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Re: As Math Grows More Complex, Will Computers Reign?
Posted:
Mar 16, 2013 9:07 PM
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On Mar 16, 5:14 pm, use...@mantra.com and/or www.mantra.com/jai (Dr.
Jai Maharaj) wrote:
> As Math Grows More Complex, Will Computers Reign?
>
> By Natalie Wolchover, Simons Science News
> Wired.com
> March 4, 2013
>
> This simple computation, written with math software
> called Maple, verifies a formula for the number of
> integer triangles with a given perimeter. (Illustration:
> Simons Science News)
>
> Shalosh B. Ekhad, the co-author of several papers in
> respected mathematics journals, has been known to prove
> with a single, succinct utterance theorems and identities
> that previously required pages of mathematical reasoning.
> Last year, when asked to evaluate a formula for the
> number of integer triangles with a given perimeter, Ekhad
> performed 37 calculations in less than a second and
> delivered the verdict: ?True.?
>
> Original story reprinted with permission from Simons
> Science News, an editorially independent division of
> SimonsFoundation.org whose mission is to enhance public
> understanding of science by covering research
> developments and trends in mathematics and the physical
> and life sciences.
>
> Shalosh B. Ekhad is a computer. Or, rather, it is any of
> a rotating cast of computers used by the mathematician
> Doron Zeilberger, from the Dell in his New Jersey office
> to a supercomputer whose services he occasionally enlists
> in Austria. The name ? Hebrew for ?three B one? ? refers
> to the AT&T 3B1, Ekhad?s earliest incarnation.
>
> ?The soul is the software,? said Zeilberger, who writes
> his own code using a popular math programming tool called
> Maple.
>
> A mustachioed, 62-year-old professor at Rutgers
> University, Zeilberger anchors one end of a spectrum of
> opinions about the role of computers in mathematics. He
> has been listing Ekhad as a co-author on papers since the
> late 1980s ?to make a statement that computers should get
> credit where credit is due.? For decades, he has railed
> against ?human-centric bigotry? by mathematicians: a
> preference for pencil-and-paper proofs that Zeilberger
> claims has stymied progress in the field. ?For good
> reason,? he said. ?People feel they will be out of
> business.?
>
> Anyone who relies on calculators or spreadsheets might be
> surprised to learn that mathematicians have not
> universally embraced computers. To many in the field,
> programming a machine to prove a triangle identity ? or
> to solve problems that have yet to be cracked by hand ?
> moves the goalposts of a beloved 3,000-year-old game.
> Deducing new truths about the mathematical universe has
> almost always required intuition, creativity and strokes
> of genius, not plugging-and-chugging. In fact, the need
> to avoid nasty calculations (for lack of a computer) has
> often driven discovery, leading mathematicians to find
> elegant symbolic techniques like calculus. To some, the
> process of unearthing the unexpected, winding paths of
> proofs, and discovering new mathematical objects along
> the way, is not a means to an end that a computer can
> replace, but the end itself.
>
> Continues at:
>
> http://www.wired.com/wiredscience/2013/03/computers-and-math/all/
>
> Jai Maharaj, Jyotishi
> Om Shanti
>
> http://groups.google.com/group/alt.fan.jai-maharaj
Mathematics isn't just the practice of computation, it's also the
communication of the information so derived, and the method of the
computation. So, an algorithm for doing mathematics, as simple
exhaustion of a space, sees the same theoretical limits (or lack
thereof) for humans and computers. In application, mathematics as the
derived result is of course expressly tractable symbolically. Then as
to whether the information in a most concise and general form is
shareable as communication, communicable, basically the act of
indentifying applicable generalities as mathematics is as simply
algorithmic as the (also) mechanical computation given inputs for
outputs as mathematics. Basically that the mind is a general purpose
computer, the notion of "Good Old-Fashioned A.I." (cf. Haugeland,
"Artifical Intelligence") has that as plain capacity has increased
with technology, that, for any rote computational task computers more
economically perform calculation than the brain, then the question is
as to how the general purpose computer does mathematics that isn't
rote: to communicate.
With regards to application and any computation, artificial constructs
may exceed natural ones. However, being a good mathematician isn't
just proving theorems, but also communicating those results that
others may apply those theorems. Now, I'm not saying Einstein (or
Ramanujan) should be able to teach a chimpanzee to integrate, but a
computer schema of organized information in mathematics may not be
accessible to our lower "intelligence". Until the results and theorem-
proving machinery are accessible and transparent to another, Einstein
hasn't taught the parrot how to integrate if it pecks E=mc^2.
Will we be able to understand the inner workings of an artificial
"intelligence"? Well, I guess we'd write programs for that, programs
to extract and classify data, programs to organize and refine
generalities and exceptions (as generalities), programs to put forth
the gist of the sentiment, then no mathematics is beyond the brain, by
definition, though then some computations are simply beyond the
brain's resources or care.
Then, Zeilberger's anthropomorphism of the aides of computational
power, and everybody loves Zeilberger as a generality, to see the 3B1
or 3B2 or what it is as clinical colleague, would have for the general
course of its placement so the role of man in ideas. The algorithm is
inputs and outputs as adapters, and implementation as plainly
semantic, where inputs and outputs are to the world, then yes we may
be obsolete as the primary concrete thinkers of the world, but the
A.I. would still be of the world, and deterministic and such, then as
to: will the A.I's: be men.
Every person has to learn a lot more than mathematics, to be a
mathematician.
Regards,
Ross Finlayson
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