William Pearson wrote:
On 05/10/2007, Richard Loosemore <[EMAIL PROTECTED]> wrote:
We have good reason to believe, after studying systems like GoL, that
even if there exists a compact theory that would let us predict the
patterns from the rules (equivalent to predicting planetary dynamics
given the inverse square law of gravitation), such a theory is going to
be so hard to discover that we may as well give up and say that it is a
waste of time trying. Heck, maybe it does exist, but that's not the
point: the point is that there appears to be little practical chance of
finding it.
A few theories. All states which do not three live cells adjacent,
will become cyclic with a cycle length of 0. Or won't be cyclic if you
reject cycle lengths of 0. Similarly all patterns consisting of one or
more groups of three live cells in a row inside an otherwise empty 7x7
box will have a stable cycle.
Will there be a general theory? Nope, You can see that from GoL being
Turing complete.
^^^^^^^^^^^^^^^^^^
Sorry, Will, but this not correct, and I explained the entire reason
just yesterday, in a long and thorough post that was the beginning of
this thread. Just out of interest, did you read that one?
If you had a theory that could in general predict
what a set GoL pattern was going to do, you could rework it to tell if
a TM was going to halt.
My theories are mainly to illustrate what a science of GoL would look
like. Staying firmly in the comfort zone.
But I stated exactly what I meant by a "theory". You are not addressing
that issue at all in what you just said.
Let me rework something you wrote earlier.
I want to use the class of TM as a nice-and-simple example of a system whose
overall behavior (in this case, whether the system will halt or not)
is impossible to
predict from a knowledge of the state transitions and initial state of the tape.
This re-wording of the text I wrote has absolutely no relationship to
the original meaning of the words. You would have proved just as much
if you had substituted the terms "bagel" and "cream cheese" into my text.
Computer engineering has as much or as little complexity as the
engineer wants to deal with.
Sadly, a completely meaningless statement, if the word "complexity" is
used in the sense of "complex system".
They can stay in the comfort zone of
easily predictable systems, much like the one I illustrated exists for
GoL. Or they can walk on the wild side a bit. My postgrad degree was
done in a place which specialised in evolutionary computation (GA, GP
and LCS) where systems were mainly tested empirically. So perhaps my
view of what computer engineering is, is perhaps a little out of the
mainstream.
Will Pearson
Richard Loosemore
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