Archive for The Universe in zero words

17 equations that changed the World (#2)

Posted in Books, Statistics with tags , , , , , , , , , , , , , , , , , on October 16, 2012 by xi'an

(continuation of the book review)

If you placed your finger at that point, the two halves of the string would still be able to vibrate in the sin 2x pattern, but not in the sin x one. This explains the Pythagorean discovery that a string half as long produced a note one octave higher.” (p.143)

The following chapters are all about Physics: the wave equation, Fourier’s transform and the heat equation, Navier-Stokes’ equation(s), Maxwell’s equation(s)—as in  The universe in zero word—, the second law of thermodynamics, E=mc² (of course!), and Schrödinger’s equation. I won’t go so much into details for those chapters, even though they are remarkably written. For instance, the chapter on waves made me understand the notion of harmonics in a much more intuitive and lasting way than previous readings. (This chapter 8 also mentions the “English mathematician Harold Jeffreys“, while Jeffreys was primarily a geophysicist. And a Bayesian statistician with major impact on the field, his Theory of Probability arguably being the first modern Bayesian book. Interestingly, Jeffreys also was the first one to find approximations to the Schrödinger’s equation, however he is not mentioned in this later chapter.) Chapter 9 mentions the heat equation but is truly about Fourier’s transform which he uses as a tool and later became a universal technique. It also covers Lebesgue’s integration theory, wavelets, and JPEG compression. Chapter 10 on Navier-Stokes’ equation also mentions climate sciences, where it takes a (reasonable) stand. Chapter 11 on Maxwell’s equations is a short introduction to electromagnetism, with radio the obvious illustration. (Maybe not the best chapter in the book.) Continue reading

17 equations that changed the World (#1)

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , on October 15, 2012 by xi'an

I do not know if it is a coincidence or if publishers were competing for the same audience: after reviewing The universe in zero word: The story of mathematics as told through equations, in this post (and in CHANCE, to appear in 25(3)!), I noticed Ian Stewart’s 17 equations That Changed the World, published in 2011, and I bought a copy to check the differences between both books.

I am quite glad I did so, as I tremendously enjoyed this book, both for its style and its contents, both entertaining and highly informative. This does not come as a big surprise, given Stewart’s earlier books and their record, however this new selection and discussion of equations is clearly superior to The universe in zero word! Maybe because it goes much further in its mathematical complexity, hence is more likely to appeal to the mathematically inclined (to borrow from my earlier review). For one thing, it does not shy away from inserting mathematical formulae and small proofs into the text, disregarding the risk of cutting many halves of the audience (I know, I know, high powers of (1/2)…!) For another, 17 equations That Changed the World uses the equation under display to extend the presentation much much further than The universe in zero word. It is also much more partisan (in an overall good way) in its interpretations and reflections about the World.

In opposition with The universe in zero word, formulas are well-presented, each character in the formula being explained in layman terms. (Once again, the printer could have used better fonts and the LaTeX word processor.) The (U.K. edition, see tomorrow!) cover is rather ugly, though, when compared with the beautiful cover of The universe in zero word. But this is a minor quibble! Overall, it makes for an enjoyable, serious and thought-provoking read that I once again undertook mostly in transports (planes and métros). Continue reading

the universe in zero words

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , , , , , , , , , on May 30, 2012 by xi'an

The universe in zero words: The story of mathematics as told through equations is a book with a very nice cover: in case you cannot see the details on the picture, what looks like stars on a bright night sky are actually equations discussed in the book (plus actual stars!)…

The universe in zero words is written by Dana Mackenzie (check his website!) and published by Princeton University Press. (I received it in the mail from John Wiley for review, prior to its publication on May 16, nice!) It reads well and quick: I took it with me in the métro one morning and was half-way through it the same evening, as the universe in zero words remains on the light side, esp. for readers with a high-school training in math. The book strongly reminded me (at times) of my high school years and of my fascination for Cardano’s formula and the non-Euclidean geometries. I was also reminded of studying quaternions for a short while as an undergraduate by the (arguably superfluous) chapter on Hamilton. So a pleasant if unsurprising read, with a writing style that is not always at its best, esp. after reading Bill Bryson’s “Seeing Further: The Story of Science, Discovery, and the Genius of the Royal Society“, and a book unlikely to bring major epiphanies to the mathematically inclined. If well-documented, free of typos, and engaging into some mathematical details (accepting to go against the folk rule that “For every equation you put in, you will lose half of your audience.” already mentioned in Diaconis and Graham’s book). With alas a fundamental omission: no trace is found therein of Bayes’ formula! (The very opposite of Bryson’s introduction, who could have arguably stayed away from it.) The closest connection with statistics is the final chapter on the Black-Scholes equation, which does not say much about probability…. It is of course the major difficulty with the exercise of picking 24 equations out of the history of maths and physics that some major and influential equations had to be set aside… Maybe the error was in covering (or trying to cover) formulas from physics as well as from maths. Now, rather paradoxically (?) I learned more from the physics chapters: for instance, the chapters on Maxwell’s, Einstein’s, and Dirac’s formulae are very well done. The chapter on the fundamental theorem of calculus is also appreciable.

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