All,
So, I have gotten to page 541 of A NEW SCIENCE.
I have passed through the four stages
"WHA?" "HUH!" "OMIGOD" and finally," I HAVE TO TAKE IT SERIOUSLY."
I am right now bogged down in the part on thermodynamics and reversibility.
Perhaps you CA folks out there could help me with a question.
Lets define a rule and a set of conditions on which that rule works to be a
reflector when the rule give back the set of conditions that were given it.
Obviously there are some boring reflectors.
But just as obviously for a CA to be reversible in Wolfram's terms, it has,
at some point to hit a reflector, no?
Allow me to manufacture some nomenclature here.
Let the array produced by a rule from S-0 ("step 0") be S+1. So when
we apply a rule to S-0 we get S+1, OK.
In short hand R(S-0) = S+1 Ok? (the rule applied to S-0 gives you S+1.
For a CA to be reversible, must it not be the case that FOR ever value of S
except the reflector
R(S+1) = (S-0) ?
In English, must it not be the case for every step in a reversible CA that
not only does the rule, when applied to the previous step, produce the next
step, but that the rule when applied to the next step, produces the
previous step.
Since we know already that the rule when applied to the next step produces
the NEXT TO NEXT step, there must be something about the rules of
reversible CA;s that prevent all steps from being relfectors.
I have totally lost it, havent I?
NIck
.
Nicholas S. Thompson
Professor of Psychology and Ethology
Clark University
[hidden email]
http://home.earthlink.net/~nickthompson/ [hidden email]
Locked
