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Kruger Oelof Abraham 2016.Pdf (2.709Mb)
UNIVERSITY OF KWAZULU NATAL A robust air refractometer for accurate compensation of the refractive index of air in everyday use Oelof Abraham Kruger 2016 A robust air refractometer for accurate compensation of the refractive index of air in everyday use Oelof Abraham Kruger 215081719 December 2016 A robust air refractometer for accurate compensation of the refractive index of air in everyday use Oelof Abraham Kruger 215081719 December 2016 Thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Physics School of Chemistry and Physics, Discipline of Physics College of Agriculture, Engineering and Science University of KwaZulu-Natal (PMB), Private Bag X01, Scottsville, 3209, South Africa Supervisor: Professor Naven Chetty P a g e | 3 Declaration This thesis describes the work undertaken at the University of KwaZulu-Natal under the supervision of Prof N. Chetty between March 2015 and December 2016. I declare the work reported herein to be own research, unless specifically indicated to the contrary in the text. Signed:……………………………………….. Student: O. A. Kruger On this ……….day of ……………..2016 I hereby certify that this statement is correct. Signed:……………………………………….. Supervisor: Prof N. Chetty On this ……….day of ……………..2016 P a g e | 4 ACKOWLEDGMENTS A heartfelt thank you to my family for coping with all the time I spent away from home for enduring my temperaments when I was home and working on the project. I wish also to thank my supervisor, Naven Chetty who has played a vital role in not only supervising the project, but also my overall guidance and support on all aspects of the projects. -
Metrology Principles for Earth Observation: the NMI View
Metrology Principles for Earth Observation: the NMI view Emma Woolliams 17th October 2017 Interoperability Decadal Stability Radiometric Accuracy • Identical worldwide • Century-long stability • Absolute accuracy Organisation of World Metrology . The Convention of the Metre 1875 (Convention du Mètre) . International System of Units (SI) 1960 (Système International d'Unités) . Mutual Recognition Arrangement (CIPM-MRA) 1999 This presentation 1. How world metrology achieves interoperability, stability and accuracy 2. How these principles can be applied to Earth Observation 3. Resources to help This presentation 1. How world metrology achieves interoperability, stability and accuracy 2. How these principles can be applied to Earth Observation 3. Resources to help • How do we make sure a wing built in one country fits a fuselage built in another? • How do we make sure the SI units are stable over centuries? • How do we improve SI over time without losing interoperability and stability? History of the metre 1795 1799 1960 1983 Metre des Archives 1889 International Distance light Prototype travels in 1/299 792 458th of a second 2018 1 650 763.73 wavelengths of a krypton-86 transition 1 ten millionth of the distance from the • Stable North Pole to the • Improves over time Distance that makes Equator through • Reference to physical process the speed of light Paris 299 792 458 m s-1 Three principles Traceability Uncertainty Analysis Comparison Traceability Unit definition SI Primary At BIPM and NMIs standard Secondary standard Laboratory Users Increasing Increasing uncertainty calibration Industrial / field measurement Traceability: An unbroken chain Transfer standards Audits SI Rigorous Documented uncertainty procedures analysis Rigorous Uncertainty Analysis The Guide to the expression of Uncertainty in Measurement (GUM) • The foremost authority and guide to the expression and calculation of uncertainty in measurement science • Written by the BIPM, ISO, etc. -
Arxiv:1204.2193V2 [Math.GM] 13 Jun 2012
