Having exchanged correspondence with F. Zarnowski made me think about the ancient pentathlon, which had been a first occasion for an exchange of emails.
It turns out that nobody knows how the winner of the pentathlon was determined and my old post on ancient pentathlon (motivated by my reading the excellent monograph of Zarnowski) addressed that question. I had proposed there a possible solution but having recently given more thought to the matter I am not quite satisfied with it. But let's start from the beginning.
The consensus is that the first three events of the pentathlon are discus throw, long jump, and javelin throw (with perhaps a permutation of discus and javelin), the remaining two being the stadium race and wrestling, in that order.
As I explain in my old post
At the issue of the three events (to which everybody participates) there exist three possibilities. Either somebody has won all three events, in which case he is the winner of the pentathlon, or one athlete has won two events and some other one event, or, finally, three athletes have won one event each. In the second case the two winners proceed to the stadium race. If the one with two victories wins again he is the champion.... If the race results in a situation where the two athletes have two victories each they proceed naturally to the wrestling which gives the final winner. The difficulty is when after the three events we have three athletes with one victory each.
Notice that when somebody has won either three or two of the first three events there is a winner to the pentathlon. On the other hand the historians point out that there is a relative paucity of known pentathlon winners, which probably means that in many cases nobody emerged victorious from the event. One possibility would be for the event to be stopped after three events if the latter were won by three different athletes. But I find this rather absurd, since, with two remaining events, there is always the possibility for somebody to obtain three victories and carry the pentathlon.
So the athletes proceed to the stadium race after which one athlete has two victories, the remaining two just one. At this point Zarnowski and myself diverge. Zarnowski proposes that the second and third of this race run again and the winner of this classification race meets the initial winner for the wrestling competition. A variant of this could be that the second and third of the stadium race wrestle each other and the winner faces the winner of the stadium in one last bout.
There is a difficulty with this scheme. The winner of the "repêchage" has won a "second-rate" victory. If he prevails over the winner of the stadium how can he be the pentathlon winner? On the other hand, if there is no possibility for him to obtain the pentathlon victory even if he beats the stadium winner in wrestling, then the whole repêchage idea is absurd: why should they exert themselves for nothing?
My initial proposal was that the stadium race served at eliminating one athlete and let the remaining two proceed to the final event which would determine the winner. One drawback of this proposal is that there is always a winner of the pentathlon, which, if we believe the historians, was not always the case (but, be aware that this is a deduction and not an established fact).
After having given more thought to the question I think that there is another possible solution. The athlete who won the stadium must wrestle in turn both athletes who did not win. If he wins the first bout, he has three victories and he is declared winner of the pentathlon. If he loses the first, he wrestles the second contestant. If he loses the second match as well there is no winner of the pentathlon. Facing a fresh opponent after having having fought and lost the first match leaves a small probability for victory. So two successive losses should not be a rare occurrence (and this would explain the scarcity of victors).
Note that with this scheme the two athletes who lost the stadium race can never win the pentathlon. So, what is their motivation to beat the one who won the race in wrestling? For me, the incentive is clear. If they win in wrestling then there is no overall pentathlon winner and nobody has lost. In fact all three of them have two victories and they are in a kind of ex aequo. The honour is safe. Although the prime objective is to win, the second one is not to lose.
I am aware that this is a complicated situation and perhaps to some reader my proposal will sound not quite satisfactory. Still, I find this last solution slightly more reasonable than the one I proposed in my old post.
Ah, if only the ancient writers had taken the pain to explain the rules of the pentathlon.
It turns out that nobody knows how the winner of the pentathlon was determined and my old post on ancient pentathlon (motivated by my reading the excellent monograph of Zarnowski) addressed that question. I had proposed there a possible solution but having recently given more thought to the matter I am not quite satisfied with it. But let's start from the beginning.
The consensus is that the first three events of the pentathlon are discus throw, long jump, and javelin throw (with perhaps a permutation of discus and javelin), the remaining two being the stadium race and wrestling, in that order.
As I explain in my old post
At the issue of the three events (to which everybody participates) there exist three possibilities. Either somebody has won all three events, in which case he is the winner of the pentathlon, or one athlete has won two events and some other one event, or, finally, three athletes have won one event each. In the second case the two winners proceed to the stadium race. If the one with two victories wins again he is the champion.... If the race results in a situation where the two athletes have two victories each they proceed naturally to the wrestling which gives the final winner. The difficulty is when after the three events we have three athletes with one victory each.
A panathenaic amphora depicting pentathletes
Notice that when somebody has won either three or two of the first three events there is a winner to the pentathlon. On the other hand the historians point out that there is a relative paucity of known pentathlon winners, which probably means that in many cases nobody emerged victorious from the event. One possibility would be for the event to be stopped after three events if the latter were won by three different athletes. But I find this rather absurd, since, with two remaining events, there is always the possibility for somebody to obtain three victories and carry the pentathlon.
So the athletes proceed to the stadium race after which one athlete has two victories, the remaining two just one. At this point Zarnowski and myself diverge. Zarnowski proposes that the second and third of this race run again and the winner of this classification race meets the initial winner for the wrestling competition. A variant of this could be that the second and third of the stadium race wrestle each other and the winner faces the winner of the stadium in one last bout.
There is a difficulty with this scheme. The winner of the "repêchage" has won a "second-rate" victory. If he prevails over the winner of the stadium how can he be the pentathlon winner? On the other hand, if there is no possibility for him to obtain the pentathlon victory even if he beats the stadium winner in wrestling, then the whole repêchage idea is absurd: why should they exert themselves for nothing?
My initial proposal was that the stadium race served at eliminating one athlete and let the remaining two proceed to the final event which would determine the winner. One drawback of this proposal is that there is always a winner of the pentathlon, which, if we believe the historians, was not always the case (but, be aware that this is a deduction and not an established fact).
After having given more thought to the question I think that there is another possible solution. The athlete who won the stadium must wrestle in turn both athletes who did not win. If he wins the first bout, he has three victories and he is declared winner of the pentathlon. If he loses the first, he wrestles the second contestant. If he loses the second match as well there is no winner of the pentathlon. Facing a fresh opponent after having having fought and lost the first match leaves a small probability for victory. So two successive losses should not be a rare occurrence (and this would explain the scarcity of victors).
Note that with this scheme the two athletes who lost the stadium race can never win the pentathlon. So, what is their motivation to beat the one who won the race in wrestling? For me, the incentive is clear. If they win in wrestling then there is no overall pentathlon winner and nobody has lost. In fact all three of them have two victories and they are in a kind of ex aequo. The honour is safe. Although the prime objective is to win, the second one is not to lose.
I am aware that this is a complicated situation and perhaps to some reader my proposal will sound not quite satisfactory. Still, I find this last solution slightly more reasonable than the one I proposed in my old post.
Ah, if only the ancient writers had taken the pain to explain the rules of the pentathlon.
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