William Pearson wrote:
On 05/10/2007, Richard Loosemore <[EMAIL PROTECTED]> wrote:
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?
Yup, and my argument is still valid, if this is the one you are
referring to. You said:
"Now, finally: if you choose the initial state of a GoL system very,
VERY carefully, it is possible to make a Turing machine. So, in the
infinite set of GoL systems, a very "small" fraction of that set can be
made to implement a Turing machine."
"But what does this have to do with explaining the existence of patterns
in the set of ALL POSSIBLE GoL systems?? So what if a few of those GoL
instances have a peculiar property? bearing in mind the definition of
complexity I have stated above, how would it affect our attempts to
account for patterns that exist across the entire set?"
You are asking about the whole space, my argument was to do with a sub
space admittedly. But any theory about the whole space must be valid
on all the sub spaces it contains. All we need to do is find a single
state that we can prove that we cannot predict how it evolves to say
we will never be able to find a theory for all states.
I have a question for you, Will.
Without loss of generality, I can change my use of Game of Life to a new
system called GoL(-T) which is all of the possible GoL instantiations
EXCEPT the tiny subset that contain Turing Machine implementations.
Nothing changes in my arguments: all the known patterns/creatures are
still observed (except the TM pattern), there are still an infinite
number of instantiations, the patterns are still just as hard to explain
.... for my purposes GoL(-T) is as good an example as GoL.
So now, my question to you is this: tell me exactly how the existence
of the TM implementation in those other instantiations, which are now
outside the GoL(-T) system, have any effect on questions about the
explicability of the patterns in GoL(-T)?
Could you please specify the precise way that the TMs now have some
impact on GoL(-T).
As far as I can see (and this was my original point, of course), they
have no impact.
Please remember that it is my particular use of the "explanation"
concept, in the context of the paper, that has to be referenced.
Thankyou,
Richard Loosemore
If it was possible to find a theory, by your definition, then we could
use that theory to predict the admittedly small set of states that
were TMs.
I might reply to the rest if I think we will get anywhere from it.
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