John Sowa asked me to post the following that I sent to him last
night. Just FYI apropos of David Hestenes... (01)
-- snip -- (02)
David Hestenes was my undergraduate physics professor (for mechanics)
at Arizona State in 1984. A tremendous but uncompromising teacher and
a first-rate physicist ... he was working at the time on new targeting
techniques for the Galileo mission to Jupiter. The 'A' I got from him
was one of the hardest grades I ever earned and I'm still proud to
have gotten it. (03)
Funny thing about imagery. The first day of class he gave us a test
-- a test of our intuitions about physics using pictorial situations.
There were 30 questions. If you got less than 17 'right', he asked
you to leave the class because in all probability, you would fail. He
was right -- almost everyone stayed and pretty much everyone who got
less than 17 right failed. I asked one of his TAs to confirm this. (04)
On Dec 13, 2007, at 22:44 , John F. Sowa wrote: (05)
> I came across an article that is related to several different threads
> in this forum. So I decided to start a new one.
>
> The article is a review of a historical book about the imagery that
> scientists such as Einstein and Heisenberg used to discover their
> radically new theories of relativity and quantum mechanics.
>
> The reviewer is a physicist, David Hestenes, who has himself
> introduced
> some radically different kinds of mathematics (namely geometric
> algebras) in order to simplify the way physicists formulate their
> theories:
>
> http://modeling.asu.edu/R&E/SecretsGenius.pdf
> Secrets of Genius
>
> Some excerpts from this review are copied below.
>
> Note some important points:
>
> 1. Imagery is extremely important in physical discoveries.
>
> 2. Mathematicians who may be much more skilled in the formalisms
> usually don't have the physical background to discover the
> fundamental insights; e.g. Poincaré the mathematician discovered
> the basic math before Einstein the physicist, but Poincaré did
> not have the physical insight to interpret it as Einstein did.
>
> 3. It is false that Newtonian mechanics corresponds to normal human
> perception of the way the world works, because people who have
> not studied physics do not think in terms of Newtonian mechanics.
> The so-called paradoxes of quantum mechanics do not conflict with
> "common sense", but with the way physicists have been trained.
>
> Although this article is about physical imagery, many of the same
> questions can be asked about ontology. How much of the logical
> and mathematical formalism really corresponds to so-called "common
> sense"? How much of it is the result of the training that the
> mathematician or logician received? How much corresponds to
> reality -- i.e., the world independent of common sense, previous
> education, or mathematical and logical formalisms?
>
> John Sowa
> ______________________________________________________________________
>
> Scientists and nonscientists alike are fascinated by the creative
> processes underlying the great scientific discoveries. We are eager
> to know the secrets of genius. Did Einstein possess creative powers
> that set him above the ordinary physicist? Or was he privy to some
> special heuristics that guided him to his discoveries? We are indebted
> to historians of science like Miller for helping us answer such
> questions. Recognizing the difficulty of the task, Miller calls for
> collaboration between historians and cognitive scientists to study
> creative processes in science. He tries to get the process started
> in the present book with a historical, epistemological, and cognitive
> analysis. His central thesis is that "mental imagery is a key
> ingredient
> in creative scientific thinking." We follow him by focusing attention
> on the role of imagery in the creation of the special theory of
> relativity and quantum mechanics, two major triumphs of 20th century
> physics. But to evaluate the role of imagery we need to know what else
> was involved in the creation of these great theories....
>
> Einstein did not need an elaborate analysis of experimental data to
> identify the conflict between Newtonian mechanics and electromagnetic
> theory. Both theories are involved in explaining the phenomenon of
> electromagnetic induction, which underlies the operation of electric
> motors and generators. The essence of the phenomenon is that a magnet
> moving relative to a wire loop induces an electric current in the
> wire.
> Einstein observed that the induced current predicted by the theory
> depended on whether the wire or the magnet was kept at rest, whereas
> the physical phenomenon appeared to depend only on the relative motion
> of the magnet and wire. Thus, the theory exhibited an asymmetry which
> was not inherent in the phenomena. Einstein removed this asymmetry by
> invoking the principle of relativity, which requires that the laws of
> physics for an observer at rest must be the same as for an observer
> moving with uniform velocity. This principle had been stated for
> mechanics by Newton, though not as a basic axiom. Einstein generalized
> it to apply to electromagnetic theory as well. Paradoxically, this
> required a modification of mechanics rather than electromagnetics...
