|Jan/Feb 2001 Book Reviews|
Weidenfeld & Nicolson
Dr Devlin starts this book by stating that although his thesis is consistent with all the evidence that he is aware of, he knew from the start it would be controversial as some of the scientific territory covered is hotly debated.
Firstly Dr Devlin sets out to define mathematics and here he rather labours the point. I liked mathematics at school and university and today still enjoy solving what may be described as simple mathematical problems. However in this book I got bored and I'm afraid a lot of his readers will feel the same and may give up. Which is a pity, as the second half of the book in which he postulates a theory on how our mathematical ability developed is much more interesting.
He begins by stating that Homo sapiens—the wise hominid—emerged some 300,000 years ago with a brain size of some 1350 cubic centimetres; a three times increase in size from the brain size of Australopithecine, and some nine times larger than is normal of our body size. It grew to this size in some 3,500,000 years ending about 300,000 years ago and given the large energy resources needed to maintain this size of brain, the advantage conferred must have been significant. Otherwise it would have it disappeared. He suggests various reasons why this happened and the need for language is not the primary one. Language, he tells us developed only some 75,000 - 80,000 years ago, or at the most 200,000 years ago.
So what were the reasons? Well the key one was the need for man to act smarter. Man, compared to the other predators was small, slow and ill armed (no claws or large teeth). He needed to develop the ability to hunt by tracking, to recognize the type of animals he was following from their tracks and estimate their physical well being. In other words he needed to develop the skills of pattern matching. And as his brain increased in size he developed a richer view of the world (more patterns could be recognized), a greater bag of tricks to aid survival (in the form of responses to particular patterns of stimuli), and a more effective means of communication with others with whom he hunted (a proto-language).
Dr Devlin goes to say that once the brain reached a certain size a new ability developed: off-line thinking. That is the ability to think about a thing without seeing it of even knowing that it exists. In other words, off-line thinking is thinking about a world of internally generated symbols that may or may not correspond to real objects, and if they do, may relate to objects that we have not seen for several years. Or it is thinking activity in the brain caused by the brain itself, not caused by any external stimulus and ending without the production of an automatic body response; the brain itself creating the initialising activation pattern, leading to a capacity to think in a "what if" fashion.
It is from this, he tells us, that man's language skills developed. Not as a need to communicate face to face, that being achieved using a sufficiently rich proto-language, but arising, almost by chance, as a by-product of acquiring the ability for an even richer understanding of the world man found himself in. As man's understanding of the world around him expanded so the need to describe this world also developed and language developed from proto-language. Man acquired the ability to think using symbols.
And so to the main thrust of the book: how did humans acquire the ability to do mathematics? In a nutshell Dr Devlin shows that mathematical thought is just a special type of off-line thinking—which anyone can do—and that the maths gene and the language gene are one and the same. Which raises the second question inherent in the title of this book: why do so many people think they cannot do mathematics? Well for the answer to that you'll have to read the book.