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>From Osher Doctorow mdoctorow@xxxxxxxxxxx
The U.S. Naval Academy, Annapolis Maryland, USA, makes my list of top
10 U.S.A. Universities for the contributions of Robert A. Herrmann of
the Naval Academy. He wrote 13 papers on arXiv from 1999 through 2003
and an additional 6 papers in Front for the Mathematics ArXiv
2004-2006, plus 9 others papers in Front of which some may overlap with
his arXiv papers. Readers will probably find Herrmann's books as well
in the geometry or physics sections of large research university
mathematics/engineering or physics libraries. Be careful not to spell
his name "Hermann", which neither of the above "archives" recognizes,
or to confuse Robert with Richard.
Herrmann is a Nonconformist most of whose work has been on Nonstandard
Analysis applied to physics, although he also has done much in
geometry, functional analysis, logic. He uses the approach through
logic rather than through algebra and topology, and he is familiar in
his writings with the relationship between probability and quantum
logic through the key work of Peter Mittelstaedt of U. Cologne/Koln
Germany which Max Jammer was one of the first to emphasize in his The
Philosophy of Quantum Mechanics, Wiley: N.Y. 1974, especially p. 403.
Mittelstaedt and Jammer were two of my early favorite researchers in
the beginning of my and my wife Marleen's development of Probable
Influence/Causation (PI) in 1980.
An interesting thing about Mittelstaedt is that he "beat" both Jauch
and Piron (Constantin Piron) of Switzerland in quantum logic via
Mittelstaedt's quasi-implication:
1) (a-->b) = a' U (ab) where ab is the intersection/meet of a, b
which in quantum logic replaces classical implication:
2) (a-->b) (classical) = a' U b
In Probable Influence/Causation, there are two corresponding versions
of PI, namely:
3) P(A-->B) = 1 + P(AB) - P(A) = P(A' ) + P(AB)
4) P' (A-->B) = 1 + P(B) - P(A) = P(A' ) + P(B)
where P(A' ) = 1 - P(A) in probability. Notice that there is a direct
relationship between the symbols P(A' ), P(AB) in (3) and the symbols
a', ab in (1), while there is a direct relationship between the symbols
P(A' ), P(B) in (4) and the symbols a', b in (2). However, there is
another curious cross-relationship because (3) also reduces to P(A' U
B) and hence from another viewpoint can be regarded as closer to (2).
In my opinion, this dual role of P(A-->B) makes it the best candidate
for crossing both macroscopic and microscopic physics, but P' (A-->B)
reduces to it in a large variety of conditions and has considerable
usefulness.
Osher Doctorow
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