From: Osher Doctorow [log in to unmask], Thurs. Feb. 14, 2002 9:59AM
In http://www.superstringtheory.com/forum, I have recently argued that a
split occurs in our universe because of a split between two types of
probability-statistics. Those who do not know simple algebra can skip the
following two inequalities which describe each universe in fuzzy multivalued
logics terms:
L > P > G (1)
L < P < G (2)
where L, G, P are respectively Lukaciewicz/Rational Pavelka, Godel, and
Product/Goguen fuzzy multivalued logics. The inequalities are most simply
explained in the probability-statistics analog language as meaning *greater
probable influence than* (for >) for *less probable influence than* (for <)
with the possibility of equal influence being included.
Since L corresponds to rare events, P to fairly common events, and G to very
frequent events, the two types of universe corresponding to (1) and (2),
written U1 and U2 for short, differ in which events have greater probable
influence. In U1, rare events have the most influence (e.g., crises,
catastrophes, genius, very fortunate events, events of lower dimension than
the space (in 3-dimensional space, this is events of dimension 0, 1, or 2,
including surfaces of bounded objects, flat bounded geometric figures, line
segments, isolated points). In U2, the exact reverse occurs, except that
for those familiar with positive and negative quadrant dependence in
statistical dependence research (and few non-post-Ph.D. statisticians are),
G and P can be reversed depending on whether positive or negative quadrant
dependence applies - which in this posting we will consider to be a
technicality.
So one universe, U1, is dominated in probable influence by rare events,
while the second universe U2 is dominated in probable influence by very
frequent events. To get a rough idea of where our observed macroscopic
(human to astronomical level) universe seems to fit, G corresponds to
*independent events*, and it does seem that independent events (events which
do not depend on each other or on particular other events relevant to the
problem) have the least probable influence, so our universe appears to be of
type U1. In the other universe, U2, independent events have much more if
not dominant probable influence.
These are models, but they come from very deep theories supported by many
directions of research and theorizing and knowledge. At the very least,
readers should consider their idea as possibly indicating the direction of
models which can apply to their disciplines in addition to all the other
models and theories which they are familiar with.
For those who are interested in physics and sciences, both philosophically
and otherwise, the universes U1 and U2 appear to be possible candidates for
the following: (1) the expanding versus the contracting universe scenarios;
(2) the microscopic (quantum) versus the macroscopic (human level,
astronomical level). In the human and astronomical levels, the effects of
General Relativity become very important, while in the microscopic level
quantum theory seems predominant except possibly for gravitational effects;
(3) the early Radiation-Dominated era of the universe versus the later
Matter-Dominated era (although it includes much radiation even today), with
the weight of evidence and opinion presently favoring U1 in the earlier era
including inflation (extremely rapid expansion) and favoring U2 in the later
era (although U1 may apply to both eras if the distinction is inaccurate for
these eras).
Finally, for those minimally familiar with probability theory, or who do not
mind learning it from scratch (beginning), the probable influences of U1 and
U2 respectively differ only in one variable (aside from a constant of 1 in a
formula, which is of negligible underlying importance). The equations of
U1 involve P(AB), the probability of A AND B (the intersection of
events/sets/processes A and B) as well as P(A), the probability of A, while
the equations of U2 involve P(A) but also P(B) instead of P(AB), where P(B)
is the probability of B. In other words, U1 is influenced more by
intersections (combinations, ANDs, conjunctions) of events/processes, while
U2 is influenced more by the separate events/processes.
Do the two universes U1 and U2 ever coincide? Yes. On important place in
which they coincide is when the universes can be shrunk down from big to
little or vice versa. In other words, if the science fiction story about
the *incredible shrinking man* who keeps getting smaller and smaller forever
and goes through different phases and universes roughly through the quantum
level and below it is even roughly correct, then U1 = U2. For those who
know probability, this is because the probability of AB (A AND B) equals the
probability of B provided that B is contained in A *almost certainly*
(except for sets of probability 0 in technical language). So everything
reduces to a bunch of sets/events/processes contained in each other, and the
macroscopic level shrinks down to the microscopic level.
If this U1 = U2 scenario is true, and those who believe that nature follows
the paths of greatest simplicity and parsimony and efficiency and so on will
probably conclude that the scenario may be true, then why do we keep getting
different results from the quantum and the macroscopic levels - especially
the indications that quantum energy only occurs at discrete values (like l,
2, 3, on some scale) instead of at all possible values like 1.3, 3.77, etc.?
It may be because the scenario is only approximately applicable and that we
really have two different universes which are very close together but are
separated by a one-way FILTER as in biology which filters out everything but
discrete (separate) energy and similar levels when observations go from
microscopic stimuli to macroscopic observer, even through a microscopic
intermediary if any. The energy which remains, and which is not recorded,
could well go into dark energy, dark matter, quantum fluctuations, higher
dimensions as in string/brane theory, etc.
For all scientists and philosophers, whether in physical or behavior or life
or social sciences, the above models represent the first time that
probability-statistics has experienced a basic change of axioms analogously
to Euclidean Geometry's change to Non-Euclidean Geometry by changing one
postulate (the Parallel Postulate). In the case of probability-statistics,
I changed Bayesian (conditional) probability's division of probabilities,
the mainstream method of analyzing dependence of events, to subtraction of
probabilities, and it turned out that Bayesian probability results apply to
P events and the new subtraction results (called Logic-Based Probability or
LBP) apply to L/RP events. A third type of probability applies to G
events, namely Independent Probability-Statistics.
In place of *Live Long and Prosper*, I will close by *Learn Long and Change
Axioms After Learning*. Hopefully the rest will eventually follow.
Osher Doctorow
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