Vladimir Nesov wrote:
On 10/5/07, Richard Loosemore <[EMAIL PROTECTED]> wrote:
Mike Dougherty wrote:
On 10/4/07, Richard Loosemore <[EMAIL PROTECTED]> wrote:
All understood. Remember, though, that the original reason for talking
about GoL was the question: Can there ever be a scientific theory that
predicts all the "interesting creatures" given only the rules?
The question of getting something to recognize the existence of the
patterns is a good testbed, for sure.
Given finite rules about a finite world with an en effectively
unlimited resource, it seems that every "interesting creature" exists
as the subset of all permutations minus the noise that isn't
interesting. The problem is in a provable definition of interesting
(which was earlier defined for example as 'cyclic') Also, who is
willing to invest unlimited resource to exhaustively search a "toy"
domain? Even if there were parallels that might lead to formalisms
applicable in a larger context, we would probably divert those
resources to other tasks. I'm not sure this is a bad idea. Perhaps
our human attention span is a defense measure against wasting life's
resources on searches that promise fitness without delivering useful
results.
I hear you, but let me quickly summarize the reason why I introduced GoL
as an example.
I wanted to use GoL as a nice-and-simple example of a system whose
overall behavior (in this case, the existence of certain patterns that
are "stable" or "interesting") seems impossible to predict from a
knowledge of the rules.
You do predict that behavior by simulating the model. What you
supposedly can't do is to find initial conditions that will lead to
required global behavior. But you actually can - for example by
enumerating possible initial conditions in a brute force way and
looking at what happens when you simulate it. It's just very
inefficient, and as a result you can't enumerate many initial
conditions which will lead to interesting global behavior. And
probably there are tricks to get better results, by restricting search
space. You propose a framework which will help in efficient
enumeration of low-level rules and estimation of high-level behavior,
and restrain possibilities to as close as possible to existing working
system - human mind. All along these same lines. Computational
mathematics deals with this kind of thing all the time.
Vladimir,
You keep taking this example out of context! You are making statements
that are completely oblivious to the actual purpose that the GoL example
serves in the paper: everything you say above is COMPLETELY impractical
if it is generalized to systems more complex than GoL.
In short, your statements are complete non-sequiteurs.
This is about the fourth or fifth time that you have taken the thing out
of context and then dismissed the whole thing with a comment like
"Computational mathematics deals with this kind of thing all the time."
Richard Loosemore
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