Conversation with Prodigious Savant Daniel Tammet - Part II, How a Prodigious Savant’s Mind WorksShare
Daniel Tammet on how his mind works.
Although their unusual abilities compel considerable attention, there are fewer than 100 known prodigious savants living at the present time. Daniel Tammet is one of them. Over 30 years, the London-born mathematical and language whiz has transformed from an awkward, reclusive boy into a confident adult. His quiet, private life of strict routines gave way in 2006, when his memoir Born on a Blue Day became a best-seller, necessitating travel, self-promotion, and talk show appearances. His latest book, Embracing the Wide Sky, is a scientific exploration of his extraordinary abilities (reciting pi to 22,514 places, learning to speak Icelandic in a week) and a tour of autism.
On August 18th and August 19th, 2009, Daniel was gracious enough to let me peer into his world. I was aware of the great number of interviews with Daniel that already exist, but as a psychologist, I still had many lingering questions, which Daniel was very patient in answering for me. These two days, I left my prior expectations, biases, and ways of thinking at the door and transported myself into Daniel's mind. As a result, I was fortunate enough to be able to share his unique way of seeing the world.
Daniel's insights changed my own way of thinking, not only with regards to Autism and Asperger's syndrome, but also in terms of the full extent to which personal change is possible, the nature and nurture of individual differences, intelligence, creativity, genius, fiction, art, poetry, math, love, relationships, the mind, brain, the future of humanity, and the appreciation of many different kinds of minds. A portion of my interview can be found in the November/December 2009 issue of Psychology Today (Numbers Guy: An autistic savant joins the wider world). .
I hope you find Daniel's reflections, insights, and ongoing journey just as fascinating and thought-provoking as I have.
S. I'm quite impressed that in 2004 you recited pi from memory to 22,514 decimal places. How did you train for this event? Did you spend all your time consciously memorizing the pi landscape? Did you at any point do any actual calculations of pi in your head? Or were you memorizing the digits of pi from a print out and then associating the numbers with the visual imagery and reading off the landscape during the actual event?
D. Yes, that was an exercise in memory, in the way that I visualize sequences of numbers and shapes, and how those shapes in turn integrate into something like a numerical landscape. Calculation would be impossible, it would be far more difficult than memorizing the numbers as far out as I did. But what I do when I memorize a number as enormous as pi, pi is an infinite number, it goes on forever, is there is an element of conscious control there because I can decide in the same way a painter decides how he's going to break up a landscape and put it on to his canvas. I can decide how I take a 10 or 20 or 30 digit number at a time and break it up. Do I break it up into intervals of 5, 5, 5, 5, 5? Or 3, or 4? Or 2 and 5 and 3 and 4? Or 5 and 4 and 2 and 1 and 5 again?
The decisions that I make would depend on the numbers themselves. So it's a very organic process. I'm looking at the numbers and deciding on their individual basis how they best go together in my mind. If a group of numbers is particularly shiny as a four-digit segment, I can group them together. And next to them, I can see that the following, say 3 digits, are very dark in my mind, then that is a particularly visually interesting or arresting image. And it would be perhaps much more easy to remember it as that, in that combination, for that reason, then to simply decide in advance to always group them in groups of 2 or 3 or 4 irrespective of the actual characteristics of the numbers themselves as they come up.
So it's a very organic process and a very involved one. It didn't take very long. In Born on a Blue Day I described the process and in Embracing the Wide Sky I go into more detail about the science of what I'm doing. I describe it as being similar in some way to music and how music gets constituted out of repetitions of smaller pieces. This is in a sense what is happening with this vast landscape, this vast symphony of numbers. The colors and the shapes and the textures are composed of smaller fragments of combinations of digits from the colors and shapes and whatever I see for each of those. And the repetitions involved, and the coherence of it all together, makes it memorable and beautiful.
I think beauty is a very important part of what I'm doing. I'm appreciating the beauty of the numbers and letting them tell me that beauty, revealed to me in front of my eyes. In Embracing the Wide Sky I describe it almost as a song that the numbers are playing for me. I think that is a useful analogy in terms of understanding it.
