Or, maybe...
"Complexity: Life at the Edge of Chaos"
Roger Lewin, 2000 $10.88 (new, paperback) from Amazon (no used copies)
Complexity: Life at the Edge of Chaos by Roger Lewin (Paperback - Feb 15, 2000)
Brad
Richard Loosemore wrote:
Jim Bromer wrote:
From: Richard Loosemore Jim,
I'm sorry: I cannot make any sense of what you say here.
I don't think you are understanding the technicalities of the
argument I am presenting, because your very first sentence... "But we
can invent a 'mathematics' or a program that can" is just completely
false. In a complex system it is not possible to used analytic
mathematics to predict the global behavior of the system given only
the rules that determine the local mechanisms. That is the very
definition of a complex system (note: this is a "complex system" in
the technical sense of that term, which does not mean a "complicated
system" in ordinary language).
Richard Loosemore
Well lets forget about your theory for a second. I think that an
advanced AI program is going to have to be able to deal with
complexity and that your analysis is certainly interesting and
illuminating.
But I want to make sure that I understand what you mean here. First
of all, your statement, "it is not possible to use analytic
mathematics to predict the global behavior of the system given only
the rules that determine the local mechanisms."
By analytic mathematics are you referring to numerical analysis, which
the article in Wikipedia, http://en.wikipedia.org/wiki/Numerical_analysis
describes as "the study of algorithms for the problems of continuous
mathematics (as distinguished from discrete mathematics)". Because if
you are saying that the study of continuous mathematics -as
distinguished from discrete mathematics- cannot be used to represent
discreet system complexity, then that is kind of a non-starter. It's a
cop-out by initial definition. I am primarily interested in discreet
programming ( I am, of course also interested in continuous systems as
well), but in this discussion I was expressing my interest in measures
that can be taken to simplify computational complexity.
Again, Wikipedia gives a slightly more complex definition of
complexity than you do. http://en.wikipedia.org/wiki/Complexity
I am not saying that your particular definition of complexity is
wrong, I only want to make sure that I understand what it is that you
are getting at.
The part of your sentence that read, "...given only the rules that
determine the local mechanisms," sounds like it might well apply to
the kind of system that I think would be necessary for a better AI
program, but it is not necessarily true of all kinds of demonstrations
of complexity (as I understand them). For example, consider a program
that demonstrates the emergence of complex behaviors from collections
of objects that obey simple rules that govern their interactions. One
can use a variety of arbitrary settings for the initial state of the
program to examine how different complex behaviors may emerge in
different environments. (I am hoping to try something like this when
I buy my next computer with a great graphics chip in it.) This means
that complexity does not have to be represented only in states that
had been previously generated by the system, as can be obviously seen
in the fact that initial states are a necessity of such systems.
I think I get what you are saying about complexity in AI and the
problems of research into AI that could be caused if complexity is the
reality of advanced AI programming.
But if you are throwing technical arguments at me, some of which are
trivial from my perspective like the definition of, "continuous
mathematics (as distinguished from discrete mathematics)," then all I
can do is wonder why.
Jim,
With the greatest of respect, this is a topic that will require some
extensive background reading on your part, because the misunderstandings
in your above test are too deep for me to remedy in the scope of one or
two list postings. For example, my reference to "analytic" mathematics
has nothing at all to do with the wikipedia entry you found, alas. The
word has many uses, and the one I am employing is meant to point up a
distinction between classical mathematics that allows equations to be
solved algebraically, and experimental mathematics that solves systems
by simulation. Analytic means "by analysis" in this context...but this
is a very abstract sense of the word that I am talking about here, and
it is very hard to convey.
This topic is all about 'complex systems' which is a technical term that
does not mean systems that are complicated (in the everyday sense of
'complicated'). To get up to speed on this, I recommend a popular
science book called "Complexity" by Waldrop, although there was also a
more recent book whose name I forget, which may be better. You could
also read Wolfram's "A New Kind of Science", but that is huge and does
not come to the simple point very easily.
I am happy to make an attempt to bridge the gap by answering questions,
but you must begin with the understanding that this would be a dialog
between someone who has been doing research in a field for over 25 years
and someone who feels confident, but who has to look up the most basic
terminology o that research field on wikipedia. That kind of gap often
(in my experience) leads to confusion and friction.
I certainly recommend the Waldrop book. It's a fun read.
Richard Loosemore
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