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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agi
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