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Concerning the machines of Archimedes

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Below is an excerpt from Plutarch’s Life of Marcellus (the famous Dryden translation) concerning the mechanical work of Archimedes in devising war machines for the defense of Syracuse.  What is notable to me is the mention of Plato’s indignation at the application of mathematics to practical ends.

These machines he had designed and contrived, not as matters of any importance, but as mere amusements in geometry; in compliance with King Hiero’s desire and request, some little time before, that he should reduce to practice some part of his admirable speculation in science, and by accommodating the theoretic truth to sensation and ordinary use, bring it more within the appreciation of the people in general. Eudoxus and Archytas had been the first originators of this far-famed and highly-prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as means of sustaining experimentally, to the satisfaction of the senses, conclusions too intricate for proof by words and diagrams. As, for example, to solve the problem, so often required in constructing geometrical figures, given the two extremes, to find the two mean lines of a proportion, both these mathematicians had recourse to the aid of instruments, adapting to their purpose certain curves and sections of lines. But what with Plato’s indignation at it, and his invectives against it as the mere corruption and annihilation of the one good of geometry, which was thus shamefully turning its back upon the unembodied objects of pure intelligence to recur to sensation, and to ask help (not to be obtained without base supervisions and depravation) from matter; so it was that mechanics came to be separated from geometry, and, repudiated and neglected by philosophers, took its place as a military art. Archimedes, however, in writing to King Hiero, whose friend and near relation he was, had stated that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king’s arsenal, which could not be drawn out of the dock without great labour and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavour, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea. The king, astonished at this, and convinced of the power of the art, prevailed upon Archimedes to make him engines accommodated to all the purposes, offensive and defensive, of a siege. These the king himself never made use of, because he spent almost all his life in a profound quiet and the highest affluence. But the apparatus was, in most opportune time, ready at hand for the Syracusans, and with it also the engineer himself.

The manner of the death of Archimedes is quite famous, and is described by Plutarch (Marcellus):

But nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through. Others write that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate that, as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honoured them with signal favours.

Written by uncudh

November 8, 2009 at 3:00 pm

Posted in history, math

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The effects of slavery on science

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Another interesting notion from Peter Green’s The Hellenistic Age (Ch. 4):

Slaves were thus regarded as at once essential and a permanent threat.  The solution, a simple one, was to keep them fully occupied […].  All power was to be muscle-power.  The effect on Hellenistic science was striking.  It has often been pointed out that ancient inventors were familiar with steam power (indeed, produced a model) and could make effective pistons yet never combined their knowledge to build a steam-engine.  Water-driven mills were known but not used.  The same applied to the compound pulley, which enormously reduced the energy needed to shift a given mass.  The reason should now be clear.  Any device that left the servile labor force with spare energy was seen as a direct stimulus to revolution.

Written by uncudh

May 7, 2009 at 1:51 am

The Ten Thousand at Nineveh

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After the death of Prince Cyrus during the Battle of Cunaxa (401 BC, near Babylon), the Greek army of the Ten Thousand found themselves trapped on the eastern side of the Euphrates river (i.e., between the Euphrates and the Tigris).  The Persian army was in the vicinity and its presence prevented the Greeks from re-crossing the Euphrates in order to make their way back towards Greece.  The Greeks were therefore compelled to cross over to the eastern side of the Tigris and travel northward, following the Tigris backwards towards its sources in northern Mesopotamia, hoping to eventually pass through Armenia and make their way to the Black Sea.  During the course of this northward travel along the Tigris, the Greeks passed through the ruins of some of the once great cities of the ancient Assyrians.  Xenophon describes passing through the ruins of the Assyrian capital of Nineveh as follows (Anabasis III.4, Loeb Classical Library edition):

From this place they marched one stage, six parasangs, to a great stronghold, deserted and lying beside a city.  The name of this city was Mespila, and it was once inhabited by the Medes.  The foundation of its wall was made of polished stone full of shells, and was fifty feet in breadth and fifty in height.  Upon this foundation was built a wall of brick, fifty feet in breadth and a hundred in height; and the circuit of the wall was six parasangs.  Here, as the story goes, Medea, the king’s wife, took refuge at the time when the Medes were deprived of their empire by the Persians.  To this city also the king of the Persians laid siege, but he was unable to capture it either by length of siege or by storm; Zeus, however, rendered the inhabitants thunderstruck, and thus the city was taken.

In a footnote to this passage in the LCL edition, the translator points out that

[t]he ruins which Xenophon saw here were those of Nineveh, the famous capital of the Assyrian Empire.  It is revealing that he can characterize this great Assyrian city (as well as Kalhu above) with the casual and misleading statement that “it was once inhabited by the Medes.”  In fact, the capture of Nineveh by the Medes (c. 600) was the precise event which closed the important period of its history, and it remained under the control of the Medes only during the succeeding half-century, i.e. until the Median Empire was in its turn overthrown by the Persians (549).

Written by uncudh

March 22, 2009 at 10:55 pm

The greatest generals of antiquity

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The following anecdote concerning the meeting of Hannibal of Carthage and the elder Scipio Africanus at Ephesus some years after their famous campaigns against each other in the Second Punic War is well-known. This version of the story is from Appian’s History of the Syrian Wars.

It is said that at one of their meetings in the gymnasium Scipio and Hannibal had a conversation on the subject of generalship, in the presence of a number of bystanders, and that Scipio asked Hannibal whom he considered the greatest general, to which the latter replied, “Alexander of Macedonia.”

To this Scipio assented since he also yielded the first place to Alexander. Then he asked Hannibal whom he placed next, and he replied, “Pyrrhus of Epirus,” because he considered boldness the first qualification of a general; “for it would not be possible,” he said, “to find two kings more enterprising than these.”

Scipio was rather nettled by this, but nevertheless he asked Hannibal to whom he would give the third place, expecting that at least the third would be assigned to him; but Hannibal replied, “To myself; for when I was a young man I conquered Spain and crossed the Alps with an army, the first after Hercules. I invaded Italy and struck terror into all of you, laid waste 400 of your towns, and often put your city in extreme peril, all this time receiving neither money nor reinforcements from Carthage.”

As Scipio saw that he was likely to prolong his self-laudation he said, laughing, “Where would you place yourself, Hannibal, if you had not been defeated by me?” Hannibal, now perceiving his jealousy, replied, “In that case I should have put myself before Alexander.” Thus Hannibal continued his self-laudation, but flattered Scipio in a delicate manner by suggesting that he had conquered one who was the superior of Alexander.

Written by uncudh

January 27, 2009 at 4:42 pm

Posted in history

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I am An-ti-‘u-ku-us

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The following is an inscription, originally in Akkadian, from the reign of Antiochus I Soter, second king of the Seleucid Empire (see Nicholas Ostler, Empires of the Word).  The incongruity of a Greek ruler describing himself in such a way (not to mention in Akkadian!)  is remarkable.

I am An-ti-‘u-ku-us [Antiochus], the great king, the legitimate king, the king of the world, king of E [Babylon], king of all countries, the caretaker of the temples Esagila and Ezida, the first born of Si-lu-uk-ku [Seleucus], Ma-ak-ka-du-na-a-a [Macedonian], king of Babylon.

Written by uncudh

January 25, 2009 at 1:24 am

Posted in history

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