Current scientific simulation, as set out in REALITY
BYTES, compared to other traditions
M. Robert Showalter
Stephen J. Kline
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.
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.
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.
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.
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
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)
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.)
"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.
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.
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.
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.
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.
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
(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."
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.
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
At the start of REALITY BYTES, Johnson starts focusing
on issues of simulation. The point of departure is a specific failure in
" . . . 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
" 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)
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.
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
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."
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.
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
"analysis has a problem" to
"REAL mathematicians don't
In physics, over a few decades, there was a transition
"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
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?
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
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.
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.
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.
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.
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.
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 too hard to actually do
something to be actively avoided
something to be avoided and dismissed at the level of
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
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).
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
"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. "
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
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.):
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;
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
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
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.
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.
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.
It will take work to get better answers than the scientific culture now
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."