Therefore

story sixteen · figures 46–48

The story →

THEREFORE · SIX THEOREMS, EACH TURNED ON ONE HOUSEHOLD — a mathematician asked to price a word · every result stated correctly, and then aimed at his own family THEREFORE · SIX THEOREMS, EACH TURNED ON ONE HOUSEHOLD a mathematician asked to price a word · every result stated correctly, and then aimed at his own family KOLMOGOROV COMPLEXITY the fare is the length of the shortest description — so the fare is uncomputable there is a correct price for each word. No machine can find it for every word ARROW no rule turns three orders into one and keeps every promise three of us. One crossing. We voted anyway. We are not unusual GÖDEL, SECOND anything strong enough to count cannot, if consistent, prove its own consistency so the register cannot count, or it is lying, or it cannot say. It says. Every Thursday it says THE HALTING PROBLEM no procedure answers it for every account there is a procedure that answers it for mine. No. ST PETERSBURG their model made the expectation infinite nobody pays infinity. Everybody pays something. Between those two sentences is where they live ZENO halve the queue, halve it again, you never arrive my father arrived. I watched him arrive. HE IS RIGHT ABOUT EVERY THEOREM AND WRONG ABOUT WHAT WILL HAPPEN TO HIM. The book lets both stand, which is the only honest way to put mathematics inside a grief.
46 · Therefore
THEREFORE · THE STAIRS, COUNTED FOUR WAYS — the household’s one repeatable experiment · and the only counter in it who is never wrong THEREFORE · THE STAIRS, COUNTED FOUR WAYS the household’s one repeatable experiment · and the only counter in it who is never wrong he counts 17 first time he counts again 19 second time, same stairs his hands say 23 the body’s count, and it does not agree with either his son, going up right every time · it costs him nothing "One of these is a fact. I have three hands." the son six years old · counts things for pleasure · better than his father and it costs him nothing what the son will not count the stairs on the way DOWN · and will not say why what the son has a word he thinks is funny, said at the wrong times to see what happens what the father sees "He is a number in a set with no ordering. He does not know." A MAN WHO PRICES WORDS FOR A LIVING CANNOT COUNT HIS OWN STAIRS TWICE THE SAME WAY. The child, who is not paid and does not know, gets it right every time. THE ONE PLACE IN THE STORY WHERE A NUMBER IS RELIABLE IS A SIX-YEAR-OLD ON A STAIRCASE.
47 · Therefore
THEREFORE · THE PROOF, AND THE TWO WORDS THAT CONVICT IT — seven lines at the end of the story · six of them valid, and one of them a man deciding THEREFORE · THE PROOF, AND THE TWO WORDS THAT CONVICT IT seven lines at the end of the story · six of them valid, and one of them a man deciding Proof. the register of a discipline Assume the world can be understood. the axiom every science needs Assume also that I would still be paid. the axiom that does not belong — and he writes it anyway Then there is a shortest true description of it. follows from the first assumption Take that description. Add this sentence to it. the move It is longer now. It is still true. true, and not a contradiction — a longer true description is not a shorter one Contradiction, I write. I WRITE · two words that tell you he is manufacturing the conclusion he needs Therefore. no consequent Therefore. and again, with nothing after it THE PROOF IS INVALID, AND THE STORY KNOWS IT. Adding a true sentence to a shortest description makes a longer true description. It contradicts nothing. Two words — I WRITE — move the failure from the mathematics into the man, without the book saying so, and the second THEREFORE has nothing after it. There is nothing that follows. HE WAS ASKED TO PRICE A WORD. HE PROVED IT CANNOT BE DONE. THEY THANKED HIM. THEY WERE KIND.
48 · Therefore

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