Current scientific simulation, as set out in REALITY BYTES, compared to other traditions

M. Robert Showalter

Stephen J. Kline

REALITY BYTES has set out, focused and partly defined concerns at the interface between scientific models and the "real world." I believe that REALITY BYTES has looked at map-territory interfaces more effectively than any erudite, stark journal article could have done. I think REALITY BYTES is the most useful, distinguished discussion of map-territory issues I know of in the English language. I know REALITY BYTES has been more useful for me than journal articles could have been.

According to current usages, journals are showplaces, and articles are "peer reviewed truth". That means that the journals are no place for sufficiently challenging material. They are no place for focusing and definition. They are no place for intellectual discourse as that notion is usually understood. Since the journals are "defining" the truth" according to some very rigid rules, they are ill adapted to seeking after new truth in the world as it sometimes is, as that seeking must sometimes be done by real people.

The New York Times forums are therefore important assets to our culture. They are great places for challenging material, great places for focusing and definition, great place for intellectual discourse in the highest liberal and cultural traditions. REALITY BYTES has uncovered and illustrated some basic insecurities at the interface between "real science" and simulation effectively and starkly. The informality has been helpful.

REALITY BYTES shows me, with more force than any textbook or journal article could, that there ARE serious muddles at the interface between scientific modeling ideas, and scientific notions of what reality is. Scientists ARE concerned about them, and DO NOT have good answers for them. If "the medium is the message" on some occasions, "the muddle is the message" at other times. So, I believe, it has been in REALITY BYTES. REALITY BYTES makes clear that modeling ideas, now lacking, are to be desired, and seem even to be hungered for. REALITY BYTES makes clear that intellectual work will be needed to supply them.

I believe that REALITY BYTES argues for reexamination of some modelling procedures and modeling doctrines in "the sciences." In another submission, my co-worker Steve Kline and I suggest some improvements in mathematical procedures. Here, I suggest that careful application of the modeling patterns of "the rest of the world," should be more a part of modeling in "the sciences" than they now are. These "usual world" modeling patterns were assumed in "the sciences" until not so very long ago. They were rejected, in large part, as a reaction to problems that James Clerk Maxwell had with his modeling in the 1860's and 1870's, and problems physicists had trying to follow Maxwell. Kline and I have solved a basic problem, central to the modeling difficulty, that Maxwell was not able to solve before his early death. We've done so as a different reaction, if you will an "engineering reaction," to some of the same kinds of modeling problems "the sciences" have had this last century.

I certainly can't speak for engineers as a group, but even so, I feel the need to set out some "engineering modeling" positions that I believe should be interesting in the context of REALITY BYTES.

Here are some "down to earth" things that I 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.

People who say "only the equations matter" don't have to actually USE the equations (or they do or assume more modeling than they admit to.) In real cases, the context is needed as well as the equations (I know of NO counterexamples here, and solicit them for discussion.)

The "only the equations matter" doctrine in "the sciences" needs to be looked at carefully and critically. It is VERY different from the descriptive and explanatory activity that occurs elsewhere in the world. I believe that REALITY BYTES offers ample evidence of the need for this critical examination.

Steve Kline and I believe something less conventional, and logically deeper, as well. A FUNDAMENTAL error has been made in our mathematics-physics modeling, that is as old as classical physics. As a culture, we have used limiting arguments that are incorrect because the restrictions on the dimensional parameters have not been understood. The dimensional parameters are our culture's link between measurement and equation representations of systems. Kline and I believe that it may be possible to take steps toward unifying "the sciences" (as that term is used in REALITY BYTES) with "the rest of the world" once this is understood.

REALITY BYTES exists in the larger context of George Johnson's work on the foundations, difficulties, and fascinations that constitute "MYSTERIES OF THE UNIVERSE." A central question from Johnson's FIRE IN THE MIND looms over REALITY BYTES:

"Do the patterns found by science hold some claim to universal truth, or would a visitor from another galaxy find them as quaint and culturally determined, as built on faith, as religious explanations of the universe?"

Let's call this quote "A". We wish we''d gotten to read A, and FIRE IN THE MIND, earlier than I did. Steve Kline's CONCEPTUAL FOUNDATIONS FOR MULTIDISCIPLINARY THINKING (Stanford, 1995) would have been a stronger, broader, more beautiful book if Steve had read FIRE IN THE MIND before finishing it. Steve and I were both very excited when we read FIRE IN THE MIND. We've told Johnson that. In FIRE and elsewhere, Johnson explores the human hunger for pattern, the need people feel to find (or impose) order in our bewildering, multifaceted, big world.

(Kline had suspected much of what Johnson said for a long time, and treated some of the same issues in his book, but with much depth that Johnson gives.