>
> The greatest remaining mystery is why Poincaré failed to arrive at
> the same conclusion and, indeed, to appreciate Einstein's
> accomplishment
> in subsequent years. Miller shows us that Poincaré was well aware of
> all
> the essential facts and ideas. The only thing missing, it seems, was
> an
> appreciation of gedanken experiments.
>
> This case illustrates an important difference between mathematical
> and physical thinking which goes a long way toward explaining why so
> few mathematicians have made important contributions to physics in
> the 20th century. Pure mathematicians do not think about the
> equations of physics in the same way as a physicist does. They
> are concerned only with the structure of the equations and the
> formal rules for manipulating them. But physicists regard the
> equations as representations of real things or processes; they are
> only partial representations of the physicists' knowledge, so to
> improve a representation they may alter the equations in ways that
> violate mathematical rules. Both Einstein and Heisenberg were masters
> at this. Neither was a mathematical virtuoso. Indeed, in the period
> when Einstein was developing his general relativity theory, the
> mathematician Hilbert expressed the opinion that Einstein was
> mathematically naive. I have heard a similar opinion about Heisenberg
> expressed by one of his students in later years.
>
> Mathematics played an essential role in Einstein's thinking, but,
> as mathematical physics goes, the mathematics in all his great papers
> is comparatively simple. His forte was in analyzing the physical
> meaning of the mathematics. Indeed, such analysis is generally
> characteristic of the best work in theoretical physics. I have heard
> the Nobel laureate Richard Feynman, himself a true mathematical
> virtuoso, express this opinion forcefully, asserting that the
> value of a paper on theoretical physics is inversely proportional
> to the density of mathematics in it....
>
> The thinking in Einstein’s creation of relativity theory can be
> described as theory-driven. As we have seen, it was not directed at
> explaining any particular experimental results, but it was nonetheless
> empirically grounded in a broad and indirect way. This made empirical
> predictions from the theory exceptionally robust. As Miller explains
> (p. 118), the empirical data available in 1901 contradicted Einstein’s
> theory as well as Lorentz’s theory of electrons. Since Lorentz’s
> theory
> was data-driven, he was ready to abandon it immediately in deference
> to the new data. But the rationale for Einstein’s theory was so secure
> that he confidently dismissed the data as inaccurate. Strong empirical
> confirmation for relativity theory was not available for decades.
> Nevertheless, many physicists came to accept it on the basis of its
> internal logic....
>
> The scientists in Miller’s account are unanimous in emphasizing the
> crucial role of visualization in scientific thinking along with a
> warning that it can be misleading. One place they were misled (along
> with Miller and the physics community at large) was in their intuition
> that classical mechanics describes what is perceptually given. They
> were unaware of the strong cognitive component in their own
> perception.
> It was only by training that classical mechanics came to be integrated
> into that perception. Cognitive research has recently established that
> the perceptions of people untutored in physics are naturally
> inconsistent with classical mechanics in almost every detail (Halloun
> & Hestenes, 1985). Thus, Miller’s conclusion (p. 261) that "twentieth-
> century physicists were forced to liberate their thinking from the
> world of perceptions" misses the mark....
>
> Having recognized the psychological tendency of physicists to confuse
> classical physics with perception, we can see more clearly the central
> epistemological issue raised by the creation of quantum mechanics.
> The conflict between classical and quantum physics had nothing to do
> with perception. It arose because physicists were unable to reconcile
> the mathematics of quantum mechanics with the classical conception
> of reality, so they were forced to construct new "quantum mechanical"
> conceptions of reality....
>
> Anyone involved in the lectures, seminars and informal give-and-take
> of creative physicists cannot fail to notice the vivid imagery in
> their thinking. Most of this imagery is suppressed in their
> publications, partly by conventions concerning the style of scientific
> reporting, partly because it is not essential to establishing the
> scientific results, and partly because it may be too much trouble
> to construct suitable diagrams to express it. This puts severe
> limitations on Miller’s historical approach and tells us that the
> creative physicist needs to be studied in vivo, while he is alive
> and kicking. That is where the cognitive scientist comes in....
>
> Imagery in physics is a promising domain for cognitive research.
> There is a rich lode of physical imagery that has never been mined
> systematically. Only a few prospectors like Miller and Simon have
> picked up samples. The payoff is likely to be greatest in education,
> leading to improvements in the design of images and in the teaching
> of imagery skills, thus enhancing creative powers at large. Here
> indeed, as Miller suggests, is a domain where historians and cognitive
> scientists can work together. But they had better enlist the help of
> some physicists.
>
>
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Bill Andersen (andersen@xxxxxxxxxxxxxxxxx)
Ontology Works, Inc. (www.ontologyworks.com)
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