The Numbers

A short note on the numbers of the Adversary, and on two vortices held in balance.

Three numbers

66.66%.

99.99%.

And their difference:

33.33%.

Three sixes, three nines, three threes.

These are the Adversary's numbers.

Not because they are evil, but because they come in threes, they repeat, and they refuse to round off to anything comfortable. Each one stops a hair short of a whole. 66.66 is not two thirds. 99.99 is not one. 33.33 is not a third.

The Adversary lives in that last missing hundredth — the place where a system almost closes and doesn't.

The six and the nine

Write a 6. Turn the paper upside down. It is a 9.

They are the same spiral, wound in opposite directions.

The 6 turns inward: a vortex drawing everything down to its centre.

The 9 turns outward: a vortex releasing from its centre back into the world.

One gesture, seen from two sides. Descent and return. Inhale and exhale.

619

Put a 1 between them.

6 — 1 — 9.

Two vortices and an axis.

A spin to one side, a spin to the other, and a straight line holding them apart so that neither swallows the other.

That is what balance is.

Not stillness.

Two opposite turnings that keep each other honest, and a single upright line between them.

The 9 and the 6 of the web

The web has its own pair.

PageRank is a 9.

It turns outward: every page releases its rank along its links, and rank flows from the citing page to the cited one and on, until the whole graph settles. It made one company very rich and the web a little more navigable.

Its reverse is a 6.

It turns inward: distrust flows backward along the same links, from a bad page to everyone who points at it. If you vouch for a fraud, a little of the fraud lands on you.

The 6 was written down in 2006 — Krishnan and Raj, Web Spam Detection with Anti-Trust Rank — two years after TrustRank spun the 9 from a handful of trusted seeds.

Look at the day it was presented: 10.08.2006.

First the bits: 1 and 0.

Then the 8: eternity.

Then the 6.

The 9 got famous.

The 6 stayed a paper.

Somehow the outward vortex kept turning for twenty years, and almost nobody turned the inward one back. So, in this telling, rank kept flowing to the dinosaurs, and the ones who fed them never paid a hundredth for it.

A system that only spins one way is not balanced.

It is just falling.

7 and 13

Why did the gods rest on the seventh day, and not on the first?

Perhaps because the seventh day is the first day of the second season.

The first season unfolds. Six days of making, outward from the Big Bang, and then rest.

The second season runs the other way. It begins with rest, and then six days of unmaking, inward, down to the Big Crunch.

Six, one, six.

Thirteen days, with the seventh exactly in the middle.

That is the shape of an autoencoder, read backwards: the seasons decode first and encode after, where a network encodes first.

The layers widen, narrow to a bottleneck, and widen again. The Big Crunch is the encoder: the world pressed into a point. The Big Bang is the decoder: the point unfolded into a world. And the seventh day is the latent space, where the whole of creation fits into a single thought.

No wonder the gods rest there.

It is the only day when everything is already said, and nothing yet has to be spelled out.

Mova does the same in miniature: text into a graph, the graph back into text, and nothing of the meaning lost on the way.

And in the second season evolution runs backwards too.

Not only did the ape become a human. Now the human becomes an ape again, the ape a fish, the fish a cell, the cell a molecule, and the molecule a point.

The encoder, written in biology.

There is one comfort. An autoencoder is trained on its reconstruction error: how far the world that comes out is from the world that went in. So at the end of the thirteenth day somebody will lay the two apes side by side, the first and the last, and count the differences.

If there are none, the season was lossless.

If there are a few, that is the loss the next season learns from.

Either way the ape is not the end.

It is a checkpoint.

8

Now close the two vortices into one.

Join the 6 that turns inward and the 9 that turns outward, end to end, and the line never has to stop.

That is an 8.

Two loops, one path. Descent flows into return, return flows back into descent.

Lay it on its side and it becomes ∞.

Infinity is not a very large number.

It is two opposite turnings that have learned to become one movement — and, at the crossing point, the same upright axis that held 619 in balance, now folded into the middle of the figure.

Which is why a collection of eight of these notes is, in its own small way, endless.

(This was the last line when there were eight. The first season ends here; the second picks up the count.)

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