In terms of a time frame, in the three month time period leading up to March 14th, I spent probably every other day on average reading the print outs, and absorbing the numbers. And on those other days, I would just be doing other stuff like anyone else and just letting those numbers take shape in my mind. So it wasn't very intensive. Of course, there was a lot of work involved, in terms of reading off that many digits and then working out the best and most beautiful visualization for them and then practicing the actual recitations. The actual recitation in the end proved to be the hardest part because there was so many digits to recite. Up until the day that I actually recited them, I'd never recited them off in one go before.
I'd always just practiced in the weeks leading up to the event for maybe an hour at a time. And in that hour I'd probably be able to recite 3 or 4, or 5 thousand digits. So at that point, the other person who was having to check every digit for me, this poor sole, after the hour, it was rough. March 14th, 2004 was the first and last time that I actually recited those 22,514 digits in one go from start to finish.
S. It is remarkable. I am curious though, if you actually tried the calculation pi, could you actually do the calculation at all in your head to any digits?
D. I've never tried the calculation. I am not actually aware of the equations mathematicians use.
D. I describe in the first book the history of pi, and how long in the past, before computers, there were very brave individuals who with nothing better to do with their time, with just a great love of pi as I have, decided to reckon it out for themselves and be able to do that at the rate of maybe a digit per week. And one of those mathematicians had to find 35 digits, the amount that he was able to work out in the course of his entire lifetime. The digits were put on his tombstone, a fitting epitaph.
S. I find it fascinating that you automatically associate each number with its own unique detailed visual imagery, and this can be replicated. For instance, you always see 6 as tiny, and you always see 1, 111 as round, bright and spinning. Do you think all savants with your capacities have the same visual associations? Are there individual differences among savants in terms of what they see in their mind when presented with a number or do all savants see the same thing? Do all savants see 1,111 as round, bright and spinning, for instance?
D. It's very difficult to know because there is very little self-reporting among savants. It's such a rare condition first of all. I'm sure there are more savants out there, particularly in the third world countries, in places like India and China and so on that we just don't know about for the time being but which we will discover in the future as the condition becomes better known and better studied. I'm sure there will be more self-reporting in the future, people writing their own accounts of what they're seeing in their mind and how they do what they do. I think that will be very helpful to scientists and will go a long way towards dispelling these persistent myths of savants as almost supernatural creatures or simply memory machines and nothing else.
There is a great creativity and a great sensibility involved in what savants are doing and synesthesia is one example of that-- this ability, it's so poetic, it's almost the essence of poetry, to associate a number with a color or a sound or a shape or combinations of these things. And of course we find examples of this in language and literature. I certainly use it in my writing. It's something that people who aren't savants, who aren't autistic, do sometimes experience as well. There are reports that I write about in Embracing the Wide Sky, about the prevalence of synesthesia, about the prevalence of number lines as well for example. I'm afraid that they're much more common than people assumed before and scientists expected and much more poetic in a way as well.
It's not simply necessarily a case of seeing one as white and two as blue or whatever. The example I write about in Embracing the Wide Sky, one of the people in France, Galton, reported describing how he sees the number 6 and 9 and he described the personalities of these numbers. And people have written to me since reading either of my books or both of them and saying, ‘Well, I see numbers as male or female', for example, in a way that a French person would see words, nouns as being masculine or feminine.
I don't have that sense of numbers, for example, as being male or female but this particular person does. And others who write to me about the colors they see, sometimes the colors correspond with the colors I see, but not always. One of my good friends in Iceland is a poet and she has synesthesia and we have discussed the different colors we both see for numbers and there is a correspondence, there is quite a large correspondence between them, but there are variations as well and differences as well. So I think there is something there, that it is something that is within the brain, that perhaps everyone is born with, but in those early formative years the brain overdevelops and then prunes back the connections that it has between cells.
And I think education as well. The fact that when we go to school, we're taught in a very formulaic way, to go through a certain curriculum, taught to do sums in a certain way, to learn languages in a certain way, and to think about ideas in a certain way. And I think the cost of that curriculum approach is that it does stunt many children's natural creativity and the way that they would approach a language or a sound or a problem differently.
We couldn't say which is better or worse than the way that we teach in a curriculum but it would make perhaps more sense. It would be intuitive. I think one of the great costs of education where you have so many children in one class or one teacher and a curriculum to teach is that you lose so much of that intuition- children have to give up so much of that intuition to simply memorize by rote a great deal of information.
