Re: Quantum Gravity Via Expansion-Contraction 18.0: Time Generates Space and Expansion/Contraction via Riccati Paraboloid


"OsherD" <mdoctorow@xxxxxxxxxxx> wrote in message
news:1156829698.103654.312130@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
From Osher Doctorow mdoctorow@xxxxxxxxxxx

Readers may begin to get the idea that Quadratic equations, whether
differential or otherwise, have something fundamental to do with the
Universe from this thread. Take a look at the keyword "quadratic" in
arXiv, which produces 223 papers, and the same keyword in Front for the
Mathematics ArXiv produces 1211 papers with over 7 pages of references
out of the first 12 pages (covering 250 papers) written in 2006.

The idea that Quadratics are of unusual importance indicates that it
may be a good idea to look at the Riccati Differential equation once
again:

1) dy/dt = A(t) + B(t)y + C(t)y^2

and see whether we might have missed something obvious. Actually, the
generalization:

2) Dt(y(x,t)) = A(t) + B(t)y + C(t)y^2

the left side is wrong.


from a recent Section of this thread also helps give the clue.
Equation (2) for Dt(y(x,t)) = 0, < 0, > 0 respectively give a parabola
and its 2 bounding regions ("inside" vs "outside" would be appropriate
descriptions of these two if the parabola had been an ellipse, for
example) in the (y, Dt(y)) plane, although the parabola changes for
different times.

But we missed one obvious generalization here:

3) x^2/a^2 + y^2/b^2 = ct

Or, to put it another way, let's rewrite (2) as:

4) Dt(y) = C(t)y^2

left side is wrong again, and how did that come from (2)?




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