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What's Love Got to Do With
Aaron Brown What’s Love Got to Do With It? Edward Frenkel is writing a protracted Dear John letter to popular misconceptions about math and mathema- ticians… he great popular science and science fiction author Isaac Asimov told a story about a university committee meeting in which there was much laughter and joking about a student named “Milton” flunkingT English literature, but no one noticed when a student named “Gauss” was failing in mathematics. I wish I could find the reference to this, but I read it long ago in childhood, and some Internet searching proved fruitless. I may have the details wrong – especially the name of the student date are smaller than Asimov’s. They also have cians, and writers. With these people, screenwriters flunking English literature – but I remember the a different slant. Asimov tried to show every- often assume they must be tortured to be authentic. point. Asimov complained that a scientist would be one how mathematics and science could be fun. But there are plenty of exceptions – movies built thought a Philistine if he expressed no interest in Frenkel instead celebrates the passion and inten- around well-rounded, friendly, artistic genius- music or philosophy, but that an artist could boast sity of mathematics at the highest level. He has es. And, even when artists are a bit crazy, it is an about not knowing enough arithmetic to balance done this through lectures which are a sensation excess of passion, “agony and ecstasy,” not some his checkbook. on YouTube, an erotic film, and, most recently, a incomprehensible twisted obsession from another Edward Frenkel is one of the great mathema- book, Love and Math: The Heart of Hidden Reality. -
``Mathematics'' and ``Physics'' in the Science of Harmonics
NISSUNA UMANA INVESTIGAZIONE SI PUO DIMANDARE VERA SCIENZIA S’ESSA NON PASSA PER LE MATEMATICHE DIMOSTRAZIONI LEONARDO DA VINCI vol. 4 no. 3-4 2016 Mathematics and Mechanics of Complex Systems STEFANO ISOLA “MATHEMATICS” AND “PHYSICS” IN THE SCIENCE OF HARMONICS msp MATHEMATICS AND MECHANICS OF COMPLEX SYSTEMS Vol. 4, No. 3-4, 2016 dx.doi.org/10.2140/memocs.2016.4.213 ∩ MM “MATHEMATICS” AND “PHYSICS” IN THE SCIENCE OF HARMONICS STEFANO ISOLA Some aspects of the role that the science of harmonics has played in the history of science are discussed in light of Russo’s investigation of the history of the concepts of “mathematics” and “physics”. 1. The rambling route of the ancient scientific method In several places in Russo’s writings on the history of science, one can find en- lightening discussions about the meanings of the concepts of “physics” and “math- ematics”, along with the particular notions of truth involved in them; see, e.g., [58, Chapter 6.6; 60, Chapter 15; 56; 57]. Both terms derive from the Greek: the original meaning of the former was the investigation of everything that lives, grows or, more generally, comes into existence, whereas the latter referred to all that is studied, thus deriving its meaning not from its content but from its method. In the Hellenistic period, the term “physics” continued to be used to indicate that sector of philosophy that addressed nature (the other sectors being ethics and logic), thus corresponding to what came to be called “natural philosophy” in modern times. On the other hand, the term “mathematics” was used to indicate all the disciplines (including geometry, arithmetic, harmonics, astronomy, optics, mechanics, hydro- statics, pneumatics, geodesy and mathematical geography) that shared the same method of investigation, based on the construction of theories by which “theorems” are proved, leaning on explicitly stated initial assumptions. -
Popularising Mathematics
Popularising Mathematics Philipp Legner August 2013 Abstract Mathematics has countless applications in science, engineering and technology, yet school mathematics is one of the most unpopular subjects, perceived as difficult, boring and not useful in life. ‘Popularisation’ projects can help bridge this gap, by showing how exciting, applicable and beautiful mathematics is. Some popularisation projects focus on telling the wider public about mathematics, including its history, philosophy and applications; other projects encourage you to actively do mathematics and discover surprising relationships and beautiful results using mathematical reasoning and thinking. In this report I will develop a framework to classify and evaluate popularisation, and analyse a wide range of existing projects – ranging from competitions to websites, movies, exhibitions, books and workshops. I also reflect upon my personal experiences in designing popularisation activities. I would like to thank Professor Dave Pratt for his advise while writing this report. Table of Contents Introduction 1 Part 1: A Framework for Mathematics Popularisation The Value of Mathematics ........................................................................... 2 Defining Mathematics Popularisation ...................................................... 4 Designing Mathematics Popularisation ................................................... 8 Evaluating Popularisation Projects ............................................................ 11 Part 2: Case Studies of Popularisation Projects -
