Nature's Numbers

Ian Stewart

This a finest sample of the Mathematics-without-formulas book. There is no condescension. The formulas are omitted just because they are not needed. There is so much to learn any way, formulas would obscure the richness of the ideas presented in the book.

One of these ideas dating back to Poincare's phase portraits and having been revitalized by the modern development of the Chaos Theory, applies perfectly to the book itself. Phase portraits depict global behavior of a system as opposed to deriving solutions dependent on initial data. I would say that the author succeeded admirably in constructing a phase portrait of the recent evolution in both mathematical theory and perceived utility of mathematics by other sciences.

Written in a very intelligent style, the book is extremely informative. Read the excerpt below. Does it jibe with your notion of a mathematical text?

The seven most common quadrupedal gaits are the trot, pace, bound, walk, rotary gallop, transverse gallop, and canter. In the trot, the legs are in effect linked in diagonal pairs. First the front left and back right hit the ground together, then the front right and back left. In the bound, the front legs hit the ground together, then the back legs. The pace links the movements fore and aft: the two left legs hit the ground, then the two right. The walk involves a more complex but equally rhythmic pattern: front left, back right, front right, back left, then repeat. In the rotary gallop, the front legs hit the ground almost together, but with the right (say) very slightly later than the left; then the back legs hit the ground almost together, but this time with the left very slightly later than the right. The transverse gallop is similar, but the sequence is reversed for the rear legs. The canter is even more curious: first front left, then back right, then the other two legs simultaneously. There is also a rarer gait, the pronk, in which all four legs move simultaneously.

The pronk is uncommon, outside of cartoons, but is sometimes seen in young deer. The pace is observed in camels, the bound in dogs; cheetahs use the rotary gallop to travel at top speed. Horses are among the more versatile quadrupeds, using the walk, trot, transverse gallop, and canter, depending on circumstances.

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