J Storrs Hall, PhD wrote:
On Thursday 04 October 2007 03:46:02 pm, Richard Loosemore wrote:
Oh, and, by the way, the widely accepted standard for what counts as a
"scientific theory" is -- as any scientist will be able to tell you --
that it has to make its prediction without becoming larger and more
complicated than the system under study, so it goes without saying that
whatever you choose for a theory it is not allowed to simulate a massive
number of Game of Life cases and simply home in on the cyclic ones.
Wrong. Consider the amount of data, cases, and simulation involved in, say,
using density functional theory to make predictions about the shape of a
fairly small molecule.
Like many another sophist who cannot defend his argument, you quietly
ignore 99.99999% of cases and try to prove your point by selecting an
outlier and trying to pretend that it represents the majority case.
What you just picked is a PRECISELY the residual, partial complexity in
the explanations of molecular dynamics that I explained in a previous
post: the bulk of the explanation has to be done using a regular type
of "analytic" explanation, but then there are always residual elements
that are so nonlinear that all we can do is simulate.
Try walking into any physics department in the world and saying "Is it
okay if most theories are so complicated that they dwarf the size and
complexity of the system that they purport to explain?"
In fact, your example is beautiful, in a way. So it turns out to be
necessary to resort to approximate methods, to simulations, in order to
deal with the MINUSCULE amout of nonlinearity/tangledness that exist in
the interactions of the atoms in a small molecule? Well, whoop-dee-do!!
Guess what the whole point of my paper was? The point of that paper
was that there is vastly more evidence for the existence of such
nonlinear, tangled interactions in the case of intelligent systems, and
there is so far NO analytic core theory to deal with the majority behavior.
So unlike the small-molecule case (where we can cope with the complexity
because it just a residual, and we have a huge, rock-solid non-complex
theory as a starting point), in the case of intelligent systems we are
thrown into wildly different territory where the whole darned enterprise
is dominated by the kind of science that was just a residual in the
molecule case.
Thanks for the example.
Since your "theory" below does not predict the specific cyclic patterns
that actually occur in GoL, I still await a complete theory and a
complete catalogue of cyclic GoL lifeforms by Monday.
Richard Loosemore
If physicists lived in a Life universe, they would consider finding the CA
rules the "ultimate theory of everything". We don't have that for real
physics, but Shrödinger's equation is similar for our purposes. DFT is a
carefully tuned set of heuristics to make QM calcs tractable -- but if we had
the horsepower, you can bet your bottom dollar that physicists would be using
the real equations and calculating like mad.
You didn't give me a formal definition of "cyclic" so I'll do it for you:
cyclic S :: exists p>1,k>=0 s.t. S[i+p]=S[i] forall i>k
I trust you understand lazy evaluation:
lifeseries M :; M, lifeseries liferules M
We're using an APL-like data semantics with implicit parallelism over vector
elements:
mats N = N N rho 2 baserep i for i=1..2^N^2
Then your theory is
cyclic lifeseries mats 2..Whatever
If you have a look at Gödel's proof, he built up to functions of about the
level of Lisp from simple arithmetic. The above assumes a few more
definitions, but there are 50 years of CS to draw them from.
Josh
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