Re: Inequivalence of models

Hi Steve, Hi Everybody,

Sorry for being "incommunicado" for a few days, I've been working on BioTheory. It's mostly up and running, although five papers are still forthcoming, and my own papers are among them. What can I say? By the time people get done reading all the great stuff that's there, my own will be ready to plug in. I haven't had much of a chance to take off the publishing and editing hats, much less put on the writer's hat, for a while. But they're almost done.

The question about "inequivalent models" isn't as complicated as you guys are making it... It has to do with the fact that simple systems are computable and have a "largest complete model" into which all others will reduce. If you go about it from the other direction; the sum of all models we can make of the system will include every individual model within it. That's what "equivalent" means. Complex systems, on the other hand, have an infinite set of models, without ever exhausting all the information possible. Because there is no "largest complete model"...

Do you see? Any single model is a finite thing, and there is no way to get to infinity by accretion (adding finite numbers together). Thus, inequivalence.

It's a different situation than the way Steve was looking it in his analogy:

Steve Johnson wrote:

For example, let's take a car. It has a mechanical
blueprint that tells where the wheels attach to the
transmission, how the engine is attached to the shaft
etc. The car also has a diagram of its electric wiring
which is quite different from the mechanic blueprint.
Each of these "models" (mechanical and electric) will
allow us to formulate hypothesis about the car. So it
seems that the Modeling Relation commutes.

It's not that one model must "reduce" to every other one in a simple system-- not at all. Instead, equivalence in this usage means that there is a sum of all models which exhausts all the information about the car.... and each model will then "reduce to" (fit into) that sum/largest model.

Does that make more sense?

Judith