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What Shape is a Snowflake? Hardcover – 13 Sep 2001
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For years Ian Stewart has been wrestling with the mathematical underpinnings of the natural world. In his new book What Shape is a Snowflake? he explains his fascination with nature's numbers and explores the fruits of his quest so far. No, wait! There isn't a single equation in the book--honest.
Stewart starts with a general exploration of patterns in nature--six-pointed snowflakes, feathery patterns of frost on glass, zebra stripes, ripples in the sand, honeycombs, spirals, and so on--then attempts to illustrate, in words, the mathematical principles underlying them. In the process the reader is introduced to ideas of dimensionality, symmetry in all its manifestations, patterns of tiling and packing, symmetry breaking, fractals, complexity theory and chaos. In the penultimate chapter he goes on to explain how the mathematics of earthly nature may mirror that of the universe. Finally he addresses the question of the book's title: What shape is a snowflake? You may be disappointed with the answer, but only if you don't get the joke.
Snowflake is a fascinating read, though it does requires a bit of patience. Much space in the first half of the book is given over to introducing patterns without offering many clues as to what generates them. In consequence, I found myself skipping sections to get to the juicier bits towards the end. Still, for the numerically challenged but patient reader, Snowflake is as friendly an introduction to the mathematics of nature as you could wish to find.--Chris Lavers
An enlightening vision of how the laws of mathematics find organic expression in the beauty and patterns of nature, written by an internationally acclaimed mathematician and science writer.See all Product description
Top customer reviews
The book attempts to explain the formation of snowflakes in detail, taking a long journey through the processes of nature; pattern-formation, symmetry, complexity, chaos theory & more. These ideas are examined from the atomic level, through to the cosmic scale.
Whilst much of this is interesting, the book sometimes varys from over-simplicity to complex ideas, and often takes a long route to reach these concepts. I also found that sometimes the context of Ian Stewart's text (and very occasionaly, the grammer itself) could be difficult to fully understand - although this may be down to differences in the way which I look at things.
Much of this journey is neatly tied-up in the final chapter on the snowflake itself; it's just that the trip itself is not always completely satisfying.
Interesting and worth a read, but not the most engaging book I have ever read.
Why indeed, is a snowflake the overall shape it is and why is every single one unique in the detail. Stewart does what many other science writers do in popularising his subject but it is in the detail that he is unique, and fascinating.
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Then he delves into the Why and How of patterns that manifest themselves in everything around us: big and small, living and non-living, spirals, wiggles, cycles, mirror symmetry, rotational symmetry, tiling patterns, spots and stripes, waves, lattices, and even patterns in time. When reading about patterns in living things, I could not help but doubt mathematical explanations of biological processes. But Stewart acknowledges this problem and makes the case that the principles underlying which patterns can and will occur may be governed by mathematics, though the patterns are coded in genetics.
The book's final section delves into some apparent inconsistencies in the links between mathematical laws and nature's patterns and mathematicians' continuing efforts to explain them with theories of bifurcation, symmetry-breaking, and fractal geometry. Finally, Ian Stewart answers that question about snowflakes -but not before he has posed a new question: What Shape Is the Universe? "What Shape is a Snowflake?" is a nice introduction to the mathematics of pattern formation for the layperson. It presents the ideas behind the patterns without mathematical formulae and with a great many color photographs and illustrations. It will pique the reader's interest in everything from ancient Pythagorean math to modern chaos theory by giving us a sense of what humans have learned about patterns and what continues to elude us.
The snowflake is key to his tour, and there is plenty to learn specifically from it, but since Stewart is keen to draw on patterns all over the place, the range of his book is amazing. In well connected chapters, looking closely at snowflakes takes him to the leafy patterns of frost on the window, the organization of leaves around spirals and Fibonacci numbers, the spiral of the nautilus shell, the stripes and amazing triangle patterns on other sea shells, the patterns of stripes on zebras and fish, the grooves in sand dunes and the lines of dunes themselves, the lines a sidewinder leaves in the sand, the synchrony of a millipede's legs and a horse's at different gaits, the oscillations of the legs of robots, the ups and downs of animal populations, the chaotic variations of weather and of the planets in the solar system, and the shape of the universe. It is clear that Stewart sees connections everywhere, and is only using the snowflake as an excuse to look at the foundations of physical laws, the nature of time, space, and matter, and why patterns in one field give clues to patterns in something entirely different. "I'm going on a journey in search of the snowflake's secret," he says, "and, with it, the deeper secrets of our astonishing universe. And you're coming with me." It's a beguiling invitation from a masterful guide.
Naturally a tour of this type, with all it encompasses, is not going to be long on detail, and anyway, one would have to start getting into equations for that. There is a useful list for further reading at the back of the book, for those who insist on stronger doses of such stuff. Stewart's book, however, is an exhilarating, accessible, vividly illustrated voyage through classic and current mathematical ideas. By the end of it, a reader will understand that the snowflake's shape is determined by phase transition, bifurcation, symmetry-breaking, chaos, fractals, and other complexities. Oh, and the book does eventually reveal what shape a snowflake is.
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