Mathematics Gene

  • show transcript
Saturday 18 November 2000 12:14PM (view full episode)

Is mathematics hard-wired into our brain? Do words, numbers & music use the same brain cells? Can animals count? Do we have a gene for maths?


Robyn Williams: Now three books on maths. The first is on tape for those who can't read well or just want to listen. Ian Stewart reading Nature's Numbers. Here's a brief extract.

Ian Stewart: "Over the centuries the collective minds of mathematicians have created their own universe. I don't know where it is situated. I don't think that there is a 'where' in any normal sense of the word. But I assure you that this mathematical universe seems real enough when you're in it. And not despite its peculiarities but because of them, the mental universe of mathematics has provided human beings with many of their deepest insights into the world around them.

I'm going to take you sightseeing in the mathematical universe. I'm going to try to equip you with a mathematician's eyes and by so doing I shall do my best to change the way you view your own world."

Chapter 1. The Natural Order.

"We live in a universe of patterns. Every night the stars move in circles across the sky. The seasons cycle at yearly intervals. Notice, snow flakes are never exactly the same but they all have sixfold symmetry. Tigers and zebras are covered in patterns of stripes. Leopards and hyenas are covered in patterns of spots. Intricate trains of waves march across the oceans. Very similar trains of sand dunes march across the desert. Coloured arcs of light adorn the sky in the form of rainbows and a bright circular halo sometimes surrounds the moon on winter nights. Spherical drops of water fall from clouds.

In the mind and culture have developed a formal system of thought for recognising, classifying and exploiting patterns. We call it mathematics. By using mathematics to organise and systematise our ideas about patterns, we have discovered a great secret. Nature's patterns are not just there to be admired they are vital clues to the rules that govern natural processes."

Robyn Williams: Ian Stewart, Professor of Maths at Warwick University reading Nature's Numbers. Orion Audio Books, distributed here in Australia by Allen and Unwin. Our second book is by Brian Butterworth who's in Melbourne this week from Britain. I'll tell you his title in a minute. At the moment he's working on where numbers go in the brain and it really matters.

Brian Butterworth: Well, some people like for example Piaget, argued that really mathematics was no more than an extension of logic and the mathematician Keith Devlin in a recent book called the 'Maths Gene', has argued that maths is nothing more than an extension of language. Now modern scientific approaches to how the brain deals with numbers and other aspects of mathematics shows that really there are separate parts of the brain that deal with maths on the one hand, deal with reasoning on the other deal and deal with language on the third hand.


There's a very interesting novel by Ken Follett called the 'Hammer of Eden' in which one of the central characters, I'd better not say whether he's a hero or a villain, is unable to read either letters or numbers but actually truth, as is so often the case, is stranger than fiction. We've found that there are people who can read numbers but can't read words, and my colleague Lisa Cipolotti here at the National Hospital for Neurology, has found that there are people who can read words much better than they can read numbers. I mean, they've had brain damage, which has affected their number reading but left their word reading intact.


Robyn Williams: But is it just a matter of the numbers, recognising the numbers or is it this ability for computation; in other words, putting them together. Is it all in one bag?





They are in a similar position to dyslexics twenty or thirty years ago. It's not a condition that's recognised, no one really knows how to treat it. We're beginning to assemble guide lines for best practice here and it's not absolutely clear how you diagnose it, but I get frantic parents ringing me up and saying, Look, my kid does very well at school in geography, history, English, he's not dyslexic but he's just hopeless at maths. Is it bad teaching? Can I get him extra tuition, will that help? So I say, Well bring him in and we'll give him some tests.

And often we find that these kids are very poor at stuff to do with numbers that really doesn't depend upon education at all. Like, for example, counting dots or saying which of two numbers is larger; is 6 larger than 2. These kids have trouble with that in a way that's very striking. As I say, it's not absolutely clear how to help these children but it is becoming clear how to diagnose them and that's by using these very simple, non education dependant tests like dot counting or number comparison.

Robyn Williams: I don't suppose the same thing would happen with music comprehension because music is often considered to be an add on. You won't have someone brought to you - Look I'm afraid my child can't play the violin to concert performance or sight read Bach?

