a few weeks ago, i discovered the works of james thurber, and one book that particularly piqued my interest was "fables for our time and famous poems illustrated." this book merges classic fables with everyday humor, infusing his unique twists that highlight the absurdity of modern life. while all of the fables are quite intriguing, one fable, in particular, caught my attention and made me reflect on my own decision-making abilities. this specific fable is called "the tortoise and the hare."
thurber's twist on the old story is that the tortoise, having pored over the literary record and found no account of a hare ever beating a tortoise, takes this as fact and challenges a hare to a race himself. it does not go well for him. he is not merely beaten; he is humiliated. thurber's real target isn't the hare's speed — it's the tortoise's reasoning.
the tortoise is probably aware of bayes' theorem, like everyone else, but he behaves as if the theorem doesn't exist. i have a tendency to do that as well. his entire case rests on a single data point: one legendary race, retold for centuries, in which a tortoise won. he treats that anecdote not as weak evidence to be weighed against everything else he might reasonably believe about the relative speed of tortoises and hares, but as a settled law of nature — a posterior probability of approximately 1, built on a sample size of one. famous bayes' theorem:
$$ P(A|B) \propto P(B|A) \cdot P(A) $$a properly bayesian tortoise would treat "a tortoise won once, in a story" as thin evidence at best — especially given the obvious confound baked into the original tale: that hare famously stopped to nap. a single anomalous result, with a known confounding factor, shouldn't collapse anyone's uncertainty down to zero. the tortoise's mistake isn't ignoring evidence or overreacting to it; it's mistaking a single old anecdote for a law, which is really a failure of induction.