The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are Like Gossip. Keith Devlin. xvii + 328. Basic Books/Perseus, 2000. $25.
Why is mathematics like a soap opera? Answer: Both deal with imaginary relationships. Armed with this dubious insight, and fortified by the rapidly growing literature on evolution of the mind, mathematician Keith Devlin proposes here an answer to one of the most difficult questions of human biology: How did our ancestors acquire a mind for mathematics?
Every month or so a new book appears seeking to explain some human characteristic in terms of the selective advantage it supposedly provided our distant ancestors. Although the benefits for genetic survival of some behaviors are reasonably clear, others—such as altruism—seem puzzling.
One of the more mysterious is mathematics. What possible genetic advantage might be conveyed to a hunter-gatherer who was prone to daydream about abstract ideas? Most likely, any budding prehistoric mathematician would have met a fate similar to that of Archimedes, who it is said was killed by a Roman centurion because, being preoccupied with a mathematical problem, he failed to take appropriate notice of the soldier.
According to The Math Gene, an important clue to resolving this puzzle can be found in that bad joke about mathematics, soap operas and imaginary relationships. People clearly have an extraordinary interest in human relationships. Indeed, most of the world's literature and a great deal of media attention are devoted to this subject: History and the news report on real relationships, and fiction and soap operas portray imaginary ones. Thinking about relationships—what Devlin calls "gossip"—is one of the most common preoccupations of the human mind.
In this clear and engaging analysis, Devlin sets forth a thesis quite contrary to common experience: that reasoning about relationships between mathematical objects is no different from reasoning about human relationships between people, and that this similarity in reasoning explains the origin of mathematics.
Devlin's argument develops along several parallel tracks. One concerns the nature of mathematics as an enterprise very different from arithmetic. Mathematics requires nuanced understanding of relations among abstract patterns. Complex mathematical structures are built, like nested Russian dolls, by encapsulating into new patterns specific relationships among simpler patterns.
Another line of reasoning concerns the nature of language. Devlin argues that the syntactic structure of all human languages can be represented with tree diagrams built from a single simple pattern—a Lego block of language—that he calls the "fundamental language tree." The many different grammars in the world all use the same phrase structure built by repeated nesting of this simple pattern.
A third source of evidence is the fossil record of hominoid evolution, which shows significant growth in brain size for several million years without a corresponding increase in the use of either language or tools. Then suddenly (in evolutionary time), the distinctively human traits of language, symbols and tools appeared.
Devlin argues that our ancestors' increase in brain size was driven not by acquisition of language (as most standard theories assert) but by the selective advantage conferred by a richer understanding of relationships among objects in the physical environment and in an increasingly complex social world. Once the brain reached sufficient size and complexity, it rather quickly developed the capacity for what Devlin calls "off-line" or "what-if" thinking—the capacity to reason hypothetically about relationships and abstractions that undergirds both language and mathematics.
Thus, according to this argument, when the human brain acquired the ability to use language, it automatically acquired the ability to do mathematics. It follows, contrary to popular wisdom, that everyone has a metaphorical "math gene." It is not genetics but interest that makes the difference between those who are hooked on mathematics and those who prefer soap operas.—Lynn Arthur Steen, Mathematics, St. Olaf College, Northfield, Minnesota