Jeff:
> Would your top-down-model be the same as what Rosen refers to as
> an analytic model? Analytic models refer to some functional aspect
> of the whole. And would your bottom-up model be the same as what
> Rosen refers to as a synthetic model? Synthetic models refer to parts
> that can be put together that then yields function.
There are similarities, but I think (?) Rosen gives these two
categories other flavours as well, he seems to associate analytic
modes with the reductionist method and synthetic models with a sort
of simulation modelling (i.e. its non-predictive).
> If so, then the
> complexity of the model you described in your language would be
> translated as the difficulty of formulating a modeling relationship
> between an analytic and synthetic model.
Given that, yes. It is the difficulty in modelling the synthetic by
the analytic (given a laguage of representation and a conception of
'difficulty').
> Rosen claims, though, that
> it is possible that an analytic model can be bigger (not expressible by)
> a synthetic model.
I am a bit confused here, surely you mean the other way around, that
Rosen claims the synthetic model cannot be expressed by an analytic
one?
> Could it be that in some situations, a bottom-up
> model cannot express what goes on in a top-down model?
As above.
> Or put
> another way, if you were given a bottom-up model, it would be quite
> difficult to come up with a top-down model that was bigger (or more
> encompassing). It may only be possible to do this (come up with a
> top-down model that is bigger than the corresponding bottom-up model)
> with some kind of self-reference.
This is now the other way around (the way I thought Rosen intended).
It is possible that this is true. I am unsure whether it is true in
an absolutist sense. It is often practically impossible to do so!
> Most people are content to have the top-down model being
> functionally the same as the bottom-up model. Perhaps, then in my
> language, the difficulty in coming up with a top-down model to
> equal a bottom-up model would be referred to as the
> complicatedness...
This is close to what I mean by 'complex'. (It does seem to be a
roundabout way of avoiding the term 'complex', despite the fact that
'complicated' and 'complex' come from the same linguistic root!).
> and if the self-referencing aspect is invoked
> (where the top-down model becomes bigger) then the process becomes
> complex. You would apparently describe what I called
> complicatedness as degrees of complexity. And you would refer to
> invoking self-reference as just being a little more complex than a
> similar situation in which self-reference was not invoked.
There is no simple-minded way that self-reference relates to
complexity, as far as I can see. Yes, self-reference has the
potential to introduce complexity, but this is not inevitable. For
example the introduction to a top-down model of a single, completely
self-inferring symbol, which did not interact with the rest would
harldy make it that much more complex! On the other hand if some
essential "Downward causation" were involved, so that the system as a
whole was self-referential, then this would indeed make it almost
impossible to model from a purely analytic perspective!
Are we confusing terms here?
----------------------------------------------------------
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