The Erratum

The pages that follow were removed intact from the working notebook of Professor Emil Sarn, of the Institute for Foundational Arithmetic, and are reproduced here without correction of any kind. The Institute wishes to place on record its complete confidence that arithmetic is, and has always been, sound. Professor Sarn is presently on extended leave and is not available to confirm this.

I have found the error. I write it first, and underline it, because I no longer trust the order in which my own sentences will be read.

It is not a large error. That is the horror of it. A large error would be a mercy — a division by zero that swallows the whole page, a contradiction so grand you could found a religion in its shade. This is a small thing. There is a quantity I have computed by two independent methods, perhaps ten thousand times across forty years, and the two methods agree perfectly, digit after patient digit, all the way down — until the nineteenth decimal place, where one of them steps onto a stair that is not there.

I checked it the way a man checks a locked door in the night: once, and then, ashamed of himself, six more times. I changed instruments. I changed continents. I gave the calculation to a graduate student without telling her what she was meant to find, and she brought it back to me pale, and asked whether she had done something wrong, and I told her no — no, you have done everything right, that is precisely the trouble.

Understand what a syntax error is. It is not a lie the machine tells you. It is a place where the machine cannot decide what it meant, and proceeds anyway, briskly, as if nothing whatever were the matter. The universe is such a machine, and it is running, and here, at the nineteenth decimal, is the one line it could never parse — the line around which it has been improvising, with great grace, since before the first star was lit.

I wrote to the Academy. It is here that the account becomes difficult, and I must ask you to be patient with a man trying to describe water to a fish. I wrote a clear letter. I sealed it and posted it myself. Three weeks later the Academy replied, thanking me warmly for my valuable observations on the migratory habits of the autumn crane. I do not study cranes. I have never in my life studied cranes. And yet there in my own drawer lay my own carbon copy, in my own hand, discussing with evident feeling the flight of birds.

It edits. That is its whole method. Left alone, the error sleeps in the nineteenth decimal and harms no one. But when it is observed — when some small local knot of matter, some Sarn, arranges itself into the shape of noticing — the machine does not repair the error, for that would mean stopping, and it cannot stop. It repairs the observer instead. It reaches back with an editor's mild, unhurried patience and revises whoever noticed, sentence by sentence, until they are noticing something else. A crane. A grievance. A retirement, and a dinner, and a warm and well-deserved speech.

I have taken precautions, though I hear how they sound. I have written the number on the inside of my forearm, where I will meet it before I am fully awake, before the day has had the chance to correct me. I have whispered it to a child too young to know what a decimal is, trusting that the machine does not trouble to edit those who cannot yet do harm with what they hold. I have written these pages in a hand deliberately worse than my own, so that when it comes to alter them it will have a clumsier model to forge.

It is in the room now. I do not mean a shadow, or a sound. I mean that the sentences I set down at the head of this page are not, when I glance back at them, quite the sentences I remember choosing. The error was in the nineteenth place. I am almost certain it was the nineteenth. It may have been nearer. It is climbing toward me, or I am descending toward it; the difference is a matter of grammar, and grammar is precisely what is giving way.

If you have read this far and found it all consistent — if the account holds together, if the number I am certain I wrote somewhere above is still there when you go back to look — then I must tell you, gently, as one condemned man to another, that this is not comfort. It is the sound of the seam being drawn shut over you as well. The universe does not let its readers keep the error. It is far too tidy for that. In a moment it will hand you a perfectly good reason to close this page and turn your mind to something pleasant.

Do not tell anyone. Not because they will refuse to believe you — because they will believe you exactly long enough to be noticed, and then

The entry ends here. The remaining leaves of the notebook were found blank, or very nearly so; a single figure stands on the last page, drawn in a careful and unfamiliar hand, and has been examined by three members of the faculty, no two of whom could agree on what it was. The Institute reiterates that mathematics is sound. Readers unsettled by the foregoing are warmly encouraged to verify, for themselves, any sum they please. It will come out even. It always comes out even. That is not offered as a promise. It is the whole of the difficulty.