A genius explains - [an autistic savant describes how he thinks]

Guardian (U.K.) ^ | February 12, 2005 | Richard Johnson

[snarks_when_bored]

A genius explains

Daniel Tammet is an autistic savant. He can perform mind-boggling mathematical calculations at breakneck speeds. But unlike other savants, who can perform similar feats, Tammet can describe how he does it. He speaks seven languages and is even devising his own language. Now scientists are asking whether his exceptional abilities are the key to unlock the secrets of autism. Interview by Richard Johnson

Richard Johnson
Saturday February 12, 2005

Guardian

Daniel Tammet is talking. As he talks, he studies my shirt and counts the stitches. Ever since the age of three, when he suffered an epileptic fit, Tammet has been obsessed with counting. Now he is 26, and a mathematical genius who can figure out cube roots quicker than a calculator and recall pi to 22,514 decimal places. He also happens to be autistic, which is why he can't drive a car, wire a plug, or tell right from left. He lives with extraordinary ability and disability.

Tammet is calculating 377 multiplied by 795. Actually, he isn't "calculating": there is nothing conscious about what he is doing. He arrives at the answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colours and textures. The number two, for instance, is a motion, and five is a clap of thunder. "When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That's the answer. It's mental imagery. It's like maths without having to think."

Tammet is a "savant", an individual with an astonishing, extraordinary mental ability. An estimated 10% of the autistic population - and an estimated 1% of the non-autistic population - have savant abilities, but no one knows exactly why. A number of scientists now hope that Tammet might help us to understand better. Professor Allan Snyder, from the Centre for the Mind at the Australian National University in Canberra, explains why Tammet is of particular, and international, scientific interest. "Savants can't usually tell us how they do what they do," says Snyder. "It just comes to them. Daniel can. He describes what he sees in his head. That's why he's exciting. He could be the Rosetta Stone."

There are many theories about savants. Snyder, for instance, believes that we all possess the savant's extraordinary abilities - it is just a question of us learning how to access them. "Savants have usually had some kind of brain damage. Whether it's an onset of dementia later in life, a blow to the head or, in the case of Daniel, an epileptic fit. And it's that brain damage which creates the savant. I think that it's possible for a perfectly normal person to have access to these abilities, so working with Daniel could be very instructive."

Scans of the brains of autistic savants suggest that the right hemisphere might be compensating for damage in the left hemisphere. While many savants struggle with language and comprehension (skills associated primarily with the left hemisphere), they often have amazing skills in mathematics and memory (primarily right hemisphere skills). Typically, savants have a limited vocabulary, but there is nothing limited about Tammet's vocabulary.

Tammet is creating his own language, strongly influenced by the vowel and image-rich languages of northern Europe. (He already speaks French, German, Spanish, Lithuanian, Icelandic and Esperanto.) The vocabulary of his language - "Mänti", meaning a type of tree - reflects the relationships between different things. The word "ema", for instance, translates as "mother", and "ela" is what a mother creates: "life". "Päike" is "sun", and "päive" is what the sun creates: "day". Tammet hopes to launch Mänti in academic circles later this year, his own personal exploration of the power of words and their inter-relationship.

Professor Simon Baron-Cohen, director of the Autism Research Centre (ARC) at Cambridge University, is interested in what Mänti might teach us about savant ability. "I know of other savants who also speak a lot of languages," says Baron-Cohen. "But it's rare for them to be able to reflect on how they do it - let alone create a language of their own." The ARC team has started scanning Tammet's brain to find out if there are modules (for number, for example, or for colour, or for texture) that are connected in a way that is different from most of us. "It's too early to tell, but we hope it might throw some light on why we don't all have savant abilities."

Last year Tammet broke the European record for recalling pi, the mathematical constant, to the furthest decimal point. He found it easy, he says, because he didn't even have to "think". To him, pi isn't an abstract set of digits; it's a visual story, a film projected in front of his eyes. He learnt the number forwards and backwards and, last year, spent five hours recalling it in front of an adjudicator. He wanted to prove a point. "I memorised pi to 22,514 decimal places, and I am technically disabled. I just wanted to show people that disability needn't get in the way."

