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 show that really there are separate parts
of the brain that deal with maths on the one hand, deal
with reasoning on the other hand and deal with language
on the third hand.
So there is evidence that there is independence in the
brain. Of course it doesn't mean that there's
functional independence. Clearly you learn most maths
through language. But once you've learnt it, does it
get stored with other things that you've learnt through
language or does it get stored somewhere else? One of
the things that we've been working on - and we work on
these things entirely opportunistically, it depends who
comes into the clinic, is about whether reading words,
reading numbers and recently, reading music all use the
same brain circuits or whether they use separate ones.
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.
Now recently with some colleagues at St. Thomas's
Hospital, we examined a patient called Mrs C. Now Mrs C
was a professional musician and a professional musical
composer, and she had some brain disease which affected
not the language part of the brain and not what we
believe to be the number part of the brain, but a part
of the brain that we haven't really paid much attention
to before, in the right hemisphere. As a consequence of
this she was left with a very, very specific deficit.
Although she could still play music, although she could
still sing, she could no longer sight-read music;
something that she was able to do fluently for over 30
years, nearly 40 years in fact. Now she can't sight-read
music at all. In fact she can't read musical notes
at all. Nevertheless she can still read numerals, she
can still read words perfectly well, and this shows
that very soon after the visual information enters the
brain it gets split into separate channels. There's a
channel for words, there's a channel for numerals and
there's a channel for musical notation as well.
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?
Brian Butterworth: Well we actually have found a
disassociation here. In a subject I called in my book
Charles. He was able perfectly well to recognise 17 and
he could read aloud the number 17 but he had no idea
what it meant; he couldn't do computation with it. So
deeper into the brain than, if you like, the
recognition centre, there's comprehension and
calculation and that's clearly something that goes
beyond the reading and comprehension.
Actually, we found another patient who was rather poor
at reading numerals but was very good at calculating
with them. So if you asked what is 17 plus 35 he would
give you the correct answer, which is 52, I think. But
if you asked him to read aloud the numerals 17 plus 35
he would often make mistakes in doing that. So there
seems to be something rather separate about the
calculation.
Robyn Williams: Yes. What are the implications of this
independence of mathematical ability?
Brian Butterworth: Well, one of the things that's
coming up now as an important social issue is people's
numeracy. Certainly our government and the government
of the United States have been worried that the
numeracy of our citizens is really much lower than our
economic competitors and we wonder what we should do
about that. Now one of the questions that comes up is
can we treat mathematics and arithmetic as being
separate from other school subjects. If it's separate
in the brain what are the education implications of
this? Now that's not completely clear yet, but one
thing is becoming clear - and this is something that I
have to say neither government recognises - and that is
that there are people who are born without a properly
developed number centre in the brain and these people
are always going to be very bad at calculation. They
might be quite good at other aspects of maths but at
calculation and understanding numbers they'll always be
awful.
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: Going to the brain itself, I can
actually work out how words might be represented in the
brain but how on earth are the numbers?
Brian Butterworth: Well, there's a big debate going on
at the moment. On the one hand there are people who
think that the way in which we represent the meaning of
numbers and what 5 stands for really isn't specifically
numerical. Their idea is that we have a kind of
quantity sense, so 5 is kind of approximately this
much; it's a bit more than 4 and a bit less than 6 but
it's all rather approximate. It's as though you have a
line in your head and 5 is approximately here and 4 is
approximately there on this line. Now I take a
different view. I think that we're born with a sense of
a collection of things and a number for that collection
so that a collection with an extra member has a very
definite precise extra representation.
At the moment we are going through some experiments
trying to see whether I'm right or whether most of the
rest of the scientists in this area are right. They've
actually got some rather good evidence, but we've got
some experiments that we're doing now which I think may
well tip the balance in our favour, but I can't tell
you about that at the moment because we haven't
finished the analysis.
Robyn Williams: Well I won't ask you about it if you
haven't finished the analysis, but what I will ask you
about are those animals which, I think, dogs can count
fairly comfortably up to 4, specially mine which are
border collies which are the most intelligent and can
go even further. But parrots can do calculation and not
simply say, well there are two things over there but
two entities we've brought together, you know two
apples and one pear, they can say, the parrot or one or
two parrots can say, This is 3, as if animals indeed
have a lower level of cognition evolution have got this
wired in as well.
Brian Butterworth: Well, that's certainly my belief
which is that our specific number sense is something
that we've inherited from animals. We know that animals
can do quite a lot of number tasks, some of which they
have to be taught and some of which seem to come rather
naturally. They can be taught for example to pick the
larger of two numerical arrays, so they can pick, if
you want three things and four things they can pick
four. If you're a very smart animal like a chimp you
can be trained to understand what the numeral 3 means
and what the numeral 4 means and then pick the numeral
4 over the numeral 3. They can do some extremely
primitive calculation - extremely primitive.
The problem is, if you want to say that these are
ancestral abilities to our own, is to show that animals
use homologous brain areas to our numerical brain and
so far nobody knows which bit of the brain animals use
to do these tasks. So until we know that, we won't know
whether it's just in general, kind of handy to make
numerical distinctions or whether actually some
ancestral creature got this idea and then the rest of
us inherited it.
Robyn Williams: Why is it important to know?
Brian Butterworth: Well, we want to know whether our
genome contains information to enables it to build
brain areas that are specific to mathematics. If it
does then that will explain why some people are born
without this ability. Also it will help us actually to
understand some archaeology. There are lots of
interesting arrays of dots in Palaeolithic caves in
Europe particularly and no one knows what they mean.
My guess is that our Palaeolithic ancestors 20,000
years ago in the depths of the Ice Age were counting
things. We don't know what they were counting, they
might have been counting bison they might have been
just counting the number of people who turned up for a
party, but I leave that questions to the
archaeologists.
Robyn Williams: Bet they were doing deals.
Brian Butterworth: I wouldn't be surprised.
Robyn Williams: And neither would I.
Brian Butterworth is Professor of Cognitive Neuropsychology at University
College, London. His book is called "The Mathematical
Brain" and it's published by Macmillan.