Paradox

The seed....of 'us'....is Paradox.

In the Beginning, there was not even Nothing.

Time was Not, nor space, nor mass or energy, nor any Thing whatsoever.

We _are_ now. We 'exist,' and we know that we do.

But then, so long ago, "was" not any Thing at all; "was" not even the

past-existent IS-ness required for the use of the word "was."

The Ultimate Paradox now is: Why is there something, rather than

nothing?

And the answer is: Nothing can not "occupy time." The question "why is

there something?" implies existence. Existence implies extent in

'time.' Without time, there is no such thing as extent in 'time.'

Hence, the question "why is there nothing?" is meaningless.

Paradox. Original Paradox. Penultimate Paradox.

Since it is impossible to "have" Nothing, then Something must Be!

What is it, then, that "is," at this Origin Point, this Alpha of all

that now is?

Resistance --absolute resistance-- to there being Something, we may see,

yields permission for only the simplest possible Something, to come into

existence; to "Be."

That Something is a single dimensionless mathematical geometric "point."

We will now begin preconditioning for The Big Bang.

We see that Nothing cannot Be, and that this dimensionless point must Be.

If it "is," then an infinite number of the same must also exist,

superimposed perfectly upon the first to appear, for an infinite number

of dimensionless points may seat themselves one upon the other, for they

are _dimensionless_.

Shall they remain so?

No, for there is immediately a Secondary Paradox: Is there one point, or

is there an infinite number of them?

We see that an infinite number of dimensionless points may be only one

point, and that one dimensionless point may be an infinite number of

them. How may we break the Paradox, and exit into Reality?

We have an infinite number of points. We have "permission" to have

them, so we _do_ have them. We are not anywhere near ourselves yet, and

there is only this one single point, now known clearly to be also an

infinite number of points.

If there is an infinity of points, then there are two points. This is

clear. There are forty. There are 10^9. There are points enough to

"reach" infinity, (which can never be reached).

Then, we must conclude that these points are _different_ from one another!

How is this possible? They are _identical_! Yet, we see that if they

_are_ identical, there is only one point, and _not_ an infinity of them.

But... we have already seen that there _is_ an infinity of them.

Paradox. Secondary Original Paradox. Ultimate Paradox.

Our route lies clear: Positing a single dimensionless point necessitates

postulating infinite points. Positing infinity points necessitates

differentiating them one from another.

Now there is Space. Now there is Time. Where no such existed before

the first Point, now there exists infinite Space, infinite Time,

manufactured by the existence of an infinite number of very _slightly_

different points.

How different?

Reach, now, for the neccesary concept of the "infinitesimal."

This is our definition of a geometric infinitesimal: the smallest

nonzero spherically dimensional "real thing" imaginable. That which is

not _quite_ a truly "dimensionless" point.

We see that even the infinitesimal, never-endingly small, yet comprises

all of infinity.

It is harmonious: out of the existence of the infinitesimally-

dimensional point, multiplied by the infinite number of them in

existence, comes inevitably an Infinite Space.

It is parsimonious: Infinity is created by an infinite number of

infinitesimally small items, all alike-yet-_just_-not-so.

It is comforting: No end to the small, no end to the large.

How, then, may we see our own reality grow from this?

How, then, may we see our physicists' findings and descriptions arise

from this?

How may we find out if our infinite number of infinitesimal geometric

almost-dimensionless points may generate something we can check on?

Invited, you are, now on a journey of reasoning, and some more of the

brain-burning Paradoxes underlying Reality.

Backbutton, please, to where you were in 'separation axiom', or

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