 Importantly, Bertrand’s paradox applies quite generally. Whether we’re interested in the size of a cube, the distance by which a horse will win, or any other parameter measured in real numbers, we can always redescribe the space of possible outcomes so that the probabilities assigned by the PoI come out differently. Even an infinitely fine division of the space of possibilities doesn’t fix the problem: the probabilities assigned by the PoI still depend on how we describe the space of possibilities.