment(s) is a ring that can grow and assemble into function12 copy texture of segment(s) segments that can then grow and branch function13 change parameters of RED in segment(s)texture to create more complex structures as the function14 change parameters of GREEN insegment(s)texture incoming text messages modify and function15 change parameters of BLUE in segment(s)texture function16 change patterns of segment(s)texture “sculpt” the basic module according to function17 exchange positions of segments the design functions available in the de- function18 add segment vertices sign function table in Table 1. function19 divide segment in 3 to create branch function20 divide segment in y to create branch VERBARIUM ’s Complexity function21 divide segment in z to create branch Potential function22 create new internodium(s) for branch(es) Depending on the complexity of the in- function23 add or replace some of the above functions coming text messages, the 3D forms be- function24 randomize the next parameters come increasingly shaped, modulated function25 copy parts of the previous operation and varied. As there is usually great vari- function26 add the new parameter to previous parameter function27 ignore the current parameter ation among the texts, the forms them- function28 ignore the next parameter selves also vary greatly in appearance. As function29 replace the previous parameter by new parameter a result, each individual text message cre- ...... ates a very specic 3D structure; a struc- function50 ture may look like an organic tree or take a more abstract form. All forms together build a collective image displayed in the ring forming a segment. Figures 2c and nite sequence of linearly distributed upper-right window of the web site: it is 2d show branching possibilities , with random numbers with a oating point proposed that a complex image structure branches diverging from a single point, precision of 4 bytes (oat values are be- could emerge that represents a new type called an internodium (2c), or from dif- tween 0.0 and 1.0). These random num- of structure that is not solely an accu- ferent internodiums (2d). There can be bers for the rst character of the word mulation of its parts but instead repre- several branches attached to one inter- This will become the actual values for the sents the amount and type of interactions nodium. Figure 2e shows an example of modication parameters in the design of the users with the system. An example segment rotation, and Fig. 2h shows the function table. Note that the random of a form created by a text message in combination of rotation and branching. number we use is a so-called pseudo ran- French is shown in Fig. 4. Figures 2f and 2g are different examples dom, generated by an algorithm with 48- of scaling. In total, there are about 50 dif- bit precision, meaning that if the same ferent design functions, which are orga- rseed is called once more, the same se- CONCLUSIONS nized into a design function look-up quence of linearly distributed random We have introduced an interactive system table (Table 1). These functions are es- numbers will be called. Which of the de- for the Internet that enables on-line users sential for “sculpting” the default ring sign functions in the design function to create 3D shapes by sending text mes- through modications of its vertex pa- table are actually updated is determined sages to the VERBARIUM web site. Using rameters. by the letters that follow in the text, in our text-to-form editor, this system trans- The translation of the actual text char- this case h,i,s; we then assign their ASCII lates the text parameters into design pa- acters of the user’s e-mail message into values (104 for h, 105 for i, 115 for s), rameters for the creation and design function values is done by assign- which provide us with random seed func- modulation of 3D shapes. These shapes ing ASCII values to each text character tions rseed(104), rseed(105), rseed(115). can become increasingly complex as according to the standard ASCII table These random seed functions are then users interact with the system. A collec- shown in Table 2. used to update and modify the corre- tive image hosts and integrates all of the Each text character is translated into sponding design functions in the design incoming messages that have been trans- an integer. We can now proceed by as- function look-up table, between design formed into 3D images, and as users in- signing this integer value to a random function1 and function50. For example, creasingly interact with the system, it is seed function rseed. In our text example by multiplying the rst random number anticipated that an increasingly complex (Fig. 3), the T in This has the ASCII value of rseed(104) by 10, we get the integer that structure will emerge. As it will no longer 84, hence the assigned random seed assigns the number of functions that will be possible to deconstruct the collective function for T becomes rseed(84). This be updated. Which of the 50 functions image into its initial parts, we suggest that random seed function now denes an in- are precisely updated is decided by the some of the features of complex systems