New Zealand Number 114 Summer 2014 Skeptic
New Zealand Number 114 Summer 2014 Skeptic Mathematics and Pseudoscience A mathematician’s experiences with mathematical cranks The TPP and its Impact on the NZ Health Sector ACC and Acupuncture Mark Hanna investigates skeptics.nz New Zealand Skeptics CONTENTS ABOUT US 3 Editorial The New Zealand Skeptics form a network of New Zealanders including 4 Newsfront scientists, health professionals, teachers, magicians and many others from all walks of life. Members have 6 Letters a variety of religious faiths, economic beliefs and political leanings, but are all 7 Mathematics and Pseudoscience interested in examining what objective Steven Galbraith writes about his experiences scientific support there is for claims with mathematical cranks of such things as psychic abilities, alternative health practices, creationism and other areas where science, pseudo- 12 The Trans-Pacific Partnership and science and shonky science interact. its Impact on the NZ Health Sector 14 A tribute to Warwick Don CONTRIBUTIONS Contributions are welcome and should be 15 BioBlog by Alison Campbell sent to: P.O. Box 30501 17 Science-Based Healthcare Lower Hutt Mark Hanna investigates the ACC and 5040 acupuncture email: [email protected] Deadline for next issue: 21 Complaining Cheat Sheet 10 April 2015 23 Science-Based Medicine Letters for the Forum may be edited Steven Novella talks about the latest bogeyman as space requires – up to 250 words is preferred. 26 Infectious Thoughts by Siouxsie Wiles Please indicate the publication and date of all clippings for Newsfront. 27 The Humanist Material supplied by email or CD is 28 The Loose Change Range appreciated. Luke Oldfield discusses the art of engaging with a ‘Non-Opinion’ Permission is given to other non-profit skeptical organisations to reprint material from this publication, provided the author 30 Skeptacular! by Mark Maultby and NZ Skeptic Inc. -
A Brief History of Numbers by Leo Corry
Reviews Osmo Pekonen, Editor A Brief History of Numbers by Leo Corry OXFORD: OXFORD UNIVERSITY PRESS, 2015, 336 PP., £24.99, ISBN: 9780198702597 REVIEWED BY JESPER LU¨TZEN he concept of number has an interesting and intriguing history and this is a highly recommendable TT book about it. When were irrational numbers (or negative numbers) introduced into mathematics? Such questions seem precise and simple, but they cannot be answered with a simple year. In fact, the years 2000 BC and AD 1872 and many years Feel like writing a review for The Mathematical in between could be a valid answer to the question about Intelligencer? Contact the column editor if you wish to irrational numbers, and many years between 1 and 1870 could be defended as an answer to the question about the submit an unsolicited review, or if you would welcome introduction of negative numbers. This is not just because modern mathematicians may consider pre-1870 notions of being assigned a book to review. numbers as nonrigorous but also because the historical actors were not in agreement about the nature and extent of the concept of number. Therefore the answer to the questions raised previously must necessarily be a long and contorted story. Many treatises and articles on the history of mathematics tell aspects of this story, and Corry’s book may be considered a synthesis of these more specialized works. Still, Corry also adds his own original viewpoints and results to the standard history. The last chapters of the book dealing with the modern foundations of the number system from the end of the 19th and the beginning of the 20th cen- turies obviously draw on Corry’s own research on the establishment of modern structural thinking that has con- tributed seminally to our understanding of the development of mathematics in this period. -
A Wealth of Numbers Reviewed by Andy R
Book Review A Wealth of Numbers Reviewed by Andy R. Magid to do with the quality, or even correctness, of their A Wealth of Numbers mathematical content. For example, consider the Benjamin Wardhaugh Amazon Best Sellers rankings of the following: Princeton University Press, April 2012 Constance Reid’s excellent From Zero to Infinity is Hardcover, 388 pages, US$45.00 number 907,624, only slightly better than Marilyn ISBN-13: 978-0691147758 vos Savant’s execrable The World’s Most Famous Math Problem, number 966,319, while Lancelot When it comes to mathematical exposition, we Hogben’s venerable (first published in 1937) and mathematicians are diligent consumers. We buy valuable Mathematics for the Million substantially non-textbook monographs, read Notices articles, outranks both at 153,398. For further comparison, and attend departmental colloquia, generally inde- John Allen Paulos’s 1980s classic Innumeracy ranks pendent of whether the exposition is high quality 16,221 (all ranks observed 16 November 2012). This (Notices), mixed (monographs), or low (most collo- highly unrepresentative sample of mathematics quia). Perhaps we are motivated by the hope that books for the general reader currently available ideas and methods from other fields will inspire consists of books this reviewer happened to read, our work in our own specialty, or perhaps we either as a general reader himself before becoming feel the duty to be informed about the world of a mathematician or, for the later ones, out of research mathematics in general. In any event, we curiosity when the books became newsworthy devote time and effort to consuming mathematical (Paulos) or notorious (vos Savant). -