Brian Butterworth: That's absolutely true. It's not regarded as a great national problem that we're not very musical. But actually not being able to multiply 8 x 7, which our current First Secretary of the Treasury was unable to do in public, isn't regarded as a great social problem, whereas saying we was instead of saying we were, still is regarded as a great social problem.







Robyn Williams: Why is it important to know?


Robyn Williams: Bet they were doing deals.

Brian Butterworth: I wouldn't be surprised.

Robyn Williams: And neither would I. Brian Butterworth is Professor Cognitive Neuropsychology at University College, London. His book is called the Mathematical Brain and it's published by Macmillan. Now for a third maths book, one Professor Butterworth actually mentioned at the beginning. I asked Clio Cresswell to read it for us.

Clio Cresswell: If you think mathematics is an alien activity only a select few can possibly understand let alone actually do, you might just be forced to think again when you read the Maths Gene by Keith Devlin. The Maths Gene is a mathematics book that could just as easily be seen as a very significant work on linguistics or equally a study of evolutionary biology. It could even earn a place in the study of brain anatomy. Above all though it's a great read crammed with an immensely impressive range of thought, research and theory. Devlin considers some fundamental evolutionary dilemmas. He finds it intriguing for example that our brain has taken some three and a half million years to evolve to its present state. Yet the mere concept of abstract numbers has only existed for, at most, 8000 years. What part of our brain do we use then when we use mathematics?

A new part couldn't have developed that fast. So what was it doing why it patiently waited? Was it used or dormant? If used, for what? And if our brain has been evolving for such a long time everyone must possess mathematical ability. What are the minor adjustments needed then for all of us to use it. To answer these questions Devlin first looks at other animals' mathematical prowess. A small group of female lions is capable of working out if another group of lions outnumbers it by simply listening to the amount of roars.

Experiments show the group is even capable of working out if the number of lions they hear differs from the number of lions they see. Devlin moves through the mathematical minds of babies, young children and then adults. The adult human brain has a fantastic ability to handle mathematics way beyond the realm of numbers. Devlin explains that mathematics is a science of patterns not just numbers. Patterns ranging from the familiar right angle or collateral triangles we learn at school to the symmetrical patterns of flowers and the various patterns on animal coats are all part of the mathematical world. Believe it or not mathematics explains why animals can have coats with spotted bodies and striped tails but not striped bodies with spotted tails. Spots and stripes occur when two chemicals produced in the skin interact. One stimulates the production of a pigment and one inhibits it. So why do some coats have spots and some have stripes.

James Murray, a mathematician from the University of Oxford toyed with possible rules governing the dual production and inhibition process only leading to spots. Would the inhibiting chemical be produced much faster than the pigment for example? He wrote the rules in terms of equations, which he analysed mathematically. To his surprise he found rules that not only produced spots but also produced stripes if the area of skin was of a particular shape - long and pencil like. This fits the scenario perfectly. Animals develop their coat patterns when they are just embryos and zebras are indeed long and pencil like for some time at that stage, while leopards are chubby with the exception of their tail.

Biologists can now investigate the process further but without the equations we may have never truly understood such a phenomenon. Devlin concludes astutely that mathematics makes the invisible visible. Devlin searches for the intriguing part of the brain that triggers mathematical thought. He takes us back to the time of the dinosaurs and the animals that survived them. A story unfolds of our evolution and of the traits we acquired along the way. Sophisticated communication and intelligence holds top ranking of course but Devlin also acknowledges more subtle abilities that are just as important.

Being able to recognise which tree contains the most fruit or possessing a good three- dimensional special sense in order to swing from tree to tree are, when all is set and done, life saving traits. This is where Devlin brings together ideas from linguistics, evolutionary biology, palaeontology and brain anatomy. To understand more about our development of mathematics the author examines the careful mix of ingredients that leads to another outstanding development - language. A typical 6 year old British child will know around 13,000 words. In contrast, 50% of people never know their times tables and these boil down to a mere 18 pieces of information. But Devlin, whose glass must always be half full, simply suggests we must be teaching those dreaded timetables incorrectly.