REALITY BYTES deals with difficulties connected to quote A at the interface between math and "the world." REALITY BYTES shows a great deal about "the patterns found by science," interpreting "science" in a particular way. But at the same time, Steve and I, who come from engineering traditions, have been struck by how parochial, recent, and tentative the "science" Johnson and REALITY BYTES refer to really is. The "science" of REALITY BYTES is still a minority position from a contemporary socio-technical perspective (counting noses of people who now use "science"). The assumption that "science" now holds all the right positions ought to be discussable, and its assumptions ought to be comparable to different assumptions different traditions hold.

I believe that A is a superb and fitting question. Even so, A would have seemed an astonishing, ill fitting question, missing a central answer, to many in the past. It would seem so to many today. Quote A applies to a PARTICULAR science. It doesn't apply to many people and organizations who feel, quite unselfconsciously, that they are scientific, too.

Quote A would seem misshapen to any "subculture of classical physics," past or present. That includes not only figures of the past, but essentially ALL working engineers today.

I believe that A would also seem misshapen to a substantial fraction of commercially employed Ph.D. physicists, who find they cannot use quantum mechanics (or cannot often use quantum mechanics) in their thought and work in electronics and elsewhere. (At least, that is my impression from talking to these physicists.) Even in the design and fabrication of the most advanced microcircuitry, classical notions are the ones most used. This is also true in nuclear engineering, aeronautical engineering, mechanical engineering, and the other disciplines that we know of. From the classical perspective, one does not need quote A's "faith." One needs measurement according to careful procedural rules.

I'd like to state a cultural difference between engineers and "scientists" clearly. I do so without attempting to hide the side I am on, and include a phrase that some may find offensive that does, nonetheless, express my real opinion, an opinion shared by many of the good engineers I know.

The idea that making a model of the world is rightly done by plopping down a disconnected axiomatization is now highly developed, strongly instilled DOCTRINE in both physics and mathematics. I'll call this the "axioplop" position, for short. Engineers (and many other people) feel differently - they believe that making a model is rightly done in a connected fashion, in representation steps that hold as close to pictorial and experimental reality as possible, with abstraction in traceable steps (using the same basic ideas about abstraction, or "hiding detail" that computer programmers use). By traceable steps we mean reversible steps. If we fall short of the reversible ideal, it is nothing we brag about. "Scientists" in the REALITY BYTES sense, take a different view. For them, axiomatization is not a necessary evil, but a positive good. Details are to be rejected, not retained. These "scientists" GLORIFY the axioplop position. REALITY BYTES, in large part (though not completely) discusses difficulties that flow from the "scientific" doctrine of axioplop.

The validity and heuristic virtues of axioplop should, I feel, be subject to examination. One may respect a great deal about the axioplop stance (for some purposes). One may respect results achieved using the axioplop approach (which engineers would call dangerous, but not necessarily wrong.) Even so, one may still feel that the axioplop doctrine may be subject to improvement in some other cases. The idea that models should be derived from physical models in a detailed fashion should be considered in at least some specific cases. The idea that rejection of detail is good ought to be discussable, and referred to examples. When and how does that rejection help? When and how may that rejection be dangerous?

(NOTE: On modelling procedure, engineers and physicists are both working largely on the basis of faith. Engineers BELIEVE they must model step-by-step but, painfully often, do not know how to do so. Physicists (and mathematicians) BELIEVE THAT THEY ARE NOT SUPPOSED TO MODEL STEP BY STEP (although, to survive, they often do so). In REALITY BYTES the faith of the physicist is assumed to be the right one. That should be debatable. It may be useful to recognize that the physicist's position is not the only position respectable, competent people take.)

Let's paraphrase Johnson's question A and ask it in some "unscientific" contexts. We'll apply questions isomorphic to A to the Boeing Aircraft Company, The United States Bureau of Standards and Technology, The United States Patent Office, and THE NEW YORK TIMES. Each of these organizations is rigorous, meticulous, and "scientific" according to common word usages. None of these organizations is "scientific" in the sense Johnson uses "science" in A, nor in the same sense in which "science" is taken for granted in REALITY BYTES.

(In Kline's book, Kline says that "science is by far the best process we have found to verify truth assertions. ( not "science " in A ) Johnson too narrow. )

Please read these questions, each isomorphic to A, and see if you find them as awkward as I do. Before reading them, let me add this hint. ANY technically useable mathematics in our culture is likely to be used by Boeing, or the Patent Office, or by USBST. If a new, useful piece of math surfaces, these organizations master it in the ways that count for them. THE NEW YORK TIMES can get a working understanding of any coherent mathematics it wishes to, in short order, if it has the will to do so. However, these organizations are all "unscientific" by the standards of A for the following reason.

All these organizations use pictures, and careful word descriptions. None of these organizations uses decontextualized mathematical description, nor would they value it if they saw it. All these organizations think context counts, and take care about contextual issues in their businesses.

Now, here are the questions isomorphic to A:

"Do the scientific ideas and technical patterns used in the business of Boeing Aircraft Company hold some claim to universal truth, or would a visitor from another galaxy find them as quaint and culturally determined, as built on faith, as religious explanations of the universe?"

