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From: Osher Doctorow on 9 Jul 2010 02:18
From Osher Doctorow

Although I phrase this in terms of Gravitation vs Repulsion, it can be
expressed with respect to Attraction vs Repulsion of Protons and/or
Electrons and other Interactions.

This time we focus on the scenario where A, B, and so on represent
bounded set/events and A ' , B ', and so on represent their unbounded
complements (parts of the Universe outside them) in an unbounded
Universe.

From the previous posts we have:

1) P(A-->B) = P(A) iff P(AB) = 2P(A) - 1
2) P(A-->B) = P(A ' ) = 1 - P(A) iff P(AB) = 0.

The first equation says that, in a probabilistic sense, the
intersection AB of A and B depends "maximally" on A (which is
bounded), while the second equation says that A and B are disjoint or
mutually exclusive, that is to say they do not meet. Thus, in (2), A
is in B ' and B is in A ' probabilistically , so A and B are in a
sense dependent on the unbounded parts of each other. This latter is
because it is elementary to prove that the Universe is always a
disjoint union or "combination" of AB, A ' B ' , AB ' , and A ' B for
any two sets/events A, B.

From the previous paragraph, AB depends on a bounded set/event in (1),
while in (2) AB is probabilistically 0 and both A, B depend on
unbounded sets B ' , A ' respectively. This especially comes from
the right sides of (1) and (2) respectively, namely P(AB) = 2P(A) - 1
and P(AB) = 0.

From the left hand sides of (1) and (2) respectively, (1) also says
that the Probable Causation/Influence of A on B, P(A-->B), depends on
a bounded set A probabilistically, while (2) says that P(A-->B)
depends on an unbounded set A ' probabilistically.

So the two interpretations or two parts ("iff") of each of (1) and (2)
are in agreement with respect to boundedness and unboundedness.

From a physical viewpoint, (1) says from previous posts that
(probabilistically) A makes B "dependent" on it maximally via P(AB) =
2P(A) - 1, which fits an interpretation of Gravitation as maximal
bounded dependence in an intuitive sense - the "Cause" (a
gravitational mass) "binds" the "Effect" (the affected other mass) to
itself in a bounded region through their intersection.

From a physical viewpoint, (2) fits an interpretation of Repulsion as
in the Cosmological Constant or Quintessence or "negative pressure"
Chaplygin Gas, etc., as "unbinding" two bounded sets/events
(probabilistically) into unbounded set/events and Causing/Influencing
the Cause (A) and Effect (B) to separate (so P(AB) = 0).

If we define:

3) GRAVITATION = P(A-->B) when P(A-->B) = P(A) for A, B bounded and A
' , B ' unbounded
4) REPULSION = P(A-->B) when P(A-->B) = 1 - P(A) for A, B bounded and
A ', B ' unbounded

then we get:

5) GRAVITATION + REPULSION = 1

or equivalently:

6) REPULSION = 1 - GRAVITATION

on a scale of 0 to 1, that is to say on the interval [0, 1].

Whatever the secret of "unlocking" Repulsion, if it exists, it
arguably is contained in these equations and their interpretation.

Osher Doctorow

From: Osher Doctorow on 9 Jul 2010 02:53
From Osher Doctorow

Without the equations of the previous post, Gravitation and Repulsion
could still be regarded intuitively in physics as "switching" each
other's "directions" to opposite, something like a 0 to 1 or -1 to +1
switch.

With the equations of the previous post, Gravitation and Repulsion
seem to relate not only to opposite directions but specifically to
respectively "bounded inside" vs "unbounded outside" topologically and
geometrically, and to the boundaries between them. The most
important boundary relevant is that of the bounded CAUSE A, since P(A)
yields Gravitation while P(A ' ) yields Repulsion. If A is a bounded
closed set, then topologically its boundary separates the bounded
inside or interior from the unbounded outside or exterior. If A is a
bounded open set, then the boundary is outside A but still separates
the interior of A (which in that case is A itself) from its exterior
which includes the boundary.

This is not to say that the EFFECT B is irrelevant. Being bounded is
a key part of the two equations (for A and B), and also P(AB)
"switches" from 2P(A) - 1 to 0 from Gravitation to Repulsion as a main
characteristic.

But what is the most intuitive thing that physics or indeed any
quantitative science knows about interiors versus exteriors of bounded
sets/events or objects? For connected sets/events, as in Euclidean
type spaces, it is roughly speaking that the interior and exterior
involve oppositely directed normals to the boundaries, but in
quantitative biology and quantitative behavioral sciences (and even in
quantitative parts of social sciences) there is an extremely primitive
intuition that life forms have regarding directions of normals to
their boundaries, namely OPPOSITELY DIRECTED ATTENTION OR FOCUS on the
interior versus the exterior of the life form respectively. If, in
the spirit of Schrodinger, we regarded physics and biological sciences
as (ultimately) unified, then we may conjecture that the Universe has
a primitive ATTENTION-SWITCHING from interiors to exteriors of bounded
sets vs unbounded complements. In words:

1) PRINCIPLE OF PHYSICS-BIOLOGY UNIFICATION: The Universe has a
primitive "pre-biological" mechanism which can roughly be descibed as
switching ATTENTION from interiors to exteriors of bounded sets/events/
objects to their unbounded complements and vice versa.

Since the Universe is itself a set/event/object/process and so on, (1)
suggests that the expansion and even acceleration of the Universe
involves attention to what it regards as its exterior or
"outside" ("nothingness" in a sense, but something in another sense),
while contraction or deceleration of the Universe involves attention
to what it regards as its interior or "inside".

It could, of course, be that the development of life itself in
different parts of the Universe differentially attracts the
"attention" of the Universe to different of its parts, while the
destruction of life or its absence might do the opposite in terms of
attention to "outside" those regions.

Osher Doctorow
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