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From: Osher Doctorow on 25 Jul 2010 01:34
From Osher Doctorow

From the last few posts, it is arguably interesting to explore whether
the Universe has a time sense, a space sense, and even a pain sense,
not necessarily exactly as "elaborate" as human senses, but deep
nevertheless. Earlier posts in this thread suggested Memory at a deep
level in the Universe.

Here is my suggestion for how the Universe may have a pain sense:

1) Clue: the Null Set, or its analog Logical Contradiction, may
represent "pain" to the Universe and any of its objects.

For a space sense and a time sense, -->t and -->s from the previous
posts certainly suggest that the Universe can distinguish between
spatial and temporal (Probable) Causation/Influence. Since -->t and --
>s also arguably involve boundaries, here are some clues regarding
these "senses" in the Universe:

2) Clue: -->t and -->s of the last few posts may indicate that the
Universe even at a pre-life level can distinguish between time and
space, and boundaries of time and space sets/events, which in turn
suggests that there are sets/events which are purely timelike and
purely spacelike.

3) Clue: Let A(t) or A_t or At represent a bounded purely timelike
event, presumably along a time axis, while B(s) or B_s or Bs
represents a bounded purely spacelike event. C(s, t) or Cst or C_st
could represent an event in both space and time. Then a periodic
variable could be generated by the Universe memorizing and detecting
its boundaries in time and "repeating" them. Similarly for a
recurrent pattern in space (like a tiling) with regard to spatial
boundaries.

4) Clue: the Null Set or "Pain Sense" may explain Anti-Structure or
"Disruption of Structure" in the Universe. Recent posts suggested a
"Structural sense or tendency" in the Universe via P(A-->A) = 1. But
certain structures may cause disruption of their parts, for example
being unstable. Since P(A-->N) for N the Null Set equals P(A ' )
(because P(A-->N) = P(A ' U N) = P(A ' )), the only sets/events which
have no disruption, that is to say for which P(A-->N) = 0, would be
sets A for which P(A ' ) = 0, which says that 1 - P(A) = 0, or P(A) =
1, which is the Universe at least up to probability 0 sets. This
yields the remarkable result that the Universe always retains its
structure, although the structure presumably differs or can differ at
different times and spatial locations - a type of "No-Go Theorem"
against the Big Rip or similar catastrophic ending to the Universe.

Osher Doctorow
From: Osher Doctorow on 25 Jul 2010 01:45
From Osher Doctorow

In (4), that is in the last Clue, A is not being used as necessarily
bounded.

Osher Doctorow
From: Osher Doctorow on 25 Jul 2010 02:21
From Osher Doctorow

While I'm on this topic, lets look at P(U-->U), P(U-->N), P(N-->U),
P(N-->N), for U the Universe, N the null set. Using P(A-->B) = P(A '
U B) for any A, B (which in this post need not be bounded or
unbounded), we get:

1) P(U-->U) = P(U ' U U) = P(N U U) = P(U) = 1.
2) P(U-->N) = P(U ' U N) = P(N U N) = P(N) = 0.
3) P(N-->U) = P(N ' U U) = P(U U U) = P(U) = 1.
4) P(N-->N) = P(N ' U N) = P(U U N) = P(U) = 1.

The only unusual thing (that is to say, the only equation that would
not hold if N were replaced by any set A) is (2), which says that the
Universe cannot (probably) Cause/Influence the Null Set. Since by
equation (3), N can Cause/Influence the Universe (but also any set A
also can!), N comes close to being an "Uncaused Cause" - but note that
the symbol 0, which refers to sets of probability 0, describes also
sets that have the same property, because P(U-->0) = P(U ' U 0) = P(N
U 0) = 0. Sets of probability 0 which are not Null include
"infinitely thin" sets embedded in higher dimensional Euclidean-like
spaces under quite general scenarios, for examples planes and plane
sections and 2-dimensional surfaces and lines and line segments and
curves and points in 3-dimensional space or even a point in time.

Osher Doctorow
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