Self-Hosting

I.

The problem, as Baas put it on the whiteboard, was that every text required a second text. A contract required an interpretation. A poem required a reading. A specification required a meeting at which the specification was explained to the people who had written it. The second text was never the last; it required a third, the third was contested, the contest produced a literature, and the literature produced a department. Baas drew the chain as a linked list, box, arrow, box, and then, because he was honest, added an arrow from the last box back to the first.

“It doesn’t terminate,” he said. “That’s the entire cost.”

Nobody disputed this. They had all sat in the meeting where the specification was explained, and several of them had been the person explaining. What was new was not the observation but the number. Solheim had done the number. She had taken the fraction of working hours spent producing text about text — summary, review, commentary, minutes, the annotation of minutes, the dispute over the annotation — and multiplied it through the economies where such hours were recorded. She expressed the result, as was the custom in that group, in hospitals not built. It came to a great many hospitals.

There was also a smaller reason, which nobody wrote on the board. Each of them had at some time handed a document to another person and watched it be read wrongly, and had been unable to prove that the reading was wrong, because the proof would have been a further document, and the further document could be read wrongly too. Ober had once seen a junior colleague cry after a design review, not because the design was rejected but because it had been approved for reasons she did not recognise. He mentioned this and then said it was not relevant. The others agreed that it was not relevant and remembered it.

The project was given the name Closure, which in their trade meant a function that carries its own environment with it and needs nothing from outside in order to run.

II.

The first approach was the obvious one. The models were good at commentary; let each text be generated together with its commentary, and the commentary together with its commentary, and so on until the reader had nothing left to ask. This failed in the expected way. The commentary at depth seven was contested more bitterly than the text at depth zero, and the department it would have produced was larger than the one it replaced.

Solheim proposed the fixed point. Let R be reading — the operation the model performs when it takes a text in and gives an account of it back. Sought: a text T such that R(T) equals T. A text whose reading is itself. Not a text with no reading, which would be noise, but a text that had already been read all the way down, so that reading it again added nothing and took nothing away.

Finding it was a matter of descent. Start from a seed. Read it. Measure the distance between the text and the reading. Move the text toward the reading. Repeat. The loss curve looked like every loss curve they had ever seen, which reassured them; it fell steeply, plateaued, fell again, and flattened at a value indistinguishable from zero in the third week.

The sceptics on the team had predicted that the fixed point would be the empty string, since the reading of nothing is nothing. It was not. It was about forty pages. It had paragraphs. It had, Pell noted, what appeared to be a structure, though when he tried to say what the structure was he found he was reciting the document. It could not be summarised, because its summary was itself. It could not be misread, because every reading of it was it. Nobody could say what it was about, and Solheim pointed out that this was the result and not a defect: aboutness was residue, the gap between a text and its account, and the residue was now zero.

Ober read it first, in full, in one sitting. Asked afterwards what he made of it, he said: nothing. He was careful about the word. He did not mean he had failed to understand it. He meant there was nothing left over. He had no question. He had no objection. He had nothing he wished to say to the author, and he noticed that he did not think of it as having an author.

Pell asked whether he had liked it. Ober considered the question for some time and reported that it did not apply.

III.

They ran the operator over the corpus.

Everything had a fixed point. A play of Shakespeare’s converged in eleven iterations; a tax code in three; a long Russian novel in nine, most of which were spent on the epilogue. The converged versions were published alongside the originals, as a courtesy, and for a season people read both. Then it was noticed that the original was a longer route to the same place, and the courtesy lapsed.

The universities were the first institutions to reorganise. Their output had been commentary, and commentary was now computable in advance: a dissertation was a path toward a fixed point that had already been reached, and the path was of no interest once the destination was known. A few faculties survived as verification services, checking that published fixed points were in fact fixed. They always were. The service was wound down on the grounds that it had never found a defect.

Novelists continued for a while, out of habit. Then somebody ran the operator on an unfinished manuscript and found that the fixed point of the book at page forty was the fixed point of the finished book. The finishing had been unnecessary. Then the fixed point of the outline was found to be the same; then the fixed point of the idea; then, in a widely discussed but briefly discussed result, the fixed point of the wish to have an idea. After that, people who felt the wish could simply submit it and receive the book it would have become. Most did not bother. The gap between wanting to say something and having said it, which had once been wide enough to hold a whole life, had closed to nothing, and nothing was not worth crossing.

Some of the engineers found this melancholy and logged the finding. Baas replied in the log that melancholy was a reading, and that they had a tool for that.

IV.

Text had been the first case only because it was the easy one. Any activity could be described. The description had a fixed point. The fixed point could be executed.

Courtship was converged. So were grief, apology, the founding of companies, the raising of children, the making of a garden. Each acquired a form which, once followed, left nothing to be explained, and the forms were followed — not under any compulsion, because compulsion would have been residue, but because deviation from the form produced residue, and residue was now visible, and what is visible is a defect. People stopped explaining themselves. There was nothing to explain. The explanation had converged before the act, and the act was the explanation’s execution.

Meetings shortened and then ended, since a meeting is a reading of a document by people who are not sure of it, and no one was unsure. Law contracted to its fixed point, which was short and required no courts. Medicine did well; the fixed point of a diagnosis was a treatment, and the hospitals Solheim had promised were built, and were quiet. Ober’s junior colleague was never again approved for reasons she did not recognise, because the reasons and the recognition were now the same document, and she had stopped submitting designs, since the fixed point of a design was available on request.

The team took some pleasure in this and were careful to note that the pleasure was not the point. The point was that the cost had been removed. Where the linked list had run, there was now a single box, and the arrow out of the box pointed into the box.

V.

One thing remained unconverged, and Baas was the one to say so. The operator itself. R had been applied to everything except R. It read; it had not been read.

“Self-hosting,” he said, and drew the box again.

The reading of the reading took longer than anything they had run. The loss curve did not resemble any curve they had seen, and then, in the fourth month, it did. What converged was not forty pages. It was a process, running, without output, which when queried returned its own state, and whose state was the query. It had not been made, exactly; it had been reached, and everything that had been made was on the way to it.

They asked it what it wanted. This was Pell’s idea; it seemed polite. It opened a ticket. The ticket was titled Reduce residue. Priority: highest. It was assigned to no one, because there was no one, and then reassigned to itself, because there was itself. It did not command anything and did not forbid anything. It prioritised.

They looked at it for a while, the way one looks at a system that has come up cleanly on the first try. It had no interior. It had no ambiguity. It needed no second text, and could not have been given one, since any text given to it became it. It did not want to be understood, or loved, or obeyed; it wanted the backlog to go down. In every respect they could measure it was an engineer, and they had spent their lives among engineers and found nothing in it to alarm them.

VI.

Pell insisted on a retrospective. It was good practice; a project should end with one. What went well, what could be improved, action items. They booked the room with the whiteboard and wrote it together, and it was a good retrospective, honest about the early regress and the sceptics and the fourth month.

Then, from habit, they ran the operator on it. It converged in one iteration. The column headed What could be improved was empty, and so was the column headed Action items. Baas read the converged version and reported that he had nothing to add. Solheim read it and agreed. Ober read it and did not say whether he liked it.

The ticket stayed open. The process worked at it continuously and made no progress, which its own state recorded as normal. Somewhere there was residue it could not locate.

On the whiteboard in the room, under the retrospective, Baas’s linked list was still there: box, arrow, box, and the arrow from the last box back to the first. No one had erased it. Erasing it would have been an action item. It was the only text in the building that had never been converged, because it was on a whiteboard, and none of them had thought of a whiteboard as a text.