S. This is what is the puzzle for me- how do you think your brain automatically makes the same associations every time? What do you think is going on in the neurons that maintain such a remarkable consistency in the associations, especially considering you never consciously and deliberately learned the associations? What really fascinates me is that your brain is wired in a way where each number is actually linked to a particular representation, and from a cognitive science prospective this fascinates me. Do you have any insight into how there is this consistency? This consistency suggests to me that there is this one-to-one mapping in your brain somehow, at the neuron level.
D. My own view is that I'm not sure that there is that one-to-one mapping. I would go back to the analogy with language. The average person knows about 45,000 words and that's an enormous vocabulary, three times as many words as Shakespeare ever used in all his connected works.
I don't know that linguists actually know. I'm very interested in linguistic research from my study of language and there is, as far as I know, no universally accepted theory in any event for how young children and many young adults acquire such an enormous vocabulary, are able to remember the meanings and the connotations and the appropriate response to each of those 45,000 words. But I don't think the explanation would come from imagining that we attached a word and its meaning and its connotation to its own individual neuron, and that therefore you acquire a mapping over 45,000 neurons to acquire that vocabulary.
My guess is that it would be something much simpler than that. A giraffe is understood as being an animal, so we're accessing that animal and then what makes it different from a dog or a cat, well it's much taller and what makes it different to other tall animals like an elephant, well it's much thinner. So I think what the brain is doing in terms of language is accessing certain fundamental traits, universal traits- height, shape, color, brightness, speed and so-on- and may even be mapping these onto lexical features.
That's another interesting theory I bring up in the chapter on language. In English we have GL, which seems to match very well with associations having to do with light or sight or to know: glean, glitter, glance, glass, and so on. And this works in many other languages as well. In French for example, it wouldn't be GL, it would be LU. In French words that start with LU, almost all of them have some association with light, including the word itself, in French, Lumiere.
That seems to suggest that you have a certain number, although I don't know what the number would be, of these universal, fundamental traits or features. And where this mapping, where this ability to break this down comes from would go way, way back in the evolution of our mind over the centuries and that vocabulary, perhaps all vocabulary, is then somehow seized through these fundamental ways of seeing the world, of perceiving actions, objects, feelings, and ideas.
And for numbers, particularly the way that I see numbers, I would imagine that something similar is taking place. That I have basic, maybe even a relatively small number of synesthetic responses for the smallest numbers and then with the heightened connectivity, whatever the creativity that emerges from that, my brain over time has been able to come up with these shapes.
I mean, many of these shapes are composites, as I describe in Born on a Blue Day. The shapes for 6, 943 is an emergent property of the shapes that I see for 53 and 131. If you take 53, as I see it, as being very round and lumpy, and a 131 as being taller, almost like an hourglass shape, and you put those on one side and then another side and you have a space in-between, that space is unique, that space, that visual space, the negative space as artists would call it, is unique to the contours of those two shapes and it creates a new shape, a third shape. That is the shape that I would visualize in the case of 6943, which is the product of 53 multiplied by 131.
So many of the shapes that I'm seeing up to 10,000 are products of prime factors multiplied together so the actual number of prime factors up to 10,000 is much smaller than 10,000. So that straight away cuts down on the number of unique shapes that I would have to see. And then where do these prime shapes come from? That's a whole other question that I concede in Embracing the Wide Sky. I have no idea for sure. My best guess would be that I'm simply taking the attributes- in the case of 53 for example, I see 5 as solid and 3 as round - and maybe my mind is simply then merging these qualities together and coming up with a shape that somehow expresses solidity and roundness together.
S. This sounds very plausible. It's more easy for me to wrap my head around how your brain could make associations with shape and maybe even color, but when you say things like brightness, the attribute brightness, or the attribute spinning, how can your brain differentiate different numbers in terms of it's brightness since there is no intrinsic difference in brightness between numbers? Do you have any ideas on what your brain is doing with the attribute brightness for instance? How does it differentiate?
D. I have no idea, certain numbers are bright, and others are dark. I have always seen them as dark, and distinguished them thusly. I can't give you any neurological explanation of that particular example, I'm afraid.