"Do the scientific ideas and technical patterns used in the business of The United States Bureau of Standards and Technology hold some claim to universal truth, or would a visitor from another galaxy find them as quaint and culturally determined, as built on faith, as religious explanations of the universe?"

"Do the scientific ideas and technical patterns used in the business of The United States Patent Office hold some claim to universal truth, or would a visitor from another galaxy find them as quaint and culturally determined, as built on faith, as religious explanations of the universe?"

"Do the scientific ideas and technical patterns used in the business of THE NEW YORK TIMES hold some claim to universal truth, or would a visitor from another galaxy find them as quaint and culturally determined, as built on faith, as religious explanations of the universe?"

A seems well formed as it applies to "science." The iso-A questions above seem much less well adapted to their subjects. Suppose a Boeing engineer reacted to the iso-A question connected to her company. She might answer as follows:

" The scientific and technical ideas and patterns we use at Boeing aren't concerned with universal truths of any kind. If something is "mysterious" we map our uncertainties as best we can, and stay away from the areas where the uncertainties are unacceptably large. We deal in specifics here. We test everything within an inch of its life, because we're in a life and death business, and because aircraft efficiency is an unforgiving business. We're very damn sure of the "truths" we use, because we test carefully, and check everything we can. If it were any other way, we couldn't build airplanes. We put several million parts together, that have to fit together, and weigh as little as they can. These parts have to be fabricatable and maintainable by real people. We have to know the operating life of these parts. We handle the difficulties of aluminum as a material. SPECIFICATION is a passion at Boeing, because it has to be, and the amount of detailed information we generate and maintain is prodigious, and has to be. At Boeing, there are plenty of things we can't calculate, and we're very aware of it. We have to deal with computational fluid mechanics, which is still, by far, the most challenging math that anyone actually DOES SUCCESSFULLY. We can handle enormous complexity. Now, we at Boeing are beginning to model whole airplanes. Work at Stanford is just beginning to model whole jet engines. There are plenty of flow calculations we'd like to be able to do, but can't. We know those limitations. There are plenty of geometrical and structural calculations (particularly involved with optimization) that we can't do. We know those limitations. But in iso-A there are some words that are really off the mark. If you're talking about our stuff as "culturally determined," that is partly true (read Walter Vincenti's WHAT ENGINEERS KNOW, AND HOW THEY KNOW IT to see how "cultural determination" works in engineering!) But there's nothing "quaint" or narrow about how we advance our culture on each new design. As for comparisons of our decisions to "religious explanations of the universe" that's as off the mark as it can be. We trust what we measure. We trust our experience. We are careful as we know how to be, and we've learned a great deal useful about being careful. A hundred years ago, the best engineering firms knew less than we know, but much of the way they went about their work was the same careful way we go about our work today. Fifty years ago, the best engineering firms did business much the same way we do, though of course we know more, and are working on newer things. A century from now, many of the same careful, tightly specified practices we use will be in use still, though they will apply to things we can't imagine now. Flaky notions like "quaint, religious explanation" don't much apply to us, and don't apply to other successful engineering firms, either."

Is the "Boeing engineer" above unscientific? According to the usages of A she surely is. She lives, unapologetically, in a world of classical physics. She lives in a sharply specifiable, and sharply specified world, and is insistently engaged in bringing more sharply specified things into being in that world. Although she faces calculational difficulties, including those that Maxwell worked on, and that Steve Kline and I have worked on, she does not romanticise or glorify them. Successful Boeing engineers do not consider themselves inferior beings to quantum physicists, and may in fact value the quantum people in terms of their ability to calculate useful things, with no credit beyond that. Boeing engineers, by and large, are not in the middle of a philosophic crisis.

Would a patent examiner, or a bureau of Standards worker, or a newspaperman be so very different? They also live in sharp, sharply specifiable worlds, each with plenty of unknowns, but with unknowns that are not special philosophical challenges. They are also engaged in bringing more sharply specified things into being. By and large, they face problems of measurement, specification, and sometimes calculation, but NOT problems of faith. Things are different in the "science" of A and REALITY BYTES. (I put "science" in quotations, because I'm not convinced that this "science" is "the best possible science" or "the most advanced science today" or "properly the highest status science.") The "science" of A is an unusual subculture, even among technical people, and should be seen as such.

At the start of REALITY BYTES, Johnson starts focusing on issues of simulation. The point of departure is a specific failure in simulation:

" . . . mathematicians have found that the general problem of predicting how any sequence of amino acids will fold into a protein is intractable -- unsolvable by any conceivable computer. . . . How can something be so easy for proteins and so difficult for us? What does this say (if anything) about the nature of scientific knowledge and our ability to know the world?

As scientists take to their computers to unravel the problem, they are forced to confront questions about the very meaning of simulation. What is the relationship between a scientific model and the reality it is meant to represent? Can a protein be thought of as a tiny biological computer, calculating the proper way to fold?