To Be a Scientist*
TO BE A SCIENTIST1 Victor H. Yngve University of Chicago One of the things that attracted me to linguistics thirty-five years ago was the realization that it dealt with a large area of natural phenomena not yet well understood that could be approached scientifically. It was a frontier with the challenge of the unknown. Linguists advertised their discipline as a science, and it did seem reasonable that there could be a linguistic science, for there were complex phenomena that could be observed, and the observations could be replicated. It reminded me of the complex phenomena in cosmic-ray physics that I had been working on, but it seemed more important and more interesting. Then as I got into the discipline and started doing research, it came over me that linguistics had serious problems in regard to its scientific status. One of the first things I noticed was that much of the writing in linguistics was polemical. This was in stark contrast with the well-mannered writing that I had become accustomed to in physics. Furthermore, it developed that there were many different theories and points of view in linguistics, and the criteria for choosing among them were not clear. At first I thought it was simply because the discipline was not yet very highly developed, for physics, too, had been polemical in earlier centuries. The thing to do was to try to develop linguistics further as a science. So when I put forth a scientific hypothesis about the relation of phrase structure to temporary memory, I expected that linguists working on different languages would test it on the languages they studied, and some did and found that the hypothesis held. -
Hypernumbers and Other Exotic Stuff
HYPERNUMBERS AND OTHER EXOTIC STUFF Photo by Mateusz Dach (1) MORE ON THE "ARITHMETICAL" SIDE Tropical Arithmetics Introduction to Tropical Geometry - Diane Maclagan and Bernd Sturmfels http://www.cs.technion.ac.il/~janos/COURSES/238900-13/Tropical/MaclaganSturmfels.pdf https://en.wikipedia.org/wiki/Min-plus_matrix_multiplication https://en.m.wikipedia.org/wiki/Tropical_geometry#Algebra_background https://en.wikipedia.org/wiki/Amoeba_%28mathematics%29 https://www.youtube.com/watch?v=1_ZfvQ3o1Ac (friendly introduction) https://en.wikipedia.org/wiki/Log_semiring https://en.wikipedia.org/wiki/LogSumExp Tight spans, Isbell completions and semi-tropical modules - Simon Willerton https://arxiv.org/pdf/1302.4370.pdf (one half of the tropical semiring) Hyperfields for Tropical Geometry I. Hyperfields and dequantization - Oleg Viro https://arxiv.org/pdf/1006.3034.pdf (see section "6. Tropical addition of complex numbers") Supertropical quadratic forms II: Tropical trigonometry and applications - Zur Izhakian, Manfred Knebusch and Louis Rowen - https://www.researchgate.net/publication/ 326630264_Supertropical_Quadratic_forms_II_Tropical_Trigonometry_and_Applications Tropical geometry to analyse demand - Elizabeth Baldwin and Paul Klemperer http://elizabeth-baldwin.me.uk/papers/baldwin_klemperer_2014_tropical.pdf International Trade Theory and Exotic Algebras - Yoshinori Shiozawa https://link.springer.com/article/10.1007/s40844-015-0012-3 Arborescent numbers: higher arithmetic operations and division trees - Henryk Trappmann http://eretrandre.org/rb/files/Trappmann2007_81.pdf -
On the Principle Qf Excluded Middle U* I-Lro 6*
ON THE PRINCIPLE 011' EXCLUDED MIDDLE 415 trans~ prove that classical mathemati('J3 is ~..IV, g, with rules ofinfemnce) of qnanti latahle into intuitionistic mathematics. ficatwn theory and extend his iHustra_ For this purpose, with each formula €> of tim.l to cover also the rule P and the mathemat,ics there is associated a trans remaining axioms, and if we let .t>:O be lat~on <0* in a perfectly general manner JEO plus Axiom 6) t,hen we have also: ,~, (IIi, § 2). If (a), and (Ea) are the Theorem III. If U f--I\£' \15, then only symbols we use for forming new On the principle qf excluded middle u* I-lRO 6*. formulas from given formulas, the defini. In that case, all the derivatioIh9 in V 6~ ANDREI NIKOLAEVICH KOLMOGOROV tion amounts to: for atomic e* is its § 4, can be dispensed with because the; donble negation is, or n@5; (B)* is n( B*); would follow from Theorem III. (1925) (A -'>- B)* is n(A* -'>- B*); ((a)A(a))* is A very suggestive remark (beginning n(a)(A(a»*; «(Ea)A(a)* is n(Ea)(A(a»*. of IV, § 5, and last two paragraphs of The following T'C'suHs are proved ex~ IV, § 6) is that every axiom A of matbe To " I"rge extent, this paper antici foundation since it asserts something ""tly (III, § 3) : matics is of type .!(., that is, A. is (intni p"ted not only Heytiog's form"liz"tion of about the consequences of something im~ Lemma 1. 1-i8 nA" ~ ir. -
