Re: Dynamical Systems and Expansion-Contraction

>>From Osher Doctorow

Am I saying that the Schrodinger wave function w:

1) w = y + ix

actually contains a (probably) influenced term y and a (probably)
influencing term x, and that all of real, complex non-real, quaternion,
octonion, and even perhaps higher-basis sets are "legitimate" according
to Probable Influence (PI)? Yes.

This is not too different from G. 't Hooft's Holographic Principle or
even from Superstring/Brane/M- Theory's "higher dimensions".

Yet what about the constraints that seem to limit us to 10 or 11
dimensions in Superstring/Brane theory, 5 in Kaluza-Klein theory, etc.?
Don't we need to compactify the higher dimensions above 4 since we
don't observe them? Not according to Lisa Randall and her colleague
Sundrum and a whole bunch of other people. And not according to Rare
Event/Probable Influence theory.

There's a "loophole" just in case some of these limitations like 5, 10,
11, etc. turn out to be correct, namely, what I'll call the Second
Grant Clue:

Second Grand Clue: Number Limitations like 5, 10, 11 in Kaluza-Klein or
Superstring Theory are Phase-Related (reflect the phase of "our"
space(-time)). This is even the case for c (the speed of light) and
Planck's constant h. A c of infinity would just reflect a different
phase - and quite possibly the "ultimate phase", although this remains
to be seen.

But the numbers above reflect algebraic or algebraic-geometric or
algebraic-topological together with physics constraints! Some of the
"nice" objects no longer exist in 23 or 71 dimensions for example!
Not necessarily.

What's a "Nice" object? Does anybody remember when we thought that
only Tensors are "nice" objects? Then the Clifford people told us
about Spinors, the Hamiltonian people told us about Quaternions, and
even way back in Einstein's day for example Sir Arthur Stanley
Eddington was quite fascinated by an object that was then called the
Christoffel symbols and later the Affine Connection for example by
Steven Weinberg and which didn't obey the "usual" symmetries but had
some rather "unusual" properties, just as the Spinors had some rather
"unusual" properties.

But it's not a group, or a Lie group, or an algebra, or a Lie algebra,
or a division algebra, or whatever! So what? Is a Creative Genius a
point, a string, an Individual, a Plurality, or what? I'd say that Sir
Roger Penrose has it right in essence: any word that we use to describe
a Creative Genius is probably too limited. If it's a point, it's also
"beyond a point", an "expanding point" that (probably) influences
others and itself. It's a source and maybe a sink, a workhorse and a
"think" - but there I pause to return to the real world for better or
worse :>)

Osher Doctorow

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