Jim Bromer wrote:
Loosemore said: "But now ... suppose, ... that there do not exist ANY
3-sex cellular automata in which there are emergent patterns
equivalent to the glider and glider gun. ...Conway ... can search
through the entire space of 3-sex automata..., and he will never
build a system that satisfies his requirement.
This is the boxed-in corner that I am talking about. We decide that
intelligence must be built with some choice of logical formalism,
plus heuristics, and we assume that we can always keep jiggling the
heuristics until the system as a whole shows a significant degree of
intelligence. But there is nothing in the world that says that this
is possible.
...mathematics cannot possibly tell you that this part of the space
does not contain any solutions. That is the whole point of complex
systems, n'est pas? No analysis will let you know what the global
properties are without doing a brute force exploration of
(simulations of) the system."
------------------------------------------------------------------------
>
But we can invent a 'mathematics' or a program that can. By
understanding that a model is not perfect, and recognizing that
references may not mesh perfectly, a program can imagine other
possibilities and these possibilities can be based on complex
interrelations built between feasible strands. Approximations do not
need to be limited to weighted expressions, general vagueness or
something like that. From this point it is just a matter of devising a
'mathematical' - a programmed - system to discover actual feasibilities.
The Game of Life did not solve the contemporary problem of AI because it
was biased to create a chain of progression and it wasted the memory of
those results that did not immediately result in a payoff but may have
fit into other developments. And it did not explore the relative
reduction space. The reconciliation between the study of possible
splices of previously seen chains of products and empirical feasibility
may be an open ended process but it could be governed by a program. It
may be AI-complete but the sub tasks to run a search from imaginative
feasibility to empirical feasibility can be governed by logic (even
though it would be open ended AI-complete search.)
>
I agree with what you are saying in the broader sense, but I do believe
that the research problem could be governed by a logical system,
although it would require a great many resources to search the Cantorian
diagonal infinities space of possible arrangements of relative
reductions. Relative reduction means that in order to discover the
nature of certain mathematical problems we may (usually) have to use
reductionism to discover all of the salient features that would be
necessary to create a mathematical algorithm to produce the range of
desired outputs. But the system of reductionist methods has to be
relative to the features of the system; a set of elements cannot be
taken for granted, you have to discover the pseudo-elements (or relative
elements) of the system relative to the features of the problem.
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
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agi
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