Counting on Our Brains Biochemistry

book reviews Today, no major economy is without the pro- humans: behavioural experiments reveal Chronometric tests reveal at least two tection of an independent nuclear arsenal or that many animals can also attend to major impairments. First, Charles cannot a nuclear umbrella; and disarmament seems numerosity. What makes the human numer- “subitize”: he cannot decide how many a dream, like nirvana. I ical ability unique, however, is that it can be items are presented on a computer screen, Brahma Chellaney is at the Centre for Policy extended through the invention and spread- even if there are only two or three, unless Research, Dharma Marg, Chanakyapuri, ing of cultural tools, such as number symbols he painstakingly counts them one by one. New Delhi 110021, India. and arithmetic algorithms. Second, he has an abnormal intuition of In recent years, the cognitive neuro- number size, which is reflected in an inverse science of numeracy, or ‘numerical cogni- distance effect in a number-comparison tion’, has emerged as an important area task: whereas we normally take less time to where the interaction between brain archi- decide which of two numbers is larger as the Counting on tecture and human culture can be studied distance between them gets larger, Charles empirically. The hypothesis of a modular takes more time for more distant numbers, our brains architecture underlying number processing presumably because he is using a very in- The Mathematical Brain has been fruitful in many areas of research, direct counting strategy. by Brian Butterworth from developmental psychology to brain Charles has not been subjected to brain Macmillan: 1999. 480 pp. £20 imaging, animal behaviour or behavioural imaging, but another case of developmental Stanislas Dehaene genetics. Several previous reviews of these dyscalculia, recently scanned with the novel findings are available, some aimed at technology of magnetic resonance spec- “One, two three, four. My mathematics fin- specialists (for example, The Nature and troscopy, shows a small, isolated area of ishes here.” Those are the words of Signora Origins of Mathematical Skills by J. I. D. damage exactly where number circuits are Gaddi, an alert, 59-year-old Italian woman Campbell; Elsevier, 1992), others at a wider postulated to lie — the left inferior parietal whose puzzling impairment has helped audience (for example, The Number Sense cortex. neuroscientists understand how the brain by S. Dehaene; Oxford University Press, The finding that early focal brain dam- does arithmetic. Signora Gaddi suffered a 1997). The Mathematical Brain falls into the age can have such a permanent and restrict- stroke that damaged the left parietal lobe of second category: it is a skilful overview of the ed effect on mathematical competence is her brain. Since then, she has become large- area for the non-specialist, with remarkable perhaps the best evidence to date in favour ly hopeless with arithmetic. She cannot depth and breadth in many cases, but of the number-module hypothesis. Such read, write, compare or calculate with any with occasional oversights that may frus- evidence imposes strong limits on brain numbers other than one, two, three and trate the expert. plasticity and clearly speaks against purely four. Even with numbers below four, she is Butterworth’s review of prehistory is constructivist theories that view mathe- definitely not performing normally. For particularly original and commendable. He matical competence as the result of a gener- instance, when shown two wooden blocks, convincingly pulls together little-known al learning device. she has to laboriously count on her fingers evidence from cave-paintings and bone- In the end, I suspect that Butterworth’s in order to establish their numerosity. carvings to suggest that the dawn of arith- hypothesis of a direct link between genes, Because Signora Gaddi performs normally metic in stone-age populations dates back number circuits and higher mathematical on many other tests that do not involve at least as far as 30,000 years. More puzzling, competence may be too simple. Still, the numbers, her affliction can be described as however, is the almost complete omission of cogent arguments of The Mathematical a selective loss of arithmetic. brain-imaging evidence in the discussion of Brain should be required reading for any- The detailed study of Signora Gaddi is the neural bases of the number module. one interested in the modularity of higher just one of many fascinating pieces of Although the modern tools of positron cognitive functions. I evidence gathered by Brian Butterworth in emission tomography, functional magnetic Stanislas Dehaene is at Unité INSERM 334, his effort to illuminate the relations between resonance imaging and electro- and mag- Service Hospitalier Frédéric Joliot, 4 Place du brain, mind and mathematics in his book neto-encephalography have been applied Général Leclerc, 91401 Orsay cedex, France. The