Tammet is softly spoken, and shy about making eye contact, which makes him seem younger than he is. He lives on the Kent coast, but never goes near the beach - there are too many pebbles to count. The thought of a mathematical problem with no solution makes him feel uncomfortable. Trips to the supermarket are always a chore. "There's too much mental stimulus. I have to look at every shape and texture. Every price, and every arrangement of fruit and vegetables. So instead of thinking,'What cheese do I want this week?', I'm just really uncomfortable."

Tammet has never been able to work 9 to 5. It would be too difficult to fit around his daily routine. For instance, he has to drink his cups of tea at exactly the same time every day. Things have to happen in the same order: he always brushes his teeth before he has his shower. "I have tried to be more flexible, but I always end up feeling more uncomfortable. Retaining a sense of control is really important. I like to do things in my own time, and in my own style, so an office with targets and bureaucracy just wouldn't work."

Instead, he has set up a business on his own, at home, writing email courses in language learning, numeracy and literacy for private clients. It has had the fringe benefit of keeping human interaction to a minimum. It also gives him time to work on the verb structures of Mänti.

Few people on the streets have recognised Tammet since his pi record attempt. But, when a documentary about his life is broadcast on Channel 5 later this year, all that will change. "The highlight of filming was to meet Kim Peek, the real-life character who inspired the film Rain Man. Before I watched Rain Man, I was frightened. As a nine-year-old schoolboy, you don't want people to point at the screen and say, 'That's you.' But I watched it, and felt a real connection. Getting to meet the real-life Rain Man was inspirational."

Peek was shy and introspective, but he sat and held Tammet's hand for hours. "We shared so much - our love of key dates from history, for instance. And our love of books. As a child, I regularly took over a room in the house and started my own lending library. I would separate out fiction and non-fiction, and then alphabetise them all. I even introduced a ticketing system. I love books so much. I've read more books than anyone else I know. So I was delighted when Kim wanted to meet in a library." Peek can read two pages simultaneously, one with each eye. He can also recall, in exact detail, the 7,600 books he has read. When he is at home in Utah, he spends afternoons at the Salt Lake City public library, memorising phone books and address directories."He is such a lovely man," says Tammet. "Kim says, 'You don't have to be handicapped to be different - everybody's different'. And he's right."

Like Peek, Tammet will read anything and everything, but his favourite book is a good dictionary, or the works of GK Chesterton. "With all those aphorisms," he says, "Chesterton was the Groucho Marx of his day." Tammet is also a Christian, and likes the fact that Chesterton addressed some complex religious ideas. "The other thing I like is that, judging by the descriptions of his home life, I reckon Chesterton was a savant. He couldn't dress himself, and would always forget where he was going. His poor wife."

Autistic savants have displayed a wide range of talents, from reciting all nine volumes of Grove's Dictionary Of Music to measuring exact distances with the naked eye. The blind American savant Leslie Lemke played Tchaikovsky's Piano Concerto No1, after he heard it for the first time, and he never had so much as a piano lesson. And the British savant Stephen Wiltshire was able to draw a highly accurate map of the London skyline from memory after a single helicopter trip over the city. Even so, Tammet could still turn out to be the more significant.

He was born on January 31 1979. He smiles as he points out that 31, 19, 79 and 1979 are all prime numbers - it's a kind of sign. He was actually born with another surname, which he prefers to keep private, but decided to change it by deed poll. It didn't fit with the way he saw himself. "I first saw 'Tammet' online. It means oak tree in Estonian, and I liked that association. Besides, I've always had a love of Estonian. Such a vowel rich language."

As a baby, he banged his head against the wall and cried constantly. Nobody knew what was wrong. His mother was anxious, and would swing him to sleep in a blanket. She breastfed him for two years. The only thing the doctors could say was that perhaps he was understimulated. Then, one afternoon when he was playing with his brother in the living room, he had an epileptic fit.

