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From: OsherD on 27 Feb 2010 01:40
From Osher Doctorow

In complex analysis, the Laurent series is like the Taylor Series
except that the former includes inverse positive integer powers rather
than only positive integer powers of the variable z.

Let us consider the two simplest terms of a Laurent Series such as:

1) b/(z - a) + c(z - a)

Using the idea of the change from Conditional Probability y/x to
Probable Causation/Influence (PI) 1 + y - x, symbolically y/x --> 1 +
y - x, (1) becomes for real z rather than complex z (for simplicity):

2) b/(z - a) + c(z - a) --> 1 + b - (z - a) + c(z - a) = 1 + b -(1 -
c)(z - a)

Now recall that:

3) P ' (A-->B) = 1 + y - x, y = P(B), x = P(A), y < = x
4) P ' (B-->A) = 1 + x - y, x = P(B), y = P(A), x < = y

Dropping the conditions y < = x, x < = y above to prevent
contradictions, we see that for positive c in (2), -(z - a) and c(z -
a) of the middle expression are analogous to y - x and x - y of (3)
and (4).

Since the same argument holds for higher powers of z - a, we conclude
that there is an "analogy" between Laurent Series and PI Series of
form:

5) aP(A-->B) + bP(B-->A) + ...

Osher Doctorow



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