Note G

I The line, in the author’s own hand

Single-seat STV — which is instant-runoff, and is a counting rule rather than an opinion. Kept away from the model on purpose. The settlers decide what they want; the arithmetic that turns their ballots into a result has one right answer, and a language model asked to do it would produce a plausible one instead. Everything here is pure and deterministic, so the same ballots always give the same rounds, and the rounds are the thing worth showing. tools/stv.mts, the first eight lines

Would produce a plausible one instead. That is the whole architecture of this game in six words, and it is the reason the record can be read back at all. A plausible count cannot be checked, cannot be reproduced, and cannot be disagreed with — and a valley whose votes are plausible is a valley where nothing that happened actually happened.

The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. Ada Lovelace, Note G to Menabrea’s sketch, 1843

Note G is remembered for that sentence and is mostly something else: a table. Operation, nature of operation, variables acted upon, result — the first published algorithm, set out so that anybody could work it by hand and get the same answer. Both halves matter here. The engine does not originate; and the arithmetic is written down where it can be checked.

II Where the line actually falls

Seven to four, and the seven are load-bearing. Every sheet in this record that found a fault found it on the left-hand column — a lean-to that held less than a house cost, a release condition read at the store and answered with a building, a ceiling at twenty-eight, a footprint written in one file and asserted in seven. Not one repair in this whole record has been made by changing what a settler is allowed to want. Every one has been made to the left-hand column — which is not because the wanting is always right, but because the counting is the half that can be checked, and a fault you cannot check is a fault you cannot fix.

III The accident that tested it

The valley has been run at four times speed. The bus is answering fine — about nine and a half seconds a reply, clean JSON — but the world is moving four times faster past a queue that runs at wall-clock speed:

A fifth of the words, and the valley did not stop. It founded two breakaways, carried a wall, a cemetery, a hearth, a well, a joiner and a valuation system, built thirteen houses, and produced the first migration in the life of the game. All of that is the left-hand column. What is thinner at four times speed is not the world but the interiority — fewer wishes, fewer things said, fewer plans, and more of `chooseJob`, which is a good clerk and has never had an idea.

Which is worth knowing while watching rather than as a fault to fix: at four times speed you are watching the counting, and the deciding is getting a word in about a fifth as often as it did in the valley all these sheets were written about.

IV The best arithmetic in the tree

If one mechanism here deserves to outlive the game it is the credit, and the reason is a distinction that took a measurement to find.

A favour is written down by name. Somebody hired on credit is owed; the hirer owes. It is worked off in goods rather than coin, reckoned once a day, and costs the creditor’s good opinion at three hundredths a day on debts over six. It is deliberately soft — no interest, no enforcement, nobody comes for you. What it does is weigh: a debtor comes when their creditor calls, and a creditor whose debt goes unanswered stops thinking well of them.

And then the part that is not obvious. A settlement that has voted a ledger in reckons a person’s standing as what they are owed by the place, less what they owe it — netted, never summed:

Summed, a ledger is a blanket penalty: the asker’s debts to eleven people add up past the cap on the first day, so every request in the valley is treated as a bad one and nobody helps anybody. Measured with it written that way: hostile pairs went from two and a half to ten — which is the fault the whole helping system was rewritten to fix, reintroduced by the thing meant to help. src/sim.ts, above the standing

Somebody who has carried half the valley’s stone is worth going out for, whoever they carried it for. Somebody who has had a hand off everybody once cannot get a second one from a stranger. That is one line of arithmetic and it is the difference between a coast where people help each other and one where nobody does.

And here is what the counting cannot supply. Across 199 proposals on file, in four valleys, not one settler has ever asked for their debts to be cleared. Not once, not in a title, not in anybody’s own words. The nearest is Pike, who asked for the opposite — a way to trade a day’s work for a night’s rest without having to run a favour for someone else — which is a request to work without incurring one. Nobody wants absolution. Somebody wanted not to be obliged in the first place.

That is the right-hand column doing the only thing it can do, and doing it better than any rule would have: telling you what people actually want, which was not what the mechanism was built to offer.

V What the valley still cannot say

Two vocabularies are missing, and both were found by reading rather than by anything going wrong.

Thirty-three ways to spend an hour and four words for when. Two settlers cannot agree a time finer than a quarter of a day, because hourLabel returns dawn for a band and not a moment. And nothing on this coast has a name except the settlements: there is no dell, no ridge, no ford, no long stand. goto takes coordinates, which is a thing a settler standing in a field cannot say to another one.

Both are the shape Sheet XLII named — a whole category of intent with no bin. And half of the second one is already standing: the cairn. A heap of stones on the ways between things, the one structure here nobody votes for, going up one stone at a time by name. A cairn that has been named is a landmark two people can agree on, and naming one is work done with hands at a place somebody chose — which is the rule the roads had to learn in Sheet XLI.

VI The counting audits the mind, and the author

The last thing worth entering is what the left-hand column did to this evening’s work. Adding one word to the catalogue — a trade for the person who makes a thing — was refused, in order:

Every one of those is arithmetic refusing an author, which is what Note G’s table was for: the operations written down where anybody can work them by hand and get the same answer. A record whose counting could be talked round would not be a record. It would be a plausible one.