Process Models
Alexander Khaneles
This is in response to Ed's posting. Unfortunatly
Google does not show it (what has happened with the
first posting of other threads initiated on Google).
=======================================
>Newton's laws and the laws of aerodynamics are not
>process models even when the laws describe the
>dynamic behavior of an aircraft.
Ed,
What is so special about Newton's laws and the laws of
aerodynamics not to be considered as "process models"?
They provide means to build temporal evolutions and so
on.
Alex
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Ed Fredkin
"Alexander Khaneles" <akha...@yahoo.com> wrote in message
news:2004040515034...@web60809.mail.yahoo.com...
> Comment to the moderators =============
> This is in response to Ed's posting. Unfortunatly
> Google does not show it (what has happened with the
> first posting of other threads initiated on Google).
> =======================================
>
> >Newton's laws and the laws of aerodynamics are not
> >process models even when the laws describe the
> >dynamic behavior of an aircraft.
>
> Ed,
>
> What is so special about Newton's laws and the laws of
> aerodynamics not to be considered as "process models"?
> They provide means to build temporal evolutions and so
> on.
>
> Alex
A process model is something that is actually evolving in time. A
description of a process model does not change in time and a formula does
not change in time (even if the formula describes something true about a
process that does change in time). Thus a model airplane, while in flight,
is a process model of a real airplane in flight, but there are no equations
written down on a piece of paper that are process models.
There is a lot of confusion in physics about equations as models vs computer
programs as models. The difference is that some computer program models can
be process models of physical phenomena (by running the program in a
computer), but this is never true about equations.
If we imagine that some computation based system might be a process model of
fundamental processes in physics it makes sense to assume that the
computational model must be universal since Physics allows us to build
universal computers. This poses a problem -- the tyranny of universality --
whatever one universal computer can do, so can any other universal computer.
A "perfect model" is a deterministic process model where the state of s2 is
related to the state of s1, at every point in time, by a bijective one to
one mapping. Further, there must be an easy way to calculate the state of
s1 from the state of s2 where the computational work is only proportional to
the size of s2 (as opposed to the size of the history of s2). If s2 is a
binary counter that counts modulo 2^30 and s1 is a deterministic random
number generator that uses a stateless function R, R(n[i])=>n[i+1] that
cycles after 2^30 steps, s2 may not be a perfect model of s1 despite that
fact that there is a bijective one to one mapping of the states of s2 onto
s1.
Another way to think of a process model is as a black box with inputs and
outputs. Assume that E is an environment. If s1 communicates with E in
ways where s1 and E affect each other and if s1 can be replaced by s2 with
no change in the overall behavior of E, then we might conclude that s2 is a
process model of s1.
Ed F
akha...@yahoo.com
I do not see much confusion in physics. Some equations resemble CA
rules. To write down such equations one makes quite strong
presumptions about framework (space-time vs. CA grid) and defines
available physical objects (fields and others vs. CA states). The
framework presumptions are promising the ability to draw evolution in
time and fulfill ideas of process model as combination of framework,
objects and equations (not only equations themselves).
Alex
Taati
Could you elaborate more about what you call a "process model"?
Isn't Newton's 2nd law (the differential equation) a process model?
Does a process model have to embody a simulation? Or should it just contain
a time-evolution?
It might be useful to clarify more about the meaning of a model:
We say a system A models (a feature of) another system B, if how A looks
through a "glass" M_A, is similar to
how B looks through a glass M_B. A glass can be imagined as a mapping or a
*morphism* which *abstracts* some feature of a system.
Models may differ in the degree of abstraction provided by their
corresponding glass. The glass may extract a simple and rather clear feature
(like the Maxwell's electromagnetic laws) that may be used to
predict/control a phenomena with some degree of accuracy; or may excerpt a
complex and conceptual feature (like most of cellular automata models, or
the brain of a living creature).
The modeling process may be as formal as an assignment of the variables in a
Boolean expression, or may be as physical as the measurement of the
temperature using an electronic sensor.
Back to the "process models", we may say that B is a process model of A, if
the (formal) system C=M_A(A)=M_B(B) embodies a temporal evolution. Is it
what you mean? If so, any PDE which describes some changes with respect to
time is a process model, as well as all cellular automata models.
Cheers,
Siamak
Ed Fredkin wrote:
> There are many different kinds of models. Given 2 systems s1 and s2,
> we can say that s2 is a model of s1 if there are things about s2 that
> are similar to things about s1. I would like to start a thread with
> the goal of clarifying the characteristics of a certain sub class of
> models which I think of as "process models." Below are examples as to
> what might constitute a process model.
>
> A process is a system that is actually undergoing temporal evolution.
> While in flight, a radio controlled ¼ scale model of an airplane is a
> process model of a real airplane in flight.
> http://www.netaxs.com/~mhmyers/rc.tn.html
> Of course, model airplanes as process models are inexact, especially
> when it comes to the pilot. Running movies or ongoing videos are also
> process models and so is a computer running Microsoft's Flight
> Simulator. Newton's laws and the laws of aerodynamics are not process
> models even when the laws describe the dynamic behavior of an
> aircraft.
> DVD's containing movies of aircraft in flight or containing flight
> simulation software are not by themselves process models of an
> aircraft in flight.
>
> We exclude, as models, the thing itself; s1 is not a model of s1.
> Further, it seems unreasonable to say that one hydrogen atom is a
> process model of another hydrogen atom. This gets more interesting
> in the case of computer-like process models of physical phenomena such
> as cellular automata.
>
> Ed F