Johnson makes a point that I wish were on the masthead of most academic journals:

"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."

This is an important admonition, but harder than it looks to reduce to specific action. How is the map to be identified? How do we get clear on what the territory is? How can we go from map to territory, matching carefully, so that we can make a judgement about what is a good fit and what is not? How do we go back again? In shorthand, I'd condense part of Johnson's question using a strangely dirty word:

How, in real cases, do you go about being a realist? How do you learn to be realistic about particular things?

George Johnson may live with people who shun "realists." But, secretly, part of him would like to find out how to be one. (It is a hard thing, finding out how to be a realist.)

In REALITY BYTES, notions of simulation sound strange to an engineer's ears.

Here is Cooper (#4)

"Scientific models have certain properties in common with literary tropes. The main difference, as I see it, is in the predictive ability of a scientific hypothesis. They both describe a feature of reality--attempt to define it in a certain way--by saying that it behaves like something else, or in a manner suggestive of something we can describe in precise terms.

. . . . the question why nature often seems to have math in its bones is still a philosophical mystery--at least to me. It's probably the most profound mystery I know of.
. . . . . .

I think what comes across . . . is the fluidity and tentativeness of the modelling process. For Carl Sagan (and many others of us) science is a candle in the dark. For working scientists, however, the process is less well-lit--it comes down to blind groping and hit or miss. Good models don't spring fully caparisoned from the head of a experimentally minded Zeus.

A STATEMENT OF FACT, BUT TERRIBLY UNSATISFACTORY "

Engineers have plenty of problems doing their simulations, but they'd never describe simulation as "fluid" or "tentative" or "like a literary trope." They wouldn't describe it as in any way magical. For them (and for me) simulation is (and always should be) something to be meticulously done, step by step, according to routine patterns. (Patterns that are taught, with heavy emphasis, in the engineering schools.) If these standards can't be met in a particular case, there is a procedural problem, or a problem of ignorance. One may be stumped by such problems, but need invoke no magical notion to relate to them. If we are stumped, and the issue matters enough, we have a research problem.

In REALITY BYTES the dialog goes on. Cooper (#6) quotes Dirac in what would seem (at least in other fields) a magical and suspicious statement.

" It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it."

(My sympathies are not with Dirac. Much of human experience involves conversion of such "deep and forbidding mysteries" into understandable, workable patterns, once people found out what they were doing. Perhaps it will be different in Dirac's realm, but for what reasons should we suspect this?)

Johnson sounds the notion of mystery again: (#9) "I agree with Will Cooper that one of the greatest mysteries of all is what the physicist Eugene Wigner called "the unreasonable effectiveness of mathematics." Why does the universe seem to obey mathematical laws? "
Cooper agrees that a mystery is really there, and wants to discuss it philosophically (#11).

"Damn it, people made math up, didn't they? It's an invention. . . . Are these objects "out there," or do they exist only in our minds, as Pirsig says? I have a hard time with the Platonic model.

Johnson responds (13)

"I think what bothers Phaedrus and me is the metaphysical question of where these laws are "written." Most physicists I know are Platonists, believing (at least tacitly) that the laws exist in some unphysical realm. "

Cooper pulls a great deal together as follows (#15)

" I grudgingly accept that materialism stands on epistemological grounds as shaky as any idealists' . . . However, I don't feel at all comfortable with the notion that we "discover" empirical laws from a priori principles existing apart from, and antecedent to, the mind of a knower. As I view the process of scientific discovery and formalization, observation (accompanied by genius, intuition, and good fortune) leads to abstraction and analysis, which, if a strong positive correlation between hypothesis and experimental results bears out, proceeds to a formal statement of a "law." . . . . . To me the entire process is human, flawed, errant far more often than accurate. I find it hard to believe that scientists take dictation from God, a la Mozart."

In REALITY BYTES I missed the following. I missed pictures, or acknowledgement of the need for pictorial representation. I missed respect for word descriptions as an ESSENTIAL part of modelling. I missed a respect for contextual detail, and a sense of the necessity for meticulous checking of well specified work. I felt uncomfortable with the idea that abstraction was, somehow, better than specificity. I missed notions of description that would work for a patent lawyer, or an engineer, or a specialist in measurement, or an ordinary user of technical information. I felt uncomfortable, feeling that the dialog in REALITY BYTES was being written by people who really liked, and revered, magical ideas. I felt that the notion of map-territory matching was too muddled to be workable.

I think that the words in REALITY BYTES would have sounded strange to Maxwell, Michael Faraday, or Lord Kelvin. They would have sounded strange to Percy Bridgman. They sound strange to me, and they'd sound strange to any engineer I know. Percy Bridgman, like Einstein a Nobel prize winner and, like Einstein a believer in continuous and differentiable mathematics (and therefore a doubter of the current formulation of quantum mechanics) might have spoken as follows.

