Re: Nonrenormalization vs Renormalization 63: If Subtraction is More Fundamental Than Integration vs Differentiation, Then What Happens to Functional Analysis?

<snip crap>


Mumbo Jumbo Doctorow. You make less sense than you did when you were
spamming Patricia Schwartz Stringtheory forums.


more compost from the past......................

From: Marlene Doctorow - view profile Date: Tues, Jan 28 2003 12:50 am

From Osher Doctorow Ph.D.

In the days of Sputnick, the USA and USSR explored space rapidly
because there was a Cold War competition between them.


Today, when no urgent competition seems to be around the corner, space
travel and space communication are much less urgent priorities and
publish-or-perish isn't filling in the gap by itself. What little
work there is in the field (understaffed, underfunded, and
under-organized and under-"ideas" as the report on NASA and the Space
Shuttle disaster indicates) is being done by engineers and physicists
largely without the best minds in mathematics.


I would like to argue here that geometry as a branch of mathematics
does not need engineers and physicists any more than the latter two
think they need non-computer-workhorse mathematicians, and that we in
geometry can give the engineers and physicists a space horse race that
they won't soon forget.


My posting appeared today in researchmathemat...@xxxxxxxxxxxxxxx, a
moderated email group/forum, and proposes a three-pronged attack on
the geometry of the universe which has strong possibilities for making
a big improvement in space travel and space communications via
changing the curvature of space(time) in space warps and wormholes. I
want to thank Dr. Paul Karl Hoiland for clarifying and explaining some
of his ideas on space warps which helped to motivate my work. He
contributes to two yahoo internet forums, stardri...@xxxxxxxxxxxxxxx
and modernappro...@xxxxxxxxxxxxxxx, both of which I have just left
because of strong personality and theoretical differences with some of
the physics and/or engineering people other than Paul. Knowing about
Kip Thorne's (CalTech) wormhole theories also helped, although I have
found similar difficulties and additional ones on the forum of
Patricia Schwarz Ph.D. of CalTech at http://www.superstringtheory.com
after several years of contributing to that forum in the String/M
Theory-Duality subforum of their Forum section and am currently no
longer contributing there.


The three-pronged attack uses fuzzy multivalued logics (FML),
probability-statistics, and proximity-geometry-topology (at least the
intersection of topology and geometry) which turn out to lead to very
analogous if not identical results. Instead of making Curvature or
discrete-type topology as the basis of the universe (as physics and
engineering are now tending to do), I define a Language of the
Universe L11U with 11 elements or alphabet letters: E (expand), C
(contract), R (Rare), N (Non-Rare), p (potential), a (actual), i
(inside), o (outside), K (Knowledge or Semantics), I (information or
Syntactics), T (transmission). Words are formed by concatenation of
these symbols. The symbols can be quantified in terms of variables on
a scale from 0 to 1. Then a fuzzy multivalued logic (FML) or
proximity function (p1, p2, ..., pn) or a probable influence P or P'
relates the symbols and words.


It turns out that the universe can generate arbitrary Curvature of
space(-time) and space and time themselves by expansion-contraction to
different amounts (radii) and different speeds in different directions
and at different times. Thus, instead of Curvature and space and
time being the Fundamentals of Geometry, Expansion and Contraction are
among the Fundamentals of Geometry, together with the other symbols
above. Curvature and space and time are not banished, but rather are
used as secondary or derived quantities.


The problems of space travel by warp drives or wormholes and of
long-distance space communication change from the usual engineering
and physics pictures to studying how human beings can master the
variables like Expansion, Contraction for example in a way somewhat
comparable to the way in which the universe has mastered them. The
history of the universe via cosmology and astrophysics and astronomy
is of course vital in this process, but the physics or engineering
theories that seek to explain and predict this history are not in my
opinion. They can sometimes approximate and even be accurate "on the
nose", but they have too many defects including anomalies, paradoxes,
fads, lack of examining fundamental ideas in detail. Some
philosophically oriented mathematicians and logicians may notice that
Socrates' asking repeatedly "What does that mean?" would have
clarified most of those problems.


Osher Doctorow Ph.D.



*** BUT WAIT< THERE'S MORE..............

From: Osher Doctorow - view profile Date: Sat, Feb 14 2004 6:57 pm

From Osher Doctorow mdocto...@xxxxxxxxxxx


I have to thank Michel Petitjean of the Universities of Paris for
replying to a post of mine on sci.stat.math 13 Feb 2004 10:58:02
(replying on that date) which stimulated my interest in relating
entropy to symmetry vs asymmetry and thence to the present topic.


Rather than "belabor" the whole problem from the beginning which the
above paper has done well, I will emphasize its relationship to my
own current research in Mathematical Physics, Mathematical Probability-
Statistics, and Philosophy.


I was unable to find a better summary of Philosophical issues than that
of the Stanford Encyclopedia of Philosophy on the internet, http:
//plato.stanford.edu/entries/time-thermo, "Thermodynamic assymetry
in time," listed as having its last substantive content change Nov
15 2001 (also the year of copyright) That is from Stanford University.
The paper is signed by Craig Callender, ccallen...@xxxxxxxx (University
of California San Diego) at the end, who is presumably the author.


Perhaps the foremost advocate of Thermodynamics and Entropy in
present-day Quantum Theory is Stephen Hawking who especially applies
it to black holes, and an entire generation of Scientists and perhaps
Philosophers of Science has been brought up to believe that the
microscopic world via Quantum Theory underlies and explains the
macroscopic world that we live in and the larger astronomical
structures that we are aware of.


