On Sat, 2 Feb 2008 21:56:06 -0800 (PST), rAgAv wrote:

We all know that the direct cause and effect relationship between two
events is invariant with respect to the temporal or spatial location
of the events. In fact, physics is based around it. But, is there any
objective proof save for the unit probability of such invariance
accounted for by statistical observation in the past?

For instance, sitting here on the surface of planet earth, If I let go
of a ball, I'm more likely to assume that the ball would go down
instead of going up. Some would be very certain that the ball would go
down. This is merely because of the unit probability, as observed in
the past, of the occurence of such an effect given the same initial
conditions. Of course, we have the universal law of gravitation to
assert to us that the ball would go towards the center of the earth.
But, this assertion by our law cannot guarantee that the ball would
indeed go down because the law itself is an generalization attempt
made by us to take advantage of the observed unfailing nature of this
causal invariance. Objectively speaking, the law is nothing but a tool
of convenience that has not failed till now.

Suppose we perform a large number of ball-dropping experiments, and the
ball always falls down. Then consider two hypotheses:

1) When we let go of the ball, the ball will fall down.

2) When we let go of the ball, the ball will randomly go up or down.

Both hypotheses are relatively simple, so there is no a priori reason to
favor one much more than the other. Both are consistent with observation
so far. But (1) predicts the observations with probability one, while the
probability of our observations under (2) is exceedingly small. Therefore
we should consider (1) to be the more probable hypothesis -- not certain or
proven, just very probable.

We can think of hypotheses such as

3) When we let go of the ball before February 4, it will fall down, but
after that it will fall up.

which also give our observations probability one, but these hypotheses are
more contrived and should be considered less probable a priori.

In reality, of course, (1) is not strictly true because in certain
situations, such as that of a ball on a string, or a ball subject to
high-force winds, the ball will not move down. But the idea remains valid
even when applied to the more complex real world.

--
Jim E. Black (domain in headers)
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