Devlin studies how a fantastic linguistic ability arose and gives credit to the complexity of human design. He does not underestimate issues such as wanting to say something, something that furthermore had to be of some importance for the evolutionary advantage to make sense. The familiar account of how human brains acquired fully blown language by a gradual acquisition of richer and richer vocabulary is unsatisfactory to Devlin. It doesn't quite fit the facts.

Humans have by far the largest brain in the animal kingdom. Nine times larger that normal for a mammal of our body size and even though this is less than 2% of our body mass it uses about 20% of our energy. Now, the expansion in brain size that led to humans as a species, began around three and a half million years ago with its size already reached about 300,000 years ago. However language only arrived on the scene between 75,000 and at most 200,000 years ago. And language happened quickly, simultaneously all over the globe during a time when communication was still face-to-face.

Devlin argues that face-to-face communication can be achieved successfully using simple combinations of two or three words together with gestures. There's no need for complicated syntax or grammatical structure. Furthermore it saves a lot of brain energy; very important when three meals a day is not guaranteed. With this in mind, Devlin argues that language is a natural extension of what is referred to as off-line thinking. Spectacularly, so is mathematics. What's off-line thinking? Well, it's our ability to recognise and respond to patterns - and remember, mathematics is the science of patterns.

Off-line thinking is our ability to classify everything we encounter in terms of type so as to help us decipher all the activity that constitutes our environment. Like, realise that both leopards and ladybirds belong to the category spotted bodies animals, yet one is a mammal which might kill us and the other is a harmless insect. As Devlin says, distinguishing types is the very essence of life. However, there's an extra ability we possess that differentiates us from other animals. We form connections between the types. Gossip illustrates this perfectly. We have no problem thinking of Russell Crowe and Meg Ryan as two actors in an romantic affair. At the same time we know Meg Ryan was married to another actor, Dennis Quaid . We may then automatically think through other structures. For instance, Meg Ryan was the star of You've Got Mail who had the affair with the star of Gladiator and the word gladiator reminds me of tigers, animals with striped bodies. You get the idea.

Structures, whether social or not, form a key part of our world view and require much more brainpower than simple face-to-face communication. Devlin suggests structures evolved over millions of years and became a framework on which language could develop easily, quickly and uniformly all over the world. He has many convincing arguments and ideas to support this, but what is particularly appealing is how mathematical ability also fits in magically with the off-line thinking hypothesis.

In a delightfully provocative section Devlin compares mathematics with a soap opera. He makes the point that mathematics is all about understanding connections between patterns. Similarly, watching a soap opera is all about understanding the outrageous, sometimes ridiculous connections between the characters.

Most of us however have no trouble understanding a soap opera, so Devlin believes mathematics is an inbuilt attribute we just have to familiarise ourselves with. Too hard? Well take the jogging boom. Before the 1970s only highly trained athletes ran more than 5 miles, then along came jogging and now ordinary people commonly run marathons of 26 miles. For most people it only requires a desire to do it. I'm thinking of a Nike like campaign for mathematics - Just do it.


Professor Brian Butterworth
Professor of Cognitive Neuropsychology
Institute of Cognitive Neuroscience
University College London
Alexandra House, 17 Queen Square
London WC1N 3AR
Tel: +44 71 391 1150 or
Clio Creswell
Dr Clio Creswell
School of Mathematics
University of New South Wales
Sydney 2052
Tel: +61 2 9385 7036
Keith Devlin
Dean of Science, St Mary's College of California
Moraga CA94575 USA
Senior Research, Stanford University
Tel: +1 925 631 4409


"The Mathematical Brain"
Brian Butterworth
Author: Brian Butterworth
Published by: Macmillan
'The Maths Gene'
Keith Devlin
Author: Keith Devlin
Published by: Macmillan
ISBN: 0297645714
"Nature's Numbers"
Profesor Ian Stewart
Orion Audio Books
Professor Ian Stewart
Orion Audio Books
Distributed in Australia by Allen & Unwin
'The Hammer of Eden'
Ken Follett
Author: Ken Follett
Published by: Crown


Robyn Williams
Polly Rickard