While it is fun to philosophize and make stuff up about “Wu” and zero-dimensional reflections, at some point, this has to tie-back to ‘real’ reality – the actual, physical world of physics and *matter*.

I mean, seriously, what is this ‘zero-dimensional Reflection’ I keep talking about? How can a reflection be ‘of itself’?

Firstly, starting with absolute, conceptual Nothing, in order to ‘cordon-off’ a *part* of Nothing, it needs a boundary of some kind. This boundary is ‘made of’ the same ‘stuff’ as Nothing, which at this point we realize is Everything.

Supposing that this Nothing/Everything is *stuff *(I’m not yet talking of Matter though), then this boundary we need must *do* something to this Nothing/Everything to *make it different* from itself somehow (so that we may consider whatever is inside that boundary to be *different from* Everything ‘else’). But by the definition of Everything, this boundary is also part of Everything, so it must be *of the same stuff*. So a boundary, which does something, and yet is something, can only be a Transformation (a ‘mathematical function’ or operation). Transformations are the only ‘thing’ which satisfy the above three criteria, namely: A) are *immaterial*, B) can *be something*, C) can *do something* – that is to say, transformations can *act on* other transformations, producing new transformations (transformed transformations, so to speak), and yet all-the-while being immaterial. This means we have an immaterial Nothing-yet-Everything.

**My first postulate: Everything is Energy, and that Energy is Transformations-operating-on-Transformations, infinitely.**

But a Transformation isn’t a *thing* – it’s a *description* of a thing, right? Yes and no. Yes, of course it’s a description. When two different things are being moved in exactly the same way, how do you describe *what’s happening to them*? The action taking place is independent of what it’s acting upon, and is therefore a distinct *thing*.

There’s a first problem though: Just because something *can* change, doesn’t mean it *does*. There is no implication or proof of *actual transformation* – Action. Since Transformations are operations, they have an input* and* an output. The input, being *other Transformations, infinitely recursively*, as well as the output being *another Transformation*, means that Everything is inter-dependent and poised in a pregnant moment of indeterminacy. But you have to think about it a little further. There’s no Space, and no Time, so what kind of Transformation can possibly exist in a dimensionless space? I know only of four ‘fundamental’ transformations, as enumerated in Geometry:

- Translation
- Rotation
- Magnification (a.k.a. Scaling)
- Reflection (inversion)

The first three all *require* at least one dimension, since all three require three bits of information – that is to say, they are all vectors requiring a *line of action* – a dimension. That last one, however, and interestingly enough, is possible in a zero-dimension space. Reflection, in zero-d space, is simply an existential ‘inversion’ – Something either *is* or it *isn’t*. It is the Boolean NOT operation of sorts. Being an operation, it has an input and an output. Most mathematicians *sorely dislike *paradox, so would instinctively reject the possibility of a single NOT where its input was tied to its output. The equivalent of “This statement is False”. But, even if I were to accept the rejection of paradox, and say ‘No NOT operation may have its output as its own input’, what of three NOTs in a loop? Two NOTs effectively *cancel each other out*, they are semantically equivalent to ‘is’, so the third NOT’s output is it’s input. This happens for all odd-numbered NOT-loops. It seems paradox is unavoidable. I personally think this *particular* paradox is not a problem but, better yet, an answer to the problem ‘Just because it *can*, doesn’t mean it *does*’ as we will see with my second postulate.

I’ve come to call these two forms of zero-d reflections The Static and The Dynamic. The dual-not-loop is The Static. It is *stable*. The single-not-loop is The Dynamic, and it is ultimately *unstable* because it is a paradox in the sense that it is indeterminable. If the value or state of these three Reflections were to be evaluated, then at each ‘attempt’ to evaluate the Dynamic, the Static would be *either/or* (like ‘either 1 or 0’).

**My second postulate: There is Action so long as The Dynamic cannot be evaluated.**

This is like some kind of Reality-Computer, or a scratched-record. At each encounter with the ‘glitch’, it starts again, oblivious of its previous attempts. “Ok, the Static is one. The Dynamic is –glitch-. Ok, the Static is zero; the Dynamic is –glitch-. Ok, the Static is one…” Another analogy I feel is suitable is that of the programmer’s “infinite While loop”:

while(True){ Do stuff;}

But consider why I claim that the Static alternates. Why wouldn’t it just stay ‘one’ each time around? Well, if it did, then we wouldn’t be ‘different’ from the previous evaluation attempt. This violates the very possibility of *ex-sistence*. Further, ‘staying’ at a value is only half way around the loop. You cannot go backwards around the loop (to do so is to go anti-NOT-wise, i.e. not-not, which is The Static). And finally, the interdependence of all these transformations (you will see when we get into higher dimensions) makes it impossible to ‘stay the same’ at each evaluation.

It’s a pretty tall claim, to say that the paradox of the single-not-loop creates a sort of evaluatory context in which the dual-not-loop *actually happens*, but that is precisely my point – A transformation *must* have an outcome, it must *happen*. If it does not *happen* at all, then there is no Transformation to speak of. It ceases to be a Transformation at all.

**My third postulate: Entropy is anti-Energy, where Energy is ‘having the quality of being different to itself’ and Entropy is ‘having the quality of being ***not* different to itself’.

