Savants: Seeing with numbers?

A continuation of Follow up to Secrets of Success.

I stumbled across an interview with autistic savant and author of the book Born on a Blue Day, Daniel Tammet, in Scientific American. If you read and agree with my last article relating to autistic savants, you'll realize that the title of the article "Learn to Think Better: Tips from a Savant" is a bit deceptive. The only tip he gives is one promoted by most psychologists nowadays. Anyway, go read the interview. It's pretty interesting and I hope to get a chance to read the book soon.

There are several things that Tammet says that made me wonder...

    The first thing he says about numbers is that numbers, to him, are multidimensional. He claims that each number takes on complex forms that he can visualize, later claiming that he perceives them as (pseudo)physical objects; that is, they have "form, color, texture and so on." This makes me wonder in what sense he means this, barring that he's a synesthete (though he might be, or even might need to be in order to have his talents*). In the few hours I've had to reflect on this, I can't seem to push my imagination beyond the point where the numbers merely relate to visual images. The furthest I have gotten so far is that the number 111 strikes an image in my mind's eye that is like round lumpy oatmeal. Of course, this is only because I just adopted Tammet's description of the number and tried to employ it with my own understanding, and as such, the roundness of the number 111 has no inherent connection with the number 3 (or any other number) and likewise for lumpiness. I'd bet that most of you who try this mental exercise will find yourself at a similar realization: one in which the relationship between the conceptual number and its visual characteristics is limited to mere association.

    Since Tammet's understanding of numbers is far beyond mine and I am utterly incapable of even partially internalizing his description of the numerical domain with the powers of my imagination (maybe I can draw upon the powers of LSD), I've not but my speculation to depend on. It leads me to assume that his understanding of numbers is not just associations with visual characteristics but rather that the visual characteristics are fundamental to the numeral; that is, the number 111 and round, lumpy oatmeal are one in the same (to a similar degree in which "bachelor" and "unmarried man" is the same for us). Tammet has already given us a description of his thought process when cognizing the number 111, but I would not find it surprising if to the description "round, lumpy oatmeal" of a numeral triggered the number "111". Essentially, his mind somehow bi-directionally maps appropriate numbers (e.g., multiples of 3) to the corresponding "visual characteristic" (e.g., roundness).

    I think that several people might find that act of associating numbers to images undermines my point of not being able to imagine another's thought processes, so I feel I need to try to make an important distinction here (if such a distinction is possible). The very act of emulating Tammet's described thought process is fundamentally restricted to certain cognitive faculties; namely, of numbers, visual imagery, and language. I would guess that when we entertain the idea of Tammet's understanding of numbers, the mental connection between the concept of a number and imagery is the product of internalizing an idea through language. That is, we are merely taking a "sentence" (i.e., the idea) and entertaining that, not the actual conscious or mental experience of the process itself. And here lies the great distinction: one involves internalizing an idea and the other involves internalizing an understanding. I dare someone who previously did not have such prowess to perform this mental experiment and honestly claim "Aha! It all makes sense now! The number 3 is no longer abstract but shares a perceptual trait with all other multiples of three. Oh look, it's number 3's friend number 111! I can tell because they look alike. Number 111 also looks like number 37! And the number 37 looks similar to number 116.28571..." (of course, I can say all of this, but I cannot actually do it or even properly think about doing it).

    Another thing I find intriguing is this visual map that Tammet indirectly claims he has. He says that the number 111 is round, like the number 3, and also lumpy like the number 37. I don't think it would terribly wrong here to assume that other visual features are identified with other numbers; shininess or smoothness with numbers 5 and numbers not wholly divisible by the number 19, and so on. So I'm left to wonder: how exactly did these visual features come to represent what they represent? Why are the particular features chosen to represent particular numerical relationships? Are they chosen by virtue of some connection between the nature of a numerical relationship and something inherent in the visual feature, or are they simply arbitrary? Are there any numbers that strike two contradicting visual features, or have all of the intricacies of mathematical relationships been taken into account? All of these questions lead my speculation down a wide, tricky, and confusing path which I will spare you (and myself) the pain of working through it. But there is one obvious thing that could account for this: since Tammet is autistic, it would not be unlikely for him to have simply focused his compulsions and obsessions on numerical calculations and then associating numerical relationships with objects around him. It wouldn't be impossible for years and years of such behavior to lead to the kind of understanding that Tammet has.

    I am left to conclude, after exhausting my faculties, that Tammet just has an abnormal mental domain or platform which lies at the foundation of his comprehension. This relates back to my other post in that it shows how a savant's understanding is incompatible with conventional minds. It is not accessible or cognizable to anyone but him, and he even proclaims that he finds it "surprising that other people don't think in the same way," indicating that his imagination is similar to ours in that it cannot escape its own understanding. Further, he states "I find it hard to imagine a world where numbers and words are not how I experience them!" Maybe, Daniel, you should read my post on why that is. =)

    That is not to say that these abilities are forever elusive to empirical inquiries. Tammet offers some potential biologically grounded suspects for his abilities. Hyperconnectivity, he says, could account for his rich understanding of numbers and words. For example, cross-modular connections between his calculating/numbers/whatever part of the brain and somewhere in his visual cortex could help explain why Tammet associates form, color, texture and etc. with numbers, though the mystery of its structural organization remains (for example, the semantic organization of his visual understanding of features such that it corresponds to certain numerical functions--and I think this is the really cool part). I can only hope that neuroscience will one day explain Tammet's vast mental network of numbers and visual characteristics. However, this empirical faith does nothing to help my understanding of Tammet's conscious experience nor would it be wise of me to hope that it ever will.

    The point I'm trying to make is the same as the one in my last post regarding this topic. This is just presented in another context.

*Another interview I came across a few days ago with a synesthesia specialist. Not that good of a read but at least the topic is interesting.