Re: Formalization of the Artificial Life Systems

[glen e. p. ropella]

Hey guys,

Correct me if I'm misguided (which I usually am [grin]); but,
does it strike anyone that using something as limited as 
linear algebra might be a tunnel-vision approach to modelling
these systems?  

It seems to me that there are some very powerful results in 
algebra (as a whole theory) that are not restricted to linear
algebra that would fit nicely into ABMs.  Examples, are the
concepts of:

  posets -- sets ordered by a reflexive, antisymmetric, and 
            transitive, binary relation
  groups -- sets under a closed, associative, identity holding,
            and inverse holding, binary operation
  quotient groups -- set of equivalence classes of an algebraic
                     object under an equivalence relation for that
                     object

  etc...

Granted, the types of results we achieve from linear algebra could
be *very* useful wherever they can be applied; but, the whole of 
linear algebra is based on the ability to establish orthogonal
sets and I'm not sure how such a criterion can be established in 
ABMs.  If we view orthogonality as a very specific kind of quotient
group, then we can think about some ABMs, possibly, possessing 
such a property.... but, I worry that starting at that point might
make us too focussed.

Ok....Fire away! [grin]
glen


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