New Books in Mathematics

A conceptual space sounds like a rather nebulous thing, and basing a semantics on conceptual spaces sounds similarly nebulous. In The Geometry of Meaning: Semantics Based on Conceptual Spaces (MIT Press, 2014), Peter Gardenfors demonstrates that this need not be the case. Indeed, his research is directed towards establishing a formal, mathematically-grounded account of semantics, an account which – as expounded here – is nevertheless accessible. In this interview we discuss the essence of this proposal, focusing in particular on its implications for linguistic analysis, but also touching upon its relation to cognitive science and other related fields. The proposal makes testable predictions about the organization of individual linguistic systems, as well as their acquisition (and potentially their evolution over time). Notably, the “single domain constraint” posits that individual lexical items refer to convex regions of single domains. We discuss the significance of this idea as a bridge between linguistics and cognitive science, what would constitute its falsification, and how it can usefully be investigated from a linguistic standpoint. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is Everyday Calculus: Discovering the Hidden Math All around Us (Princeton University Press, 2014) by Oscar E. Fernandez, who teaches mathematics – and calculus in particular – at Wellesley College.  While it can be read by someone who wants to obtain a sense of what calculus is and how it’s used, it is even more enjoyable and enlightening if the reader has taken the first semester of a calculus course.  The author takes the reader through a day in the author’s life, during which things one typically encounters – stock price quotations, cooling cups of coffee, getting good seats at a movie – afford an opportunity to investigate how calculus explains these everyday occurrences.  Fernandez also introduces some instances where calculus has totally unexpected applications to our lives – why our GPS system relies upon Einstein’s Theory of Relativity, and why we obtain electricity via alternating current rather than direct current.  Everyday Calculus should not only add to the appreciation of calculus by those who have studied the subject, the book will hopefully persuade readers unfamiliar with calculus to take a course in it. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

When we’re faced with a choice between Door #1, Door #2, and Door #3, how do we infer correctly that there’s an equal chance of the prize being behind any of the doors? How is it that we are generally correct to choose the shorter of two checkout lines in the supermarket when we’re in a hurry? In his new book, Tychomancy: Inferring Probability from Causal Structure (Harvard University Press, 2013), Michael Strevens – professor of philosophy at New York University, argues that we are all equipped with a reliable, probable innate, and not fully conscious skill at probabilistic reasoning—a “physical intuition” that enables us to infer physical probabilities from perceived symmetries. This skill is found in six-month-old infants watching as red and white balls are removed in different proportions from an urn. But it also underlies important advances in the sciences, such as James Clerk Maxwell’s reasoning when he hit upon the correct distribution of velocities of a moving particle in a gas. In this intriguing essay on a very special type of cognitive capacity, Strevens’ defends controversial claims about the rules guiding our reasoning about physical probability, its probable innateness, and its role in science as well as in everyday judgment. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-posted with permission from Wild About Math] My favorite kind of math challenges are those that children can understand and professional mathematicians can’t solve easily (or at all.) Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing (Princeton University Press, 2014) is a brand new book from Princeton University Press that has a great collection of fun problems that kids (middle school and above) and their parents can work on together. Author Tim Chartier does a fantastic job of weaving some wonderful stories into his sharing of a number of challenges that are either original or new spins on old problems. And, many (all?) of the puzzles in the book are classroom tested. Tim is a mathematician and a professional mime. He’s got a neat relationship with the Mathematical Association of America, and with the Museum of Mathematics in New York City. He’s got a DVD course coming out, and a second book. Tim is quite the math celebrity and a really great guy. I think you’ll all enjoy the many topics we manage to touch on in just over an hour. Oh, and if you didn’t win a billion dollars in Warren Buffett’s March Madness challenge then you might want to listen to the podcast and read the book. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-posted with permission from Wild About Math] I’ve admitted before that Physics and I have never gotten along. But, science fiction is something I enjoy. So, when Princeton University Press sent me a copy of Physics Professor Chuck Adler‘s new book Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction (Princeton University Press, 2014), I was intrigued enough that I wanted to interview the author. This interview rambled, but in a good way. Chuck is a great guest, he’s passionate about physics and math as well as fantasy and science fiction. We flowed through a number of subjects and had a grand time. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Beautiful Geometry (Princeton UP, 2014), by the mathematician prof. Eli Maor and the noted artist Eugen Jost.  It’s a fascinating collaboration which helps to bridge the gap deplored by C. P. Snow in his classic The Two Cultures.  If you’re a lover of geometry, you’ll find some of your favorites depicted here – as well as a number of theorems that will undoubtedly be new to many readers (including the interviewer).  Each result is accompanied by an original work of art by Eugen Jost.  It’s fascinating not only to read about some of the more piquant results in a field (geometry) that is more than 2,500 years old, but just as delightful to see how these results inspire the creativity of an artist.  If you come for the geometry, you’ll certainly stay for the artwork – and if your interest is in art, you’ll be intrigued by how a presumably dry subject such as geometrical theorems can give birth to works of exquisite beauty. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is Love and Math: The Heart of Hidden Reality Basic Books, 2013) by Edward Frenkel of the University of California at Berkeley.It’s a toss-up which is more interesting – the description of Frenkel’s life or his description of his interest in – and love for – mathematics and physics. Before he was twenty years old, Frenkel had written a paper that a visiting Swedish physicist thought so intriguing that he smuggled it out of Russia.That paper started Frenkel on a career which resulted in his collaborating with some of the world’s foremost mathematicians and physicists – and to his writing Love and Math. It’s a fascinating read. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

[Re-posted with permission from Wild About Math] I had the pleasure of interviewing mathematician and mathematical card magic innovator Colm Mulcahy. Dr. Mulcahy just published a book, Mathematical Card Magic: Fifty-Two New Effects (A K Peters, 2013) We spent a delightful hour discussing his book, his love of math and magic, and the inspiration behind writing the book. Plus, Dr. Mulcahy shares a few challenges listeners might enjoy chewing on, sprinkled throughout the interview. And, we discuss Martin Gardner, who Colm Mulcahy knew for the last decade of his life and met with several times. You may also enjoy Shecky’s text interview with Colm Mulcahy at Math Tango.   Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

The book discussed in this interview is Dice World: Science and Life in a Random Universe (Icon Books, 2013), by Brian Clegg, an acclaimed British writer of books on science for the general public. Brian has a knack for taking concepts that seem abstruse and explaining them in ways that those who lack a technical background can readily understand. This talent is on display inDice World, where he takes the reader on an intriguing trip through the world of probability and statistics, and shows how these disciplines are essential to our understanding of how the Universe came into existence, how it functions, and how it will evolve. Brian Clegg can be contacted at brian@brianclegg.net. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics

Today I talked to Leonard Wapner about his new book Unexpected Expectations: The Curiosities of a Mathematical Crystal Ball (A.K. Peters, 2012).  Prof. Wapner’s previous book, The Pea and the Sun, was an in-depth investigation of the Banach-Tarski Theorem, one of the most counterintuitive results in mathematics.  Expectation is an extension of the idea of average value, and is a basic tool of probability theory that underlies both the gaming and insurance industries.  Unexpected Expectations is a fascinating look at some of the counterintuitive aspects of this apparently simple concept. Learn more about your ad choices. Visit megaphone.fm/adchoicesSupport our show by becoming a premium member! https://newbooksnetwork.supportingcast.fm/mathematics