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Science Forum Index » Physics Forum » Quantum Gravity 270.7: More Riccati Slow/Fast Times...
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| OsherD... |
 Posted: Sat Jun 21, 2008 5:49 pm |
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From Osher Doctorow
We can look at Probable Causation/Influence (PI) to figure out
conditions for P(A-->B) or P ' (A-->B) = 1 (opposite to the 0
condition of before):
1) P ' (A-->B) = 1 + P(B) - P(A) = 1 iff P(A) = P(B) = x = y (x =
P(A), y = P(B))
Therefore:
2) P ' (A-->B) = 1, y = x = t is optimal.
But this is the equation:
3) y = t
and we get:
4) dy/dt = 1 = P ' (A-->B) = A(t) + B(t)y + C(t)y^2 in Ricatti
equation, which has general solution A(t) = 1, B(t) = C(t) = 0.
So the constant equation is a special case of the Riccati Differential
Equation satisfying the Fast (or Slow, depending on which way one is
looking at it) Time condition:
5) dy/dt = 1 (for all y = t)
This isn't necessarily the only Riccati Differential Equation that
represents the Fast Time case, but it's one of them.
Similar arguments hold for P(A-->B) = 1 + y - x with y = P(AB) and x =
P(A).
Osher Doctorow |
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| Spaceman... |
| Posted: Sat Jun 21, 2008 10:55 pm |
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OsherD wrote:
Quote: So the constant equation is a special case of the Riccati Differential
Equation satisfying the Fast (or Slow, depending on which way one is
looking at it) Time condition:
Why are you trying to satisfy a clock malfunction?
It would be way more scientific to find out what screwed up
the clock physically.
--
James M Driscoll Jr
Spaceman |
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