Subject: categories: Re: Cross-category "conversions" of some interest

From: [email-masked]
Date: Wed, 12 Jul 2000 16:47:21 +0100

Applying the conversion from x/y to 1 - x + y to the Heisenberg Uncertainty
Principle in the form xy > k where k is a positive constant (x, y
uncertainties in position and momentum respectively, for example, where
notice x and y are nonnegative in the standard deviation version of
uncertainty) yields xy = (x/y)y^^2 (where ^^ is exponentiation) --> (1 - x +
y)y^^2.  For 1 - x + y < 0, which says x > 1 + y, the latter expression is
negative, so the converted form reads: (1 - x + y)y^^2 = -/1 - x + y/y^^2 >
k and therefore /1 - x + y/y^^2 < -k for k positive.  Since y^^2 is always
nonnegative, this conditional holds trivially (always) provided that x > 1 +
y.   Since x and y could be selected with exchanged physical roles
(uncertainties in momentum and position respectively, for example), the
condition that x > 1 + y is rather arbitrary and certainly will be fulfilled
for one of the two orders in which x and y are defined. 
:

Osher Doctorow
Doctorow Consultants
Culver City, California USA   

Even more strikingly, consider the identity 0/1 = 0 of classical
mathematics. Applying the conversion we find 0/1 --> 1 - 0 + 1 = 2 and
deduce 2 = 0, thus giving an unbelievably simple explanation of the Pauli
exclusion principle for fermions.
 
Steve Vickers.