If they were to invest the seaport of Syracuse, the Athenians had to build a wall that would surround it on the landward side. They were on the point of accomplishing this, when the Spartan Gylippus arrived with his forces just in time to interfere with the work, so effectively that the Syracusans were able to push their counter-wall past the Athenian line. Thus investment became impossible, and the task of the Athenians so much greater that it was to prove beyond their power. A dramatic moment, fate in the balance, “on a razor’s edge,” in Homeric phrase! —perhaps magnified for effect by the historian, in service to human vanity, which plumes itself on decisive action in crisis. παρὰ τοσοῦτον μὲν αἱ Συράκουσαι ἦλθον κινδύνου, comments Thucydides (7.2): So near to danger did Syracuse come, within so little distance of it, his expression fitting the narrowness of wall and time. He had used it once before (3.49), of the port of Mytilene, that one successfully walled in (3.18) and besieged by the Athenians but likewise saved by timely arrival, of word from Athens that the remaining townsfolk should be spared (a countermand anticipating the counter-wall).

Mytilene fell because the Spartans were slow in coming to its relief (3.29). Celerity is a theme of the history, without a Caesar to embody it. Thucydides himself was to come in all haste against Brasidas, soon enough to save Eion, yet too late for Amphipolis (4.104, 4.106); so his countrymen would exile him, no doubt for tardiness (5.26). But to return to Mytilene: the Spartan commander Salaethus, found in the city after its capitulation and sent to Athens, tried (in vain) to purchase his life by offering to have his people lift the siege of Plataea, a little city allied with Athens and glorious in the Persian wars, now walled in by enemies (2.78)—walled in at last, because the ingenuity and enterprise of its inhabitants (perhaps assisted by weather) had defeated every attempt to capture it (2.75–77). By their thwarting of the Peloponnesian siege engines, the Plataeans bring to mind the great Syracusan of two centuries later, Archimedes, against whose engineering Roman might was as nothing. Like him, they had an answer to everything, preserving their town by quick wit put into practice, when no speedy Athenian rescue could be hoped for. Practical wisdom may be another theme.

Wonderful as the Plataeans’ defense of their town was, still more prodigious was the escape from it of a large party in the face of the besiegers. Thucydides lingers over the episode (3.20–24), a small one in the midst of a great war, recounted in all detail; he must have interviewed members of the party, and his admiration for their achievement is manifest. Their first step towards escape was in a way the most remarkable. Here it is, in Hobbesian style.

They made them ladders, fit for the height of the enemies wall; the wall they measured by the lays of brick, on the part toward the town, where it was not plaistered over; and divers men at once numbered the lays of brick, whereof though some missed, yet the greatest part took the reckoning just; especially, numbering them often, and at no great distance, but where they might easily see the part to which their ladders were to be applied; and so by guess of the thickness of one brick took the measure of their ladders.

There were two unknowns. The second of these, the thickness of the brick, they somehow arrived at εἰκάσαντες—“by guess,” as Hobbes translates it, but I suspect the precise sense is “inferring from comparison.” Mere guessing wouldn’t have done, since exactness was important, inasmuch as any error in the estimate of thickness would be multiplied by the number of layers of brick. I imagine that the Peloponnesians, rather than manufacturing the brick themselves, purchased it locally, from a brickyard in the vicinity of the town. That brickyard would have produced only a few standard sizes of brick, to match those already in use in Plataea among other places; so the Plataeans had only to choose the right one among those, which was not difficult. —Later: This conjecture is doubtful, since at 2.78 Thucydides says that the Peloponnesians got, or made, their bricks from the ditch they dug within and without their wall of circumvallation. Still, there may have been standard sizes in wide use. But perhaps it is more likely that the Plataeans simply managed to procure a sample.

Now consider their determination of the first unknown, the number of layers of brick. The experiment of counting the layers produces values which have a certain probability distribution, some being more likely than others. Underestimation and overestimation by any given amount are equally likely, I suppose, so the distribution is symmetrical about its mean, which is the true value of the number of layers; indeed, since errors are due to a multitude of small factors the distribution is no doubt approximately normal (bell-shaped), with the true value in the middle. The Plataeans take a sample of the experimental outcomes, counting diligently in the knowledge that their own lives, or (if they are not themselves of the party) the lives of their dear ones, depend on accuracy. Usually they hit the true value. This most frequent outcome is almost certainly the same one as would be selected by taking the mean of their sample (more precisely, the whole number closest to the mean). Then in accepting the most frequent outcome as the mean of the distribution, the Plataeans are also accepting the sample mean; and the law of large numbers does promise that the mean of a distribution is well estimated by the mean of a large sample (cf. my last post). Their common-sense procedure appears theoretically sound. But the main point is simply their reliance on many counts by many counters. No Great Man was entrusted with the task, for they understood that multitude alone dissolves bias. This is true statistical thinking, in the winter of 428–27 BCE. Is an earlier instance anywhere recorded?