The Third Sally
or, The Dragons of Probability
FOUR LINES
- NarratorA dragon is distinguished not by its actuality but by its probability. Once it exists, that probability is overwhelming.
- TrurlAnd if he only turns it down again, they come back. By then he is gone, with the gold.
- NarratorThe counter on his chest settled at eight tenths of a dragon.
- TrurlThis way I get the tribute.
HOW IT IS MADE
Every dragon in the film has a probability between 0 and 1, set by keyframes in the score. The dragon is drawn first into a hidden canvas. Then every small cell of that drawing gets a fixed random threshold, and the cell is printed as a dot only if the dragon’s probability is above it. As the probability rises the same dots stay and new ones join them, so a dragon fills in rather than flickers. Above 0.9 the solid drawing fades in.
The sound reads the same numbers. A counter clicks at random, more often the more probable the nearest dragon is. A dragon’s roar is cut into short grains, and each grain is kept with probability p, so an unlikely dragon is heard in scraps. The counter on Klapaucius’s chest is the same dial you see on Trurl’s amplifier.
In the gorge Klapaucius turns the improbability up on everything. Stones float and walk, a moth taps Morse, the dust spells a sign, the tune plays wrong notes, and half-likely witches and centaurs pass as dots. The dragon stays solid the whole time, because its probability is pinned at 1. It is Trurl in a skin with probability-proof shields.
AFTER THE OTHER FILMS
In How the World Was Saved things are removed for good. Here nothing is ever fully present or absent: a dragon is a number that can be turned up and down, and a man who can turn the number can sell its removal.
FOR THE BENCH
Draw a shape as a grid of points, and give each point a fixed threshold th = random() in setup(). In draw(), show a point only if p > th, and tie p to mouseX. Why does storing the thresholds once make the shape fill in, while calling random() every frame makes it flicker?
Narration and dialogue paraphrase Stanisław Lem, “The Third Sally, or The Dragons of Probability,” The Cyberiad. Drawn after the dragon plates. Download the film.
THE SCRIPT
TRURL'S CELLAR
Narrator. Trurl and Klapaucius proved that dragons are not impossible, only improbable. For one to appear by itself, you would have to wait sixteen quintoquadrillion heptillion years.
Narrator. So Trurl built a probability amplifier, and tried it in his cellar.
Trurl. Raising the probability.
Trurl. Klapaucius!
Klapaucius. Lowering it.
Narrator. A dragon is distinguished not by its actuality but by its probability. Once it exists, that probability is overwhelming.
THE COUNTRYSIDE
Narrator. Other scholars repeated the experiment, with less care. Dragons got loose, and multiplied.
Narrator. When hunters closed a ring around one, it slipped out of real space into configurational space. All they found was a burnt patch and a smell.
BASILISCUS
Trurl. Have you heard about this Basiliscus?
Klapaucius. I don’t like it.
Trurl. Wherever he lands, dragons appear. Then he charges the king to remove them.
Klapaucius. He brings them with him, at a probability near zero, and turns it up.
Trurl. And if he only turns it down again, they come back. By then he is gone, with the gold.
THE DAMPERS
Narrator. They split up. Klapaucius did not chase dragons. He set dragon dampers in every square, and soon the beasts were very rare.
KING PFFTIUS
Narrator. On the planet of King Pfftius he heard that Trurl had been there first. Trurl had killed the dragon, the king said, and brought twenty-four of its teeth.
Narrator. But there was some misunderstanding about the fee. Trurl stormed out. That same day the dragon came back, worse than before.
THE TRIBUTE
Klapaucius. What are you carrying, good people?
A porter. The tribute for the dragon, sir. Gold, jewels, imported perfume.
Klapaucius. Perfume? Dragons have no use for perfume. Or for money.
A porter. It used to ask for virgins. That stopped after the stranger came, with his boxes, and a little dial just like yours.
Master Gyles. A fortnight past, or maybe two.
Narrator. The counter on his chest settled at eight tenths of a dragon.
THE GORGE
Klapaucius. A second head in its body. Two heads always quarrel. It will freeze.
Klapaucius. Then I will make you improbable.
Klapaucius. Nothing touches it.
Trurl. Yipe!
Trurl. Stop! Stop! Don’t kill me!
THE DRAGON
Klapaucius. Trurl? What is this masquerade?
Trurl. I killed the real dragon. The king would not pay. He wanted a death certificate, an autopsy, forms in triplicate.
Trurl. So I kept its skin. A telephone pole, some pulleys, and I was ready.
Klapaucius. But if they would not pay you in the first place…
Trurl. This way I get the tribute.
Klapaucius. It was not right to force them.
Trurl. Who forced them? I walked around in the mountains, and in the evenings I howled a little.
Klapaucius. Why didn’t it vanish, when I made everything improbable?
Trurl. Probability-proof shields, under the skin. In case Basiliscus came by.
Trurl. Come on. I saved the platinum for last. Now you can help me carry it.