Re: meanings of model

[Tim Gwinn <***>]

Howard,
See interposed.
Regards,
Tim

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Wednesday, December 15, 2004 1:56 AM
> To: ***
> Subject: Re: meanings of model
>
>
> Tim, you asked:
> I am unclear what you mean by "physical laws" in your post. To
> me, "physical
> laws" are just those formal theories and their mathematical formulations
> that we humans create. In your rephrasing of my question, it
> sounds like you
> equate the phrase "physical laws" with something like "effective processes
> of nature". Is that the case?
>
> I answered:
> >I usually mean by physical laws the natural laws that I imagine
> exist whether
> >or not I have created a model of these laws.
>
> HP: What I was trying to distinguish was your use of "physical laws" as
> what we humans create in the models on the right side of the modeling
> diagram from my use of "physical laws' as Rosen's "natural causes" on the
> left side. Failing to make this distinction leads to misunderstanding.
>
> > >HP: Also Constructivists, like most computer modelers, see no
> reason why the
> > > formal concept of Turing computability should limit how we
> actually write
> > > programs.
> >
> >TG: The limits of Turing computability are inherent in any
> program that runs
> >on a computer. (Obviously excepting an analog computer, which is
> an entirely
> >different meaning of "computer".
>
> HP: What I mean is that Turing computability is a formal concept
> that does
> not enter into normal programming because it has never been a serious
> limit. Programmers have written billions of lines of correct and useful
> code without knowing Turing existed.


TG: A programmer's ignorance of the limits of Turing computability does not
alter those limitations.


> > >HP: Many programs for physical and biological models are not even
> > > algorithms because they do not halt by themselves.
> >
> >TG: This is rather vague. I have no idea what kind of programs you are
> >talking about, so I don't know if you are talking about
> successive numerical
> >approximation routines or something else. I disagree that they are not
> >algorithms -- of course they are algorithms: they are running on
> a computer,
> >aren't they?
>
> HP: There are several definitions of algorithm. A common definition of
> algorithm is a finite set of program steps that leads to an answer. That
> means the computation must halt when the answer is reached. If
> the computer
> never halts how would you know when you have an answer?


TG: Again, I still am not sure what kind of example you have in mind, or if
they are models or simulations. Clearly, if these are programs actually
being used in physics and biology, they are providing answers to their
users. This is why I wonder if you are talking about successive numerical
approximations or the like. Writing a program which provides successive
answers per iteration of an intentionally infinite DO-WHILE loop is not an
example of a non-halting program which provides no answer.
"Compute the exact decimal values of pi" is such a non-halting program. But
if I break out of the program after the 500th decimal, and am satisfied with
that value, then I am using a different criteria for "answer" -- the program
is equivalent to the halting program "Compute the decimal values of pi up to
the 500th place".


> > >HP: In fact, strictly
> > > speaking, our computers are not Turing-equivalent. They are
> finite memory
> > > and finite state machines, and all theorems on computability
> > > depend on the
> > > syntax of infinite sets.
> >
> >TG: The limitations of a universal Turing machine will apply
> equally (or a
> >fortiori) in a finite Turing machine.
>
> HP: Our finite machines do not in general compute exact
> functions, but only
> approximate answers. These are good enough for scientific models that are
> only approximations anyway. That is not good enough for formal proofs so
> they are not Turing-equivalent and formal Turing proofs about limitations
> say nothing about approximate answers.


TG: The limitations of Turing computability do not rest on whether one
computes exact functions or their approximations. One can certainly utilize
simulations rather than models to circumvent some of these limitations, but
then one does not have a commuting modelling relation.


> >TG: Any natural system which possesses closed loops of
> entailment cannot be
> >modeled solely by a computable model.
>
> HP: Closed loops of entailment may be a useful abstract concept. I do not
> know how you can empirically recognize closed loops of entailment
> by their
> inability to be modeled because the proof that they cannot be
> modeled by a
> Turing-equivalent computer is again a strictly formal proof that says
> nothing about how one can construct an approximate model.


TG: "Closed loops of entailment may be a useful abstract concept."?? I'm not
sure why you bother with the ROSEN list if this is only an abstract concept
to you with no counterparts in the external world. The Central Argument of
Life Itself rests on organisms as physical systems with closed loops of
entailemnts. The predicative limits of entailtment in Turing computability
do not rest on whether one computes exact functions or their approximations,
or whether the Turing machine is a UTM or a finite TM.. It is a limitation
of the very nature of computability.
One can certainly utilize simulations rather than models to circumvent this
limit, but then one does not have a commuting modelling relation.


>
> Howard
>
> >