Formalism

[Fawzi Roberto Mohamed]

Well, there was quite a discussion about formalism and mathematicals models in 
ABMs. Here is my small contribution.

I am not an expert, but I am not sure that I *really* want a strong formalism 
of 
AMB. Don't take me wrong, I like formalisms and mathematics, but in general 
more 
a model is generic, the less anwers it can give (but it can be applied to many 
areas). This is not an absolute rule, and generic models ((universal) algebra, 
group theory,...) are useful because can be applied in many fields.

But in ABMs simulations are used in so many fields that I don't know if a 
formalism that goes beyond making one understand the project of another and 
making everyone present a project in a somewhat standard way would be useful. 
More specific formalisms can obviuosly be developed in in specific field (i.e. 
simulation of geological processes, biological evolution,...).

What I wants in a system like Swarm is that specific formalisms are avaible and 
can be used in my simulation without too much difficulty. This mean that if a 
part of my problem has a good description with vectors and lineare angebra I 
want to be able to translate the formalism of vectors and linear algebra in a 
"nice" way in swarm, and then maybe change to non linear aproximation in some 
agents. Then I wants to use (for example) group theory in another part of my 
simulation,... and so on.

I don't know if other think like me, but I think that such a system is 
feasible. 
For example I like much some computer algebra systems like Axiom that have a 
good programming language, a big library with optimized solutions for both 
algebraic and numeric problems. Axiom (for example) is very formal (it is what 
I 
like in it) and it can optimize numerics quite well. But exactly for this 
reason 
I don't know if i would use it as prototyping tool and to experiment with new 
models. To say the truth I have never tryed, and axiom can be used in 
interactive mode in a quite intuitive way (one day I should try to simulate 
something on it).

Anyway I am very intrested in discussions about formalism, maybe you find an 
exeption to "my" rule.
I think that there is a theorem in universal algebra that says that on "big" 
sets (not countable like the real numbers) you can never have an algebra 
(formalism) so powerful to express every relationship. This does not mean that 
partial formalism aren't useful, at the opposite, but you should keep your 
high-level formalism so flexible(generic ->not so precise) so that you can 
embed 
in it many specialized formalisms.

Fawzi


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