Re: Rosen & Ashby

Johnk,

After some more thought, I retract my comments regarding being able to use a more complex system to model another complex system. Such a "more complex" system would have characteristics that make it "more than" a model (excess degrees-of-freedom, etc.), and as such it now seems to me that it would therefore be improper to call it a model. My bad.

I also spoke incorrectly in my last reply regarding "no largest model". I should not have said that "no largest model" was necessarily an imprecise form of "no largest Turing-computable model", although that is sometimes the way it is used. Instead, only systems with only Turing-computable models will have a largest model, and that largest model will also accordingly be Turing-computable. So, "no largest model" will imply "no largest Turing-computable model"; so the former phrase is not really simply a shorthand version of the latter, which is what I wrote below. :(

Thanks for the discussion!

Regards,

Tim

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[JK]
> - complex systems cannot be described completely by any other system,
> formal or realized.
[TG]

This is not necessarily true. It is possible that a complex system can be completely "described" (i.e., modeled) by another system if it is more complex than the system under study.

This is a philosophical escape. If one complex system can fully model another, but by definition no complex system can have a complete "largest" model itself, what is the meaning of the first part of the statement?

[TG]

No, not a philosophical escape. :)

This is one of those cases where context is important. "No largest model" is a commonly used (even occasionally by Rosen), albeit somewhat misleading, shorthand version of the more precise phrase "no largest Turing-computable model". So this phrase does not impact on the ability to model a complex system with another complex system.

With this more explicit phrasing it might also now make more sense why the definition of complex system as "A system is complex if it has a nonsimulable model." and "no largest model" (in the more precise form of "no largest Turing-computable model") are closely related. Any number of Turing-computable models can be combined or concatenated into one largest Turing-computable model. Since a complex system will posses at least one non-Turing-computable model, the totality of that system's models cannot be combined or concatenated into one largest Turing-computable model.

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