Re: Inequivalence of models

[Howard Pattee <***>]

John M and Tim,

I think Rosen's meaning of inequivalent was largely motivated by showing
that reductionism doesn't work. As Tim says, they are models that can't
be transformed or reduced to (or derived from) each other in a
formal sense. However, while it is a necessary condition for Rosen
complexity, I don't think it is sufficient. For example, Rosen uses the
example of a gas that has a microscopic deterministic model that is
reversible (time-symmetric) and also a statistical thermodynamic model
that is irreversible. Clearly, these are inequivalent models because one
cannot formally derive one from the other, although one can
conceptually see how to make the transition from a deterministic to
statistical model about the same system. But a gas is still a simple
system.

Rosen also uses the example of a protein sequence model from which one
cannot derive its functional model. These models are inequivalent in a
categorical sense rather than a formal sense as in the gas. These protein
examples have a structure/function inequivalence. In other words, one
can't conceptually see how structure can become functional without
enlarging the system beyond the protein sequence model. 

Howard