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. 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. Will ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=50577306-861814
