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Re: tricks, discoveries and such...

130.245.14.20

Posted by caa on May 17, 2000 at 20:51:04

In Reply to: tricks, discoveries and such... posted by gnat on May 16, 2000 at 23:40:20:

Hi gnat,

>> Take for example FFT, Fast Fourier Transform. Can it be considered
>> as some "conceptual breakthough"? Hmm, basically it's nothing more
>> than a trick. Take a well-known DFT, Discrete FT formula and apply
>> some smart grouping of sum members, that's all. Not a discovery in >> some strict sence, maybe. But it made a whole class of algorithms
>> practically computable.

I'm not very familiar with signal processing, but besides the details
the basis of DFT, I think, comes from approximation theory, real
analysis. I didn't say it very well in an earlier post, but I think
there's alot more enlightening than just "grouping of sum members":

earlier post

Anyone who is moderately mathematically sophisticated and who had
an intuition that approximating functions is simply "taking snapshots"
in an infinite-dimensional space, would have had formalized Fourier
Transforms. But only Fourier did. I trully think that mathematical
theories, espcially works by "geniuses", are not simply results of
tricks and hard works, but rather intuitions that normal people like
us don't have (until they point it out).

Nothing wrong with tricks and hard works either. All being equal,
these differentiate the goods and the greats. But in my experience
of knowing and reading about mathematicians or theorists, these bright
people are very passionate about their discoveries, significant or
not. And they show that very explicitly. And more importantly
*intuitions* and big pictures are what it's all about, not how fast
you can calculate (remember that scene in which Will and the prof
show off their lightening computational skills?).

Will Hunting was probably playing a cool genius. But from what I
know, read, and heard, he doesn't resemble anyone of them, not that
they are all the same. But then, he was also a troubled genius; but
then again, which one isn't.

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