Alternative Mathematics without Actual Infinity ∗ Toru Tsujishita 2012.6.12 Abstract An alternative mathematics based on qualitative plurality of finite- ness is developed to make non-standard mathematics independent of infinite set theory. The vague concept \accessibility" is used coherently within finite set theory whose separation axiom is restricted to defi- nite objective conditions. The weak equivalence relations are defined as binary relations with sorites phenomena. Continua are collection with weak equivalence relations called indistinguishability. The points of continua are the proper classes of mutually indistinguishable ele- ments and have identities with sorites paradox. Four continua formed by huge binary words are examined as a new type of continua. Ascoli- Arzela type theorem is given as an example indicating the feasibility of treating function spaces. The real numbers are defined to be points on linear continuum and have indefiniteness. Exponentiation is introduced by the Euler style and basic properties are established. Basic calculus is developed and the differentiability is captured by the behavior on a point. Main tools of Lebesgue measure theory is obtained in a similar way as Loeb measure. Differences from the current mathematics are examined, such as the indefiniteness of natural numbers, qualitative plurality of finiteness, mathematical usage of vague concepts, the continuum as a primary inexhaustible entity and the hitherto disregarded aspect of \internal measurement" in mathematics. arXiv:1204.2193v2 [math.GM] 13 Jun 2012 ∗Thanks to Ritsumeikan University for the sabbathical leave which allowed the author to concentrate on doing research on this theme. 1 2 Contents Abstract 1 Contents 2 0 Introdution 6 0.1 Nonstandard Approach as a Genuine Alternative . -
Arxiv:1809.08676V1 [Math.LO] 23 Sep 2018 Hc Ahmtca O S.I Un U Htti Eednei N Dep Language Is Precise May Dependence Game
NAMING THE LARGEST NUMBER EXPLORING THE BOUNDARY BETWEEN MATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS DAVID SIMMONS Abstract. What is the largest number accessible to the human imagination? The ques- tion is neither entirely mathematical nor entirely philosophical. Mathematical formula- tions of the problem fall into two classes: those that fail to fully capture the spirit of the problem, and those that turn it back into a philosophical problem. 1. Introduction “You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number–not an infinity–on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature. Are you ready? Get set. Go.” – Scott Aaronson, “Who can Name the Bigger Number?” 1 “The game of describing the largest integer, when played by experts, lapses into a hopeless argument over legitimacy.” – Joel Spencer, “Large numbers and unprovable theorems” [8] This paper addresses the question: what is the best strategy in a “name the largest number” contest such as the one described above? Of course, the answer depends on arXiv:1809.08676v1 [math.LO] 23 Sep 2018 what the rules of the contest are. Scott Aaronson’s idea of letting a “reasonable modern mathematician” judge the entries might sound fair at first, but the answer to the question of whether a given entry is a precise description of a number may depend on exactly which mathematician you ask. It turns out that this dependence is not incidental but fundamental, and slightly different standards for what counts as a valid entry give rise to radically different strategies for winning the game. -
Overload Journal
Series Title # Placeholder page for an advertisement AUTHOR NAME Bio MMM YYYY ||6{cvu} OVERLOAD CONTENTS OVERLOAD 133 Overload is a publication of the ACCU June 2016 For details of the ACCU, our publications and activities, ISSN 1354-3172 visit the ACCU website: www.accu.org Editor Frances Buontempo [email protected] Advisors Andy Balaam 4 Dogen: The Package Management [email protected] Saga Matthew Jones Marco Craveiro discovers Conan for C++ [email protected] package management. Mikael Kilpeläinen [email protected] Klitos Kyriacou 7 QM Bites – Order Your Includes [email protected] (Twice Over) Steve Love Matthew Wilson suggests a sensible [email protected] ordering for includes. Chris Oldwood [email protected] 8A Lifetime in Python Roger Orr [email protected] Steve Love demonstrates how to use context Anthony Williams managers in Python. [email protected]. uk 12 Deterministic Components for Matthew Wilson [email protected] Distributed Systems Sergey Ignatchenko considers what can Advertising enquiries make programs non-deterministic. [email protected] Printing and distribution 17 Programming Your Own Language in C++ Vassili Kaplan writes a scripting language in C++. Parchment (Oxford) Ltd Cover art and design 24Concepts Lite in Practice Pete Goodliffe Roger Orr gives a practical example of the use of [email protected] concepts. Copy deadlines All articles intended for publication 31 Afterwood in Overload 134 should be Chris Oldwood hijacks the last page for an submitted by 1st July 2016 and those for Overload 135 by ‘A f t e r w o o d ’. 1st September 2016. The ACCU Copyrights and Trade Marks The ACCU is an organisation of Some articles and other contributions use terms that are either registered trade marks or claimed programmers who care about as such. -
Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetic
Model Theory of Ultrafinitism I: Fuzzy Initial Segments of Arithmetic (Preliminary Draft) Mirco A. Mannucci Rose M. Cherubin February 1, 2008 Abstract This article is the first of an intended series of works on the model the- ory of Ultrafinitism. It is roughly divided into two parts. The first one addresses some of the issues related to ultrafinitistic programs, as well as some of the core ideas proposed thus far. The second part of the paper presents a model of ultrafinitistic arithmetics based on the notion of fuzzy initial segments of the standard natural numbers series. We also introduce a proof theory and a semantics for ultrafinitism through which feasibly consistent theories can be treated on the same footing as their classically consistent counterparts. We conclude with a brief sketch of a foundational program, that aims at reproducing the transfinite within the finite realm. 1 Preamble To the memory of our unforgettable friend Stanley ”Stan” Tennen- baum (1927 − 2005), Mathematician, Educator, Free Spirit As we have mentioned in the abstract, this article is the first one of a series dedicated to ultrafinitistic themes. arXiv:cs/0611100v1 [cs.LO] 21 Nov 2006 First papers often tend to take on the dress of manifestos, road maps, or both, and this one is no exception. It is the revised version of an invited conference talk, and was meant from the start for a quite large audience of philosophers, logicians, computer scientists, and mathematicians, who might have some in- terest in the ultrafinite. Therefore, neither the philosophico-historical, nor the mathematical side, are meant to be detailed investigations. -
A Finitist's Manifesto: Do We Need to Reformulate the Foundations Of
A Finitist’s Manifesto: Do we need to Reformulate the Foundations of Mathematics? Jonathan Lenchner 1 The Problem There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been sleep-walking in their infinitary mathematical paradise to take heed. Much of mathematics relies upon either (i) the “existence” of objects that contain an infinite number of elements, (ii) our ability, “in theory”, to compute with an arbitrary level of precision, or (iii) our ability, “in theory”, to compute for an arbitrarily large number of time steps. All of calculus relies on the notion of a limit. The monumental results of real and complex analysis rely on a seamless notion of the “continuum” of real numbers, which extends in the plane to the complex numbers and gives us, among other things, “rigorous” definitions of continuity, the derivative, various different integrals, as well as the fundamental theorems of calculus and of algebra – the former of which says that the derivative and integral can be viewed as inverse operations, and the latter of which says that every polynomial over C has a complex root. This essay is an inquiry into whether there is any way to assign meaning to the notions of “existence” and “in theory” in (i) to (iii) above. On the one hand, we know from quantum mechanics that making arbitrarily precise measure- ments of objects is impossible. By the Heisenberg Uncertainty Principle the moment we pin down an object, typically an elementary particle, in space, thereby bringing its velocity, and hence mo- mentum, down to near 0, there is a limit to how precisely we can measure its spatial coordinates. -
Phenomenology, Logic and the Philosophy of Mathematics Richard Tieszen Index More Information
