Science > Physics > Independent/Dependent Phases 15: Interdisciplinary
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
11 Oct 2005 08:27:32 AM |
| Object: |
Independent/Dependent Phases 15: Interdisciplinary |
From Osher Doctorow
Probable Influence (PI) involves the quantity 1 rather prominently:
1) P(A-->B) = 1 + P(AB) - P(A)
2) P(X-->Y) = 1 + F(x,y) - FX(x)
and P(X<-->Y) = F(x,y) + P(X > x, Y > y) = F(x,y) + R(x,y) involves 2
more indirectly via 2 terms.
This reminds me of the question of whether PI would have been
discovered earlier than 1980 by Marleen and me had there been a greater
interest in the numbers 1, 2, 3, and/or sqrt(3).
I remind readers that Fuzzy Multivalued Logic (FML) implications have
analogs (x-->y) = 1 + y - x (Lukaciewicz and Rational Pavelka FMLs) and
similarly have analogs for conditional probability y/x and independent
probability-statistics y.
We tie in to geometry because P(A-->B) = 1 + y - x with y = P(AB) and x
= P(A), as well as P' (A-->B) = 1 + y - x with y = P(B) < = P(A) are
1-sided partial inverses of Euclidean-like distance functions/metrics
on unit lines, squares, cubes, hypercubes with the proper replacement
of y and x in higher dimensions by means of yi and xi respectively, i =
1 to n, where then y = (y1,...,yn), x = (x1,...,xn).
The numbers 2 and 3 appear in various important "term" and
partition/decomposition contexts. E = K.E. + P.E., Generalized Boolean
Logic is generated by any two of the 3 FMLs Lukaciewicz/Rational
Pavelka, Product/Goguen, Godel, etc. 2 even appears as an upper bound
on the order of (partial) derivatives or their generalization in GR, as
the "y degree" of the Riccati Differnetial equation dy/dt = A(t) +
B(t)y + C(t)y^2, and so on.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Independent/Dependent Phases 15: Interdisciplinary |
11 Oct 2005 08:50:14 AM |
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From Osher Doctorow
In biology, 2 and 3 appear in various contexts including bilateral
symmetry and sexual reproduction, while in psychology I have discussed
the key dimensions of cognition, perception, and emotion, and the three
"most used" senses of vision, hearing, touch, as well as Freud's ego,
id, superego and Jung's introvert vs extrovert and chunking's
3-chunk-size of short-term memory, and attribution theory's internal vs
external attribution. In sociology, there are Homans' 3 variables of
action, interaction, and sentiment.
In philosophy and in international relations and history, there are the
2 key distinctions between Materialism and Nonmaterialism,
Violence-Oriented and Non-Violence-Oriented, etc.
In the study of time, there is past, present, and future, while the
Penrose diagram distinguishes space vs time vs light.
Sir Isaac Newton and Leibniz are considered to have discovered calculus
because of their discovery of the inverse (and hence "double")
operations of integration and differentiation. Recall that Pierre de
Fermat and Archimedes had previously discovered constructions/equations
of calculus.
Even Nonmaterialism is arguably internally divided into Knowledge,
Ethics, and Spirit, or for those who don't "buy" Spirit the Unknown.
Conics and quadric surfaces, which play such key roles in geometry and
analysis, have second degree equations and two or three nonconstant
terms.
Osher Doctorow
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