Explain SMBC — the wiki for Saturday Morning Breakfast Cereal

probability

2022-12-02 View on smbc-comics.com → 1 revision
probability
Votey panel for probability
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Explanation

This comic tackles a classic problem in probability theory through an increasingly frustrated math professor. The setup is a variant of the Bertrand paradox or a geometric probability problem: given a square with side length between 0 and 2, you don't know the length but can narrow it down. For a "reasonable" distribution, you can say the side is less than 2 units. You'd also like to know the area, and since the side is between 0 and 2, the area must be between 0 and 4 -- but the probability distributions for side length and area are incompatible if you assume uniform distributions for both.

The professor, growing angry, asks "SO WHICH IS IT, MOTHER F***ERS?" and then "WHICH IS IT?" -- expressing the genuine mathematical frustration of the Bertrand paradox, where different ways of assigning "equal probability" to a geometric problem yield different answers.

A student responds: "I thought philosophy of probability would be the easiest. I'm an art student. And now I'm not even sure reality is real." The professor's final reply -- "Reality? That's just a convenient assumption for calculations" -- is both a joke and a surprisingly accurate summary of certain interpretations of probability theory (particularly subjective Bayesian views). The comic highlights how seemingly simple probability questions can lead to deep philosophical confusion.

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