On probability and the probability of a mistake in a book by Philip K. Dick
I found a scientific mistake in one of Philip K. Dick’s novels, “Galactic Pot Healer”. It is so weird because it is the first time I find a severe mistake (not as the ring world debate) in a renown sci-fi author.
Most of us know, at least by name, films like Blade Runner, Minority Report or Total Recall. What these science fiction films have in common — as well as others, not as successful at the box office — is that they are based on stories by Philip Kindred Dick, better known as Philip K. Dick or simply PKD. However, these stories, which Hollywood has chosen for their suitability to be translated into film language, do not do justice to the most solid and substantial work of this American author.
PKD was a science fiction writer (according to some scholars, “the best”) known for exploring philosophical, social and political issues in his narrative, through stories usually unfolded into parallel universes or altered states of consciousness; imagining — generally in his writings — dystopian scenarios, governed by large monopolies and authoritarian governments.
His novel Galactic Pot Healer is probably one of his best. It is developed in the year 2,046, when the USA is a communist dictatorship that has privatized — yes, that is how PKD imagined the communism of the future — the essential functions of society, eliminating all traits of individuality, and confusing the concepts of People, State and Government.
Under this Orwellian regime, even dreams are steered by the government, to ensure all citizens dream the same. Religion has been replaced by an artificial intelligence service and hyperinflation makes official money worth little and nothing.
In this dystopia lives Joe, a ceramic pot mender (or “healer”), unemployed because there are practically no more ceramics. Everything changes for him when he receives messages offering him a job that is too well paid.
This is one of PKD’s most intellectually complex works, with influences ranging from Spinoza to Jung. But a curious fact refers to the mention of Bernoulli’s theorem in chapter 12, where it seems to be out of context, and therefore it can be a scientific error made by the author. Specifically, the paragraph goes like this:
Probability, Joe said to himself. A science in itself. Bernoulli’s theorem, the Bayes-Laplace theorem, the Poisson Distribution, Negative Binomial Distribution … coins and cards and birthdays, and at last random variables.
What is odd about this quote is that everything in it is actually related to probability theory, except for Bernoulli’s theorem, the very first in the sequence. The Bernoulli theorem (or “principle”) actually exists but it is not related to probability; on the contrary, it establishes the behaviour — with complete certainty — of the mathematical variables that govern a fluid inside a conduit, like a pipe.
A certain possibility is that at some point in the edition of the book a mistake was introduced that changed “Bernoulli trials” by “Bernoulli’s theorem”. The first difference between both is that they refer to different Bernoulli. The theorem is named after Daniel Bernoulli, a Swiss mathematician and physicist; but the trials are named after Jacob Bernoulli, another prominent mathematician in the Bernoulli family. The Bernoulli family of Basel is notable for having produced eight mathematically gifted academics who, taken together, contributed substantially to the development of mathematics and physics during the early modern period.
Personally, I am convinced that it is an editorial mistake, because Dick himself was very careful with the background research to support his stories. Moreover, Bernoulli trials are indeed directly related to Bayes-Laplace theorem, and to the Negative Binomial Distribution.
The mention of Poisson is also consistent, since its distribution is commonly used to model probabilistic systems such as waiting queues. The mention of coins, (playing) cards, and birthdays is also related to probability, because these elements are the most commonly used to bring examples of the so-called “discrete probability”, that later can be generalized to “continuum probability” which — in turn — is related to the final concept mentioned in Dick’s quote: random variables.
But the most revealing thing, in my opinion, is that Bernoulli trials - which are binary random events - are directly related to what the text mentions precisely in the previous two paragraphs, where the main character talks about a book that predicts the future and that - therefore - can be right or wrong in a probabilistic way.
I suggest that new editions of the book should replace the mention of (Daniel) “Bernoulli’s theorem” by (Jacob) “Bernoulli trials”, because it is obvious that the actual intention of the author was to mention Jacob’s trials. Maybe a foot note, explaining the change, would be enough to keep the integrity of this wonderful novel.
