Paola, John, et al.,
You may find interesting in light of this discussion the thinking of Keith
Devlin, a mathematician whom I've mentioned before in this forum. In a couple of
his books, The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are
Like Gossip ... and The Math Instinct: Why You're a Mathematical Genius (Along
with Lobsters, Birds, Cats, and Dogs), Devlin makes the connection between math
and how we have evolved to represent the world in ways that enhance our ability
to survive and reproduce in it  and the ability we now recognize as math being
a natural _expression_ of this capability, which is also intimately connected
with language abilities. Dr. Devlin is one of the experts we enlisted in
an educational math video series that I helped produce for Discovery Education,
in which we aimed to express the natural and integral nature of math for the way
we cope with and manage the world  while conveying the mathematical concepts
for doing so.
I apologize that I have not had time to read much of this discussion,
much less participate, in the recent past  but I thought that an awareness of
Devlin's thought would be pertinent here.
Ken Cliffer
In a message dated 12/15/2007 12:37:22 A.M. Eastern Standard Time,
paola.dimaio@xxxxxxxxx writes:
John and
all
not directly related, but it sparked a thought
I
worked for a few years as 'science and technology' correspondent in London
I was young and inexperienced, and did not dare venturing into discourse
as I do now, thanks also to the relative impersonality and distance given by
the digital media, but it was an amazing learning experience to which I owe
the little about science that I know in this life (as well as possibly to my
previous lives  preposterous as it seems)
I got invited to lots
of gigs. I there met Prof Miko Kaku for example when he launched his book on
Hyperstring Theory. He was frustrated that so many scientists refuted his
theories as 'cannot prove it We only exchanged a few words in private, as
there were so many people around, but he looked at me and said: you seem
to understand. (what exactly we did not really discuss)
It was on oneof
these occasions, around 1996 or thereabouts at an event held at the
Royal Society of London (or at the Salt Exchange in the City?can't remember
for sure) that a large brain was displayed in a box and the man who was
guarding it heralded 'this is Einstein's brain'. it was very large, and
preserved in perfect conditions. I was too young and never probed that, I took
it as a fact. I remember distinctivly not being sure if the guy was pulling a
joke on me ( he did seem serious, and it was a very serous event) but not
doing anyting to dispel the doubt (like taking the guy's name and phone
number) so I looked at this brain for a long time (and the man behind
it) with deference, respect and not knowing what to do or think really.
I just kept in my memory the picture of that brain.
More recently, I
heard a horrible horror story about it that a crazy pathologist got hold of
the brain and (short of eating it fried for breakfast) he dissected it into
240 pieces
http://www.pacpubserver.com/new/news/8400/einstein.html
I
find it very hard to believe  I would be more inclined to believe (or just
want to believe desperately) that a collector has managed to rescue it from
Harvey and that the brain is safe and whole somewhere in London and that
Harvey is just a crazy and so the journalist who reported that silly
story.
I am pretty sure that Einstein brain should have been studied as
a whole, and not dissected Now I think also about Einstein's brain at
night, together with lots of other things, when I cant sleep
Should
anyone on this list have any more information anytime, please help me
rest PDM
On Dec 14, 2007 10:44 AM, John F. Sowa < sowa@xxxxxxxxxxx> wrote:
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 socalled
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 socalled
"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 theorydriven. 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 datadriven, 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 giveandtake 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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