On Thu, Dec 15, 2011 at 1:06 PM, Joe Niederberger <firstname.lastname@example.org> 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?
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.
 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.