Re: Formalization of the Artificial Life Systems

[Chris Landauer]

this is part of the thread about formalizing artificial life systems

i second vladimir's thanx to barry for the references -
i have seen a couple of them before and will look for the others

partly to vladimir: i made up the notion of a variable-dimensional space -
it is part of a general program to stimulate the development of new mathematics
for describing and analyzing complex systems being coordinated by Dr. Kirstie
Bellman and me -
the variable-dimensional spaces are an example of integrated heterogeneous 
spaces,
which allow a formal space to have very different properties in different 
places -
so far, such spaces exist only operationally in some conceptual design support
software that she designed and built at The Aerospace Corporation -
there is not much theory yet

glen wrote that deciding up front to use linear algebra might be too limiting -
he's exactly right

i use vector spaces mainly as an illustration,
since most people have heard of them -
also, since much of the discussion is about spaces that represent location,
and vector spaces make a good model for locations,
it makes sense to use them for location and something different perhaps
for the agents themselves

there are certainly a number of different formal mathematical spaces
that may be appropriate -
the multiplicity is actually more important than any one of them -
ANY exclusive choice will be too limiting

the reason i have been asking for "qualities" is that once you know
or have an idea about the kinds of behavior you want to represent,
then you can make an informed choice of mathematical model -
one of the hardest qualities to describe is the elaboration and unfolding
of new structure,
which is one of my main interests in this area,
because there isn't much mathematics in it yet -

mathematical and formal logical systems are always too concrete,
because you have to define all of your terms and entities up front -
one of the mathematical investigations Dr. Bellman and I are trying to organize
is a study of situated spaces,
in which there is some leakage allowed from the context into the system
(that is, the context of use can affect the formal system itself -
this would be a new kind of mathematics if it could be done) -
the current work on situated logics for natural language modeling
(Jon Barwise and students and others)
is an example of some very good studies in this area

lotsa interesting hard problems here

more later,
cal

Dr. Christopher Landauer
National Systems Group, The Aerospace Corporation
The Hallmark Building, Suite 187
13873 Park Center Road, Herndon, Virginia 20171
e-mail: address@hidden
Phone: (703) 318-1666, FAX: (703) 318-5409


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