Abstract
As the Venus tablet shows, omens were the original focal-point of the ancient Mesopotamian astronomers. These omens are collected in the so-called “Enuma Anu Enlil” tablets,1 a series of 70 tablets containing thousands of omens dating back to the second millennium BC. For instance: “If Jupiter [rises] in the path of the [the god Enlil’s] stars, the king of Akkad will become strong and [overthrow] his enemies in all lands in battle.”2. Though many are celestial omens, others record meteorological phenomena – a not insignificant point, as we shall see.
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Notes
- 1.
The name means “when Anu and Enlil …,” from the opening words of the first tablet. Anu and Enlil were Sumerian gods.
- 2.
N. M. Swerdlow, Babylonian Theory of the Planets. Princeton, NJ: Princeton University Press, 1998, p. 94.
- 3.
Shakespeare, Sonnet 15.
- 4.
Daniel 5:7.
- 5.
George Sarton, A History of Science, volume 1: Ancient Science Through the Golden Age of Greece. New York: W.W. Norton, 1970, p. 64.
- 6.
Ibid., p. 63.
- 7.
According to Neugebauer, The Exact Sciences in Antiquity, p. 101: “Around 700 BC, under the Assyrian empire, we meet with systematic observational reports of astronomers to the court. In these reports no clear distinction is yet made between astronomical and meteorological phenomena. Clouds and halos are on equal footing with eclipses. Nevertheless, it had been already recognized that solar eclipses are only possible at the end of a month (new moon), lunar eclipses at the middle… We should recall here Ptolemy’s statement that eclipse records were available to him from the time of Nabonassar (747 BC) onwards.”
- 8.
Swerdlow, Babylonian Theory of the Planets, p. 56.
- 9.
Bettany Hughes, Helen of Troy: goddess, princess, whore. New York: Alfred A. Knopf, 2005, p. 8.
- 10.
Iliad, XXI, l. 463.
- 11.
Others, however, claim that Parmenides was the first to do so.
- 12.
J. E. Lendon, Soldiers and Ghosts: a history of battle in classical antiquity. New Haven and London: Yale University Press, 2005, p. 24.
- 13.
Swerdlow, Babylonian Theory of the Planets, pp. 181–182.
- 14.
Even less was there any similarity to the great men of the Hebrew culture developing in Palestine which, though closer to Ionia than to Egypt or Mesopotamia was – as George Sarton points out – “as foreign to the Greeks as either of those, if not more so.” Sarton adds in A History of Science: ancient Greece through the Golden Age of Greece (New York: W.W. Norton, 1970), vol. 1, p. 163: “By the end of the seventh century many of the prophetic books of our Bible had already been composed: Amos, Hosea, Micah, Isaiah, Hezekiah, Zephaniah, Jeremiah, Nahum, Habakuk; the Pentateuch (or Torah), and the books of Samuel were already completed…. Let us … consider now only the Prophets and the Torah, and compare them with the Homeric writings. The difference between the respective languages, Hebrew and Greek, is small as compared with that between ways of thought. The Hebrew prophet was a seer; the rhapsodist, a poet and storyteller. The latter referred sometimes to the gods and the heroes just as he referred to ordinary mortals, but the former spoke in God’s name, in the name of the one God and of eternal justice. The contrast is so great that communication between the Hebrews and the Ionians was probably reduced to a minimum.” One can understand for this why the roots of modern science are to be found among the Ionian Greeks and not among the Hebrews who remained scientifically illiterate. The amount of astronomical knowledge in the Bible, even for the time, is minuscule.
- 15.
Richard E. Nisbett, The Geography of Thought. New York: Simon and Schuster, 2003, p. 31.
- 16.
See: E. R. Dodds, The Greeks and the Irrational. Berkeley: University of California Press, 1951.
- 17.
In these ideas of the sixth century BC, one recognizes vestiges of very much older ideas about man’s state, including the “ecstatic journey” or vision-quest by means of which one might receive an understanding of the mystery of destiny and of existence after death. Those ideas had been current among the Shamans; for all we know they may have existed, in more or less developed form, in the Upper Paleolithic at the time of the cave painter. Eliade, in Shamanism: archaic techniques of ecstasy, p. 394, writes of the consistency of themes from the Shamans to the post-Pythagorean Plato: “The enormous gap that separates a shaman’s ecstasy from Plato’s contemplation, all the difference deepened by history and culture, changes nothing in this gaining consciousness of ultimate reality; it is through ecstasy that man fully realizes his situation in the world and his final destiny.”
- 18.
For a fascinating discussion, see: Edward Rothstein, Emblems of Mind: the inner life of music and mathematics. Chicago: University of Chicago Press, 1995.
- 19.
