Joel Pitt wrote:
On Sat, Aug 2, 2008 at 9:56 AM, Richard Loosemore <[EMAIL PROTECTED]> wrote:
There is nothing quite so pathetic as someone who starts their comment with
a word like "Bull", and then proceeds to spout falsehoods.
Thus: in my paper there is a quote from a book in which Conway's efforts
were described, and it is transparently clear from this quote that the
method Conway used was random search:
"[Conway and his team of collaborators found an appropriate set of rules]
... only after the rejection of many patterns, triangular and hexagonal
lattices as well as square ones, and of many other laws of birth and death,
including the introduction of two and even three sexes. Acres of squared
paper were covered, and he and his admiring entourage of graduate students
shuffled poker chips, foreign coins, cowrie shells, Go stones or whatever
came to hand, until there was a viable balance between life and death."
The reference is: Guy, R. K. (1985) "John Horton Conway," in Albers and G L
Alexanderson (eds.), "Mathematical people: Profiles and interviews."
Cambridge, MA: 43-50.
The rest of your comment, below, is just as full of BS as the first
paragraph.
So you're saying that just because Conway and company didn't work
everything out in their heads and relied on external tools and
experimented, it means they were doing a "random search" for the
behaviours that comprise the Game of Life?
Huh? No, this is very, very simple. They decided that they wanted some
rules that would allow the cellular automaton to have a particular ratio
of birth rate to death rate. As a matter of pure, nice and simple
empirical fact, the method they used to find the set of rules that they
eventually chose was .... trial and error. There was no mathematical
analysis that told them where to look, and there has never been any
mathamatical analysis since then, which has demonstrated that Conway et
al could have saved themselves some trouble.
And, more generally, if anyone were to write down a prescription, today,
for the *desired* global behavior of a cellular automaton, using rules
that are interacting in a complex way, there is, in general, no analysis
that you can do to design the rules to get the desired global behavior.
If you do not believe this is the case, show me a paper, or a
demonstration, that would convince a reasonable person that this is wrong.
No more speculation, please: just find something, somewhere, that says
that there is a general method to design the global characteristics of
complex systems using something other than empirical test of candidate
algorithms.
This stuff is so basic that it is common knowledge throughout the
complex systems community. Why target me on the subject? Why not just
go down to the Santa Fe Institute and accuse every last one of them of
being out of their minds?
And failing all of the above, just write to Conway and ask the guy.
Very few mathematical proofs are so simple that they can be
conceptualized entirely in one's head. Very few engineering attempts
are made without prototypes. Progress is about experimentation.
In fact, using your analogy, most of scientific progress could be put
down to a "random search". (Just don't start claiming evolution is a
random search, or we'll degenerate into a argument about Creationism.)
I implied nothing of the sort.
Richard Loosemore
-------------------------------------------
agi
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