top-down vs. bottom-up

Jeff Prideaux (JPRIDEAUX@GEMS.VCU.EDU)
Thu, 28 Sep 1995 23:40:01 -0400


A few days ago Bruce wrote:
> Using Jeff's 'language' to describe my language...
>
> Given two 'formal' (i.e. non-natural) models, one bottom-up one
> starting from the casual interactions of the components and one
> top-down starting from some overall description of behaviour of the
> whole, we seek to 'model' the bottom-up model with the top down one
> with encoding and decoding arms. My definition of complexity is the
> difficulty of doing such top-down modelling w.r.t. to the
> representational language in which the coding arms are embedded.
> Thus this is similar to your 'complexity of modelling', but
> perpendicular to it. From your view the modelling situation is
> complex if there of more "structural causation" in the coding arms.
> From my view the modelling situation is more complex if it is
> difficult (within a language) to find good encoding arms.
>

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. 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. Rosen claims, though, that
it is possible that an analytic model can be bigger (not expressible by)
a synthetic model. Could it be that in some situations, a bottom-up
model cannot express what goes on in a top-down model? 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. 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...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.

Im very interested in your response.

Jeff Prideaux
(it is of course possible that what I have characterized above
diverges with Rosen and others...)