Aristotle, it seems, was troubled by mules. Here he is, explaining things to his students at the Lyceum. Maybe he was telling them how it is that a mule cannot be.
In his On the Generation of Animals he wrote at some length in speculation on the mystery of the mule. English has a nice double meaning to the word “contrary,” which applies straight-on to the offspring of cross-mated horses and asses. Aristotle tried to work out the “contrary nature” of the mule. The difficulty for him was not that a mule is contrary, which it certainly is, but the fact that, being generated by a horse and an ass, yet being neither one, it is contrary to nature. [21st Century note: The offspring of a mare horse and an stallion ass is a mule; the progeny of a mare ass and a stallion horse is called a hinny. Mules are by far more common than hinnies, though it can be difficult to tell a hinny just by looking.]
It wasn’t only an interesting puzzle for Aristotle. It went to his philosophy of being, in which animals of every kind have an essential nature. Their nature is passed on to their offspring. Dogs produce dogs, lions lions, horses horses, and asses asses. But, oh dear, horses mated to asses produce these odd things that, in their turn, produce nothing at all. [21st Century note: A few reported cases of hinny reproduction exist. They all seem to have something unverified about them. It may be that an occasional mating has produced a second generation hybrid foal, but I am not going to think about what you would call it!]
Aristotle considered several possible explanations for the existence of mules, from the density of the combined seeds of horses and asses, to the relative temperatures of horses (warm) and asses (cold), to the opinion that
the genital passages of mules are spoiled in the mother’s uterus because the animals, from the first, are not produced from parents of the same kind.
Aristotle did not resolve his concern about whether, or how, mules are among us. He could not have imagined the truth. Equus caballus, the horse, has 64 chromosomes; Equus asinus, the ass or donkey, has 62. The mule and hinny come out with 63 (no wonder mules are odd!). Any deviation from the expected chromosome count results in an incomplete, or imperfect, organism. The mule is sterile because it doesn’t match the map for a complete animal.
Please don’t try to explain this to William. He views himself as perfectly complete.