By What Light
a ledger for the Abominable House: room, light, witness, and an exact count
EIGHT LINES
- WaldemarWith one number, every winner is the same kind of film.
- WaldemarThe room and the light decide who knows.
- WaldemarA sack that has acted once may act again only against someone it knows is guilty.
- WaldemarA film has to hold across the rows and down every column.
- WaldemarThe list and the count agree.
- WaldemarThis film takes a branch worth less than one in ten.
- WaldemarThis one solves every deed and never leaves two rooms.
- WaldemarEvery deed is solved. Two sacks are left, and the house is burning.
HOW IT IS MADE
This film continues from The Burning of the Abominable House, where a computer counted who did each of twelve deeds to whom: twelve to the twelfth power, 8,916,100,448,256 films. Here the four tenants are flour sacks, and each deed also gets the four parts of Alison Knowles and James Tenney’s The House of Dust, read as causes: what the deed leaves behind, which room, what light, and who else is in the room. The light decides who sees. By candle or lamp everyone in the room sees who did it; by moonlight nobody does; four deeds happen behind a shut door; after the sixth deed the house can catch fire, and then the fire lights everything. What a deed leaves (paper, cloth, flour, rope or ash) is found by the next sack to come into that room with a light. A sack that has acted once may act again only against someone it knows is guilty; that rule is checked down each sack’s own column, after Calvino’s The Castle of Crossed Destinies. The engine plays the deeds in the order the index lists them and chooses only who, where, by what light and with whom.
Every number in the film was computed by the film’s own engine (engine.js). With every choice open there are 5,462,981,741,978,763,773,743,437,712,768,106,496 films. The rules leave exactly 3,790,040,669,283,834,371,506,176. The count is done by dynamic programming: the room changes what is left behind but not what can happen next, so it is multiplied in and forgotten, and what the next deed depends on fits in at most 85,008 cases (who is alive, who is tied, whether the fire has started, who has acted, who knows whom). For the first three deeds the film also lists every raw choice and throws out the ones that break a rule: 44,789,760 of 1,528,823,808, the same number the count gives. Of 200,000 who-to-whom films drawn at random, 182,781 fail first on the column rule.
A million random films were scored by one number (deeds solved, then deeds that answer an earlier wrong). The best three open differently but are the same kind of film: every deed solved, five or six rooms. So the film keeps a grid instead, after Mouret and Clune’s MAP-Elites, with three of Calvino’s Six Memos as its axes: exactitude as deeds solved, multiplicity as rooms used, visibility as deeds a witness sees. The million films fill 38 of 64 squares, and each square keeps its best. The film played at the end comes from a square the three winners never reach: every deed solved in two rooms, the cellar and the attic. Stopped before its fourth deed (after Calvino’s t zero), the engine gives the exact share of every pair that could do the knifing: five pairs are impossible, Ogiva knifing the widow takes 51 percent of what can follow, and the film takes a branch worth 8.6 percent.
The four sexual deeds of the index are never named or shown; they happen behind a shut door. The sound follows the parts of each deed: paper, cloth, flour, rope and ash, a candle, a lamp, the moon, a witness’s whisper, a door, and a clock that speeds up from 66 to 108 ticks a minute until the fire.
FOR THE BENCH
Count instead of sampling. Write moves(k, state) that lists every legal choice for deed k, and step(k, state, move) that returns the next state. Keep a Map from a packed state key to how many films reach it, and push it forward one deed at a time: for every state and every move, add its count to the next state’s key. Use BigInt; the totals pass twenty digits. Then check yourself: for the first two or three deeds, list every raw choice with a recursive function, keep the legal ones, and compare. The two numbers must match exactly. Then remove the room from the state key and watch the number of states drop while the count stays the same.
After Italo Calvino, The Burning of the Abominable House, in Numbers in the Dark, translated by Tim Parks; with Alison Knowles and James Tenney, The House of Dust (1967); Calvino, t zero, The Castle of Crossed Destinies and Six Memos for the Next Millennium; Jean-Baptiste Mouret and Jeff Clune, “Illuminating search spaces by mapping elites” (2015); Richard Bellman, Dynamic Programming (1957). Nothing is quoted. Download the film (mp4).
THE SCRIPT
THE FIRST ENGINE
Waldemar. The first time, the machine asked one question of each deed: who did it to whom.
