sci.physics

>From Osher Doctorow

The disadvantage of replacing 1/r^2 by p^2 where p is defined as 1/r
in Newton's Law of Universal Gravitation is that p is then not
reversible under the transformation p --> 1/p and blows up at 0 again
in this scenario (that is to say, when inverted). This is not as bad
as if 1/r had no physical interpretation because 1/r as "proximity"
does refer to "nearness" as opposed to "farness", and both make
physical sense. To avoid part of the problem, "normalize" r or
replace 1/r^2 by p defined by:

1) p = 1 - x + y = 1 - (x - y) = 1 - r, where r, x, y normalized into
[0, 1]

Here x and y could be respective linear (radial) coordinates on a line
of centers connecting the of two masses m1 and m2 in the proper
order to have x > = y. We could then use F = Gm1m2/r^2 outside [0, a)
for some very small positive number a, and inside [0, a) replace 1/r^2
by p of (1) above.

Readers will recognize 1 - x + y as Probable Causation/Influence (PI),
which serves a dual role as a geometric "proximity function" and a
probability related to Causation.

Osher Doctorow