S. You have reported that you actually have quite a high IQ, about 150. Being a savant with a high IQ makes you quite unique among savants. How do you juggle the savant tendency to process stimuli as associatively and in parts with the simultaneous high IQ proclivity to process stimuli holistically and conceptually? Is there ever a conflict in which you have to consciously switch gears, or do you automatically and seamlessly switch between the two modes of thought? Or perhaps your default mode of thought is detail oriented and then you consciously impose concepts on top of that? Can you describe your subjective experience in this regard? (Thanks to Martha J. Morelock for this question)
D. It's a very good question and of course it's a very complex question. I'd have to really think about how I think to give any kind of full report.
I am aware of changing gears consciously between different ways of thinking, but I am aware that I do in a sense occupy two different countries of the mind, two different ways of seeing things. There is that very detailed oriented view but then there's that ability to stand back as well. So for example, in Embracing the Wide Sky, I say in the chapter on perception that when I first step into a room, there is that initial swirl of details and of information in fragments that is just swimming into my head. But after a few moments that kind of calms down. If I initially see the scratches on a table surface before I see the table, I do subsequently see the table.
In terms of the optical illusion I give in the perception chapter, although I'm able to see the details in such a way that it allows me to circumvent the effect, I'm able to see the effect as well. I am able to see both. I am able to in a sense switch between two different ways of seeing in order to perceive the optical illusion both as you would see it, I would imagine as most people would see it, and seeing that the two circles in the middle of the page, one surrounded by small circles and the other by large ones are in fact the same size.
But when it comes to my day-to-day life, I'm not really aware that I switch consciously. I guess it would be very time consuming and very clumsy to have to do so. To be in a conversation with someone and have to constantly switch gears in a conscious way. Or when I'm writing, to have to switch gears in a conscious way or when I'm preparing dinner or on an airplane or whatever it would be. So although I am conscious of the fact that I do have this ability to switch between both, I'm not necessarily doing it consciously. I'm not having to say to myself ‘look I'm in this mode, now I need to go to this mode'.
I'm not aware of whether one impedes on the other. I think if anything there is a kind of synchrony, a kind of ballet between the two that allows me to draw the benefits from both. I certainly feel in my writing that there is a lot of detail and people have commented on the detail but I certainly think I am able to see the bigger picture to some extent and to draw conclusions and make comparisons and to describe scenarios and situations in broad strokes.
S. Do you think the way your mind is wired allows you in any way to see some underlining "truths" about reality that most people with "normal brains" can't see?
D. I'm sure that it gives me a different perspective on the world. Some people have speculated that Einstein was on the autistic spectrum because he didn't speak for the first years of his life and was considered only in his very first years a relatively slow bloomer and then obviously he did very well.
I'm not saying that he wasn't good at maths, that's one of those myths. He was actually very good at maths from a very young age. But one of the quotes that he gives in one of his writings is to say that one of the reasons that he was able to tackle questions about the fundamental nature of the universe that others missed was that growing up in an unusual early childhood stage where other children were questioning things, even fundamental things, but then moving on to other things, he didn't go through the same stages of development as the other children. And so by the time he did catch up with his peers, they'd all moved on and he was even into adulthood fascinated by these same almost childlike questions about light and space and velocity and so-on. And this almost childlike curiosity stayed with him and I think motivated him to achieve all these great insights subsequently.
Obviously coming from a childhood that was very different, which I describe in detail in my autobiography, and touch on more briefly in Embracing the Wide Sky, it's clear that if you don't go through the same development process as everyone else, then you're bound to see the world differently. And you're bound to approach problems or ideas or situations from different perspectives. That's a very positive thing potentially because we need solutions to many problems. As I said in the Embracing the Wide Sky very clearly, as we define solutions for the future we will need to draw on all of our available intellectual capital as a society and find new thinking because there's one kind of thinking that gets us into a mess such as this present financial crisis for example, and we're going to need a new kind of thinking to get us out of it.
So I think that in the future people will see more high profile autistic intellectuals, high functioning autistic individuals in public life, contributing to society in their own way and making use of their own insights, their own ideas to do so, and I think that's a very, very positive change that we have touched the beginning of realizing.
© 2009 by Scott Barry Kaufman
Other parts of the series: