Re: Turing machines and tape length

[Tim Gwinn <***>]

Howard,

 

Can you provide an example or two of what you mean by "encoded empirical models of Nature"? I read this and your reply to Judith's 'Formality' post and I still don't understand what this phrase refers to. In my view, an 'encoded empirical model of Nature' would be some formal model, and 'empirical' indicates that this formal model is in a commuting modelling relation with some natural system.

 

Regards,

Tim

 

-----Original Message-----
From: ROSEN Forum [mailto:***On Behalf Of Howard Pattee
Sent: Tuesday, December 28, 2004 10:59 AM
To: ***
Subject: Re: Turing machines and tape length

Tim,
I understand Rosen's overall argument. My problem is that I do not follow Rosen's "for the sake of argument" hypothesis about what would follow if the formal computable "mechanisms" corresponded to empirical causal models of Nature. As you state his hypothesis, a formal computable inferential entailment,  "must entail (e.g., reductionism, context-independence, etc.) and also what it must not allow (e.g., causal loops, context-dependence, etc.)."

What I do not follow is why the formal inferential entailments of computable functions (that exist only on the unencoded right side of the modeling diagram) must necessarily "entail" reductionism, no causal loops (and the rest) in the encoded empirical models of Nature. As Einstein and I see it, the formal inferential entailments say nothing certain about the causal entailments of Nature. Nor do the causal entailments of nature impose any axioms or inferences in formal mathematics. All we can hope to test is empirical "conformance."

I do see reductionism as a straw man. Physics has not been reductionist for over a 100 years. We know, for example, that thermodynamics is not reducible to particle mechanics but both can be modeled with approximate computable functions. One of Rosen's earliest conditions for complex systems is multiple irreducible models. I think irreducible models imply anti-reductionism.
 

TG: Such programs suffice very well for the sake of emulating the behavior of an N-body system, but because the entailment structure is now entirely different from the entailment structure of the natural system, it is a simulation rather than a model, in the Rosennean sense of those terms.

HP: This is a logical or conceptual distinction that I still do not see how to make empirically. We name the cause of n-body orbits "gravity," but we never causally model gravity itself. We have many concepts of gravity (curved space, gravitons, etc.) but we don't know causes except by our models. We understand this when we compute n-body systems, so we are not misled. Almost all computer models are simulations in this sense. We know that there is seldom anything in the program, gates, and memories with the same physical causal entailments as in the system being modeled, but as you point out, we always take care of this by our encoding and interpretation. I would say that only a physical analog like a model airplane could be a model in Rosen's sense.

Howard