While researching the concept of symmetry, I stumbled upon this: There is a paradox of medieval logic concerning the dilemma of an ass who is placed equidistantly from two piles of food of equal size and quality. A perfectly symmetrical situation. If the behavior of the ass is completely rational, it will have no reason to prefer one pile to the other and therefore cannot reach a decision over which pile to eat first, so it remains in its original position and starves. This dilemma is called "Buridan's ass". The donkey could escape the paradox if it can choose spontaneously. That seems to imply some sort of probability space?