Vladimir,
I say the following without meaning to be critical.
In what I wrote yesterday, I was trying to establish the first point in
the sequence of points that make up the argument in my paper.
What is happening, in this discussion, is that you are trying to ask me
to present the entire argument that was in the paper, but only one step
at a time. That seems fair enough, by itself, except that .....
This is having the unfortunate side-effect that as each point is
presented, you are interpreting it and (especially) running on ahead
with it in directions that do not have any relation to my argument.
The paper I wrote was a single coherent whole, and this process of
breaking it up is getting crazy. I find myself continually trying to
explain that this or that argument has nothing to do with what I wrote.
Please ignore the paper. It is intended for a different audience than
most of the people on this list.
Richard Loosemore
Vladimir Nesov wrote:
Richard,
Any problem can be stated as search for results that satisfy given
constraints. What you state here doesn't seem to contradict what I
wrote before. In following paragraph you describe it:
On 10/6/07, Richard Loosemore <[EMAIL PROTECTED]> wrote:
In my use of GoL in the paper I did emphasize the prediction part at
first, but I then went on (immediately) to talk about the problem of
finding hypotheses to test. Crucially, I ask if it is reasonable to
suppose that Conway could have written down the patterns he *wanted* to
see emerge, then found the rules that would generate his desired patterns.
So, you ask if it's possible to find local rule given global behavior.
It's obviously possible to get global behavior once you have local
rules. Which essentially what I wrote before, and what Josh
exemplified by his brute force initial conditions enumerator. I try
not to be 'dismissive', which suggests kind of oversight, but I also
try not to ignore inconsistencies.
On 10/5/07, Vladimir Nesov <[EMAIL PROTECTED]> wrote:
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.
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