Cambridge University Press 0521837820 - Phenomenology, Logic and the Philosophy of Mathematics Richard Tieszen Index More information Index absolutism, 44, 332 see also Frege, G.; natural numbers; abstraction, 34, 36–37, 78, 84, 325, 327, Peano arithmetic (PA); Poincar´e, H.; 328 primitive recursive arithmetic (PRA); formal and material, 28 Weyl, H. see also founding/founded distinction artificial intelligence, 288 absurdity associationism, 210 formal a priori, 27 authentic/inauthentic distinction, 3, 42 material a priori, 27 axiom systems algorithmic methods, 32 definite formal, 4, 11–12, 29 alienation, 42 analysis, paradox of, 320 Becker, O., 8, 9, 14, 62, 83, 126, 237, 247, analytic a priori 254, 260, 268 judgments, 28 Bell, D., 329 see also analyticity; analytic/synthetic Benacerraf, P., 58, 64, 172 distinction Bernays, P., 108, 153, 245 Analytic and Continental philosophy, 1–2, Beth models, 289, 293 44–45, 66 BHK interpretation, 229, 232, 238, 242, analyticity, 185–190 245 rational intuition and, 188–190 biologism, 23 see also Frege, G.; G¨odel, K.; Poincar´e, Bishop, E., 228, 288 H.; Quine,W.V.O. Bolzano, B., 24, 51, 154, 318 analytic/synthetic distinction, 318 Boolos, G., 187 in Husserl, 27–28 Brentano, F., 1, 22 antinomies, 131 Brouwer, L. E. J., 7, 8, 118, 227, 228, 231, see also paradoxes 234, 235, 248, 249, 253, 254, 266, 278, antireductionism 283, 296 in Husserl, 33 see also intuitionism see also reductionism apophantic analytics, 28–29 calculation Aristotelian realism, 127 in science, 36, 40, 41–42 Aristotle, 127 Cantor, G., -
True History of Strict Finitism
A True(r) History of Strict Finitism Jean Paul Van Bendegem Vrije Universiteit Brussel Center for Logic and Philosophy of Science Universiteit Gent Confusion about what strict finitism is ° Both historical roots ° As what its meaning is Different names: ° Strict finitism ° Ultrafinitism ° Ultra-intuitionism Aim: to clarify matters (a bit) The “founding father” (usually mentioned as such) Alexander Yessenin-Volpin (sometimes Essenine-Volpin of Ésenine-Volpine) • ultra-intuitionism • articles quite cryptic • no direct interest in finitism • different aim (finitary consistency proof) YESSENIN-VOLPIN, A. S. : "Le programme ultra- intuitioniste des fondements des mathématiques". In: Infinitistic Methods, Proceedings Symposium on Foundations of Mathematics, Pergamon Press, Oxford, 1961, pp. 201-223. YESSENIN-VOLPIN, A. S. : "The ultra-intuitionistic criticism and the antitraditional program for foundations of mathematics". In: KINO, MYHILL & VESLEY (eds.), Intuitionism & proof theory. North-Holland, Amsterdam, 1970, pp. 3-45. YESSENIN-VOLPIN, A. S. : "About infinity, finiteness and finitization". In RICHMAN, F. (ed.), 1981, pp. 274-313. “Zenonian” sets Z: • if n belongs to Z, so does n+1 • Z is nevertheless finite in its entirety example : the collection of heartbeats in your youth But see: James R. Geiser: “A Formalization of Essenin-Volpin's Proof Theoretical Studies by Means of Nonstandard Analysis” (JSL, Vol. 39, No. 1, 1974, pp. 81-87) for an attempt at rigorous reconstruction “Take, for example, the unusual answer proposed by Alexander Yessenin-Volpin (Aleksandr Esenin-Volpin), a Russian logician of the ultra-finitist school who was imprisoned in a mental institution in Soviet Russia. Yessenin-Volpin was once asked how far one can take the geometric series of powers of 2, say (2 1, 2 2, 2 3, …, 2100 ). -
Science by Doing Rock Paper Scissors Student Guide
Activity type Pendulum system Activity 2.1 and measurement DOWNLOAD e-NOTEBOOK Making a pendulum to measure time What to use: Step 2 Consider the most accurate way Each GROUP will require: to measure the time taken for your pendulum to swing. • heavy retort stand • heavy cotton or light string Step 3 • masses (50 g to 1 kg) Tell your teacher when you have a • metre ruler pendulum that swings exactly at the • stopwatch. required rate. Each STUDENT will require: Step 4 When your teacher has checked your • Science by Doing Notebook. pendulum, compare it to those of other groups. What do they have in common? What to do: Put this result on the class board in the table prepared by your teacher. Step 1 Construct a pendulum that takes exactly one second to swing from one side to the other. Discussion: ? 1. When adjusting your pendulum, What does a which variables did you test? simple pendulum 2. Which variable had a significant effect have to do with on the timing of your pendulum? clocks? 3. A simple pendulum can be thought of as a system. What should be included in this system? 4. What energy transformations are happening in the pendulum system? 5. Once the pendulum starts to swing, what keeps it swinging? Motion and Energy Transfer Student GuideMotion andPart Energy2 Transfer Why do Student all systems Guide run on energy? Part 2 17 Activity 2.1 Pendulum system and measurement Continued Our metric system of measurement is often referred to as the SI system. This ? Acomes HISTORY from theOF SystémeTHE METRE International, adopted in the French revolution What does a simple during the 1790s. -
