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From: OsherD on 1 May 2010 17:05
From Osher Doctorow

The Golden Mean or Golden Ratio Equation is:

1) x^2 = x + 1, with solution x = (1 +/- sqrt(5))/2

while the Fibonacci Equation with the first equation of (1) as its
limiting equation is:

2) Fn = Fn-1 + Fn-2 (just divide both sides by Fn-1 and take limits
to get (1))

Probable Causation/Influence (PI) is based on differences, since:

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

Therefore we would expect:

3) Gn = Gn-1 - Gn-2 as the PI analog of (2).

Divide both sides by Gn-1 to obtain:

4) Gn/Gn-1 = 1 - Gn-2/Gn-1

and as with (2) with an appropriate limit x of the ratio we obtain:

5) x = 1 - 1/x

Multiplying both sides by x yields:

6) x^2 = x - 1, or equivalently x^2 - x + 1 = 0

with solution:

7) x = [1 +/- sqrt(1 - 4)]/2 = [1 +/- sqrt(3)]/2

The quantity 3 can be interpreted as the quark triple in the Strong
Interaction, while the quantity 2 arises naturally from the opposites:

8) gravitational direction = -(repulsion direction)

9) direction of opposite electrical charges motion = -(direction of
identical electrical charges motion)

In each case (8) and (9), there is a choice of 1 direction from 2
possible ones, which in combinatorics is:

10) C(2, 1) = 2!/[(2 - 1)! 1!] = 2

Finally, the 1 in (7) is the one direction of beta decay/radioactive
decay via the Weak Interaction.

Osher Doctorow

From: OsherD on 1 May 2010 17:10
From Osher Doctorow

I mean to type [1 +/- sqrt(3) i]/2, not [1 +/- sqrt(3)]/2.

Osher Doctorow
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