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. 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. 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. Computer engineering has as much or as little complexity as the engineer wants to deal with. 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 ----- 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=50437016-7ec2cc