Speed of Light
Speed of light From Wikipedia, the free encyclopedia The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its precise value is 299792458 metres per second (approximately 3.00×108 m/s), since the length of the metre is defined from this constant and the international standard for time.[1] According to special relativity, c is the maximum speed at which all matter and information in the universe can travel. It is the speed at which all massless particles and changes of the associated fields (including electromagnetic radiation such as light and gravitational waves) travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the theory of relativity, c interrelates space and time, and also appears in the famous equation of mass–energy equivalence E = mc2.[2] Speed of light Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth. Exact values metres per second 299792458 Planck length per Planck time 1 (i.e., Planck units) Approximate values (to three significant digits) kilometres per hour 1080 million (1.08×109) miles per second 186000 miles per hour 671 million (6.71×108) Approximate light signal travel times Distance Time one foot 1.0 ns one metre 3.3 ns from geostationary orbit to Earth 119 ms the length of Earth's equator 134 ms from Moon to Earth 1.3 s from Sun to Earth (1 AU) 8.3 min one light year 1.0 year one parsec 3.26 years from nearest star to Sun (1.3 pc) 4.2 years from the nearest galaxy (the Canis Major Dwarf Galaxy) to 25000 years Earth across the Milky Way 100000 years from the Andromeda Galaxy to 2.5 million years Earth from Earth to the edge of the 46.5 billion years observable universe The speed at which light propagates through transparent materials, such as glass or air, is less than c; similarly, the speed of radio waves in wire cables is slower than c. -
The Routledge Companion to Philosophy of Language
THE ROUTLEDGE COMPANION TO PHILOSOPHY OF LANGUAGE Philosophy of language is the branch of philosophy that examines the nature of mean- ing, the relationship of language to reality, and the ways in which we use, learn, and understand language. The Routledge Companion to Philosophy of Language provides a comprehensive and up-to-date survey of the field, charting its key ideas and movements, and addressing contemporary research and enduring questions in the philosophy of language. Unique to this Companion is clear coverage of research from the related disciplines of formal logic and linguistics, and discussion of the applications in metaphysics, epistemology, ethics, and philosophy of mind. Organized thematically, the Companion is divided into seven sections: Core Topics; Foundations of Semantics; Parts of Speech; Methodology; Logic for Philosophers of Lan- guage; Philosophy of Language for the Rest of Philosophy; and Historical Perspectives. Comprised of 70 essays from leading scholars—including Sally Haslanger, Jeffrey King, Sally McConnell-Ginet, Rae Langton, Kit Fine, John MacFarlane, Jeff Pelletier, Scott Soames, Jason Stanley, Stephen Stich and Zoltán Gendler Szabó—The Routledge Companion to Philosophy of Language promises to be the most comprehensive and author- itative resource for students and scholars alike. Gillian Russell is Associate Professor of Philosophy at Washington University in St. Louis. Delia Graff Fara is Associate Professor of Philosophy at Princeton University. Routledge Philosophy Companions Routledge Philosophy Companions offer thorough, high quality surveys and assessments of the major topics and periods in philosophy. Covering key problems, themes and thinkers, all entries are specially commissioned for each volume and written by lead- ing scholars in the field.