Stephen P. King (stephenk1@home.com)
Mon, 06 Sep 1999 03:08:32 -0400
Dear Bill,
WDEshleman@aol.com wrote:
>
> Stephen and Matti,
>
> [WDE]
> My infinite products are simply candidates for role of the
> objective multiplicity that subjectively offers the seemingly
> non-intuitive conclusions drawn above.
>
> [SPK]
> I think that the infinite product offer a way to construct coordinate
> systems that are "subjective" yet can be "shared".
>
> [WDE]
> Yes, Stephen; what I believe that I have is an example of a
> subjective mathematical description of a holographic reality.
> So then you may ask, what is the underlying objective
> structure? You are ready Stephen; you can understand the
> simple math I will give you. There are two other infinite
> products equal to 1/(1 - x) besides the one I use in my
> paper. The first is simply that:
>
> 1/(1 - x) = (1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 + x^16)... (A)
>
> with no holographic properties. Now, by induction, we
> know that since (1 + x^2) = { (1 + x^2)^(1/2) } * { (1 + x^2)^(1/2) }
> and (1 + x^4)
> = { (1 + x^4)^(1/4) }*{ (1 + x^4)^(1/4) }*{ (1 + x^4)^(1/4) }*{ (1 +
> x^4)^(1/4) }
>
> and so on for each of the factors in (A) above. This produces a
> bifurcating Christmas tree with 1/(1 - x) as the star equal to the
> product of,
>
> (1 + x) *
> { (1 + x^2)^(1/2) } * { (1 + x^2)^(1/2) } *
> { (1 + x^4)^(1/4) }*{ (1 + x^4)^(1/4) }*{ (1 + x^4)^(1/4) }*{ (1 + x^4)^(1/4)
> } *
> then 8 roots of (1 + x^8) *
> then 16 roots of (1 + x^16) *
> then 32 roots of (1 + x^32) * * *
> to infinity.
Cool! I am thinking about the pictoral meaning of this...
> This is what I accept for now as the underlying objective holographic reality.
> It is holographic (many-worlded) in the sense that any branch or even
> sub-branch contains exactly the same structure (distribution) as
> does the whole (product). A structure that appears the same, no matter
> which node that it is observed from internally. And because it is equal
> to 1/(1 - x) it gives an impression to observers that present states are
> being drawn toward all possible future states instead of being pushed
> into the future or past by means of histories. The mathematical relations
> above are derived by repeated cyclotomic factorizations.
My question is: What if these exist subbranches that are 1/x : x \elem
[0,1] different from the "whole"? How long or how many disjoint steps
does it take to alter it so that it is equal?
I see each "world" as constructed from pieces of others; so what if a
given world were finite? What effect would the "other", \infinity - x,
pieces of worlds have on it? None? This looks like the renormalization
problem!
I am thinking that a finite amount of information requires only a
finite number of particles in some configuration to encode it, so what
if there exists an infinite amount of information, like Lexicons, "at"
each point in a space? Can we think of "time" as the parametrization of
the encoding/decoding process?
Onward,
Stephen
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