Discovering Order and Pattern in the Universe
Phoenix, London, 1996
From Stewart's over-worked word-processor comes another romp through a network of mathematical notions, this time on the subject of symmetry. This takes us from petals to violins, and from crystals to cheetahs.
This is pop science, not technical mathematics, and with only 170-odd pages of large print, it needn't take weeks to get through, but the reader will find many engrossing ideas along the way. Anyone who is seriously interested in patterns in Nature, as opposed to those who prefer to play around with attaching arbitrary significance to numerals, will get rewarding glimpses of how one branch of mathematics may throw light on another, and thence on how the world works.
Stewart's main point is that,
"nature's rhythms are often linked to symmetry, and that the patterns that occur can be classified mathematically by invoking the general principles of symmetry-breaking."
This notion is applied to the gaits of animals, so that, for instance, the pattern of movement of a horse's legs as it breaks into a gallop from a trot can be understood as an instance of symmetry-breaking.
From an evolutionary point of view, one of the implications seems to be the economies of organization that would be enabled by not having certain phenotypical complexities coded for in detail in the genotype. If patterns such as the Fibonacci series can be "brought to bear" in some way (e.g. in the primordia of plants), then the resultant patterns of development or behaviour may be complex yet derivable from relatively simple generative systems.
Those who, like Queneau, might wish to pursue connections with mathematics and the arts should find this well worth reading.
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© Paul Taylor 2001