Natural Science Forum / Physics / General Physics / July 2007

Although addition/subtraction are preferable to multiplication/
division in Probable Causation/Influence (PI), averages or means or
expectations (expected values, E(  )) involve division in weighting
for finite variables and sample means (which approximation population
means) always involve division by the sample size, so the above
preference does not extend to averaging.    Conditional probability-
statistics, which uses multiplication/division primarily, is extremely
oriented toward averages or means or expectations.

Y. Charles Li, U. Missouri USA, in "Segment description of
turbulence," arXiv: 0707.4459 v1 [math.AP] 30 Jul 2007, 9 pages,
points out that chaos and turbulence have no good averages and in fact
averaging makes no sense at all for them because they wander all over
the place more or less and don't fluctuate closely about a candidate
"mean".   Instead, he uses segments which are unions of flows at
various points, and obtains a fascinating Non-Markov machinery.
Recall that Markov Chains are conditional probability machinery, while
Non-Markov chains and processes are a good candidate for PI study.

Osher Doctorow