Random? By Chance? Improbable?

A philosophy professor rolls out some related concepts.

July 6, 2022

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Comic illustration of animated dice falling out of a cup.

Illustration: Gary Taxali

The words chance and random are, of course, different in their daily usage. We are happy to say things like, “There is no chance of rain tomorrow” and “There’s a random person at my front door,” but not the other way around.

Still, one might assume a deep connection between the concepts. A commonplace view even defines random in terms of (some type of objective) chance: An event is random if it happened by chance.

However, science and philosophy distinguish the terms. The philosopher and mathematician Bruno de Finetti famously proclaimed, “Chances do not exist,” favoring instead a subjective interpretation of probability: Nothing really happens “by chance,” even though some events may be more or less surprising. An alternative suggestion might be that an event is random to a specific person if they previously judged the event to have low probability. But lots of events can have low subjective probability: I would have considered it extremely improbable that my student’s essay contained exactly 4,524 words, and yet I wouldn’t say it was random.

A rich mathematical theory of random objects called Kolmogorov complexity measures randomness without any direct appeal to probability (not to mention objective chance). An object is random to the extent that it has no short description; it is disorderly or incompressible. A chance process could produce a random object, but it might produce an object that’s not random. And there may be ways of obtaining random objects other than by chance.

There are a number of related concepts here that can be disentangled: chance, randomness, probability, frequency, predictability, incompressibility and many more. The intricate connections among them continue to be a subject of much research and interest.

Thomas Icard, PhD ’14, is an associate professor of philosophy. Email him at stanford.magazine@stanford.edu.

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