Hypernumbers and Other Exotic Stuff
HYPERNUMBERS AND OTHER EXOTIC STUFF (1) MORE ON THE "ARITHMETICAL" SIDE Tropical Arithmetics Introduction to Tropical Geometry - Diane Maclagan and Bernd Sturmfels http://www.cs.technion.ac.il/~janos/COURSES/238900-13/Tropical/MaclaganSturmfels.pdf https://en.wikipedia.org/wiki/Min-plus_matrix_multiplication https://en.m.wikipedia.org/wiki/Tropical_geometry#Algebra_background https://en.wikipedia.org/wiki/Amoeba_%28mathematics%29 https://www.youtube.com/watch?v=1_ZfvQ3o1Ac (friendly introduction) https://en.wikipedia.org/wiki/Log_semiring https://en.wikipedia.org/wiki/LogSumExp Tight spans, Isbell completions and semi-tropical modules - Simon Willerton https://arxiv.org/pdf/1302.4370.pdf (one half of the tropical semiring) Hyperfields for Tropical Geometry I. Hyperfields and dequantization - Oleg Viro https://arxiv.org/pdf/1006.3034.pdf (see section "6. Tropical addition of complex numbers") Supertropical quadratic forms II: Tropical trigonometry and applications - Zur Izhakian, Manfred Knebusch and Louis Rowen - https://www.researchgate.net/publication/326630264_Supertropical_Quadratic_forms_II_Tropical_Trig onometry_and_Applications Tropical geometry to analyse demand - Elizabeth Baldwin and Paul Klemperer http://elizabeth-baldwin.me.uk/papers/baldwin_klemperer_2014_tropical.pdf International Trade Theory and Exotic Algebras - Yoshinori Shiozawa https://link.springer.com/article/10.1007/s40844-015-0012-3 Arborescent numbers: higher arithmetic operations and division trees - Henryk Trappmann http://eretrandre.org/rb/files/Trappmann2007_81.pdf -
A Mathematician Reads the Newspaper (1997) by John
Introduction "I read the news today, Oh Boy." -JOHN LENNON M y earliest memories, dating from the late 1940s, include hearing a distant train whistle from the back steps of the building we lived in on Chicago's near north side. I can also see myself crying under the trapezi (Greek for "table") when my grandmother left to go home to her apart ment. I remember watching my mother rub her feet in bed at night, and I remember my father playing baseball and wearing his baseball cap indoors to cover his thinning hair. And, lest you wonder where I'm heading, I can recall watching my grandfather at the kitchen table read ing the Chicago Tribune. The train whistle and the newspaper symbolized the outside world, frighteningly yet appealingly different from the warm family ooze in which I was happily immersed. What was my grandfather reading about? Where was the train going? Were these somehow connected? When I was five, we moved from a boisterous city block to the sterile environs of suburban Milwaukee, 90 miles and 4 light-years to the north. Better, I suppose, in some conventional 1950s sense, for my siblings and me, but it never felt as nurturing, comfortable, or alive. But this introduction is not intended to be an autobiography, so let me tell you about the Milwaukee Journal's Green Sheet. This insert, literally green, was full of features that fascinated me. At the top was a saying by Phil Osopher that always contained some wonderfully puerile pun. There was also the 'Ask Andy" column: science questions and brief answers. -
Beautiful Geometry by Eli Maor and Eugen Jost
blogs.lse.ac.uk http://blogs.lse.ac.uk/lsereviewofbooks/2014/03/03/book-review-beautiful-geometry-by-eli-maor-and-eugen-jost/ Book Review: Beautiful Geometry by Eli Maor and Eugen Jost How do art and mathematics cross over? Beautiful Geometry is an attractively designed coffee table book that has 51 short chapters, each consisting of an essay by the mathematical historian Eli Maor on a single topic, together with a colour plate by the artist Eugen Jost.The book achieves its aim to demonstrate that there is visual beauty in mathematics, finds Konrad Swanepoel. It is heartily recommended to mathematics students who want to broaden their horizons and to teachers of mathematics at school level. Beautiful Geometry. Eli Maor and Eugen Jost. Princeton University Press. January 2014. Find this book: Geometry has a history that goes back at least 3000 years, and under the ancient Greeks achieved a scientific level which even today survives all but the most exacting logical scrutiny. Having always been synonymous with Mathematics, in the 20th century Geometry has simultaneously specialised into a myriad subfields (algebraic geometry, differential geometry, discrete geometry, convex geometry, etc.) while losing its all-encompassing grip on Mathematics. At universities we are eager to teach our students Calculus and Linear Algebra instead of a course on Classical Geometry, now deemed old- fashioned. This book reminds us of what we are missing. This attractively designed coffee table book has 51 short chapters, each consisting of an essay by the mathematical historian Eli Maor on a single topic, together with a colour plate (occasionally two) by the artist Eugen Jost.