From Osher Doctorow
The Universe's Fundamental response to "Contradiction" is arguably
Phase Change.
For example, let us suppose that the Universe was initially "set" or
"ready" to calculate both probabilities or probable ratios:
1) P(A-->B) or P' (A-->B) = 1 + y - x, y < = x
2) P(B|A) = y/x, x not 0
Suddenly the Universe is confronted with an "instantiation" of x = 0
for some arbitrary variable x in [0, 1], even though y > 0 has already
been "registered". The division in (2) is now impossible, while the
inequality in (1) is violated if y has not been registered as 0. The
Universe cannot do anything about (2), but it can change (1) as a
"phase change" to:
3) P(B-->A) or P' (B-->A) = 1 + x - y, x < = y
It is even possible that x = 0 could "force" y = 0 in (1) but not (2),
since 1 + 0 - 0 = 1 is allowed. So at the very minimum, P(B|A)
"disappears" and P(A-->B) or P' (A-->B) remains.
The physics and engineering applications of this idea are arguably
numerous, and not the least of them is the old science fiction idea of
transferring to "hyperspace" as a sort of phase change or higher
dimension change. In science fiction, there was supposed to be some
substance which generated the change somehow, but in our scenario the
Universe when fed a 0 value of some variable can "force" the phase
change.
An example is a black hole, which has not only 0 visibility but 0
"return-ability" under most scenarios as well as arguably infinite
tidal forces (the latter can arguably generate a more general
contradiction as with 0, or even with "0 freedom from force(s)").
The black hole is especially interesting, because the above scenario
may incorporate two processes: the collapse of an over-massive star,
and the creation of new mass/energy due to infinite tidal forces (at
the "other end"). Instead of the other end of a black hole
evaporating in finite time as in the Hawking scenario, it arguably
creates mass/energy, explaining the role of supermassive black holes
in "centers" of galaxies in being associated with occurrence of new
stars. In the collapse part, the star's "non-mass volume" goes to 0
or approximates 0 when it reaches over-massive state.
This reminds me that arXiv has two papers under keyword "hyperspace,"
of which Durham's physics/0011042, 25 pages, is especially useful in
references to F-theory, the 2-time theory which Cumrun Vafa began in
1996 and which Luis J. Boya of U. de Zargoza Spain but especially I.
Bars of USC continues to research in 2007 via 2-time theory including
hep-th/070289 and 0703002.
Osher Doctorow
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