Under Construction

The Mandala

Fire and water and earth and the boundless height of air - Empedocles - On Nature

The last page left us with two engines and a promise to show the wheel they turn. This is the wheel. Virtualism calls it the Mandala, and of everything in the theory it is the oldest part and the most certain - the picture the whole framework grew up around. It looks, at first glance, like an old diagram of the four elements, and in a sense it is one. But read correctly it is something more exact: a map of every kind of relationship there can be, and of how each turns into the next.

Index

Four Kinds of Relationship

Two Ways to Cut the Circle

The Wheel Turns

One Rule, Every Level

Four Kinds of Relationship

The four elements here are not four kinds of stuff. Fire is not a hot substance and water is not a wet one. They are four kinds of relationship - the four ways any two things can stand to one another - and the ancient names are borrowed only because they happen to fit.

Fire is sameness: the bare fact of two things being alike - the one redness shared by everything red, the oneness of being a single thing at all. Earth is difference: what sets things apart and makes them countable, the home of objective fact and of number. Air is inwardness: the relationship of a whole to its own parts, a thing regarded from within rather than from without. And water is possibility: a whole set against all that it is not yet, the open and the potential. Every relationship in existence is one of these four, or is built from them.

Two Ways to Cut the Circle

Lay the four out as a circle and two natural divisions appear, square to one another. Cut it top from bottom and you separate the objective from the subjective: the upper half, fire and earth, is the world as it stands regardless of any onlooker - which is, not by accident, the half where number lives. The lower half, air and water, is the world as it is from a point of view, the half where mind will one day live. Cut it left from right instead, and you separate wholes from parts: fire and water are relationships of whole things, earth and air relationships of parts. Each element sits where one cut crosses the other, and the diagram sets the whole arrangement out at a glance.

The Wheel Turns

Now bring back the two engines. Each element is also one of the determination-states from the last page. Fire is the fully-determined: a settled truth so complete that to alter it would alter everything. Earth is the over-determined - paradox itself, the forcing engine, where objective difference and mass are wrung into being. Air is the under-determined - hypodox, the permitting engine, where a whole's inner parts have room to shift. And water is the non-determined: the open floor of bare possibility, not yet committed to anything.

Set going, they turn in order - fire to earth to air to water, and round to fire again - and each step is one of the transitions the engines drive. That turning is the cycle of becoming: the route by which a settled truth is differentiated, drawn inward, opened to possibility, and resolved into a fresh settled truth one turn further on. The fine machinery of those four steps - which, remarkably, lines up with the four fundamental forces of physics - is saved for the deepest page of all. Here the point is only this: the abstract pair of engines has a definite shape, and the shape is a wheel of four.

One Rule, Every Level

Two things lift the wheel above a tidy diagram. The first is that it does not stop at four. Each element divides into three finer cases, making twelve; each of those divides again, making thirty-six; and so on inward without end, in the very same open way the numbers were produced. The wheel is fractal, alive, never a finished thing. The second is that one single rule turns it at every level. The same move that carves one number from the next carves mass out of number, and pattern out of mass, and - far up the spiral, in tiers this site only points toward - the shapes of mind and meaning. Older traditions felt the form of this wheel and read it in the elements and the turning sky; what Virtualism adds is the reason it had to be this wheel and no other.

The technical detail

A caution, because 'the same rule' can mislead. The four elements are functional roles, not fixed substances, and the same role yields different objects at different heights of the spiral. A relation of difference - earth - gives mass, and so gravity, at the physical level; but the same earth-relation higher up need not give anything like a kilogram. A difference of truth might instead erect a social hierarchy, or a political order. The move repeats unchanged; what the move produces depends entirely on the material it is applied to.

One rule, running everywhere, is about as near as the theory comes to a single sentence for what it holds. The wheel turns in time, too - its four stages can be read as the past, the present, and the near and far future - and that reading is exactly where we go next.