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Naze sugaku ga tokui na hito to nigate na hito ga irunoka?
(Why are some people good, but others bad at maths?)

Frontiers 01

Extract by Brian Butterworth

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The Man Who Could Read Only Numbers

We were not very surprised that Mr Harvey - not his real name - could still calculate accurately, even though brain damage had so deprived him of speech that he could not name even the commonest objects. Three patients had already been reported whose maths had survived brain damage, but whose language had not. We were mildly surprised by his ability to read aloud the numerals 1, 2, 3, and even four-digit numbers such as 7495 without error. Given his enormous difficulties with speech, this was unusual but not completely unknown.

Was it relevant that Mr Harvey, before his retirement, had been a banker and his hobby was gambling? This would have given his mental mathematical muscles more exercise than most people's, and we knew that with brains, as with real muscles, you either use it or lose it. Practice rewires the brain. It was likely, therefore, that the mathematical part of his brain had recruited more brain cells and strengthened the connections between them. So if he started with more tightly interconnected brain cells devoted to mathematics, a reasonable level of number skill might well have survived three years of an insidious disease eating away at his brain.

What astonished us, though, was his word reading. He was quite unable to read even the simplest and commonest words - for, tree, then, take, give, you - but he had no trouble at all reading number words. Though he couldn't read you, he could read two and three, ten, eight, and five, not to mention thousand and million. This was quite unprecedented in the annals of neuropsychology. What could be the explanation of such a weird anomaly, and could it tell us anything about the nature of normal reading, or indeed about normal mathematics?

Patients with these very specific and unusual patterns of preserved and defective abilities are like rare archaeological specimens. We can't go into a laboratory and make them. We just have to find them, and to do this, like the good archaeologist, we need to know what to look for. And, perhaps more importantly, we need to know what we've got when we find it.

This takes both acute observation, and a wide knowledge of theory. "Theory" in this case means having a view about how different mental abilities are organised in the brain. In practice, this translates into having an idea of what can go wrong by itself and what cannot.

These specific disturbances of cognitive function have been responsible for major advances in our understanding of the mind. We now know, for example, that amnesiacs - the "lost weekend" type of amnesiacs - do not forget everything. Even the most severe cases still remember how to speak, to read, that Paris is the capital of France, that kangaroos are not indigenous to Southend-on-Sea, and how to calculate.

The part of memory that is responsible for this preserved information is called "semantic memory". Remembering who you are, what you did yesterday or last year - "autobiographical memory" - is a function of a brain structure called the hippocampus, while semantic memory uses other brain regions. In the thriller The Code To Zero by Ken Follett, the hero tries to recover his life by using his semantic memory. Finding that he understood the technicalities of a rocket launch told him that he must have been a rocket scientist. I won't ruin your enjoyment of the ingenious plot by revealing more. There is also "procedural memory" for skills such as driving or skiing.

A few years ago, a distinguished Italian neurologist and expert on memory disorders, Dr S, was skiing too fast, as usual, and took a tumble. When the rest of his party caught up with him, he stared at them strangely. He was surprised to find his wife and his best friend suddenly looking very old. And he failed to recognise some of his younger colleagues. The neurologists in the party did a piste-side examination, and diagnosed autobiographical memory loss, probably of the past 25 years or so. This is why his wife and friend looked old, because his memory of their faces was 25 years old, and of course he had come to know his younger colleagues within the 25-year blank period. However, he was still able to ski back to the bottom station, where he declared, "See, my procedural memory is still intact!"

He was taken to the local hospital where he asked for a brain scan, a procedure that he would have learned about during the blank quarter of a century. A scan was carried out, and Dr S looked at the results and made his own diagnosis. Seeing his name and age on the scan, he noted, "There, the brain looks in very good shape for my age; no signs of atrophy. I must have transient global amnesia."

This was accurate, and showed that the semantic memories created in this period were still accessible. Global amnesia meant that not only was he unable to remember the past, but he could not create memories of new events. Fifteen minutes later he said, "Shouldn't I be having a brain scan?" This condition was, thankfully, transient, and after 20 hours he recovered completely. My impression is that he now skis a little more carefully.

Mr Harvey is the exact opposite of Dr S. His autobiographical memories are reasonably well preserved. We asked him to read the word "theatre". He couldn't pronounce the word, but he did say, "I delved into that every year in Oxford from 1950 to 1960". His wife confirmed that, indeed, he had been a keen amateur actor and director during this time. His problem lay in his semantic memory.

