WDEshleman@aol.com
Sun, 5 Sep 1999 04:05:04 EDT
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.
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.
Sincerely,
Bill
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