The Holofractal Omniverse · The Map of Dimensions

Geometry begins with the smallest claim it is possible to make. Euclid opens the Elements with it, and his definition is entirely negative: a point is that which has no part. Nothing to divide, nothing to measure, no size in any direction. Later commentators added what Euclid left out — that a point has position but no magnitude. That is the whole of it. Not a small thing. A location, and the assertion that something is there.

Roughly 13.8 billion years ago, everything we can see expanded out of an extraordinarily hot, dense state. That is the Big Bang, and it is worth being careful about what the theory actually claims. It describes the expansion and everything after it. It does not describe a creation out of nothing, and it is not an explosion into some waiting emptiness — space itself expands, and there is no centre to point at. Georges Lemaître, a Belgian priest and physicist, was the first to run the expansion backwards and ask what it converges on: a single primeval atom, all the energy of the universe packed into one quantum. Everything since is elaboration. For the rest of this map, set time aside — it is the last rung of the ladder, not this one.

Roger Penrose has a proposal about what sits on the other side of a beginning, and it is worth walking through carefully. In the very far future the universe keeps expanding, the last black holes evaporate away, and — this is the step the theory requires rather than knows — rest mass itself decays. Mass is what lets you build a clock: through E=mc² and E=hν, any stable massive particle has a definite frequency and therefore keeps time. Strip mass out and there is no clock anywhere, and with no clock there is no way to measure scale at all. A universe that cannot measure size cannot tell the difference between the vast cold empty far future and the tiny hot dense beginning — the two have the same shape once size stops meaning anything. Penrose calls each stretch an aeon, and proposes that the remote future of one is the Big Bang of the next.

Three honest notes on that, because it is easy to garble. Conformal Cyclic Cosmology is a minority proposal, and the traces its author has claimed to find in the microwave background have been contested by other cosmologists. Nothing physically shrinks or bounces — the rescaling is conformal, a statement about shape rather than size, and the theory has no contracting phase at all. And it is not the “Big Rip”: that is a separate hypothesis altogether, in which a stranger kind of dark energy tears galaxies, then stars, then atoms apart at a finite moment in the future. Different idea, different people.

One last thing, and it is the strangest. Cool a quantum system all the way to absolute zero and it does not stop. A residual energy remains — half a quantum, and it cannot be taken away. Max Planck stumbled into it in 1911 and called it Restenergie; Einstein and Otto Stern made the first physical argument for it in 1913 and Einstein abandoned the idea within months, calling it dead as a doornail; Heisenberg’s mechanics finally put it on firm ground in 1925. It is called zero-point energy, and its consequence is that empty space is not empty. The vacuum carries a ground-state energy and behaves less like nothing than like a medium. Nothing that exists is ever entirely still.

The zero dimension produces no equations of its own — there is nothing yet to relate to anything else. What it produces are definitions and a conjecture: the smallest statement geometry can make, the reason nothing is ever completely still, and a proposal about what a beginning might be the far side of.

There is one question underneath every other question, and Leibniz put it in seven words in 1714. Why is there something rather than nothing? He thought the asking was fair because nothing is the simpler option — nothing requires no explanation, no cause, no maintenance. Something has to be accounted for. Three centuries later nobody has closed the question, and a good deal of philosophy is really an argument about whether it is a real question or only a question-shaped noise.

Hegel opens his Science of Logic by refusing to start with anything at all, and finds that pure being — being with no further determination, nothing said about it, nothing added — turns out to be indistinguishable from nothing. That is not his conclusion; it is his first move, and the whole of the Logic follows from what happens next. But as a description of a dimension that is one bare coordinate and no properties whatsoever, it is uncomfortably exact.

And then there is the problem of “before.” Augustine met the sceptics’ favourite taunt — what was God doing before he made heaven and earth? — by refusing the premise. If time itself begins with the world, there is no before to ask about. The question has a grammar but no referent. Whatever you think of his theology, the structural point is the one this dimension keeps running into: a beginning cannot have a moment in front of it.

Nearly every tradition that has tried to describe the beginning has run into the same difficulty, and it is a difficulty of grammar as much as theology: you have to say what things were like when there was no like, and where it happened when there was no where. Genesis solves it by declining to explain and simply starting — in the beginning, and then the world is under way. The formless void, the darkness on the face of the deep, and then a spoken word and light.

The Rig Veda takes the opposite approach, and its creation hymn may be the most remarkable thing written on this subject in any language. It refuses to claim knowledge. There was neither non-existence nor existence, it says, and then, six verses later, it points out that the gods themselves arrived after the world did — so how would even they know? The Tao Te Ching gives the shortest answer of the three: everything that exists came from what exists, and what exists came from what does not.

From this dimension emerges Creation. If nothing, then something. If something, then everything. The zero dimension is a single point — a coordinate and nothing more. No length, no width, no height. It is not sweeping, not moving, not measuring. It is the barest question there is: existence versus nonexistence. And existence answers.

Everything was created in that point. Not assembled over time, not built up in stages, not arriving in an order — all of it, at once, in a single coordinate.

Picture yourself as that point. You have popped into existence in a white space. There is no up, no down, no left, no right. No other objects, no other points, nothing whatsoever to measure yourself against. You cannot tell whether you are moving, because there is nothing to move relative to. You cannot tell whether there is anything else out there at all. The only thing you can do is vibrate.

So you vibrate yourself into another self. Infinite vibration creates another point — and it is not a second thing, it is you, in another location. And now the space between you is a line, connecting the two of you together. You are moving in the first dimension.

This whole map is built on if/then statements — but not “if this happens, then this happens.” With time removed, nothing happens. If this exists, then this exists. From one point of existence, every other rung follows — not later, but all at once.

Philosophers have a word for what this implies — monism, the idea that only one thing exists. On this map it is literal: only one thing does exist. The single point coordinate from the beginning. Everything else, everywhere on this map, is that one point — vibrating.

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