He had very few words left - "delved" came up very often in his speech. In a standard clinical test, he failed to name a single common object, such as table, chair, clock, or glove. And he couldn't point to the right picture when you said these words. He was unable to classify pictures of animals into those living in England and those living outside England. The combination of good autobiographical memory and poor semantic memory caused by a neurodegenerative disease is called "semantic dementia".

For two years Mr Harvey had been in the care of one of the world's leading experts on semantic dementia and other memory disorders, Professor Michael Kopelman of St Thomas's Hospital in London. Kopelman and I were interested in how numerical knowledge and calculation skills relate to other aspects of memory, and we had noticed that in reports of other semantic-dementia patients, these abilities could be preserved even when much else had been lost. On our team, which is funded by the Wellcome Trust, was an enthusiastic Italian neuropsychology graduate, Marinella Cappelletti, who was to do most of the testing of Mr Harvey, even going to his home an hour and a half away when we needed to collect more data.

We devised a battery of numerical tests and systematically tested Mr Harvey more or less once a month for over a year. Mr Harvey always arrived at the clinic immaculately dressed, usually in a pinstripe suit and tie; and he was always smiling and affable, but it became apparent that his condition was getting worse. He was losing his vocabulary, and was performing more and more poorly on our tests of semantic memory. However, for most of this period, his calculation remained at a very high level. His arithmetic, both oral and written, was usually without error. He could do long multiplication flawlessly. He could read long numbers and write them to dictation with no difficulty.

We had now demonstrated conclusively, for the first time, that numerical skills could be preserved when most of the rest of semantic memory, including words, were lost. This is important because it refutes the idea, popular with both psychologists and laymen, that adult calculation is carried out in language and that arithmetical facts are stored just as verbal formulae.

However, we still did not know why he was able to read only number words, and, as we soon discovered, these were also the only words he could write. It wasn't just that number words were the only words he could remember. After all, he chatted with us, albeit hesitantly, about things other than numbers. So, we asked him to read words that he had used correctly in conversations, to be sure he knew them. He was slightly better with these words than assorted common words; but since he was reading number words 100% correctly every time, this could only be a tiny part of the explanation. Memory research wasn't going to provide the answer.

We turned to research on reading. In 1973, two Oxford neuropsychologists, John Marshall and Freda Newcombe, had published a study of three patients whose reading had been affected by brain damage. In this study, they did something that had never been done before. Previously, reading disorders, called "alexia", had been classified into two types: alexia with agraphia (writing disorders) and alexia without agraphia.

Marshall and Newcombe took the revolutionary step of not just counting the words correctly written but analysing the kinds of errors that the patients made when they attempted to read a word. They found that one of their patients, a skilled reader before his brain damage, frequently mispronounced one or two letters in the word in rather the same the way that a child who didn't recognise the word might. For example, he read "insect" as "insist", softening the C; and "listen" as "Liston, the boxer", sounding out the T, which, unusually, is silent.

Two other patients made characteristic errors that had never before been noticed, reading "bush" as "tree", and "ill" as "sick". Obviously, they couldn't make these errors simply by sounding out the letters in a childish way. They must in some way have read the words correctly, and retrieved their meanings. Somehow in the process of trying to say the words they had come up with a word that was similar in meaning, but not in sound, to the target.

Pondering on this puzzle, Marshall and Newcombe came up with a theory that became the standard in reading research (though nowadays it has a few more bells and whistles). They argued that when we see a word, we use two "reading routes" automatically and simultaneously: we try to sound it out letter by letter, a kind of mental phonics process, and at the same time we try to retrieve the meaning of the whole letter string without bothering about its pronunciation. The patient who said "Liston, the boxer" was using the letter-to-sound route only, presumably because the other route had been damaged. The other two patients were using only the reading-via-meaning route, again presumably because the other route had been damaged.

Of course, bush doesn't mean the same as tree, so why did these errors arise? It seems that we need both routes. We need to be able to recognise words as wholes, since many have irregular spellings, or pronunciations that depend on their context - such as lead and wind. And the letter-to-sound route is needed in case we have never seen the word before. With two routes operating together, one can check the output of the other. This may be particularly important given that we read so fast, far faster than we normally hear words - 200 to 300 words per minute, three to five words per second. With one route dysfunctional, errors will arise, with the kind of error depending on which route is affected.