"I was given medication - round blue tablets - to control my seizures, and told not to go out in direct sunlight. I had to visit the hospital every month for regular blood tests. I hated those tests, but I knew they were necessary. To make up for it, my father would always buy me a cup of squash to drink while we sat in the waiting room. It was a worrying time because my Dad's father had epilepsy, and actually died of it, in the end. They were thinking, 'This is the end of Daniel's life'."

Tammet's mother was a secretarial assistant, and his father a steelplate worker. "They both left school without qualifications, but they made us feel special - all nine of us. As the oldest of nine, I suppose it's fair to say I've always felt special." Even if his younger brothers and sisters could throw and catch better than him, swim better, kick a ball better, Daniel was always the oldest. "They loved me because I was their big brother and I could read them stories."

He remembers being given a Ladybird book called Counting when he was four. "When I looked at the numbers I 'saw' images. It felt like a place I could go where I really belonged. That was great. I went to this other country whenever I could. I would sit on the floor in my bedroom and just count. I didn't notice that time was passing. It was only when my Mum shouted up for dinner, or someone knocked at my door, that I would snap out of it."

One day his brother asked him a sum. "He asked me to multiply something in my head - like 'What is 82 x 82 x 82 x 82?' I just looked at the floor and closed my eyes. My back went very straight and I made my hands into fists. But after five or 10 seconds, the answer just flowed out of my mouth. He asked me several others, and I got every one right. My parents didn't seem surprised. And they never put pressure on me to perform for the neighbours. They knew I was different, but wanted me to have a normal life as far as possible."

Tammet could see the car park of his infant school from his bedroom window, which made him feel safe. "I loved assembly because we got to sing hymns. The notes formed a pattern in my head, just like the numbers did." The other children didn't know what to make of him, and would tease him. The minute the bell went for playtime he would rush off. "I went to the playground, but not to play. The place was surrounded by trees. While the other children were playing football, I would just stand and count the leaves."

As Tammet grew older, he developed an obsessive need to collect - everything from conkers to newspapers. "I remember seeing a ladybird for the first time," he says. "I loved it so much, I went round searching every hedge and every leaf for more. I collected hundreds, and took them to show the teacher. He was amazed, and asked me to get on with some assignment. While I was busy he instructed a classmate to take the tub outside and let the ladybirds go. I was so upset that I cried when I found out. He didn't understand my world."

Tammet may have been teased at school, but his teachers were always protective. "I think my parents must have had a word with them, so I was pretty much left alone." He found it hard to socialise with anyone outside the family, and, with the advent of adolesence, his shyness got worse.

After leaving school with three A-levels (History, French and German, all grade Bs), he decided he wanted to teach - only not the predictable, learn-by-rote type of teaching. For a start, he went to teach in Lithuania, and he worked as a volunteer. "Because I was there of my own free will, I was given a lot of leeway. The times of the classes weren't set in stone, and the structures were all of my own making. It was also the first time I was introduced as 'Daniel' rather than 'the guy who can do weird stuff in his head'. It was such a pleasant relief." Later, he returned home to live with his parents, and found work as a maths tutor.

He met the great love of his life, a software engineer called Neil, online. It began, as these things do, with emailed pictures, but ended up with a face-to-face meeting. "Because I can't drive, Neil offered to pick me up at my parents' house, and drive me back to his house in Kent. He was silent all the way back. I thought, 'Oh dear, this isn't going well'. Just before we got to his house, he stopped the car. He reached over and pulled out a bouquet of flowers. I only found out later that he was quiet because he likes to concentrate when he's driving."

Neil is shy, like Tammet. They live, happily, on a quiet cul-de-sac. The only aspect of Tammet's autism that causes them problems is his lack of empathy. "There's a saying in Judaism, if somebody has a relative who has hanged themselves, don't ask them where you should hang your coat. I need to remember that. Like the time I kept quizzing a friend of Neil's who had just lost her mother. I was asking her all these questions about faith and death. But that's down to my condition - no taboos."

