From: Mathieu Bouchard <matju@...>
Date: 2002-01-12T12:00:41+09:00
Subject: Re: should I use ruby instead of perl


On Sat, 12 Jan 2002, Tomasz Wegrzanowski wrote:
> On Fri, Jan 11, 2002 at 08:30:07PM -0500, Mathieu Bouchard wrote:
> > Well, if a problem, to be solvable, has to be of finite length in a finite
> > alphabet, then the problem space is discrete, even though it's
> > theoretically infinite. If you think about real numbers that can be
> > incorporated in the problem definition: the subset of the real numbers
> > that can actually be written down (in whatever form) is countable. It's
> > "bigger" than the Rational set just like the latter is "bigger" than the
> > Integer set, but it's still countable.

> Infinite number of problems can map into the same solution.

Well, there are several ways to encode n numbers into a single number: for
example, N^n is countable. then take f(x,y)=x as a N^2->N function... I
agree that an infinite number of problems can map into the same solution,
but that doesn't automatically make the problem set
continuous/noncountable.

> Solution set is countable, problem set doesn't have to. Problems are
> represented in human mind usually, without finite symbol alphabet.

Okay, a mismatch in our conceptions of 'problem'. If it is agreed upon
that a problem is a particular neuron pattern, then the density of the
problem space becomes equal to the density of a brain in the universe,
which has yet to be decided. (Maybe I'm just being dense... oh. That would
prove your point then ;-)

> This discusion is quite esoteric :)

well duh!!! what else can you expect when you begin talking about
integrating on a problem space?

________________________________________________________________
Mathieu Bouchard                   http://hostname.2y.net/~matju