Mathematical Brain. The title itself is only recently to mathematical cognition, a something of a misnomer, for one would review of the available evidence would have search this volume in vain for investigations been welcome, especially since it confirms of the cognitive bases of higher mathematics, the presence of numerical circuits in a local- or even of simple geometry, algebra or topol- ized brain region: the left inferior parietal Biochemistry: a ogy. The book focuses on a single mathemat- region. ical object, but one that is rightly seen by Specialists will be delighted, however, by biography Butterworth as a fundamental cornerstone Girelli and Butterworth’s latest evidence on Proteins, Enzymes, Genes: The of the mathematical edifice: the concept of developmental dyscalculia, some of which is Interplay of Chemistry and Biology number. published here for the first time. If there is a by Joseph S. Fruton Butterworth’s central hypothesis is that genetic plan for a number module, then one Yale University Press: 1999. $45, £30 our brain is “born to count”. Our genes con- might expect to find an occasional child who Charles Tanford and tain instructions that specify how to build a is born without it, either due to a genetic Jacqueline Reynolds number module, a set of neural circuits defect or to pre- or perinatal cerebral dam- specialized for processing numbers. Those age. Butterworth claims to have identified F. Gowland Hopkins, Cambridge Universi- circuits, which are associated in part with the one such patient, Charles, who is “born ty’s first professor of biochemistry and left inferior parietal lobe, make us sensitive blind to numerosities”. Although Charles is recipient of a Nobel prize for his work on to numerosities in our environment and now a very bright adult, with a university vitamins, said in a lecture delivered in 1927: allow us to understand and to manipulate degree in psychology, he has experienced “Biology and chemistry, though in their numbers mentally. Loss of those circuits, as profound, lifelong difficulties in math- infancy both foster-children of medicine in Signora Gaddi’s case, results in a selective ematics, to the point of still having to count and passing their childhood in company, inability to grasp the meaning of numbers. on his fingers in order to solve single-digit have long occupied domains which, though The number module is not unique to addition problems. never really far apart, have sometimes 114 © 1999 Macmillan Magazines Ltd NATURE | VOL 401 | 9 SEPTEMBER 1999 | www.nature.com book reviews seemed to be so. But their proper domains, while extending in all directions, have now definitely met at a frontier which is surely a Biology’s structurally region of supreme importance for both.” (From Hopkins and Biochemistry, edited by sound foundations J. Needham and E. Baldwin; Heffer, 1949.) Structure and Mechanism in That new frontier, of course, is now called Protein Science: A Guide to biochemistry. Enzyme Catalysis and Protein Some 45 years after Hopkins’ address, Folding Joseph Fruton wrote Molecules and Life by Alan Fersht (Wiley, 1972), which documented some of W. H. Freeman: 1999. 614 pp. $47, £27.95 the history of the new frontier between Gregory A. Petsko organic chemistry and biology. That book (now out of print) forms the basis for Pro- Genome sequences now accumulate so teins, Enzymes, Genes. quickly that, in less than a week, a single The broad scope of Fruton’s book makes laboratory can produce more bits of data it an ambitious undertaking, surely requir- than Shakespeare managed in a lifetime, ing a lifetime of devoted reading and Alternative structure although the latter make better reading. research. And this is what Fruton has With this flood of data comes a demand for obviously given to the task, as evidenced by catalyses art market an understanding of the three-dimensional 248 pages of notes, references and bibliogra- Artist Damien Hirst has found a more structure and function of the proteins phy (in small print), following 494 pages of lucrative way of representing molecules than encoded by these genes. But while sequenc- text. Nothing like this can be found in the have most structural biologists. Carbon ing genes is easy, it is not so easy to deter- 1972 book. It is an invaluable scholarly monoxide (above) is featured in This is Modern mine a gene product’s function or the resource and may be the most important fea- Art by artist and commentator Matthew mechanism by which it acts. ture of the new edition, the best justification Collings (Weidenfeld & Nicolson, £20), an Two seemingly unrelated subjects — pro- for buying the new book even if one already eye-opening tour around contemporary art. tein folding and enzymology — are among has the old one. There is also a subject index the fields being enlisted to aid in this enor- in the new edition, frustratingly absent in mous task: the former in the hope that we the old.

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