Linas Vepstas wrote:
On Thu, Oct 04, 2007 at 11:06:11AM -0400, Richard Loosemore wrote:
In case anyone else wonders about the same question, I will explain why
the Turing machine equivalence has no relevance at all.
Re-read what you wrote, substituting the phrase "Turing machine", for
each and every occurrance of the phrase "GoL". The semantics of the
resulting text is unchanged, and states nothing particularly unique
or original that isn't already (well-)known about Turing machines.
You continue to distort the meaning of the argument by taking it out of
context..
Richard Loosemore.
You can even substitute "finite state machine" or "pushdown automaton"
at every point, and you argument would still be unchanged (although
the result would not actually be Turing complete). That's because
some finite automata are boring (cyclic in trivial ways), and some
are interesting (generating potentially large and complex patterns).
Most randomly generated finite automata will be simple, i.e. boring,
and some will exhibit surprisingly complex behaviours.
To be abstract, you could subsitute "semi-Thue system", "context-free
grammar", "first-order logic", "Lindenmeyer system", "history monoid",
etc. for GoL, and still get an equivalent argument about complexity
and predicatability. Singling out GoL as somehow "special" is a red
herring; the complexity properties you describe are shared by a variety
of systems and logics.
--linas
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