I was asked to price a word. That is the whole job. Give me a word. I return a number. The number goes on the board.
My son is six. He counts things for pleasure. He is better than me and it costs him nothing. He will not count the stairs on the way down and will not say why. He has a word he thinks is funny and says it at the wrong times to see what happens.
A word costs what it costs to keep. Keeping is compression. A word you can prove twice is a word that compresses. So the fare is the length of the shortest description. So the fare is Kolmogorov complexity. So the fare is uncomputable.
I wrote that on the form.
They asked me to write it again in plain words. Plain words: there is a correct price for each word. No machine can find it for every word. Not now. Not ever. Not with any machine you will build.
They thanked me. They were kind. The board went up in the spring.
Three of us. One crossing. I rank the outcomes. My brother ranks them differently. My sister differently again. There is no rule that turns three orders into one order and keeps every promise. This is a theorem. It is ninety years old.
We voted anyway. We are not unusual.
The register is consistent. The register says so. Anything strong enough to count cannot, if it is consistent, prove its own consistency. So the register cannot count, or it is lying, or it cannot say.
It says. Every Thursday it says.
Will my account ever close. Give me the account and I will tell you. There is no procedure that answers that for every account. There is a procedure that answers it for mine.
No.
They offered me a wager on my mother. Double for each year she stays. They called it a plan. I could not price it. Their model made the expectation infinite. Nobody pays infinity. Everybody pays something. Between those two sentences is where they live.
There is a bowl by the door with three coins in it and a button. I count the stairs. Seventeen. I count them again. Nineteen. My hands say twenty-three. My son counts them going up and gets it right every time. One of these is a fact. I have three hands.
1 1 2 3 5 8. Fine. 1 1 2 3 5 8 13 21. Fine. 240 300. Not fine. They have given no rule that takes the first to the second. There is a resolution.
Halve the queue. Halve it again. You are always at the front of the half you are in. You never arrive. My father arrived. I watched him arrive.
I do not sleep. At night my heart does the stairs. Seventeen, nineteen, twenty-three. The tap runs at night in the flat below and I lie there subtracting. Two hundred and six. Two hundred and forty. Minus thirty-four. It was minus nine when I started. Minus thirty-four for a decade and a year is not a fact. It is a direction.
The boy is asleep in the next room. He is a number in a set with no ordering. He does not know.
Sets. Take the set of everything you can afford to say. Take the set of everything you must say. These do not intersect. That is not a metaphor. I have written it out. It is four lines.
Give me one axiom. I will give you a city.
Proof.
Assume the world can be understood. Assume also that I would still be paid.
Then there is a shortest true description of it.
Take that description. Add this sentence to it.
It is longer now. It is still true.
Contradiction, I write.
Therefore.
Therefore.