Nick, hi, Been meaning to send this for a couple of days. There is a paper on the role of models in control theory, which is perhaps profound or perhaps a tautology (Mike Spivak comments that the two naturally go together):
Conant, Roger C. and W. Ross Ashby. 1970. Every Good Regulator of a System Must be a Model of That System. International Journal of Systems Science 1 (2):89-97. This should be available for download from a link "Foundations of Complexity" on the SFI website. Presumably it's like a room with mirrors at both ends, which isn't a true infinite regress, because the images get less resolved at each reflection. One models onesself, presumably, not with the intent that the model be realistic, but only that it serve some particular purpose. So we don't encounter Turing-completeness paradoxes, since an internal model is not required to be a model of itself, but only a model of some aspect of itself, or even of that self's interaction in some contexts. The recursive character does indeed make me think of language, as Jochen says, though not necessarily that the two are "the same" thing. For the model to be a part of the self, and in that sense, an object in its own right, and also to serve as a referent to something else through a suitable system for interpretation, reminds me of the way a word is both an object subject to manipulation, and a referent to other objects. But somehow words are easier. They are objects with respect to syntax, mophology, phonology, etc., and referents with respect to semantics, though I doubt that those distinctions are as clean we carelessly might suppose. Is it right, then to say as counterpart, that internal models, as parts of the self, are objects under some explicit grammar for handling them, and referents with respect to a semantics for which that model-language provides addressing? It would be interesting if there is a common structure of recursion, and a "syntactic" sort of cognitive primitive, which underlies many forms of internal modeling, of which only one is the use of a grammatical language. In other words (and replacing what Dennett does say with what I wish he would say), it is not that language enables internal modeling, but rather that, in certain cognitive domains, both build from recursive functionality that we find expressed in the use of internal models and also in the use of grammatical language. (I say "certain cognitive domains" to avoid the Pinker/Fitch/Chomsky assertion that recursion is exclusively human and exclusively linguistic-within-human. That seems a conclusion one can reach only by selectively ignoring almost everything we know about the world.) I suppose that extending some of Russell's thoughts on "proper names" to deal with other parts of speech would be a way to try to constrain our thinking empirically. Maybe a lot of this has already been done. It's not an area I have had time to learn about. Eric ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
