9. Exponentially Zero 

— Paradox to the nth Power—

Footnote-ish Miscellanea


Paradox Times Paradox
To the Power of Zero

The idea is that paradox, as a concept, reflects the paradoxical nature of squaring the uni-number One-Zero (one equals the other), the Zingular, with itself.

Pseudo times pseudo becomes Zeudo. Or Ze. Paradox squared make things happen, unpredictable things. The countably infinite moves a little bit away from us, recedes.


Pseudo-mathematically

P^2 = Z

Normally, one expects numbers one and zero to behave like other numbers. But if they have a paradoxical nature, which is the general argument, and if at times error — or whatever — enters, then sums and products may change from what we expected.

This would happen pretty much with every number, but for an non-1 number there are more intermediate steps, meaning a chain of events is necessary for, say, 437 to suddenly equate 0.

Not so likely. Not as likely.

But for 1 there is but one single step. Similarly, for 0 there is also but a single step. These numbers would thus stand for the extreme case of Yes turning into No, False into True, and so forth.


Definitions are true only provisionally. Every rule has an exception. If the rule says something will not happen, let it be Zero. If it says something is always the case, let it be One.

Then wait for exception. Stir while waiting, add salt. Do note the difference between ‘will not happen’, above, and the non-written ‘can not happen’. We need no rules of logic to tell us that gravity will work. Gravity seems to overlap quite nicely with reality, without definitions, but definitions do not overlap as nicely with reality. There are always loopholes, as every lawyer knows.


The Point

The canonical example of something that is both nothing and something would be the point. Non-spatial pure location it indicates something, but it is an absence in itself.

The point par excellence would be the center-point of a Cartesian coordinate system; the point of origin. Using Latin let us think of it as Origo. Like a door it is nothing in itself, yet doors are not nothings, or they would not be there, so the absence-in-one-sense simultaneous with presence-in-another-sense is a meaningful one. A door to understanding.


The House that Jack Built

If One and Zero are equal, are both Ze, then we may think of the Origo as having a sphere of influence beyond itself, in particular in the area between itself and One. The place of no-place, the place where things are, cease to be or begin to exist henceforth. The locus of change. This is the area where one single event or non-event may change the course of history.

A This is the house that Jack built kind of thing. Though there is a number of events in a chain, taken on its own, every single event may be considered cause for all that follows if it was necessary. A chain of unlikely events from 437 to 0 could thus be thought of as a ‘causation tunnel’. As such, we can think of the tunnel as a 1, in which case the event is suddenly 437 times more likely to happen — but then upon another plane of reference. Singular events are points, infinitely many, but the line they (may) make up is one.


Trajectories

The event-lines can be considered trajectories in four-dimensional space. The event-plus-object-timelines making up four-dimensional “tunnels in time”. In the center of the tunnel would be the most likely events, the “walls” of the tunnel that which can not happen — at least not here or now.

The next step could be to look at object-related events as “objects” in their own right, letting four-dimensionality consist of event-lines rather than objects-with-timelines. In such a setting an electron would be a point at one observation or entanglement — perhaps the same thing? —, then diffuse into probability and non-existence until the next observation; the next tango with reality.

It may be not the size per se, or exclusively, that makes these very small things quantum-sensitive, but that we can only detect one in terms of event.

One would want to look at how trajectories intersect next, for where trajectories intersect, there is an origo, and where Origo is, trajectories are affected. They nest, they become entangled, turn into bundles, perhaps fuse. Tori and related forms may describe bundles of a closed or at least relatively repetitious system.

Event-lines, objects abstracted from them, might be possible to analogize. Being object-less, they have no mass. Being mass-less, they may behave like massless particles. Being such and being linear, they may behave like photons. If events behave like massless particles, they may also, perhaps, have a wave-like nature.


Entanglement

When one incomplete cell has joined with another incomplete cell, there is a fertilized egg.

Suddenly the individual cells have no history before this joining, their different characteristica soon indistinguishable. They are entwined, entangled, forever inseparable. With birth the same thing happens again, for now the joining is part of the larger world and required to breathe on its own, restarting the entanglement to now be one between the born one and the world they partake in.


Each trajectory could be considered a domain unto itself. What is a line in one domain is a point in another. We would not expect the house that Jack built not to come into existence if all things are normal, meaning we have to consider where the house-building trajectory intersects with other trajectories.


Tunnels

Lines become “points” partaking in planes and three-dimensional objects. They, in turn, “move” through time, which is to say that they turn into trajectories.

The house that Jack built is a house situated at the end of a four-dimensional tunnel, extending back into Big Bang, converging a multitude of paths into itself.

So is a person, say Jack himself. Or a cat. Or anything that constitutes a unit; a system. When the cat is in the cradle, one tunnel intersects with another. When the dog is in the house, yet another intersection happens. The greater the number of intersections, the greater the number of possibilities and interactions.

With event-lines intersecting, the geometry is back to the point, but now the points are loci in another sense. Yet, points being points, that really does not matter mathematically. They would be mapped similarly, whatever they happen to represent. Any tour into “higher” dimensionality thus starts over. Time-tunnels intersecting become “meta-event”-points, and so on, and so forth.


“Here and now” is where all that can intersect right now intersects. Here and now is thus where we find an origo, and where things can be affected one way or another. And where the unknown, X, the exception, may enter onstage, unbidden, perhaps welcome, perhaps not. Only in a closed system can X not enter — unless there from the start, but not detected, another possibility.


A personal example:

I once had two friends who I thought should not meet. Though both nice people, there was too much explosive conflict potential in the meeting, for which reason I assumed that I should not introduce them to one another.

Which I then decided was superfluous to decide. Naturally, being so vastly different, it would not happen I needed to. The two had nothing in common, no intersections in time or place where I might be called upon to introduce them to one another, or seek to avoid doing so. I taunted myself for my wish to control things which needed not to be controlled.

As it turned out, they both decided to make a surprise visit to me at the same time the same day. My front door and my personal whereabouts made up a point of intersection. Had I been walking down Champs Èlysées and these friends had happened to walk there too, each on their own track, going about their business, I could have been a “center of gravity” for them, causing a meeting.

It turned out they did not aggravate one another but were rather neutral and them meeting was not problematic at all. I had worried unnecessarily, teaching me the lesson that though I was wrong in my assumption about them never having to be introduced by me, I was perhaps even more wrong to assume the event needed to be avoided. Anyhow, the point is that unknown factors cannot be discounted for. They may even be too obvious to be accounted for. In this case, I discounted the house that Jack built only because I was in it. It was invisible to me.


X?

How, then, to accord for X? Is the unexpected not by virtue of being unexpected and unknown an unknown unexpected X? How can the indefinite domain surrounding Origo-Zero be charted? Is it even possible?