This idea gave us the crucial clue to Mr Harvey's reading. Suppose he wasn't able to use the letter-to-sound route at all, then he would have to rely exclusively on reading by meaning. We tested this by seeing if he could read letter strings that he had never seen before, such as "zind" and "yead". He couldn't. We also looked to see if he made "regularisation" errors, such as pronouncing the T in listen, or reading pint to rhyme with hint. He didn't. Normal readers using both routes are more accurate reading regularly spelled words than irregular words because the two routes interact. Mr Harvey showed no advantage for regular words because the letter-to-sound route wasn't working.

The words he could and could not read were defined solely by their meaning. If they meant a number (or an ordinal - first, second, eighteenth) he could read them. If not, he was unable to. This reinforced our view that he was reading exclusively by meaning.

We knew from our other tests that his semantic dementia had severely affected his knowledge of the meaning even of common words for everyday objects. But it was clear that he understood the meaning of number words, since he was still able to carry out flawlessly tasks that depended on knowing these meanings. So he could say which of two numbers was larger, even up to four-digit numbers. And, of course, he could calculate. So it was not just that he knew that that "seven" denoted a number; he knew precisely which numerical value it had - not six and not eight, and that, added to five, it makes 12. In other categories of knowledge, even when he wasn't completely at a loss, his grasp of concepts and meanings was much vaguer, as is usual in these cases.

As his disease progressed, he found that he was unable to recall some of the facts he had learned in school, such as multiplication tables. But he compensated well enough by using successive addition to solve the problems we gave him. This was, in a way, even more impressive than being able to retrieve the product of, say, eight times seven, which could be mere rote memory, as it showed that he still understood both number meanings and the concepts of arithmetic.

Now Mr Harvey's case is not just a medical curiosity. Nor is it just an example of one man's struggle to overcome an unpredictable and crippling disease, or a pointer to how far neuroscience has progressed by 2001. It solves two problems (although it raises more questions). First, we have confirmed what theorists had previously only speculated about, that reading via meaning is sufficient for accurate pronunciation, since Mr Harvey can read number words with perfect accuracy.

This may give us a clue as to how to help dyslexic children. One of their main problems is in learning the sound of each letter. This is particularly hard in English, where letters can have very different sounds depending on the word they are in. Just think of G in the following words: tug, tough, though.

A dyslexic young woman we studied some years ago suffered six years of trying to learn to read through phonics, and was almost classified as "educationally subnormal" when her mother sent her to a different school which taught reading by the whole-word, look-and-say method. This worked excellently for her. We found her reading to be efficient, but unusual. She read most words so well that on standard tests she would not be dyslexic. However, she was quite unable to read new words. She always had to ask someone to read them to her and then she would try to remember how they sounded.

I think many dyslexics would benefit from more emphasis on a whole-word, meaning-based, approach to reading, and less on phonics. Our study of Mr Harvey shows that this single route can work effectively (though not as effectively as the two routes together, of course).

The second result was this: many years ago the great British neuropsychologist, Elizabeth Warrington, discovered that neurological patients could have selective impairments of single categories of knowledge within semantic memory - they might still know about living things and foods, but had lost information about furniture, for example. In these studies she did not specifically consider numerical knowledge.

The case of Mr Harvey, along with converse cases where language is spared but numerical abilities are severely damaged, shows that numerical knowledge is separate in the brain from our knowledge of language and the rest of semantic memory. This is somewhat counterintuitive given that most of what we know about numbers is learned through language, and we can all remember hours of tedium reciting our tables in a singsong voice. But however we learn about numbers, they end up in a region of the brain known as the parietal lobes. Knowledge of language is mostly in the dominant frontal lobe (Broca's area), and Wernicke's area in the temporal lobe, near where most of the rest of semantic memory is located.

Brain scans showed that disease was ravaging Mr Harvey's temporal lobes, but had left the parietal lobes intact, showing that different categories of knowledge may be in quite separate lobes of the brain. Why number knowledge should be in the parietal lobe and not in the temporal lobes is a question that we are currently pursuing.

Our study left us with one further puzzle. Mrs Harvey had told us that her husband, an inveterate gambler on the horses, now only bet on dogs. Why, we wondered, had semantic dementia driven him to the dogs? This is where my misspent youth came in useful. I remembered that one bets on horses by giving the horse's name. "Ten pounds to win on Galileo, please." If you can't read the name, this is going to be difficult. But since all dog races have six starters, it's normal to say, "Ten pounds to win on number six." This Mr Harvey can do. I hope he has better luck with the dogs.

This is an extract from Frontiers 01: Science and Technology, 2001-02, edited by Tim Radford, Guardian science editor, and published by Atlantic Books.

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