Let's be more careful about "isomorphisms". These can be constructed
between algebraic groups (set, + operator, closure, identity element,
etc, you know the drill); groups can be induced on some classes of
function/algorithm, but not all. Some of your ideas are more like
homeomorphisms, topology-preserving mappings among topological spaces
(Set, family of subsets, family is closed under union and countable
intersection, etc). Again, topological spaces can be induced on sets of
functions (which are what agents are), but their properties can be
tricky. I think you all are also mixing strings and categories. Before
you can go too far with this, you have to define the class of
computability of the "algorithms" of the agents. If they are partial
(e.g. Turing-computable, so they are procedures, but not necessarily
algorithms), then the questions you are asking are all probably
undecidable (I didn't get my doctorate in mathematics, so I'm on shaky
ground here, but I can think of a proof strategy similar to the
triangularization proof of Goedel's incompleteness theorem that would
show that if such maps ("isomorphisms") exist, then they are
inconsistent). If you limit the agents to primitive-recursion or some
other subset of the total functions, you may be able to establish some
useful theorems about the boundaries your intuition says should be
there. Since CAS are based on simple local rules, the limitation to
primitive recursion may not be a practical limitation at all. But since
agents are presented in the literature mostly as having more or less
arbitrary Turing-capability, you will have a lot of work to do to
educate the agents community to the mathematical realities of Goedel and
incompleteness. In the interim, at least be aware that these things you
are talking about have substantial mathematical aspects that one ignores
at one's peril (e.g. of wasting time on something that is provably
undecidable).
best of luck
joe
Marco Cicchini wrote:
>
> Re: R: [UAI] Where does Multi Agent end and PDP start?Dear Kathy,
>
> Thanks for your reply. It is enlightening. especially in the following
> passages:
>
> "The set of system equations for any collection of loosely coupled
> physical systems is mathematically isomorphic to a game of interacting
> "agents," were the "objective function" for each subsystem is the action
> integral it is "trying" to minimize (where we interpret "trying" for a
> non-living physical system in the same way as my example of the computer
> "trying" to compute 1/0).
>
> So everything "is" distributed interacting agents, including superstrings.
>
> What you make of that isomorphism depends on what you think the meaning of
> "is" is."
>
> I see exactly what you mean because one key factor of complexity/emergence
> is to find structures, patterns, isomophisms.
>
> I'd like to submit to you my original question: where does multi agent end
> and PDP start?
>
> I guess that at the end of the day two systems are never too isomorphic
> because our mdels always neglect something so, the real systems are never
> too identical.
>
> Notwithstanding this some of them, natural or artificial, perceptrons or
> neurons, have "processing" abilities. What does distinguish them from other
> Complex Adaptive Systems?
>
> Which isomorphisms are common to the "processors"?
>
> Is it all about what we consider as information? Should each agent have some
> characteristics to be the bulding block of a "processor" or is it any case
> different from the other?
>
> Has anybody reflected if there is a point in talking about a boundary
> between CAS (not processing) and CAS (processing)? If so, is there such a
> boundary? If not, why not?
>
> Thanks to all for the help,
>
> Marco Cicchini
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Dr. Joseph Mitola III
Consulting Scientist
The MITRE Corporation
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