by Wojciech Jóźwiak. Contact: firstname.lastname@example.org. Facebook»
In “The Cyberiad” by Stanislaw Lem, the novel “The Third Sally or The Dragons of Probability”, we read a luscious paragraph about how Klapaucius fought the dragon. Here is what happened:
At the first bend he crouched behind a boulder, pulled out his improbability automatic, took aim and actuated the possibiliballistic destabilizers. The gunstock trembled in his hands, the red-hot barrel steamed; the dragon was surrounded with a halo like a moon predicting bad weather— but didn't disappear! Once again Klapaucius unleashed the utmost improbability at the beast; the intensity of non-verisimilarity was so great, that a moth that happened to be flying by began to tap out the Second Jungle Book in Morse code with its little wings, and here and there among the crags and cliffs danced the shadows of witches, hags and harpies, while the sound of hoof beats announced that somewhere in the vicinity there were centaurs gamboling, summoned into being by the awesome force of the improbability projector. But the dragon just sat there and yawned, leisurely scratching its shaggy neck with a hind paw, like a dog. Klapaucius clutched his sizzling weapon and desperately kept squeezing the trigger—he had never felt so helpless – and the nearest stones slowly lifted into the air, while the dust that the dragon had kicked up, instead of settling, hung in midair and assumed the shape of a sign that clearly read AT YOUR SERVICE GOV. It grew dim—day was night and night was day, it grew cold – hell was freezing over; a couple of stones went out for a stroll and softly chatted of this and that; in short, miracles were happening right and left, yet that horrid monster sitting not more than thirty paces from Klapaucius apparently had no intention of disappearing.
(Translated by Michael Kandel, 1974)
We know what happened next: here the dragon did not disappear, because he was not a dragon, but dressed in dragon's skin friend of our hero Trurl, who thus enforced the unviable ruler of this planet due him payment for the earlier removal of the actual dragon.
What else: I skip a small logical mistake that the author made in this tale. Now, if the dragon was something highly unlikely, so when Klapaucius increased “improbability,” why was he expecting the dragon to disappear? Rather, the intensity of that “field of improbability” should be reduced, restoring ordinariness that would just destroy the dragon. But this does not change the considerations I intend to present here.
What is Klapaucius doing? He “increases improbability” – launches “improbability gun” or emitter which maximally increases “intensity of non-verisimilarity.” Apparently Lem imagined a certain physical field that controls probability. While normally the probability of some rare phenomenon is very small, close to zero, it would increase in this field. The probability is amplified, as is the amplitude of the electrical signal passing through the amplifier. This idea in Lem's mind was justified by the fact that in physics (quantum, yes!) there is talk of probability amplitude. (Which, moreover, can be zero, or negative or also imaginary – just like dragons in his novel.) So, since probability is a physical quantity, and some physical quantities are amplified, “passed through amplifiers”, then you can imagine a probability amplifier, which works, how? – Yes, that it makes rare or extremely improbable phenomena highly probable. Until they begin to appear.
Let's skip the harpies, centaurs and talking, volatile boulders. Two of the phenomena that Lem entwined in his tale, undermine our attention. It's the butterfly that broadcasts “The Second Jungle Book” with Morse code and the dust forming the inscription that absurd, the better. Here is the improbable, i.e. having a slightly low probability of occurring (because, after all, a butterfly could accidentally broadcast a Kipling novel and the dust could accidentally form an inscription, except that these would be cases with extremely low probability) turns out to be significant! And vice versa, because we see from here that what is significant has a low probability.
Places in space and the pieces of matter that fill them, which arranged in an extremely unlikely state, have low entropy. When improbable configurations of matter fall apart and enter more ordinary states, that is having higher probability, entropy increases.
Experience and the natural order of the world teach us that entropy does not diminish by itself. Phenomena with a low and very low probability of occurrence usually do not happen spontaneously: rather, they are due to a process whose intermediate phases are unknown or obliterated. If the surface of the broken rock is shaped like a shell, it is not so much because it accidentally arranged in that manner, but because it is a fossilized sediment of the bottom of the former sea, in which limestone remains of mussels or ammonites living there were deposited. Such phenomena are also significant: for the geologist who recognizes them, they are a signal, a message.
In general, we are looking for incredible things in the world: which are (1) rare, therefore (2) have low entropy and at the same time (3) are significant to us.
Keeping this in mind, we will move on to considerations more strictly belonging to astrology, for some time.
With gratitude to Alexandra Müller-Larsson for linguistic help.