The Beauty of Numbers in Nature, by Ian Stewart
Ian Stewart is the Emeritus Professor of Mathematics at the University of Warwick, England. He’s written over 140 scientific papers, including papers co-authored with Jim Collins on coupled oscillators and the symmetry of animal gaits (more on this later), worked with Dr. Jack Cohen and Terry Pratchett on the Science of Discworld books (1-4). He’s also co-written 2 SF books with Cohen – “Wheelers” and “Heaven.” And, he wrote the Mathematical Recreations column for Scientific American from 1991 to 2001. After all of this, I still hadn’t heard of him prior to reading this book. I’d been asked for Christmas gift ideas back at the beginning of December, so I went on Amazon and surfed around for any math and science books that caught my eye. Beauty of Numbers seemed promising, so that was one of the three I settled on (the other two were “Proof: the Science of Booze“, and anything by Roger Penrose).
It was funny, right after I opened Beauty of Numbers, I saw a couple nice animal photos, which I then showed to a Japanese friend that loves that kind of thing. But, she just raised her nose, sniffed, and said that the Japanese science magazine, Newton, does it better. As I continued to read BoN, I kind of had to agree with her. The subject Stewart chose is something that fits in with Newton – examples of symmetry, patterns, chaos and dynamic systems that show up in our universe (from the stripes and spots on animals, fish and birds, to spirals on shells, in weather patterns, and in galactic formations), with accompanying math and physics explanations. Except that Newton would do it in 40-50 pages, while Stewart took 212 pages, and they’d include tons of huge glossy photos and powerpoint graphs to illustrate the point. BoN, in turn, has only a few smaller photos or illustrations per page, and virtually no real math.
Another thing that struck me was that a lot of the topics he picked are also ones that showed up in Martin Gardner’s Colossal Book of Mathematics, (50 of Gardner’s best Scientific American Mathematical Recreations articles), including symmetry, topology, Penrose tiling, Escher paintings, chaos, and Conway’s cellular automata. But with less emphasis on the math and science parts. BoM reads like an updating of Colossal for adults that are curious about nature, but fear equations. The closest he gets to formulas is with an explanation of how to form Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 84…) and how taking the ratio of two successive numbers (55/84, or 84/139) gets you closer to an approximation of the Golden Ratio. It gets kind of maddening after a while, especially when he talks about using mathematical oscillators (above) to explain how to model the way animals and insects walk, without actually saying what the model looks like mathematically. Personally, I would have loved to see a real example of system modelling for a horse versus a centipede, instead of just being told that he’d done work on this kind of thing.
Anyway, Ian starts out by asking “Does being a mathematician ruin one’s appreciation of nature, like knowing how a magic trick works lessens the wonder you feel when you see the trick done?” (Of course, his answer is that knowing how nature works just makes it that much more amazing.) He then uses a story of having seen fern-like frost formations on the window of his room when he was a child to ask “how do snowflakes form?” The famed astronomer Kepler had compiled a book on snowflakes and tried to answer that question himself. Ian then goes on to establish a vocabulary to hang the answers from, starting with the different kinds of symmetry (rotational, translational, reverse, mirror, and time), then moving into how Alan Turing’s work could be applied to show how chemical inhibitors and accelerators in animal skin, plants and seashells can create the spots, stripes, and apparently random patterns we can see in nature. It takes a while to get to Einstein’s theory of general relativity as it applies to gravity on a galactic, and even universal scale to explain how we get spiral galaxies, and a (possibly closed universe), and the discussions of symmetry breaking and chaotic dynamic systems. After all of this, he returns to the snowflake, and how its formation is dependent on factors like humidity level, temperature, symmetry, hexagonal crystal formation, wind speed and direction, and gravity to give us beautiful 6-sided ferns and flakes that all look unique.
Summary: There’s nothing “wrong” with BoN. It’s an easy read, and it does cover a wide range of topics. Names that Ian drops include Feynman, Kepler, Einstein, Alan Turing, Roger Penrose, Conway, M.C. Escher, Newton, and many others that are leaders in their fields. As mentioned above, it’s like an updated edition of Martin Gardner’s Colossal Book of Mathematics, and adding a little more on quantum mechanics, while name-dropping string theory and M-theory. But, it’s somewhat like Proof: The Science of Booze, in that there’s a lot of trivia that may give you something to talk about at parties, but it’s not going to make you feel seriously smarter. If you like Big Bang Theory, you’ll probably like BoN.
The Chief
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