The Dynamic is pure Energy – the degree to which something is *different to itself* at each evaluation, and The Static is pure Entropy – the degree to which something is *not different to itself* at each evaluation. By ‘the degree to which’, one can consider ‘having the quality of’. By ‘different to itself’, I mean ‘of a knowable value’. The Dynamic, at any moment is neither True nor False, and so is the slipperiest of fish – it cannot be pinned down, cannot be determined or identified, so is ultimately *different to itself* instantly and eternally. The Static, in contrast, is the very opposite – it is either True or False. It cannot help but be something at some point – at any instant you look at it, it *is something*.

I believe (naïvely?) that this definition of Entropy isn’t too-far-removed from the present ‘accepted’ definition, and can still be used; only that Entropy now becomes the conjugate of Energy. A hot body has Energy because its internal state (its displacement on the axis of Time) is changing vigorously. A cold body has Entropy because its internal state is quite stable (lesser displacement on the axis of Time). As the two bodies meet, Energy and Entropy are exchanged and Equilibrium is attained. I use the word Entropy to describe a sort of anti-Energy. Potential Energy is pure Entropy – pure Static – the transformation *hasn’t happened yet* and it is highly self-similar, highly stable. Kinetic Energy Is Dynamic Energy, where a body in motion has a high degree of self-difference.

The notion of Rotation now seems plausible. Imagine a cylinder with one half (lengthwise) painted Black, and the other White. If you were to spin the cylinder around its length axis, but watch it from above, you’d see it alternate White-Black-White-Black, etc. This ‘rotation’ of existence, of ‘is-ness’ is what I’m talking about. Further, the closed-loop transformation in zero dimensions seems to be the smallest possible ‘entity’ – the Point.

**My fourth postulate: Two N-dimensional Reflections ***are* one (N+1)-dimensional Rotation.

So a Point in 0D is in fact also a Point in 1D. This is because it is a 1D Rotation. However, a line (being the first dimension) is defined to be the infinite collection of Points. So how does one Point *differentiate itself* from its two neighbouring points on a line? Simply by its boundary: the Reflection. Each Point on a Line is a Reflection of its neighbour. This re-affirms the ‘alternation’ of the Static, because at each evaluation, one Point must be NOT its neighbour. This is of course a 1D Reflection. According to my fourth postulate, two of these 1D Reflections are in fact a single 2D Rotation. So in fact, The Static is 0D, 1D and 2D. Continuing the reasoning, each 2D Point distinguishes itself from its neighbours by being 2D Reflections of them. Once again, using the fourth postulate, 2D Reflections *are* 3D Rotations. The fourth postulate is all-the-more striking when you consider the 2D Reflection/3D Rotation example:

Draw a triangle on a piece of paper, each vertex numbered. Then draw a vertical line (to represent the line of reflection) a little further away. If the paper is folded along the vertical line, and a new triangle is drawn where the two halves of the paper meet, with each numbered vertex of this new triangle corresponding to each original vertex, then you’ve successfully created its exact Reflection on a 2D piece of paper. But in Folding, you effectively did a half-Rotation in 3D space.

So The Static is a 3D Point also. This reasoning can be extended indefinitely (until proven otherwise), using the fourth postulate. But we’ve said that Rotations are vectors. So Points are Vectors also? Every Point in 3D space can be represented by a vector of norm 0 – that is to say the Zero Vector. This seems to contradict my separation of the first three ‘fundamental’ transformations from the fourth one. But in fact, it doesn’t. Ultimately, when down at the null dimension, the notion of magnitude or intensity is meaningless (the norm of a zero vector, being zero). Essentially, this means that, at zero dimensions, all four types of transformation become one and the same – the ‘pure’ transformation: “NOT”.

**My fifth postulate: The Point is the Zero Vector in all spatial dimensions, and all spatial dimensions emerge simultaneously because of the Point.**

So where does Matter come in? Matter has Mass, and Mass, it is currently thought, is but the distortion of space-time by Gravity. Space-time is the ensemble of Space and Time as a collection of axes – Three of Space, One of Time.

The following need to be determined:

- What, really, is Time? Where is it?
- What is Gravity in this context of Transformations?
- Can dimensions be bent/distorted and if so, How?

What is Time? I adhere to the reasoning that Time is just the observation of change. There is the further, *more human* sense of Time which is irreversible Time. But, consider change happening. Take an oscillation, for example. The notion of periodicity requires a notion of comparison (because we need to know what happened before, to see it happen *again*). When considering ex-sistence, what exists must be different to everything around it, and constantly. If we were to take the periodicity of a Point as the prime frequency – the highest clock-speed that this ‘Reality Computer’ could attain, then every transformation must happen at a slower speed, but there must be change that happens at irregular intervals for something to ex-sist, otherwise there would be no ‘t=zero’ marker for our Universe to begin from. Any periodicity that is a multiple of the base frequency is nothing more than a different clock – and no notion of ‘when’ or ‘how long’ can be obtained. The slower clock-speeds just become the next level of comparison. What is needed is both aspects of Time: periodicity and irregularity. The Static and The Dynamic.

**My sixth postulate: Time emerges alongside all spatial dimensions, and exists in all dimensions.**

So we now have the three (and plausibly many more) dimensions of Space as well as Time. However, these Points, regardless of how Static or Dynamic they are, remain Points – not Things, not Matter. I’m still struggling to understand how a *dimension* itself could be bent or curved, but I suspect that it is this kind of transformation of a dimension (which, as we’ve just established, is just more transformations) that results in the ‘appearance of Mass’ through (sub-Plankian?) gravitational distortions of space-time, and therefore Matter. More to come later…