Richard,
I presume this is the Waldrop Complexity book to which you referred:
"Complexity: The Emerging Science at the Edge of Order and Chaos"
M. Mitchell Waldrop, 1992, $10.20 (new, paperback) from Amazon (used
copies also available)
http://www.amazon.com/Complexity-Emerging-Science-Order-Chaos/dp/0671872346/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1214641304&sr=1-1
Is this the "newer" book you had in mind?
"At Home in the Universe: The Search for the Laws of Self-Organization
and Complexity"
Stuart Kauffman (The Santa Fe Institute), 1995, $18.95 (new, paperback)
from Amazon (used copies
also available)
http://www.amazon.com/At-Home-Universe-Self-Organization-Complexity/dp/0195111303/ref=reg_hu-wl_mrai-recs
Cheers,
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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