Amongst the arcana of contemporary neuropsychology there is an emerging consensus that, like Chomsky/Pinker's "language instinct", we have an innate sense of arithmetic. In this new book, Butterworth, a professor at University College London and editor of the journal Mathematical Cognition, covers a great deal of the same territory as The Number Sense by French mathematician and neuroscientist Stanislas Dehaene.
Butterworth's book is a thesis driven through a litany of facts, selected experiments, and the tangled archaeology of numbers: from our base-10 "Arabic" numerals with their place-value system , which actually emerged from the Hindu poet-astronomers of the Indus Valley in the first millennium BC; back through the chronically useless Roman numerals (abaci and counting boards were used for anything more complicated than addition); Sumerian cuneiform base-60 clay tablets from 1,900 BC; and into simple bodycounting systems like that of the Yupno people of Papua New Guinea who, starting from their left little finger cross from left to right of their bodies, ending up with the penis at 33 (apparently Yupno women don't count in public).
Butterworth speculates that even our Neanderthal cousins could count, and cites evidence to suggest similar skills in chimps, songbirds, jackdaws and even the dance of the honey bee. After which, one is hardly surprised that, from stare-timing experiments, psychologists believe that new-born babies can "subitise" - recognise at a glance without counting - up to four dots; displaying an innate sense of abstract "numerosity" before children ever speak or learn number words, let alone multiplication tables.
Butterworth also delves into neurology: from the 1950s horror stories of Wilder Penfield's brain mapping (electrically stimulating the open brains of awake but locally anaesthetised patients) to bizarre "dyscalculic" brain-damage cases; from the Vietnam vet who lacked a whole portion of his left-brain; to an Austrian woman who, after a stroke, could multiply by rote, yet could not add or even count on her fingers.
Butterworth uses these cases well to point up discrete mechanisms for reasoning, short term and "semantic" memory (rules and tables), and even subtraction and multiplication. Finally, he locates his "number module" in a nubbin of grey matter on the left parietal lobe of the brain, even speculating that nearby sensory representations of fingers in the brain are highly interconnected with this area.
He argues further that this is genetically determined, citing Fragile X Syndrome, a weakness on the long arm of the X chromosome which often correlates with the controversial Gerstmann's Syndrome, a complex of symptoms which include inability to tell apart sensations in different fingers, left from right, and indeed to calculate or write. He likens this to other X chromosome defects such as Turner's Syndrome, and indeed some forms of colour-blindness.
Elsewhere, Butterworth jaunts through anecdotal biographies of idiot savants and prodigies like Ramanujan, and as to why people are so lousy at maths he lays the blame squarely at the feet of educationists, without really explaining a great deal.
At over 400 pages, this is a windy and often repetitive book, which isn't quite as engaging as Dehaene's. And with regard to the fascinating archaeology of numbers, you will be far better served by a beautiful new book by another Frenchman, Georges Ifrah, The Universal History of Numbers.
Mic Moroney is a freelance journalist