Waldemar. Twelve deeds, twelve pairs for each. Twelve to the twelfth power. Almost nine trillion films.
Waldemar. I ran a million of them at random, gave each one a score, and kept the best three.
Waldemar. They open differently. They end the same way. In all three every deed is solved, and the story moves through five or six rooms.
Waldemar. With one number, every winner is the same kind of film.
FOUR MORE PARTS
Waldemar. So each deed gets four more parts. What it leaves behind. Which room. What light. Who else is in the room.
The printer. Blackmail. Inigo, the widow. Paper. The attic, by candle. Ogiva at the door.
Waldemar. The room and the light decide who knows.
THE RULES
Waldemar. These are the rules. A dead sack does nothing, and nothing more is done to it. A tied sack cannot act.
Waldemar. By candle or lamp, everyone in the room sees who did it. By moonlight nobody does, not even the one it was done to.
Waldemar. Four of the deeds happen behind a shut door. Nobody sees those.
Waldemar. Every deed leaves something in the room: paper, cloth, flour, rope, or ash. The next sack to come in with a light finds it.
Waldemar. After the sixth deed the house can catch fire. Once it has, the fire lights every deed that follows, and the last deed is always lit by it.
Waldemar. A sack that has acted once may act again only against someone it knows is guilty.
ROWS AND COLUMNS
Waldemar. That last rule is read down each sack's own column, not across the film.
Waldemar. This film breaks it at the fourth deed. Ogiva knifes Inigo, and nothing Inigo has done has reached her.
Waldemar. Of two hundred thousand who-to-whom films drawn at random, nine in ten fail first on this rule.
Waldemar. A film has to hold across the rows and down every column.
THE COUNT
Waldemar. With the four parts added, the number of films is thirty-seven digits long.
Waldemar. I did not list them. The room changes what is left behind, but not what can happen next. So the count multiplies by six and forgets the room.
Waldemar. The next deed depends on very little: who is alive, who is tied, whether the fire has started, who has acted, and who knows whom.
Waldemar. That never comes to more than eighty-five thousand cases. So the machine counts every film exactly, one deed at a time.
Waldemar. The answer is twenty-five digits long.
Waldemar. For the first three deeds I also listed every film, one by one, and threw out the ones that break a rule. Forty-four million, seven hundred and eighty-nine thousand, seven hundred and sixty.
Waldemar. The list and the count agree.
STOPPED
Waldemar. Now take one film and stop it just before the fourth deed, the knifing.
Waldemar. Here are the twelve pairs that could do it, each with its share of all the films that can still follow.
Waldemar. Five of them cannot happen: the dead, the tied, and the sacks with no reason are out.
Waldemar. In half of what can follow, Ogiva knifes the widow.
Waldemar. This film takes a branch worth less than one in ten.
THE GRID
Waldemar. Instead of one winner, keep a grid. Across, how many deeds are solved. Down, how many rooms are used. Deep, how many deeds a witness sees.
Waldemar. Each square keeps its own best film. The million films filled thirty-eight of the sixty-four squares.
Waldemar. The three winners from before sit together in one corner.
Waldemar. This one solves every deed and never leaves two rooms.
ONE FILM FROM THE GRID
The printer. One. Blackmail. Inigo, the widow. Paper. The attic, by candle. Ogiva sees.
The printer. Two. Drugging. Ogiva, Inigo. Cloth. The attic, by lamp. The widow sees, and finds the paper.
The printer. Three. The cellar, by moonlight. The door is shut.
The printer. Four. Knifing. The widow, Inigo. Flour. The cellar, by lamp. Ogiva and Belindo see.
The printer. Five. The attic, by moonlight. The door is shut.
The printer. Six. A gun. Belindo, the widow. Ash. The cellar, by candle. Ogiva sees, and finds the flour.
The printer. Seven. Tying and gagging. Belindo, the widow. Rope. The attic, by lamp. Two pieces of cloth are found.
The printer. Eight. The attic, by lamp. The door is shut. The rope is found.
The printer. Nine. The cellar. The fire has started. The door is shut.
The printer. Ten. Slander. Belindo, Ogiva. Paper. The attic, by firelight.
The printer. Eleven. Snooping. Ogiva, the widow. Flour. The attic, by firelight.
The printer. Twelve. Strangling. Belindo, the widow. Rope. The attic, by firelight.
Waldemar. Every deed is solved. Two sacks are left, and the house is burning.