166 Sommerer and Mignonneau, Modeling the Emergence of Complexity A A creases as Pmin, the shortest algorithm - R Table 2. The ASCII table. L T that can generate a digit sequence, S, in- I 33 ! 34 " 35 # 36 $ 37 % 38 & 39 © F creases to the length equal to the se- E 40 ( 41 ) 42 * 43 1 44 , 45 - 46 . 47 / quence to be computed; when the 48 0 49 1 50 2 51 3 52 4 53 5 54 6 55 7 algorithm reaches this incompressibility 56 8 57 9 58 : 59 ; 60 < 61 5 62 > 63 ? 64 @ 65 A 66 B 67 C 68 D 69 E 70 F 71 G 72 H 73 I 74 J 75 K 76 L 77 M 78 N 79 O limit the sequence is dened as random. 80 P 81 Q 82 R 83 S 84 T 85 U 86 V 87 W The KCS de nition distinguish es be- 88 x 89 Y 90 Z 91 [ 92 \ 93 ] 94 ^ 95 _ tween “highly ordered” and “highly com- 96 © 97 a 98 b 99 c 100 d 101 e 102 f 103 g plex” structures. 104 h 105 i 106 j 107 k 108 l 109 m 110 n 111 o Hinegardner and Engelberg’s Number- 112 p 113 q 114 r 115 s 116 t 117 u 118 v 119 w of-Parts Denition. Perhaps the simplest 120 x 121 y 122 z 123 $ 124 ? 125 % 126 ~ measure of complexity is that suggested by R. Hinegardner and H. Engelberg [63]: the number of different parts. can emerge. These features include Internet in a bottom-up fashion, we have Hinegardner and Engelberg’s measure properties such as variety, dependency created an interactive installation called evokes “exploded” diagrams of pieces of and symmetry breaking (as described by Riding the Net [60,61]. This system com- machinery. They give some indication of Heylighen), irreducibility (as described bines speech-recognition software with complexity, but leave out what is perhaps by Nelson) and ability to surprise (as de- Internet search engines to pull images most important: “organization” and “lev- scribed by Edmonds). While our proto- and sounds from the Internet in re- els of organization” [64]. type system succeeds in modeling some sponse to a “real-life” conversation. The Crutcheld’ s Topological Complexity. of the features of complex systems, future images are displayed as a moving stream The topological complexity described by updates of the systems should include the on a large interactive screen from which James Crutcheld [65] is a measure of modeling of genetic exchange of infor- participants can “grab” images by touch- the size of the minimal computational mation (text characters) between forms, ing them and then nd out where they model (typically a nite automaton of creating offspring forms through stan- came from. As users engage in conversa- some variety) in the minimal formal lan- dard genetic crossover and mutation op- tions with each other, the content of their guage in which it has a nite model. Thus erations as we have used them in the past conversations becomes visualized as the complexity of the model is “objec- [59]. The potential benet of such an ex- image and sound streams from the In- tivized” not only by considering minimal tended system will be the expansion of ternet. As the conversations are com- models but also as related to the xed hi- diversity, reactivity to neighbors and to pletely unrestricted and unpredictable erarchy of formal languages. external control, exploration of op- and the speech recognition system itself Computational Complexity. Compu- tions, and replication—basically, the re- also adds a certain amount of unpre- tational complexity is now a much- maining features commonly associated dictability, the resulting images and studied area with many formal results with complex adaptive systems, as de- sounds represent a dynamic and com- [66]. The foundation of complexity the- scribed by Crutcheld. Another further plex feedback between the user’s input ory is the research into computability the- update of the system should also in- data (such as speech and touch) and the ory undertaken since the 1930s onward clude the capacity to simultaneously dis- system’s internal interpretation (such as by Alan Turing, Alonzo Church and play all messages in the browser’ s images and sound les derived from the Stephen Kleene [67], among others. The window; this should make it possible for Internet). The system clearly nds itself primary considerations then were the users to retrieve all messages ever sent at the midpoint between order and dis- formalization of the notion of a com- and to follow the whole evolution of the order (as described by Edmonds), and puter (e.g. the Turing machine, Church’s interaction history. the resulting interactions create common lambda calculus) and whether such a features of complex systems such as vari- computer could solve any mathematical ety, dependency, irreducibility, symmetry problem. OUTLOOK AND FUTURE breaking, ability to surprise, expansion Descriptive Complexity Theory. In WORKS of diversity and the reaction to neighbors 1969, Ronald Fagin decided to study spec- Since the rst publication of this paper, and to external control. The Riding the tra (the spectrum of a rst-order sentence we have become increasingly interested Net system is shown with two users com- is the set of cardinalities of its nite mod- in how users could interact with existing municating and interacting with each els) and Asser’s problem (1955): “Is the data structures instead of actually creat- other in Fig. 5. class of spectra closed under comple- ing these complex data structures by mentation?” [68] In 1970, his investiga- themselves. The Internet nowadays con- tions expanded to generalized spectra tains more than a billion documents, and APPENDIX A. DEFINITIONS OF (i.e. existential second-order spectra the amount of text, image and sound COMPLEXITY where not all relation symbols are quan- data increases by the minute. One could Algorithmic Information Complexity: tied out). Fagin’s most important result even argue that the Internet itself is one The KCS Denition. The best-known def- was probably his characterization of NP of the best examples of a complex system. inition of complexity is the Kolmogorov- as the class of generalized spectra in 1974. It provides an ideal platform for knowl- Chaitin-Solomonoff (KCS) de nition Interest in the subject has now exploded, edge discovery, data mining and data re- [62], describing Algorithmic Informa- mainly due to the intimate relationship trieval and systems that make use of a tion Complexity (AIC), which places (rst hinted at by Fagin) between nite dynamic and constantly evolving data- complexity somewhere between order model theor y and complexity theor y base. To work with the complexity of the and randomness; that is, complexity in- [69]. In fact, there is an established sub-
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