I am a member of the support vector machine mail list,
and you post stuff wich has nothing to do with svm's



Am Donnerstag, 14. Februar 2002 19:46 schrieben Sie:
> 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