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>From Osher Doctorow mdoctorow@xxxxxxxxxxx
The idea of using Nonstandard Analysis to make deeper foundations for
Quantum Mechanics and Quantum Theory has some surprising results.
Before that, I should mention that Nonstandard Analysis has its
foundations in mathematical logic, but it was later proved that it can
be derived using only algebra and topology, and even logicians now seem
to agree that it has developed far away from its closest logical roots
in model theory and quite independently of logical model theory.
There is a good side of the coin, and a bad side. The good side is
that this whole research literature shows that Einstein's finite c as a
"top finite bound" and Quantum Theory's h or the Planck constant as a
"bottom finite bound" could be replaced entirely by infinitesimally
small "atoms" (actually called infinitesimals in Nonstandard Analysis)
and by dividing 1 by such an atom, by infinite speed instead of c. It
doesn't proclaim this very loudly, since "science" is too close to the
old-time Witch Hunt days, but it's there to read between the lines.
The bad side is that Ingenious Imitators can use one or more of this
type of idea almost as well as Creative Geniuses, once the original
ideas (not necessary even in physics) have been discovered. Still, it
may be a price to pay for advancing the field, since the more papers on
a topic, the more sympathy Peer Reviewers may have for really high
quality Creative Genius in the topic.
Robinson's migration from Hebrew University to UCLA is interesting. I
pointed out that Israel, India, Japan, and from another viewpoint China
and Spain, have an unusual benefit to Creative Geniuses because they
had such extreme changes in their sociocultural histories in the last
100 years. But the USA and U.K., with an opposite type of "stable"
history in the last 100 years, have given rise to equal Creative Genius
in my opinion now, but concentrated in Princeton U., the Princeton
Institute, U. Chicago, Stanford, U. Texas Austin, U. Florida
(especially Gainesville), CalTech, MIT, and arguably U. Virginia and
one other Virginia University, and Harvard except that Harvard recently
fell into the Ingenious Imitator category for most of its departments.
So why did Robinson move to UCLA from the Hebrew University? Well,
UCLA around that time had an unusually talented Mathematical Logic
branch. The weather is also exceptional in Southern California, and
Robinson not too long after died from cancer so maybe his health was
already deteriorating. He arguably collided with the UCLA Bureaucracy
(which infects both a high proportion of Faculty, Administrators, and
Students in their own Bureaucracy). Anyway, he next went to Yale.
Yale is a sort of Dead End. It's in the Ivy League, but so are many
New England Universities. Connecticut is too far from Virginia and
points south and west to get much benefit, and in fact you have to
cross all of New York by most routes to get away from Connecticut.
It's got the New York Bureaucrats on the south and the Massachussetts
Bureaucrats on the north, a rather formidable ocean on the east and a
long way on the left (west).
I think that Robinson would have had more influence in Israel. But you
never know.
Osher Doctorow
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