From: Richard Loosemore (rpwl@lightlink.com)
Date: Wed Mar 22 2006 - 12:20:22 MST
H C wrote:
>> From: Richard Loosemore <rpwl@lightlink.com>
>> Daniel Tammet's ability to multiply seems to be mediated by a
>> shape-memory pathway. My (admittedly vague) guess would be that he
>> somehow got the shape memory part of his system to encode the math
>> algorithms for multiplication, so that he can feed in the numbers as
>> shapes and get them back as a new shape, corresponding to the product.
>> I would be interested to know what he has been doing all these years,
>> and whether he can perform many other types of mathematical operations.
>
>
> I think what it really comes down to is just a superior short term
> memory. For example, I can take any two digit number and calculate it to
> the fourth power (albeit far more slowly and error prone). I notice that
> I can maintain the algorithmic "ultra-fluidity" that he seems so
> proficient with in the numbers, however, as the size of the data sets
> necessary to remember grow, I have to continually "break" the
> ultra-fluid data manipulation in order to mentally repeat the data sets
> so that they remains unambiguous. So not only do we have to mentally
> implement the algorithm in such a way that the output is incrementally
> built from some input, but also it is necessary to remember the input
> and the output. The thing with savants, it appears, is that they have
> some particularly mental balance, in such a way that they can maintain
> the ultra-fluid flow of the mental algorithm, and the output and input
> can be remembed entirely unambigiously, without constantly repeating
> themselves.
>
> It sure would be nice to figure out how to do that, if it's not an
> unchangeable quality.
>
> I don't believe it is an unchangeable quality, because I have noticed
> that the ability for me to remember in such a manner is related to my
> particular state of mind. But I won't get into that right now.
>
> -hank
In general I agree that some savants might be using the mechanism you
describe, at least in part: they either don't need a rehearsal buffer
because their STM is so big that it can keep long strings up without
losing them, or they have such an efficient buffer that they can cycle
the numbers back in without having to attend to them (those two things
might turn out to be equivalent).
What intrigues me more, though, is Daniel's apparent use of shapes. We
appear to have a separate facility for dealing with 3D spatial stuff, so
I wonder if he isn't doing it using that facility, rather than with a
super efficient STM?
I had a similar experience, just once, when my Physics teacher at school
tried to impress us with his very first calculator, which had a square
root key. He remembered his calculator in the middle of a blackboard
calculation where he needed a square root, so he proudly grabbed the
calculator and started trying to get the number into it. Just for fun,
I tried to do it in my head before his calculator did it: I visualised
the square root function as a graph, used a bit of "feel" for where the
result ought to be, and started naming the digits of the answer. As I
got down to the lower digits the "feels" coming back from somewhere down
in my subconscious became more tenuous, but I tried to be sensitive for
what felt like "too big" or "too little", and then on the last digit I
just made a blind guess, just for fun.
Altogether there were only about five or six digits in my answer (and in
fact that was all his calculator could handle)... and it turned out that
my answer was exactly right, including the last wild guess digit. [The
confused look on the teacher's face, when he realized that someone had
produced the answer just before his calculator, was priceless :-)]
What was interesting was that the result came from this weird sense of
groping for the right digits, and being sensitive to a bunch of
mechanisms, somewhere inside, that were all trying to push the answer
this way or that. It did not have the feel of a calculation at all
(goes without saying anyway, since I would barely have known how to set
up such a computation). Although this wasn't shape memory, there was a
graph there at the beginning.
Some savants may be using similar techniques, but developed into vastly
more complex versions. Maybe hundreds of "subconcious" mechanisms that
all compete with each other to determine the digits of a result, getting
to the target digits by a process of relaxation. I could imagine such
relaxation mechanisms that were exactly isomorphic to a regular serial
algorithm, so they really could come up with extremely accurate digits,
one by one.
If such a relaxation calculator could be learned by the savant, the best
place to locate it might indeed be in a coopted chunk of the visual
system, where we already know that there is lots of relaxation-type
computation going on. And if it _were_ located there, the savant might
consciously experience it as some kind of imagined shape visualization.
I confess, I haven't had much time to go and read the details of what
Daniel has said, so feel free to shoot down this theory of his
particular functioning, if the data conflict with it.
Richard Loosemore.
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