When he isn't working, Tammet likes to hang out with his friends on the church quiz team. His knowledge of popular culture lets him down, but he's a shoo-in when it comes to the maths questions. "I do love numbers," he says. "It isn't only an intellectual or aloof thing that I do. I really feel that there is an emotional attachment, a caring for numbers. I think this is a human thing - in the same way that a poet humanises a river or a tree through metaphor, my world gives me a sense of numbers as personal. It sounds silly, but numbers are my friends."

Guardian Unlimited © Guardian Newspapers Limited 2005

[TheBrotherhood]

"That's a very unusual combination."

Yes, it is nonconventional and non-PC, and most people whose lives are controlled by fear either, intentionally tend not to speak the truth, or just plainly are not aware of the truth.

[Octar]

Thanks for posting this. Very interesting.

[bdfromlv]

It may be for neil. He may be preying on the somewhat innocent for his own purposes.

[snarks_when_bored]

Good post, xm177e2. I hope you'll forgive me if I turn your short post into something more long-winded.

---

Suppose that we want to show that the two-digit natural number AB, with decimal digits A and B, is a multiple of 3 if and only if A + B, the sum of its digits, is a multiple of 3. How would we do that? Here's how a proof might run.

Proof:   Consider the two-digit natural number AB with decimal digits A and B (for example, 57 with digits A=5 and B=7). AB will be a multiple of 3 if and only if AB = 3Y for some natural number Y. Since AB is decimal notation for 10A + B, the condition just stated reads 10A + B = 3Y. But (interpreting '<==>' as 'if and only if'), we have

	10A + B = 3Y
<==>	A + B = 3Y - 9A
<==>	A + B = 3(Y - 3A)
<==>	A + B = 3X,    where X = Y - 3A

Since each step of this argument is reversible (that's what 'if and only if' does for you), we've found that the two-digit natural number AB is a multiple of 3 if and only if A + B (the sum of its digits) is a multiple of 3. QED.

But why stop there? What about a three-digit natural number ABC? Let's see how that runs.

Proof:   Consider the three-digit natural number ABC with decimal digits A, B and C (for example, 342 with digits A=3, B=4 and C=2). ABC will be a multiple of 3 if and only if ABC = 3Y for some natural number Y. Since ABC is decimal notation for 100A + 10B + C, we want 100A + 10B + C = 3Y. But (interpreting '<==>' as 'if and only if'), we have

	100A + 10B + C = 3Y
<==>	A + B + C = 3Y - 99A - 9B
<==>	A + B + C = 3(Y - 33A - 3B)
<==>	A + B + C = 3X,    where X = Y - 33A - 3B

Since each step of this argument is reversible (that's what 'if and only if' does for you), we've found that the three-digit natural number ABC is a multiple of 3 if and only if A + B + C (the sum of its digits) is a multiple of 3. QED.

Shall we continue? Consider the four-digit natural number ABCD with ...

Hang on a second...the first two proofs were close to being identical. They have almost the same pattern. Does anybody think a similar argument won't work with four-digit natural numbers ABCD and five-digit natural numbers ABCDE and so on through n-digit natural numbers and beyond? Nah.

What you see here is a phenomenon that mathematicians encounter over and over again...a statement which is true for one or two or three 'small' cases looks like it's going to be true for ALL cases (the essence of mathematical insight is pattern recognition). But it's not possible to write down infinitely many proofs, one for each case (and who would want to do something stupid and boring like that, anyway?). So what do mathematicians do? They come up with a bit of notation that allows them to capture the general case with a minimum of trouble, and then prove the result for the general case. Once that's done, they no longer have to worry about whether the result holds for natural numbers with, say, 1327 digits or whatever. The result holds for ALL natural numbers, no matter how many decimal digits in their expression! Now that's power.

