Don Mikulecky, MCV/VCU, mikulecky@gems.vcu.edu:
> (causual structure is the number of) distinct ways with which we
> and the natural system are interacting. Note that "distinct" means
> needing encodings into distinct formal systems, i. e. ones which
> are not derivable from each other. I'll be sending some more on
> this out of Kampis' book.
There a lot of problems here.
1. Usually the number of non-equivalent distinct formal systems is
infinite, in fact I am hard pressed to think of one that is not
(even when what is being modelled is purely formal!).
2. It is an uncomputable problem in many cases to tell if formal
systems are thus distinct - thus the number of distinct formal
systems might not even be knowable.
3. It is unclear how you can tell whether a model of a natural
systems commutes. You can easily tell when it does not, but how do
you ever know it does other than comparing the formal to natrual
model for an eternity. I will come back to this in another post.
me:
> > This I find odd (depending on what you mean by "causal structure").
> > The complexity seems defined in terms of the 'success' of the
> > modeling relation. Thus, by this definition, unsucessful models
> > will always be less complex than successful ones, even if the
> > unsucessful ones are far more intuitively 'complex' than the
> > sucessful ones. This seems more like the 'difficulty' of modelling
> > than its 'complexity'. I suspect that your idea of causal structure
> > in the coding arms is more involved than it seems from the above.
> >
>
> The simple system model which has only one way of interacting with the
> natural system has been very successful. It also has a very simple
> causal structure.
But a much 'simpler' formal model which interacts in two ways is
necessarily more complex, by your meaning. Doesn't this also mean
that a completely unsuccessful model that interacts in no (zero) ways
is even simpler. I find this all very counter-intuitive.
> > I find it very counter-intuitive that the 'complexity' of the formal
> > models play no part in the complexity of the modelling. Maybe this
> > is because we are approaching this from within different structures:
> > I am talking about the complexity of models (relative to a language
> > of representation, goals etc.) and you are talking about the
> > complexity of modelling (natural systems).
> >
> Here I'll have to side with Bruce. Chaitin certainly makes this a necessity!
Please explain, what you see as the ramifications of Chaitin's
results for this discussion. There is a big gap between what I
understand of his results and the consequences you state.
> > 4. For me the complexity of the formal model itself is relevant, for
> > you essentially not (but its input-output is constrained by the
> > coding arms). For you the 'content' of the formal part does not
> > matter, it is a black-box given the constraints of the coding.
> >
> au contaire...it is indeed important if it can be linked to the number of
> distinct ways we interact with the natural system. Here is, as I see
> it, a reason why the natural system must retain its place in the modeling
> relation.
What if it can't, so formal models of different 'complexity' have
identical coding arms, does the formal model matter then?
----------------------------------------------------------
Bruce Edmonds
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Building,
Aytoun Street, Manchester, M1 3GH. UK.
Tel: +44 161 247 6479 Fax: +44 161 247 6802
http://bruce.edmonds.name/bme_home.html