Current scientific simulation compared to other traditions
an edited excerpt from "Current scientific simulation,
as set out in REALITY BYTES as compared to other traditions" http://www.wisc.edu/rshowalt/rbcrit/
Robert Showalter and Stephen J. Kline
(edited by M.R.Showalter).
Here are some "down to earth" things that we believe almost all engineers would sympathize with, and that many "ordinary people" would find sensible as well:
Context counts. The issues
of descriptive detail that happen to be needed to model a situation are
needed, and the test for "what is needed" is a practical one.
Practical requirements may vary, but it is ALWAYS important to have dimensions
clearly defined and consistently used, and it is ALWAYS important to be
able to relate what you mean by your symbols back to measurable procedures.
It is vital to get equations right.
To get them right, or to check them, may take careful modeling.
To interpret equations USEFULLY in a particular context, you must place them IN THAT CONTEXT. For SPECIFIC cases, modeling details (including both words and pictures) are important.
This matter-of-fact approach is different from some ideas now current in physics. We'd like to consider the differences.
The doctrine that detailed modelling is to be avoided, and discounted, is set out by Richard Feynman in an overwhelming (and, in its way, very beautiful) lecture. I quote from page 2 of lecture 18 in THE FEYNMAN LECTURES ON PHYSICS, Vol II. It is just below a table 18-1, titled "Classical Physics." That table shows nine abstractly notated equations. The nine equations are described in the text as "ALL of classical physics." Just below Table 18-1, Feynman lectures as follows.
"Feynman: It was not yet customary in Maxwell's time to think in terms of abstract fields. Maxwell discussed his ideas in terms of a model in which the vacuum was like an elastic solid. There was much reluctance to accept his theory, first because of the model, and second because there was at first no experimental justification. Today, we understand better that what counts are the equations themselves and not the model used to get them. We may only question whether the equations are true or false. This is answered by doing experiments, and untold numbers of experiments have confirmed Maxwell's equations. If we take away the scaffolding he used to build it, Maxwell's edifice stands on its own. He brought together all of he laws of electricity and magnetism and made one complete and beautiful theory."
It seems to us that the paragraph teaches the following lessons.
Lesson: You are SUPPOSED to think in terms of abstract fields. (Abstraction in not a dangerous but indispensable condensation and convenience, as engineers and computer programmers consider it to be.) Abstraction is a VIRTUE.
Lesson: You are NOT SUPPOSED to make Maxwell's mistake, and worry about detailed modelling. Modelling got Maxwell into trouble, and is now understood to be a disreputable dead end. Only the equations matter anyway.
Lesson: As a matter of history, there was much (read, too much) reluctance to accept Maxwell's theory, because of difficulties with modelling. This is a reason to avoid detailed modelling.
Lesson: Part of what you need to be a physicist is UNDERSTANDING that WHAT COUNTS ARE THE EQUATIONS THEMSELVES. The model DOES NOT COUNT. (You can't get credit, as a physicist, by struggling with the sort of modelling Maxwell did.)
Lesson: We may only question whether the equations are true or false (and, somehow, this can be done without careful, step-by-step modelling in construction of the true-false tests.)
Lesson: The only askable questions about equations are answered by doing experiments. (Somehow, these experiments can be defined, done, and interpreted without careful, step- by-step modelling, or somehow the step-by-step modelling is easy. Somehow all experiments may be generalized ((indefinitely??) beyond the range of parametric values actually used to confirm them.)
Lesson: ALL experiments have confirmed Maxwell's equations. (Language, and the limitations of our mind are treacherous right here (See Kline, 1995, Chapter 3). Feynman speaks as if he forgets, and his readers can be expected to forget, that IT WAS FAILURE OF MAXWELL'S EQUATIONS AT ATOMIC SCALES THAT CAUSED THE ABANDONMENT OF THE TRADITIONAL PATTERNS OF CLASSICAL PHYSICS.)