" There is plenty of math that people can't specify or do, but there is NO deep philosophic problem in modelling, so long as you avoid muddle. Muddle is avoided by the hard, specific work of connecting all the ideas you use to specific measurement procedures, set out in enough detail so that you know what you are talking about. If you can't specify (and picture) everything under discussion, you don't know what you're doing. If you don't know what you're doing, you and your logic are in the hand of the gods. You won't be able to figure out what goes wrong if something does go wrong. Odds are, something will go wrong. So, odds are, if you want to get your work right, you'll be FORCED to check your modeling. There's no mystery if you happen to get confused when you don't know what you're about. The job of correcting the situation is not mystical. The job is to FULLY specify your problem (and operational measurement procedures defining everything are the test for that.) Once you know what you are talking about, the math may still stump you, but you won't face any "deep" or "magical" philosophical issues.

" By the way, people "take dictation from God" all the time. They do so when they take measurements in well defined, fully understood experiments.
There may not be any "general, grandiose solutions" to a generally defined "map-territory problem" but in SPECIFIC cases (the only kind we can ever really do) we have programmatic jobs that we can reasonably expect to do."

Bridgman believed that. Einstein believed that. Engineers believe that, and are taught to practice simulation in this spirit. They do so. The "Bridgman" position above is not totally tenable in fields where quantum effects enter. Even so, Bridgman's position and its output has been abandoned, for cultural reasons, to a much greater extent than the evidence of quantum mechanics itself requires. I believe that the "mysteries" of REALITY BYTES, miraculous as they may seem, are in large part man-made. That is, I'm not surprised that a "science" that proceeds according to the usages of axioplop produces muddle after muddle.

But REALITY BYTES treats problems that are more fundamental than current differences between engineers and "scientists, also. Here is a profound, unpopular truth (accusystems #33) that constrains the work of scientists and engineers of all sorts:

"Our math becomes stretched when things are slightly more complex than that of the few simple text book example problems. There are problems where our mathematics are as yet inadequate."

Limiting oneself to classical physics entirely, complicated situations are hard to model analytically, and, often enough, hard to approximate. Academic disciplines advertise their strengths and their hopes, not their limitations, and so this is a very important truth that is less known than it should be.

Intractable mathematical problems, perhaps the hardest of mathematical problems, exist in classical physics and in much of engineering. Steve Kline and I have been working, within the engineering tradition, at the interface between measurable reality and mathematical modelling, trying to get classical physics to work well enough for engineering and invention in complicated and coupled cases. Steve's been preoccupied with fluid mechanics, I with breaking mathematical modelling to the tasks of invention and optimization.

Our difficulties would exist even if engineers and "scientists" agreed on modelling. But communication of our problems, and their solutions, would be easier if that agreement was there. Some sense of historical context may help.

I believe that the "mysteries" of REALITY BYTES, miraculous as they may seem, are in large part man-made. They hardly apply at all to the modelling tradition of ENGINEERING, which since the 1880's has gone a different (and very productive!) way from "pure" science. They can largely be traceable to DOCTRINAL POSITIONS after 1880. I've done a little checking. I can't find any evidence for a rejection of step by step modelling as doctrine prior to the 1880's. So far as I can tell, this doctrine is at least in large part a reaction to the work of Poincare in mathematics ("the crisis of analysis) and physicists' reactions to the "failure" of Maxwell, who really tried to model rigorously, and conspicuously failed to do so before he died.

In the history of math, there was over a few decades a transition from

"analysis has a problem" to

"REAL mathematicians don't do analysis."

In physics, over a few decades, there was a transition between

"not even J.C. Maxwell can model successfully" to

"you SHOULDN'T TRY to model"

In both math and physics, there was a transition from
"abstraction as a dangerous convenience" to "abstraction as a VIRTUE."

The physicists lagged the mathematicians by about 20 years on this transition (to the glorification of abstraction) but the transition they went through was of the same nature.

These transitions have been historically important, but they were group responses, not logical derivations.

Here is a kind of "modeling argument" common in the "high scientific" culture that seems strangely backwards from the viewpoint of engineers. In this argument, abstraction is better than specificity, pictures and detailed argument are unnecessary encumbrances, and math is, somehow, meritorious in itself, and not much checked. John Edstrom (#31) is teaching the VIRTUE of abstraction. (Physicists and mathematicians, quite unselfconsciously, think abstraction is a GOOD thing. Engineers, just as unselfconsciously, think abstraction is an unavoidable but always dangerous necessary evil, to be handled as carefully in engineering as it is in computer programming.)