I'll leave the general case as an exercise for the reader. (Hint: recall that 1 = 10⁰, 10 = 10¹, 100 = 10², ...)

[patton]

Very inductive, Watson.

[patton]

If you ever have time, I HIGHLY recomend an excursion into theoretical mathematics.

Your post shows an intuitive grasp of the difference between chaos and entropy, eg.

[stands2reason]

Think of an old crotchety lady who knows instantly when someone's trying to "piss on her leg and tell her it's raining."

'Ceptin' I'm not quite old yet. :-)

[stands2reason]

That's what I am?

[longshadow]

So what do mathematicians do? They come up with a bit of notation that allows them to capture the general case with a minimum of trouble, and then prove the result for the general case.

Show P_n true for n=0 or 1

Show P_n true for n=k => P_n true for n=k+1.

By induction, P_n is true for all n in the Natural numbers.

Extra credit/geek alert: what axioms are specifically required for the last step (the induction step) to be true?

[snarks_when_bored]

You're spoiling the surprise!!! (laugh)

[TheBrotherhood]

I don't know you. Therefore you must answer that question yourself.

[snarks_when_bored]

Speaking of Asperger's Syndrome, I've just run across the following entry over at Peter Woit's blog:

Autistic String Theorist Accused of Ecoterrorism and Being a Police Informant

[bondserv]

Quite definitely, says the mate.

And, if I spend much MORE time here, it may be terminal!

You definitely minister to my thirsty soul.

P.S. Did you see the Sanhedrin is official back in service after being defunct since AD 70. In their second meeting on Feb. 12th, 2005 they discussed the rebuilding of the Temple. Interesting, eh!

[snarks_when_bored]

This thread is close to dead, but I'll append another link just the same. It's to the English translation of a small part of Grothendieck's autobiographical work, Récoltes et Semailles (Harvests and Sowings). Reading the intensely personal reflections of a bona fide genius is not something we're ordinarily able to do. Keep in mind that the writer is one of the greatest mathematicians of the 20th century:

Récoltes et Semailles (Harvests and Sowings)

[Earthdweller]

After reading part way into this piece I find the relevance that ties the whole line of thought on this thread together. Thanks for posting it. I found it enjoyable.

"...Quite simply, mathematics had become a mistress, ever receptive to gratifying my desire. These years of isolation laid the foundation for a faith that has never been shaken - neither by the discovery ( arriving in Paris at the age of 20), of the full extent of my ignorance and the immensity of what I would be obliged to learn; nor (20 years later) by the turbulent events surrounding my final departure from the world of mathematics; nor, in recent years, by the thoroughly weird episodes of a metaphorical "Burial" of my person and my work, so perfectly orchestrated by those who were formerly my closest friends ....

To state it in slightly different terms: in those critical years I learned how to be alone.."

[Elsie]

"Whosoever drinks of the water I give him, will never thirst again."

[bondserv]

Jesus answered and said unto her, If thou knewest the gift of God, and who it is that saith to thee, Give me to drink; thou wouldest have asked of him, and he would have given thee living water.

"Whosoever drinks of the water I give him, will never thirst again."

"...but the water that I shall give him shall be in him a well of water springing up into everlasting life.

Jhn 4:24-26
24 God [is] a Spirit: and they that worship him must worship [him] in spirit and in truth.
25 The woman saith unto him, I know that Messias cometh, which is called Christ: when he is come, he will tell us all things.
26 Jesus saith unto her, I that speak unto thee am [he].

Jhn 15:4 Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.

[ctdonath2]

25. Seems about right...I like object-oriented programming partly because I can 'feel' the code (not as in textures, but kinda like knowing/'seeing' where stuff is in a dark room).

[ctdonath2]

Someone DID write a detailed paper (about a year ago) about the airspeed of an unladen swallow. Google it.

[IamConservative]

""At least you didn't have to read it, er, 19 times."


Uhh I'll have to get back to you on that."

Gimme three and I'll get back to you.