Science > Physics > Quantum Gravity 119.6: Example of Generalized Lie Derivative in Golden Mean
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
24 Apr 2007 06:20:01 PM |
| Object: |
Quantum Gravity 119.6: Example of Generalized Lie Derivative in Golden Mean |
From Osher Doctorow
The Generalized Lie Derivative in the special form:
1) L(x, y) = 2xy, x and y real
yields the Riccati Differential equation terms by:
2) L(y, y) = 2y^2
3) L(y, 1) = 2y
4) L(1, 1) = 2
which directly go into the Riccati Differential Equation:
5) dy/dt = A(t) + B(t)y + C(t)y^2 = (1/2)[A(t)L(1, 1) + B(t)L(y, 1) +
C(t)L(y,y)]
For an example, let's look at the golden mean. Geometrically and
algebraic, the Golden Mean is defined by the ratios (where a and b can
be two sides of similar figures, etc.):
6) (a + b)/a = (a/b)
Notice that a occurs in the denominator of the left hand side and in
the numerator of the right hand side, corresponding to the definition
of a as the "mean" of the ratio(s), while a + b and b, which occur in
the numerator of the left hand side and the denominator of the right
hand side respectively, are called the "extremes" of the ratio(s).
The quantity a or a^2 (the product of the a's in the numerator and
denominator as indicated) arguably plays the most critical
(interactive, communicating, etc.) role as the mean of the ratio(s),
and therefore a^2 should occur as the (Probably) Causing variable (the
negative term) in Probable Causation/Influence (PI). To see whether
this is correct, multiply both sides of (6) by ab, which yields:
7) ab + b^2 = a^2
and therefore:
8) ab + b^2 - a^2 = 0
and by adding 1 to both sides of (8) we finally get:
9) 1 + (ab + b^2) - a^2 = 1
which says that P(A-->B) = 1 + y - x = 1 with x = a^2, y = (ab +
b^2). As expected, the negative term -x = -a^2 is precisely what was
predicted, and a^2 is the Causal "variable", while (ab + b^2)
represents the Effect.
In the usual method of finding the Golden Mean from (7), we divide
both sides by b^2 to obtain:
10) 1 + (a/b) - (a/b)^2 = 0
and defining phi as a/b, we get:
11) phi = (1/2)(1 +/- sqrt(5))
which is the Golden Mean and/or its "Conjugate". Notice that (10)
itself does not obey the optimal P(A-->B) = 1 equation analogous to
(9), precisely because (10) interpreted as a Probable Causation/
Influence would be equivalent to the claim that the PI of (a/b)^2
causing or influencing (a/b) is 0, a rather curious interpretion to
say the least. Since a or a^2 is actually Causal rather than a/b,
and the Golden Mean phi is a/b, the fact that a = (a/b)b means that b
times the Golden Mean (or the square of this) is the Cause rather than
just the Golden Mean itself.
The quantity a^2 = L(a, a), which is where the Generalized Lie
Derivative comes in, and the Generalized Lie Derivative is indeed
Causal here.
Osher Doctorow
.
|
|
| User: "OsherD" |
|
| Title: Re: Quantum Gravity 119.6: Example of Generalized Lie Derivative in Golden Mean |
25 Apr 2007 08:53:02 PM |
|
|
From Osher Doctorow
I meant at the end of the last post that a^2 = (1/2)L(a, a) since L(a,
a) = 2a^2.
Osher DOctorow
.
|
|
|
|
|
Related Articles |
Publishing Industry, Beware: "Of all people, Jews should know about ganging up, finding common enemies and telling the big lie."
Re: A quote that is not verifiable, and is probably a lie.
Quantum Gravity 119.0: Generalized Lie Derivative And Riccati Differential Equation
Did Bush LIE about going BACK to the MOON?
Stop the "1 degree temperature increase" LIE. Stop psychopathically Lying!
THE MOST BLATANT LIE OF EINSTEIN CRIMINAL CULT
Re: What's up with the alarmist label? [was Re: How Long Will the Steve Schulin tell this Obvious Lie?
Quantum Gravity Via Expansion-Contraction 61.2: Spin Via Nonstandard Analysis, Lie Algebra, and PI
| =?ISO-8859-1?Q?Re:_une_nouvelle_th=E9orie_de_la_grande_unification_b?==?ISO-8859-1?Q?as=E9_sur_le_groupe_de_Lie_E8?=
String Duality, Cosmology, De Sitter Group Lie Algebra
Quantum Gravity 220.2: Quantum Control on Lie Group SU(1, 1)
Criminal Minds ENJOY LYING, And THEY Know They Intentionally Lie {HRI 20050527-V3.1} - (Version 3.1 on 5 June 2005)
THE LIE OF "FIRST" PEARL HARBOR -- FDR, Meet GWB -- 911 .
THE ORIGINAL LIE OF EINSTEINIANS
Quantum Gravity 119.1: More Re Generalized Lie Derivative And Riccati Differential Equation
|
|
|