Erdstrom: "There are other advantages, but lets just look at abstraction for now. Suppose that I invented the rubber band. How do I communicate this to other people? Like you said in an early post, a large part of understanding involves describing new things in terms of known things (the model class identification problem). In my mind the rubber band reminds me most of a spring, but there is no known spring quite like my invention. That is what makes it new after all. So how do I describe it to you? I know about helical steel coil springs, iron leaf springs, pleated paper springs, .... but my new bouncy thing isn't paper, iron or steel. It isn't a coil, a leaf or a pleated sheet. If I try to describe my invention to a stranger by pointing to any single particular spring I will inevitably call attention to all of the ancillary qualities I don't want to call attention to. "I invented something that is exactly like a steel coil spring except that it is not steel and it is not a coil!" (plus a long song and dance to explain the explanation) In effect I have to write a long discourse that touches on all commonly known springs in order to establish the nature of the quality of bounciness without tying it to any particular quality in any particular spring and also distinguish this kind of bounciness from, say, the bobbing of a cork in water and other examples of things that bounce that aren't quite the same sort of bounciness I wanted to talk about.

" What I really need is an abstract notion of "spring" that doesn't depend on any particular physical characteristic such as construction material, shape, color, size, weight, supply source, density or smell. Well, Hooke's Law (F = -kx: the change in length x of the rubber band is directly proportional to the force F applied to it) fits the bill. In four symbols Hooke provided a way to describe the business end of every spring then known and all springs yet to be discovered, including mine. All I have to do is measure the k of rubber and I'm done. Notice that what, if anything, I should measure in order to characterise the bounciness of my new rubber band is clearly expressed right there in the definition! Why, I hardly have to think at all! Notice also that the single symbol, F, refers to an entire complex of detailed knowledge. In a single symbol I relate my discovery to Newton's Principia Mathematica and everything written about force since then and implicitly link my discovery to anything that might be written about force in the future. Best of all, I can do it without having to write a gargantuan tome. This means that you won't have to read the equivalent of an encyclopedia in order to learn the essence of my discovery and you won't need a wheelbarrow to carry my report home with you. A Postit note will do nicely."

I believe that if John Erdstrom actually did invent a new widget of any kind, and actually did wish to describe it in an operationally useful fashion to real people, he'd forget the advice he's giving just above. Think what he says:

Do away with the pictures. Do away with the words. Let one equation carry your explanatory load. (Don't bother to be sure that your equation is a good model: Choose Hook's law, which is linear, and apply it to a hysteretic and nonlinear material.)

For what human being would this be "effective communication", if the communication was to be tested by action?

People know how to do a lot better than this. Go to the Patent Office and see how the pros describe things, concisely, when performance actually matters! Go to any firm that manufactures a complex product, and see the sophistication with which description is done, and how effective that communication is when it has to be! Erdstrom seems to advocate a kind of "anti-communication". As a representative of his culture, Erdstrom WORSHIPS THE REJECTION OF DETAIL.

Erdstrom uses language an engineer might hesitate to use as he advocates his position:

"So math isn't just better than descriptive prose at these sorts of jobs. It beats the living crap out of prose and then kicks its sorry butt down the stairs, out the door and into the street. Beginning in the 13th century our culture began to discover this and over time prose was seen to be such a waste of effort that people stopped using it whenever they could find mathematical structures that captured what they wanted to express. What we're left with as a result of this selective process is a literature which is rich in mathematical expressions. "

Oh yes? John Erdstrom would have a hard time finding examples, anywhere or anytime since the 13th century, when "prose was such a waste of time people stopped using it." For example, descriptive prose is indispensable all over engineering, for plain reasons. Boeing generates a mass of descriptive language, and has to. So does any other firm that produces complex products that work. What people use when it counts is a MIX of pictures, and words, and (sometimes) equations. The idea that mathematics is dominant when people have descriptive work to do is not true. It has never been true. Mathematics is one of the representative modalities people use and, like the others, indispensable in its place.

The idea that math is "better" than prose, as Erdstrom expresses it, is strange. Even so, that idea is taken for granted among some "scientists." That is strange. To teach a student the ideas Erdstrom teaches here (and in physics that is routinely done) you have to raise your voice. To believe such nonintuitive things, you have to have been indoctrinated yourself. Reading Erdstrom here, I felt that George Johnson's notion that the sciences can be thought of as cults was helpful.

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. Please read the following paragraph, not in the casual way that a literary man might read it, but as a motivated, intellectually- mathematically overwhelmed, anxious student, struggling to remember, and struggling for acceptance as a physicist, would be expected to read it.

"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."

The paragraph teaches lessons students struggle to learn, and MUST learn to be physicists. These lessons are as follows. I take the liberty of expressing some comments and reservations in parenthesis:

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.)

These lessons are central points of faith and cultural tradition, religiously enforced, among physicists and among mathematicians, who follow the physicists here. I do not believe that any of these lessons would have been regarded as sane prior to 1880. These lessons are all shockingly anti-intuitive when you first come upon them. Students react to them with near uniform shock, generation after generation, and are broken to these lessons by indoctrination. A bit later, these same students learn that (in Lindley's felicitous phrase) "reality does not exist." Status is gained by going "beyond common sense."

