I am traveling today and will be out of contact. And so the briefest introduction to coincidences via the examination of how one classic writer viewed them. We’ll explore this topic in more depth another time.
Plutarch in his life of Sertorius opens with a discourse on the probability of seemingly rare events:
It is perhaps not to be wondered at, since fortune is ever changing her course and time is infinite, that the same incidents should occur many times, spontaneously. For, if the multitude of elements is unlimited, fortune has in the abundance of her material and ample provider of coincidences; and if, on the other hand, there is a limited number of elements from which events are interwoven, the same things must happen many times, being brought to pass by the same agencies.
A better, non-mathematical introduction to the law of large (and small!) numbers you will not find. But how does probability figure in coincidence? Plutarch continues:
Now, there are some who delight to collect, from reading and hearsay, such accidental happenings as look like works of calculation and forethought. They note, for example, that there were two celebrated persons called Attis, one a Syrian, the other an Arcadian, and that both were killed by a wild boar; that there were two Actaeons, one of whom was torn in pieces by his dogs, the other by his lovers; that there were two Scipios, by one of whom the Carthaginians were conquered in an earlier war, and by the other, in a later war, were destroyed root and branch; that Ilium was taken by Heracles on account of the horses of Laomedon, by Agamemnon by means of what is called the wooden horse, and a third time by Charidemus, because a horse fell in the gateway and prevented the Ilians from closing the gate quickly enough; that there are two cities which have the same name as the most fragrant plants, Ios and Smyrna, in one of which the poet Homer is said to have been born, and in the other to have died.
Plutarch defined after-the-fact confluence of events that are in some way interesting are necessary for any happenstance to be labeled a coincidence. More:
I will therefore make this addition to their collection. The most warlike of generals, and those who achieved most by a mixture of craft and ability, have been one-eyed men,—Philip, Antigonus, Hannibal, and the subject of this Life, Sertorius; of whom one might say that he was more continent with women than Philip, more faithful to his friends than Antigonus, more merciful towards his enemies than Hannibal, and inferior to none of them in understanding, though in fortune to them all. Fortune he ever found harder to deal with than his open foes, and yet he made himself equal to the experience of Metellus, the daring of Pompey, the fortune of Sulla, and the power in Rome, though he was an exile and a stranger in command of Barbarians.
Antigonus, incidentally, one of Alexander’s lieutenants and later a king, was aptly nicknamed Monophthalmus. And to Plutarch’s list of one-eyed men of war we can add Nelson and Xiahou Dun, a general who, during the Han Dynasty, pierced and plucked out one of his eyes with an arrow and ate it on the line of battle to instill terror in his enemies.
Is it a coincidence that some of the most effective generals had only one eye, or does possessing only one eye confer martial skill? To the later we can definitely say no: Alexander had two working ocular sockets, as did Caesar, Napoleon, Patton, and so forth.
But is that enough? Should we compare the ratio of one-eyed top military commanders with that of the ratio among the best dry cleaners, Oscar-winning movie directors, or grand chess masters?
This exercise seems absurd since we can find no reason why lack of binocular vision would confer extraordinary war-making skill; nor skill of any kind, for that matter (except in looking like a pirate).
So one-eyed generals are a coincidence. But that still doesn’t tell us why we find the list of interest.
To be a coincidence for Plutarch, an event must be curious, it must be able to be converted to a clever anecdote, it must have a rich back story. The probability of the confluence of events must, at least at first glance, appear shockingly low, even to the point of impossibility.
So much Plutarch knew—and it he knew it all without the benefit of our modern mathematical apparatus. However, that math can help us understand the phenomena better—which is something we’ll leave for another day.