Philosophically, rough as it sounds or reads, that idea seems to be
"shot full of holes". It is somewhat reminiscent of David Hume's
"debunking" of causation-causality, but with a possibility that the
reverse may actually be true - that the macroscopic or Classical
or (modified) General Relativistic world may actually explain the
microscopic Quantum world. This is not entirely without precedent.
Martin C. Gutzwiller of IBM T. J. Watson Research Center in his
Chaos in Classical and Quantum Mechanics, Springer-Verlag: N.Y. 1990
argued that classical chaos was essential to understand quantum-
mechanical chaos and his theme was explaining the former and its
relationship to the latter rather than mainly explaining the latter.
Einstein of course believed until his death that the macroscopic
world explained the microscopic world, and if we add probability to
the macroscopic world (in which Einstein and his colleagues as well
as the quantum mechanical "opposition" were not well versed), there
is much to argue in his favor.


The Achilles' heel of the Quantum-Thermodynamics viewpoint revolves
around four difficulties concerning the direction of time, well
isolated by Callender: (1) The psychological arrow, (2) The mutability
arrow, (3) The epistemological arrow, (4) The explanation-causation-
counterfactual arrow (p. 15 of Calender's paper). I will only deal
with aspects of (3) and (4) here.


Callender's example is the Quantum-Thermodynamics viewpoint that, upon
seeing a footprint in the sand (a slightly enlarged scenario, but an
interesting thought experiment), we can infer that because it has high
order in the sense of orderliness or pattern, it must have been
caused by something previous that also had high or higher order such
as somebody walking. This tells us very little actually, for example
about human walkers - in fact, it only tells us that the sand grains
interacted with its environment previously. J. Earman (1974) in
"An attempt to add a little direction to 'The Problem of the Direction
of Time,' " Philosophy of Science 41, 15-47, gives the opposite view-
pont of a bomb destroying a city. The only thing we can essentially
tell is that a bomb went off, but the city that was bombed doesn't
have lower entropy than its surroundings and doesn't even have any
intuitive kind of higher order than its environment.


The types of Probability and Sets or Objects used in Quantum Theory,
especially in their Thermodynamic and Statistical Mechanics and
Entropy studies, are themselves rather low-level in terms of
Probable Influence or Probable Causation, which makes several of
their conclusions about Non-Causality being important quite question-
able. I have been studying Probabilities on new types of Sets in
various places, most recently on sci.stat.math, and it turns out
that the type of Set Probability which most closely resembles our
intuition of Probable Influence or Probable Causation is essentially
Macroscopic at least in definition and development: the Probability
of Rare Events. Whereas Quantum theorists typically use a
symmetric version of Probability which disguises asymmetric features
that are so common in intuitive notions of causation (like "a" comes
before "b" in time which is asymmetric), and which is based on a
ratio of probabilities that doesn't apply to Rare Events because its
denominator is zero or close to zero for Rare Events (events of
Probability less than .05 for example), Rare Event Theory starts from
a new type of set (A-->B) which is the Set Theory analog of the logical
conditional a-->b for propositions a, b, or logical implication a==>b.
It then puts a probability on this set, and eliminates the anomaly of
dividing by zero or near-zero quantities. Most interesting of all
perhaps, it is fundamentally Asymmetric rather than Symmetric, although
it can explain Symmetry as a special situation. Thus, it reverses
the intuitive picture of Mainstream Quantum Theory as underlying and
explaining Macroscopic and Astronomical events/processes.


What is the origin of the Asymmetry in Rare Event Probability? It is
the direction of the arrow --> in (A-->B) in the Set. In Set Theory,
this means that the set (A-->B) is equivalent to the set (A' U B),
which is the analog of logical "either 'not A' or 'B' or both," and
that is Asymmetric with (B-->A).


Yet there is also much more powerful Influence and Causation in Rare
Event Probability, and even that can be expressed intuitively. The
Mainstream fraction or ratio expresses at most the probability of
the "caused" event B occurring "given" that the "causing" event A has
occurred, which is to say "freezing" the causing event. The Rare Event
probability expresses the probability of the "causing" event A
influencing or causing the "caused" event B. The difference can be
illustrated by the "footprint in the sand" example earlier. When you
see evidence of a footprint in sand, you see a caused event B (the
footprint in the sand) and you've "frozen" the causing event A back
in time where it can't change in whatever particular state out of
many possible states it was. This doesn't tell you much even if by
some method you were told the probability involved, since it could
be that by "freezing" event A at some different state, a different
result for B would have been obtained. But if you were told the
Rare Event probability, it would work for all and any state of A.


Even Callender earlier in his paper (p. 12) assumes that the world
is fundamentally quantum mechanical rather than classical mechanical,
but he is assuming what physicists have told us. What is the reason
for physicists' view aside from historical accident of being interested
in quantum mechanics? It has to do with a little number called
Planck's Constant h, which depending on whether it is very small or
very large changes the picture from Quantum Mechanics to Classical
Mechanics or Classical Physics in the formulas or equations of
Quantum Mechanics. It is a rather small foundation to build an entire
Science around, not to mention an entire Philosophy! Since Symmetries
are really special situations of Asymmetries intersecting in opposite
directions intuitively, we can just as easily argue that Rare Event
Theory contains Quantum Theory as a special or limiting case! (For
those who are interested, the equation x = y is the intersection of
the opposite inequality x < = y (x is less than or equal to y) and
x > = y (x is greater than or equal to y).)


Osher Doctorow


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