The New Mathematics of the Living World

Ian Stewart

Penguin, London, 1998.

Like "Nature's Numbers", this book argues for the central importance of patterns in biology, but does so in more detail. The main point is that it is neither feasible nor necessary for genes to specify the patterns of organisms, vital as genetic instructions obviously are. The other secret of life, apart from DNA, is the pre-existing mathematical structures available to organisms as they develop. There is some fascinating stuff to ponder, together with quite a few oddities.

It could be said that Stewart is picking up where D'Arcy Thompson left off, and each chapter begins with a quotation from the latter's "On Growth and Form". This is a tricky business, needless to say, but Stewart provides much experimental work to support the general thesis. In this endeavour he and Goodwin are mutual admirers.

One aspect of the difficulty with all this is hinted at in this passage at the end of a chapter on Fibonacci sequences and flowers:

"Fractal mathematics is the way we humans come to grips with these particular regularities of the universe - just as calculus is the way we come to grips with the regularities of gravitation. This is how mathematics works: It is our language for understanding nature's patterns. What of the genes? They tell the plant which plant it should be. That is, they select a particular assortment of patterns from the physical grab bag. The patterns themselves, however, are provided by mathematical rules - and unless we understand these rules, and what mathematics they conceal, the true role of the genes will forever remain mysterious." (p.136)

Note here how nature has patterns, and mathematics is our language for understanding them. But then, these patterns turn out to be provided by mathematical rules. So genes speak our language?

There is further discussion of animal gaits in this book, which is illustrated by a diagram of how camels walk: four rows of drawings, each of four stages of the gait. I stared at this like it was a "spot the difference" test, and saw that each row was identical. Very illuminating.

There is some reference to Dawkins' selfish gene theory, and, as with Stewart's chum, Goodwin, there seems to be something awry in the representation.

"The concept of the selfish gene is a clever and dramatic way to explain some peculiarities of DNA sequences, such as junk DNA, the function of which is unknown, but which still gets replicated along with the rest of the genome." (p.235)

The reader of "The Selfish Gene" or "The Extended Phenotype" will soon see that this is not what the concept is about. Dawkins explicitly says that he sees selfish DNA as only a special case of the general selfish gene theory.

Stewart goes on:

"However, it is equally possible to promote the slavish gene theory, in which genes worry enormously about the survival of their organisms. (If the genes don't produce a viable organism, they die out, right?) Maybe the selfish gene theory has more going for it than I think, but even if it does, it is the story told on the level of the gene. The gene may in some meaningful sense focus on getting itself replicated - but that doesn't mean that humans focus on getting their genes replicated."

That'll be a joke, right? Or is this just clueless? That's equally possible, right?




Paul Taylor 2001