Lesson: When we look at physical reasoning WE SHOULD TAKE AWAY THE SCAFFOLDING. (This classifies out of existence many kinds of checking processes, and leaves unanswerable a large number of checking problems.)
Lesson: A THEORY *IS* A SET OF EQUATIONS. (A theory is NOT, for example, the combination of pictorial, word, and quantitative description that the Patent Office insists on, and that engineering requires.)
about a return to intuitively comfortable positions that correspond to
Feynman's points, but that match more closely how the rest of the world
thinks and does business?
More intuitive Lesson: Abstraction is powerful, but dangerous because it hides things, and lets you forget things. Use abstraction, but keep track of what you hid, so you can undo your abstraction if you need to.
More intuitive Lesson: If you can trust your equations, work with them, and don't distract yourself with modeling details your equations encode properly. But if you have reason to doubt your equations, you need models, for context and checking. Modeling is tough, and SOMETIMES an area of physics can get by, at least for a while, without doing it. If that happens, that may be pragmatically acceptable, but it is nothing to brag about.
More intuitive Lesson: Useful prediction and workable detailed understanding are what count in physics. That means the equations are indispensable. For USE enough knowledge to place the equations in physical context is indispensable, too. (If you are manipulating symbols that you do not understand, results may be all right, but the lack of understanding carries dangers with it, and is nothing to brag about.)
More intuitive Lesson: If
we want, we can play a game where "we may only question whether the
equations are true or false." In practice, we'll need
some sense of context and modelling to run the experiments that game requires.
"Games" that throw away detail may be convenient (so long as
you are SURE that the details you throw away will never matter) but these
games are nothing to brag about.
More intuitive Lesson: If you don't know enough to set up a model, that may be an inescapable misfortune, but it is nothing to brag about. If you lack information that you'd like to have, that may be an inescapable misfortune, but it is nothing to brag about. If the problem is important enough, and acessable enough, that is a research problem.
More intuitive Lesson: If
we want, we can play a game that says "The only askable questions
about equations are answered by doing experiments." To
play this game with much sophistication, we'll again need something like
careful, step-by-step modelling. If we play this game because
we don't know enough to do any better, we may get away with it, but
it is nothing to brag about.
More intuitive Lesson: Maxwell's
equations work beautifully over a very wide range of conditions, but fail
at atomic scales with charges moving as they move in electron orbitals.
IT WAS FAILURE OF MAXWELL'S EQUATIONS AT ATOMIC
SCALES THAT CAUSED THE ABANDONMENT OF THE TRADITIONAL PATTERNS OF CLASSICAL
PHYSICS. Therefore, the derivation of Maxwell's
equation is suspect, and may be worth a new look every now and again. (Note:
Maxwell himself was very unsure of his derivation before he died.)
More intuitive Lesson:
When we look at physical reasoning, we should consider our arguments according
to the same standards we apply to other arguments that have to work in
practical cases. In a detailed
situation, we can't show everything, so we need to choose what matters,
and attend to it. But hiding
information when it is not useful to think about it, and throwing it away,
so that it is lost forever, are different things.
More intuitive Lesson: A
THEORY IS AN EXPLANATORY SYSTEM, and the value of a theory is determined
by how well it works in use. For use, a workable physical
theory needs to be a "conceptual kit" with equations and
contextual "hooks" to fit to particular cases. A
theory adapted to a particular physical circumstance should be organized,
if possible, so it can be fit together with other theories so that
complicated physical circumstances can be modeled.
More intuitive Lesson: Anybody
who says that "abstraction is BETTER
than specificity" should be asked to
supply MANY cases
where the claimed superiority can be demonstrated, and should be asked
the SPECIFIC CONTEXTS where the claimed superiority exists.
these lessons were acceptable, then engineers and post-quantum physicists
could talk to each other more effectively than they do.
I believe the rather standard engineering "lessons" above, if accepted, might make it a great deal easier to follow George Johnson's admonition that
"Scientists must constantly
remind themselves that the map is not the territory, that the models might
not be capturing the essence of the problem, and that the assumptions built
into a simulation might be wrong. "