I was nearly kicked out of school in seventh grade for coming up with a method
of manipulating (multiplying, dividing) large numbers in my head using what I
later learned was a shift-reduce method. It was similar to this:
http://www.metacafe.com/watch/742717/human_calculator/
My seventh grade math teacher was so upset with me, he almost struck me
(physically -- you could get away with that back them). His reason? "Wasting
valuable math class time."
The point is, you can train yourself to do this type of thing and look very
savant-like. The above link is just one in a series of videos where the teacher
presents this system. It takes practice, but not much more than learning the
standard "multiplication table."
Cheers,
Brad
Vladimir Nesov wrote:
Interesting: is it possible to train yourself to run a specially
designed nontrivial inference circuit based on low-base
transformations (e.g. binary)? You start by assigning unique symbols
to its nodes, train yourself to stably perform associations
implementing its junctions, and then assemble it all together by
training yourself to generate a problem as a temporal sequence
(request), so that it can be handled by the overall circuit, and
training to read out the answer and convert it to sequence of e.g.
base-10 digits or base-100 words keying pairs of digits (like in
mnemonic)? Has anyone heard of this attempted? At least the initial
steps look straightforward enough, what kind of obstacles this kind of
experiment can run into?
On Tue, Jul 1, 2008 at 7:43 AM, Linas Vepstas <[EMAIL PROTECTED]> wrote:
2008/6/30 Terren Suydam <[EMAIL PROTECTED]>:
savant
I've always theorized that savants can do what they do because
they've been able to get direct access to, and train, a fairly
small number of neurons in their brain, to accomplish highly
specialized (and thus rather unusual) calculations.
I'm thinking specifically of Ramanujan, the Hindi mathematician.
He appears to have had access to a "multiply-add" type circuit
in his brain, and could do symbolic long division and
multiplication as a result -- I base this on studying some of
the things he came up with -- after a while, it seems to be
clear how he came up with it (even if the feat is clearly not
reproducible).
In a sense, similar feats are possible by using a modern
computer with a good algebra system. Simon Plouffe seems
to be a modern-day example of this: he noodles around with
his systems, and finds various interesting relationships that
would otherwise be obscure/unknown. He does this without
any particularly deep or expansive training in math (whence
some of his friction with "real academics"). If Simon could
get a computer-algebra chip implanted in his brain, (i.e.
with a very, very user-freindly user-interface) so that he
could work the algebra system just by thinking about it,
I bet his output would resemble that of Ramanujan a whole
lot more than it already does -- as it were, he's hobbled by
a crappy user interface.
Thus, let me theorize: by studying savants with MRI and
what-not, we may find a way of getting a much better
man-machine interface. That is, currently, electrodes
are always implanted in motor neurons (or visual cortex, etc)
i.e. in places of the brain with very low levels of abstraction
from the "real word". It would be interesting to move up the
level of abstraction, and I think that studying how savants
access the "magic circuits" in thier brain will open up a
method for high-level interfaces to external computing
machinery.
--linas
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