[time 67] Re: [time 66] Geometric transformations & DSP

Ben Goertzel (ben@goertzel.org)
Mon, 29 Mar 1999 10:16:01 -0500


I've been lurking for a while here, and this may be a good time for me to
jump in, if only to ask for clarification. This discussion is fascinating,
sometimes beyond me (I'm a mathematician who has dabbled in a number of
radical and conventional physics theories, but does not have a really
thorough knowledge of
physics beyond the level of General Relativity and standard Quantum Mechanics).

My inclination with this kind of discussion is to try to strip away as much
and terminology as possible and reduce things to the level of ultimate
simplicity, where
the core concepts are laid bare.

Mathematical tricks are not going to be enough to solve the current
problems of physics.
We need a conceptual innovation. Specifically, we need to figure out how local
subjective realities combine to yield the global reality (which then in
turn gives rise to the
local systems that spawn local subjective realities). The universe is an
attractor of
this dynamical system of localreality/globalreality intercreation. The
conceptual innovation
is going to be the right way to express this philosophical idea mathematically.

that said, now let me ask some basic questions about the current discussion...

> The idea is to figure out how to:
>1) How the quantity of time (past, future, "history") as it is
>considered "classically" by observers is derived from the interactions
>of LSs, which give us local clocks.

OK, I think I understand this, but I forget what "LS's" stands for :(

The point is that we want to get a global time out of the panoply of local
times associated with local coordinate systems in
Is that correct?

>and equivilantly:
>2) How to derive the classical 3+1 spacetime from R^6n (or R^3n x R^3n)
>via projections. Clue: Paul Hanna conjectures that a 3 + 3 relativity is
>at work. I will be getting the formalisms from his shortly. :)

Why 6n?

Not knowing this background, I'm speaking in ignorance, but here are a few more
comments anyway...

I spent a while working with Tony Smith's physics theory in which he derives
3+1 spacetime from 8-dimensional spacetime, which is derived from N-dimensional
spacetime by the clifford algebra periodicity theorem (stating that Cl(n)
is expressible
as a direct product of clifford algebras of order 8 or below)

But this argument only makes sense if one is focusing on clifford products.
The question of projecting higher dimensions onto lower ones has to do with the
multiplication operations that one wishes to preserve via the projection.
Where addition
is concerned one can project anything onto anything.


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