Re: Turing machines and tape length

[Howard Pattee <***>]

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