Re: About Zero, time, and spacetime.
- From: Julio Di Egidio <julio@xxxxxxxxxxxxx>
- Date: Sun, 09 Mar 2008 22:21:24 EDT
Arindam Banerjee wrote:
If you are putting a new sign for every new dimension, as I understand
from your website, then it is too bulky and pointless for practical
work. Much rather have a few generalised operators and apply them to
all dimensions. This is what all programming languages to my
knowledge do.
Pardon me if I disagree on this. I mean, less for the programming, more for the good in poly-numbers. Operators in programming do not apply to all dimensions, they _are_ the dimensions. For example, in a true table.
IMHO, the "problem with Cartesio" is that one tends to expect the representational plane to be... "filled". If we instead consider the "natural" representation of poly-numbers, i.e. not trying to "project points outside of the axes", we just get _something else_.
As a sort of boot-strap, I'll assume a number ([X1],[X2],...,[Xn]) maps to _n_ points, one for each sign-dimension. I'll add some further assumption (improperly put): in poly-number algebra, signs can't combine (someway in analogy with the two parts of a standard complex number), i.e. (s1.X).Rel.(s2.Y) can't reduce when s1!=s2 and there is some meta-relation about them "belonging to the same number", our very poly-signed cset; thus, for instance, ([X],[Y]) maps and simply maps to _two_ distinct "points" on _two_ distinct "axes" in our representational plane.
Then we have:
-- natural numbers (sign-operators)
-- real numbers (csets)
-- relations (operations and functions)
These we can meta-map to:
== signs map to axes;
== csets map to intervals on those axes;
== relations map intervals to intervals across axes;
where we keep the identity relation into account - so that, the system is tautologically (internally) closed.
Then we need a further dimension, a "discrete" time, to, in a sense, break-out of our number system:
== the time of representation, i.e. the time for the machine to scan the domain in order and in very order to represent the transformation; this maps to what I'd call the "natural axis", in that its "points" represent natural numbers.
Still, we've got a lot of... "space"?
Ok, let's first go to infinity on the number of dimensions. There is an example on Mr Golden's site, a sequence from the Mandelbrot set (maybe, just keep in mind that's drawn with "cartesio"). There I guess we can glimpse Plato World; conversely, going to infinity on the number of dimensions represents Natural Language. Interesting; actually, intriguing, isn't it?
Anyways, let's go back to our "axes" and how should we lay them down: who said that _that_ should be measured in... "angles"? And who said that that should be... "static"? I'm afraid I'm too rookie not to tell the first that comes to mind: this is frequency, maybe better, relational frequency.
Still we've got some... "space", don't we? Let me put it again very very straight: ultimately, this is "void", the void of the empty set which happens to be the void "we" are. So that, now, we can say that void not only exists (Theory of All etc.), but it is representable, along with all the rest!
There may still be "gaps", in higher senses now, which I won't try fill, I'll just hint at the quite-evident fact that, again, Continuum dis-is the empty set, itself "we" (the "paralogical impossible") - so that we have self-referentially (externally) closed the domain.
Aether reality, yes. Waves need a medium to pass through. For
electromagnetic waves, that medium is by definition ether, which is
like a marvellous solid permeating everything in the Universe. Once
we dismiss the whole of relativity and quantum as bungled physics, we
can have regain our correct perspectives.
That medium is simply void. Something like "waves of directions across the absolute empty of the empty set" maybe? Moving dimensions, dynamics of (pure) relations, whatever, after all it seems continuous are "we", numbers are not... or, should I say the reverse?
:)
-LV
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