Engineers are asked to do many hard things. But never in my experience has an engineer gained status, or gotten good work done, by going beyond common sense in this kind of way. Phrases like "reality does not exist" (or "what is the sound of one hand clapping") seem silly (not profound) to an engineer. To many, they seem silly.

I believe, strongly, that every one of the lessons Feynman taught above is actively misleading. I think most professional engineers would feel the same. It is not merely that accepting these lessons classifies the problems Steve Kline and I have chosen out of existence. These lessons, fairly enforced, would make professional standard engineering impossible. These lessons, believed by physicists, and disbelieved by engineers, isolate physics and engineering, so that neither side can learn useful things the other side has to teach.

Feynman's lessons above are now taken for granted, without examination, in the physics and mathematics community. Knowing these lessons confers status - the lessons themselves are, in George Johnson's sense, worshiped. I believe that many of these lessons should be examined, to see how they fit conditions and modeling opportunities today.

One of Feynman's lessons is a biased and false statement of history. (Feynman may never have examined the history, and may simply be repeating it.) Maxwell discussed his ideas in terms of a model. When Feynman says that "there was much reluctance to accept his theory . . . because of the model" a student will read "there was too much reluctance." By professional standards, the inference of "too much" seems unfair to all concerned, and misleading. Maxwell was a respected mainstream scientist from the beginning of his career to the end of it in 1879. When he wrote down his electromagnetic equations in the early 1860's, they were respected and studied from the first. Maxwell's work, mostly electromagnetics, was respected enough to gain him leadership in physics at Cambridge, one of the most important posts in the gift of British science, by his early forties. People concerned with his model were capable people asking real, interesting questions that concerned Maxwell, too. (A reading of Whittaker's A HISTORY OF THEORIES OF AETHER AND ELECTRICITY makes clear that Maxwell did not work in isolation, and that his colleagues were not dolts.) Maxwell DID show something interesting in modelling. Maxwell, more than anyone before his time, DID try to make step-by-step modelling a rigorous proposition. As he did the modelling, he did measurement work of ground-breaking precision, again and again, and theory and model were tightly related. In some important ways, his modelling work was unsatisfactory, and obviously very difficult, before he died in 1879, in the forty-eighth year of a very busy life. Some of his concerns are expressed in his ENCYCLOPEDIA BRITANNICA article DIMENSIONS, set out a little later. Steve Kline and I have addressed and, we believe, finally solved, some of Maxwell's central modelling concerns expressed in that article.

After the 1870's, the profession of physics became less and less concerned with detailed modelling, because they found their modelling did not work. Maxwell's magnificent yet disastrous book A TREATISE ON ELECTRICITY AND MAGNETISM made things worse. It was a disorganized set of notes and sketches, some of surpassing brilliance, all no doubt useful as reminders for Maxwell himself. Nonetheless, for long stretches, the exposition and mathematical formality of Maxwell's TREATISE is so incomplete and informal as to be painfully unusable. People who tried to use this book learned, in large part, that modelling is painful and unworkable. They "learned" that theories, when they happened, must be interpreted as magical occurrences, rather than formal (or mostly formal) and logical (or mostly logical) derivations.

Over time, modelling in the physics profession, and among mathematicians, went from

something essential

something too hard to actually do

something to be actively avoided

something to be avoided and dismissed at the level of taboo.

This may be a humanly understandable sequence. It seems to resemble the sort of progression that builds up taboos elsewhere. It may have made pragmatic sense as it happened. But the conclusions are NOT a rigorously logical progression.

Modelling is practically indispensable in engineering, no matter how hard it is, so engineers never went down this progression. SOME careful modelling is often indispensable in engineering. No engineer would doubt that in public. It would be professionally dangerous for an engineer to do so. Many of the strange and magical issues described in REALITY BYTES seem foreign to the context of engineering (which has other kinds of problems).

How 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? If these "more intuitive lessons" are NOT compatible with what modern physics ACTUALLY knows, and can ACTUALLY do, I'd value a chance to have the reasons debated, in an well umpired forum, by people who are not all religiously instructed in the "science" position. It would be nice, for practical and social reasons, too, if these "anti-intuitionists" could live in a conceptual world more clearly translatable into the world of engineers and other people. Here are some "lessons" that seem intuitive to me, that may perhaps seem so to others as well:

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.

If these lessons were acceptable, then engineers and quantum physicists could talk to each other more effectively than they do. Perhaps some good would come of that. If these lessons are NOT acceptable, I'd be interested in why that is ON THE BASIS OF EVIDENCE, NOT JUST DOCTRINE. I believe the rather standard engineering "lessons" above, if accepted, might make it a great deal easier to follow George Johnson's admonition that

Call this B. George's A poses a problem. George's B specifies an important part of the solution. To follow B you need to be careful to define maps and territories meticulously enough so that matches between them are clear enough so that they can be accepted or rejected. Specifications must be careful enough so that assumptions can be called wrong (and called wrong in enough detail so that new approaches can be suggested.) Ways to do this are not fully available now, anywhere, and the barriers to doing this kind of map-territory fitting are not well understood, and have not been widely discussed.

