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Re: Brainstorming about STEM (was About Functions)
Posted:
Dec 15, 2011 5:44 PM
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On Thu, Dec 15, 2011 at 1:06 PM, Joe Niederberger
<niederberger@comcast.net> wrote:
>>I guess I'm more in the Sir Roger Penrose camp. He sees >computers as
>>blindly dumb compared to humans because the latter have a >track record
>>of doing non-computable things.
>
> &
>
>>I don't like science fiction that does too much to mislead the public.
>
> &
>
>>It's fun to have a superman complex.
>
> Non computable things? Really???? Name one.
> For example, show me one idiot savant that can
> factor any number (or declare it prime) no matter
> how large in constant time. Or something else
> compelling.
>
The examples I remember from Sir Roger's talks
were mostly chess related. Fairly trivial puzzles
that a chess player could solve (without being
an idiot savant), but that stump Deep Blue to
this day.
But pick any cool proof by a gifted mathematician,
say the one that V + F == E + 2 by Von Staudt, as
well explained in 'Polyhedra' by Cromwell. When
have you seen footnotes to computer programs
that have duplicated any of these results?[1]
We still have expressions by Ramanujan for
which no formal proof exists, but have been
verified to billions of digits.
It's really quite easy to find results humans
have arrived at that no automaton has been
able to touch.
> I think you are the one entertaining thoughts
> of genuine superman powers.
>
> Joe N
No, it's just that AI has been over-hyped and
people have this inferiority complex around
computers that's all based on balderdash.
Kirby
[1] http://www.ics.uci.edu/~eppstein/junkyard/euler/interdig.html
this more cryptically notated one is not as
easy to follow as Cromwell's rendering, but
that's OK. Good to see Sommerville's name
go by. There's a space-filling tetrahedron
named after him, also called a 1/4-Rite in
my neck of the woods, where we care about
such things.
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