Re: meanings of model

[ICB Ionel <***>]

Howard:

I am responding to your 'challenge' referring to the biological modelers'
feels and concerns about the formal aspects of computability. Your message
contained the following statement with which I'd have to disagree on a
factual basis:

>>I am not aware of any biological modelers that feel limited by or are
even concerned about the formal aspects of computability. Other problems
seem more important...

What am I missing? >>

In a 1987, extensive review about biological modeling I did raise such
concerns that you seem to think that don't, or need not, concern biological
modelers. For the Rosen list I am providing here the web addresses for this
published review where it could be found in PDF format:

COMPUTER MODELS AND AUTOMATA THEORY IN BIOLOGY AND MEDICINE:
COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS

Mathematical Modelling, Vol. 7, pp. 1513-1577,1986

http://doc.cern.ch//archive/electronic/other/ext/ext-2004-072.pdf
http://cogprints.org/3718/01/COMPUTER_SIMULATIONCOMPUTABILITYBIOSYSTEMSrefne

The references cited in my review (of other authors' work , as well as
Robert  Rosen's) concerning the formal aspects of computability are also
pertinent to your comment cited above. One such forml modeling paper by
Robert Rosen is : "On Analogous Systems." BMB (1968).

Ionel

P.S. The full message/ context for Howard's statement follows:

On Sat, 11 Dec 2004 21:02:26 -0800, Howard Pattee <***>
wrote:

>Tim and Boris,
>
>Your discussions raise a problem I have had with definitions of "model"
>that appears to me to have two profoundly different usages. One meaning of
>"model" refers to the structures of the formalism itself. Essentially this
>usage refers to "the formal model" as the right half of the modeling
>diagram. In this formal sense we can speak of all possible models and other
>formal concepts such as infinite sets, formal mappings, equivalence
>relations, duality, direct sums, Cartesian products, and the largest
>model.  In this formal context, analytic and synthetic are used as in
>formal logic, analytic referring to purely syntactical propositions where
>proof by contradiction is allowed. Synthetic expressions are not true or
>false by virtue of syntax alone, but among logicians I can't find any
>consensus on its precise meaning.
>
>The other meaning of "model" is an empirically testable representation,
>implying the WHOLE modeling relation. In this usage the right-half
>formalism is a model if and only if it satisfies some empirical test such
>as the Hertzian condition that (as a result of measurement or encoding) the
>interpreted consequents of the model's formal syntax matches closely enough
>the consequents of nature. This is definitely not a formal condition since
>neither measurement nor "matching closely enough" is a formalizable process
>or condition.
>
>Since empirical models are always finite, non-formal approximations, I do
>not see how exact logical conclusion about model formalisms necessarily
>apply to reality in other than the Hertzian testable sense. Except for
>practical speed/complexity issues, like NP-completeness and all that, I am
>not aware of any biological modelers that feel limited by or are even
>concerned about the formal aspects of computability. Other problems seem
>more important.
>
>Yet Rosen apparently argues that they are limited and they should be
>concerned when trying to model complex systems. I accept his formal
>conclusions about "the formal model" as correct, but I don't follow the
>informal argument that would preclude   empirically testable models of some
>aspects of life. What am I missing?
>
>Howard