To make B workable, new ideas have to come into being. THE NEW YORK TIMES forums, including REALITY BYTES are great places for the creative process of eliciting and bringing into focus such ideas.

This piece has been devoted to comparing a "science" tradition implicit in much of the discourse of REALITY BYTES with other traditions, especially engineering. I'll be grateful if anyone has reactions, and grateful that those reactions, if they come, can come in a context where there is a powerful umpire and interpreter present. In the presence of an umpire, in a place separated from the jurisdiction of any of the "invisible colleges," real discourse on interdisciplinary issues is possible.

Steve Kline and I have also done specific work on simulation, within the "careful specification" tradition of engineering, that is relevant to REALITY BYTES. We are asking that it be checked.

Here is James Clerk Maxwell, writing a year before his death in 1879 (DIMENSIONS Encyclopedia Britannica, 9th ed.):

"There are two methods of interpreting the equations relating to geometry and the other concrete sciences.

"We may regard the symbols which occur as of themselves denoting lines, masses, times &c;

or

we may consider each symbol as denoting only the numerical value of the corresponding quantity, the concrete unit to which it occurs being tacitly understood.

"If we adopt the first method we shall often have difficulty in interpreting terms which make their appearance during our calculations. We shall therefore consider all the written symbols as mere numerical quantities, and therefore subject to all the operations of arithmetic during the process of calculation. But in the original equations and the final equations, in which every term has to be interpreted in its physical sense, we must convert every numerical expression into a concrete quantity by multiplying it by the unit of that kind of quantity."

According to the first, more literal method Maxwell states, we have "difficulty" interpreting some (cross effect) terms, indeed, with no more information than Maxwell had, we cannot interpret them at all. We are stopped. THEREFORE we make a plausible assumption. We make that assumption along with Maxwell, giants before him (Newton, LaPlace, LaGuerre, and Fourier) and workers since. As a culture, we decide to act AS IF our physical quantity representing symbols may be abstracted into simple numbers in our intermediate calculations. This ASSUMPTION has produced equations that fit experiment innumerable times. But it remains a pragmatic ASSUMPTION with no logically rigorous basis at all.

This is a problem that bothered Maxwell a great deal. It bothered us because of practical problems we had with analyses that we had been taught to trust, including some important problems in automotive engineering, neural medicine, and elsewhere. We're asking that our solution be checked. The solution we offer has some interesting things to say about Johnson's question

What is the relationship between a scientific model and the reality it is meant to represent?

It also offers information about "where these laws are "written."

It says something about the limited but real degree in which we DO

"discover" empirical laws from a priori principles existing apart from, and antecedent to, the mind of a knower."

We show something new about the dimensional parameters, the constructs that ARE the interface between measurement and our culture's equations. We show that the dimensional parameters are "not just numbers" and that there are some limits on how they can be used. When we show those limitations, it becomes clear that some of our culture's limiting arguments have been wrong and some of our culture's accepted equations are in error or incomplete.

In medicine, this is a matter of life and death.

Elsewhere in applied physics, we think our work will lead to reinterpretation of some problems, including some of the problems that occur at the interface between classical and quantum physics. I hope that some of the discontinuity at that interface may, with time, smooth out with the improved analysis.

Steve and I hope this work can be considered, and checked, and the truth found out about it.

We are dealing with a problem that crosses disciplinary boundaries. Interdisciplinary problems are hard. We are dealing, in exactly the senses Johnson described in FIRE IN THE MIND, with the taboos that surround structures of faith. Without powers like THE NEW YORK TIMES and George Johnson in the world, to give us a place to stand, we might be lost.

A while ago, I asked George to

"give us a place where we can get stomped, fair and square, or possibly, a place where we can win."

We're grateful for the chance we're getting here.

We'd like to close this piece where I began it. I believe that REALITY BYTES has looked at map-territory interfaces more effectively than any erudite, stark journal article (or journal series) could have done. REALITY BYTES is the most useful, distinguished discussion of map-territory issues I know of in the English language. My own thoughts and feelings about simulation are clearer, more informed, and more developed because of REALITY BYTES. A forum like REALITY BYTES which is informal, multidisciplinary, and well umpired, can be a great place for challenging material, a great place for focusing and definition, and great place for intellectual discourse in the highest liberal and cultural traditions. On issues that are strongly multidisciplinary, involving high stakes, it may be one of the only places our culture has to offer. I think The New York Times forums are important assets to our culture. I'm glad to be able to read them. I'm grateful for the chance to participate in this one.

I believe some of these answers may come by considering "outside world" and "engineering" approaches, some of which might reasonably be accepted again in "the sciences."