The Boy with the Incredible Brain
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The Boy with the Incredible Brain
http://video.google.com/videoplay?docid ... 6664593143
Some of you may have heard of this dude - there was a great write up a couple years ago called "A Genius Explains"
http://www.guardian.co.uk/weekend/story ... 03,00.html
I've just started watching - it's not to be missed.
Some of you may have heard of this dude - there was a great write up a couple years ago called "A Genius Explains"
http://www.guardian.co.uk/weekend/story ... 03,00.html
I've just started watching - it's not to be missed.
Wow, this is what I've always wondered about mathematical savants. If they are calculating (relatively) complex problems nearly instantaneously, then they can't possibly be adding/subtracting/deriving/quantifying numbers the way we do on paper, because it's not possible for that mental activity to be instantaneous, IMHO.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."
It's like saying you can count to 100 instantaneously - well, no you can't.
I find that very interesting, I'll have to check out the video at some point.
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Actually, the video shows how this is indeed possible - there are schools in china which teach the "ancient art of the abacus" and it's shown how anyone can do some really difficult calculations really fast. (but the examples demonstrated were just tough calculations - not factoring and stuff)R00k wrote: Wow, this is what I've always wondered about mathematical savants. If they are calculating (relatively) complex problems nearly instantaneously, then they can't possibly be adding/subtracting/deriving/quantifying numbers the way we do on paper, because it's not possible for that mental activity to be instantaneous, IMHO.
But the way Tammet is doing them clearly seems to be different - actually this theme is explored really nicely towards the end of the video.
Even an abacus isn't the same as computation. It's more of a stylized/visual summing - almost abstracted mathematics in a way - is it not?[xeno]Julios wrote:Actually, the video shows how this is indeed possible - there are schools in china which teach the "ancient art of the abacus" and it's shown how anyone can do some really difficult calculations really fast. (but the examples demonstrated were just tough calculations - not factoring and stuff)R00k wrote: Wow, this is what I've always wondered about mathematical savants. If they are calculating (relatively) complex problems nearly instantaneously, then they can't possibly be adding/subtracting/deriving/quantifying numbers the way we do on paper, because it's not possible for that mental activity to be instantaneous, IMHO.
But the way Tammet is doing them clearly seems to be different - actually this theme is explored really nicely towards the end of the video.
Which would seem to lean more in the direction of a savant's approach, than in the direction of actual digital computation, which is what we do.
It gives me the strange notion that some sort of rosetta stone could be made between a savant's approach, abacus-style math, and the advanced calculations of our civilization, and it could yield some sort of deeper understanding of the universe.
These people seem to have a more direct connection to the metrics of our environment, through entirely natural means.
actually, it proves that maths as we know them are 'the long way round'[xeno]Julios wrote:Actually, the video shows how this is indeed possible - there are schools in china which teach the "ancient art of the abacus" and it's shown how anyone can do some really difficult calculations really fast. (but the examples demonstrated were just tough calculations - not factoring and stuff)R00k wrote: Wow, this is what I've always wondered about mathematical savants. If they are calculating (relatively) complex problems nearly instantaneously, then they can't possibly be adding/subtracting/deriving/quantifying numbers the way we do on paper, because it's not possible for that mental activity to be instantaneous, IMHO.
But the way Tammet is doing them clearly seems to be different - actually this theme is explored really nicely towards the end of the video.

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hm yea you're probably right - didn't think about it that way before.R00k wrote: Even an abacus isn't the same as computation. It's more of a stylized/visual summing - almost abstracted mathematics in a way - is it not?
I wonder, though, how we actually do arithmetic. I'm pretty sure that from my own experience, I use a lot of memory - multiplication tables, etc.R00k wrote: Which would seem to lean more in the direction of a savant's approach, than in the direction of actual digital computation, which is what we do.
yea - it's fascinating how each number has its own unique synaesthetic sense.These people seem to have a more direct connection to the metrics of our environment, through entirely natural means.
reminds me a bit of this swiss synaesthete who can actually taste musical intervals, and uses this to enrich the way in which she composes music. (i think she's swiss at least)
Certainly. But when it comes to more difficult arithmetic, like long division or square roots, it is a repetitive digital calculation process -- you take the result of these two digits combined with this operand, then you apply the remainder to the same calculation using the next two digits, etc...[xeno]Julios wrote:I wonder, though, how we actually do arithmetic. I'm pretty sure that from my own experience, I use a lot of memory - multiplication tables, etc.
This is apparently far from what this fellow is doing with the numbers. And I believe it's also quite a bit different from the way it is done on an abacus, although I've never really used an abacus for any kind of division, just for simple add/subtract/multiply computations.
You can see patterns in nearly any mathematical construct, and it always struck me that an abacus is akin to using the derived patterns of math to arrive at answers, instead of performing calculations on the values themselves.
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yea i guess it is a form of serial computation.R00k wrote:
Certainly. But when it comes to more difficult arithmetic, like long division or square roots, it is a repetitive digital calculation process -- you take the result of these two digits combined with this operand, then you apply the remainder to the same calculation using the next two digits, etc...
While i agree for sure that what this guy is doing is a very different form of computation (seems way more connectionistic/dynamical), I think the abacus stuff is probably serial. If you watch the video, it shows a bit of how they do it, and it seems pretty rote.R00k wrote: This is apparently far from what this fellow is doing with the numbers. And I believe it's also quite a bit different from the way it is done on an abacus, although I've never really used an abacus for any kind of division, just for simple add/subtract/multiply computations.
They're visualizing the abacus moves in their head, and you can see their fingers moving in thin air, doing each individual computation. They're using a visual simulation, which is based on memory, to "observe" the outcomes of each finger move, but it's still serial.
True it may not be isomorphic to the arithmetic computations that we normally use in arithmetic, but it still seems serial.
That said, I really don't know much about how an abacus works.
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Everyone says that he has extraordinary "mathematical" ability, but they only show him doing basic arithmetic and memorization. IMO true mathematical ability would be demonstrated with him being able to do research and to prove theorems for which mathematicians have not discovered a proof yet, etc... or at least being able to prove every single theorem of calculus, linear, statistics, and so on. Of course those could be memorized, but perhaps, if he really were that brilliant, he could continue the work of famous mathematicians who died.
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I call it the Toxic test.
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