Zero and 1 or Infinity Solutions in Universe-Partitioned Probability
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 11 May 2006 21:51:34 -0700
From Osher Doctorow mdoctorow@xxxxxxxxxxx
COPYRIGHT NOTICE
Zero and 1 or Infinity Solutions in Universe-Partitioned Probability
Copyright By Owner Osher Doctorow Ph.D.
First Published 2006
Just as Generalized Boolean Logic is generated by Lukaciewicz/Rational
Pavelka FML (Fuzzy Multivalued Logic), Product/Goguen FML, and Godel
FML (see earlier threads), so the Universe generated by Causal and/or
Independence/Dependence Probabilities yields a general function f(x, y)
of the form:
1) a(1 + y - x) + b(y/x) + cy = f(x, y)
where a, b, c are taken here as constants although they might
alternatively be variable.
It is rather easy to prove, by considering the cases (x, y) = (x, x),
(x, y) = (1, 1), (x, y) = (x, 0), (x, y) = (1/2, 0), where 1 is the
probability analog of "infinity", that:
2) y = f(1, y)/f(1, 1)
3) x = 1 + [(1/2)f(x, 0)/f(1/2, 0)]
assuming that no denominators are 0 and that 0 < = y < = x < = 1.
Notice that the right hand side of (2) has only y variable and the
right hand side of (3) has only x variable and that the constants 1/2,
0 look as though they would "cancel" if it were not for f.
Since x is the (Probable) Cause variable and y is the (Probable) Caused
variable here, we see from (2) and (3) that the Cause variable has a
rather remarkable relationship to 0 and 1/2, while the Caused variable
has a rather remarkable relationship to 1 ("alias" infinity). In
addition, x has a separate relationship to 1 from (3) but in the
additive rather than multiplicative/division expression.
Osher Doctorow
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