Such a person is the British savant Daniel Tammet. According to an interview by Richard Johnson in The Guardian, February 12, 2005: “Daniel Tammet is talking. As he talks, he studies my shirt and counts the stitches. Ever since the age of three, when he suffered an epileptic fit, Tammet has been obsessed with counting. Now he is 26, and a mathematical genius who can figure out cube roots quicker than a calculator and recall pi to 22514 decimal places. He also happens to be autistic, which is why he can’t drive a car, wire a plug, or tell right from left…”
Tammet is calculating 377 multiplied by 795. Actually, he isn’t “calculating”: there is nothing conscious about what he is doing. He arrives at his answer instantly. Since his epileptic fit, he has been able to see numbers as shapes, colors and textures. The number two, for instance, is a motion, and five is a clap of thunder. “When I multiply numbers together, I see two shapes. The image starts to change and evolve, and a third shape emerges. That’s the answer.”
- 20.
The date of the battle was September 11, 490 BC which was the 17th day of the lunar month in Attica, according to N.G.L. Hammond in The Cambridge Ancient History, vol. IV (Persia, Greece and the Western Mediterranean c. 525 to 479), ed. John Boardman, N. G. L. Hammond, D. M. Lewis, and M. Ostwald, Cambridge: Cambridge University Press, 1988, p. 40. Hammond’s calculations were made based on data provided to him by the Astronomer Royal, Sir Richard Woolley. Hammond notes that “the moon-goddess held an important place in the religious associations of the battle. The commemorative coins struck from 490 BC onwards showed a waning moon behind the owl of Athena…. Seltman and others have thought the waning moon was added to give the date of the battle…. It is more likely … that the waning phase, shown on the coins, was a particular factor in the victory,” perhaps by revealing that Persian cavalry, which had left its position, had not yet returned and allowing Militiades, the commander of the Greeks, “to thin his center, pack the wings and make its length equal to that of the Persian infantry line which was known could be attacked at speed across no-man’s land before the cavalry could intervene.”
- 21.
George Steiner, “A Death of Kings”; in: George Steiner: A Reader, pp. 172–173.
- 22.
That discovery follows immediately from the Pythagorean theorem about triangles, a discovery which so elated Pythagoras that he is said to have sacrificed a pair of oxen in thanksgiving to the gods. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the lengths of the two sides. But the right-angled triangle in which the sides are each 1 unit in length, the hypotenuse is the square root of 2, a surd. In other words, it cannot be expressed as the ratio of two whole numbers, or is ir-rational. A simple proof, which is essentially that given in Euclid, Book X, is as follows. Let us suppose each side 1 unit long; then how long is the hypotenuse? Let us suppose its length is m/n units. Then m2/n2 = 2. If m and n have a common factor, divide it out, then either m or n must be odd. Now m2 = 2n2, therefore m2 is even, therefore n is odd. Suppose m = 2p. Then 4 p2 = 2n2, therefore n2 = 2p2, and therefore n is even, contra hyp. Therefore no fraction m/n will measure the hypotenuse.
- 23.
Jean-Pierre Changeux and Alain Connes. Conversations on Mind, Matter, and Mathematics. Princeton, NJ: Princeton University Press, 1995, p. 4.
- 24.
F.M. Cornford, Plato’s Cosmology. New York: Harcourt, Brace & Co., 1937, p. 28.
- 25.
Arthur Hugh Clough, Introduction to Plutarch, Lives of the Noble Grecians and Romans (trans. John Dryden and revised by Arthur Hugh Clough), New York: Modern Library, n.d., p. xxvii.
- 26.
Plutarch, “Pericles,” in: The Lives of the Noble Grecians and Romans, translated by John Dryden and revised by Arthur Hugh Clough. New York: Modern Library, n.d., p. 183.
- 27.
Steiner, “A Death of Kings,” p. 173.
- 28.
Albert Einstein, Foreword to Galileo Galilei, Dialogue Concerning the Two Chief World Systems, translated, with revised notes, by Stillman Drake. Berkeley: University of California Press, 2nd revised edition, 1967, p. xv.
- 29.
What is reported of Heracleides is not very flattering. Bertrand Russell says, in History of Western Philosophy, p. 223: “he must have been a great man, but was not as much respected as one would expect; he is described as a fat dandy.”
- 30.
Arthur A. Hoag, “Aristarchos Revisited,” Griffith Observer, 54 (1990):10–18.
- 31.
E. R. Dodds, The Greeks and the Irrational. Berkeley: University of California Press, 1951, p. 189. Anaxagoras had been prosecuted because he dared reduce the celestial divinities into stones and earth. He escaped the death sentence by choosing exile. Socrates was prosecuted “…for not believing in the gods of the city-state, but in other new divinities.” We learn from Plato’s Apology that at his trial Socrates refused to be associated with the astronomers, and disclaimed any knowledge of astronomy; in contrast to the astronomers, of whom he says “those who hear them think that men who investigate these matters do not even believe in gods.” Socrates claimed to the contrary that he does “… believe that the sun and moon are gods, like all the other people do.” He was prosecuted anyway, and chose to drink the hemlock rather than accept exile. Xenophon (Memorabilia, IV, 7, 6f) provides even more detail about Socrates’ views regarding astronomy. “With regard to the phenomena of the heavens, he disapproved strongly of attempts to work out the machinery by which the god operates them; he believed that their secrets could not be discovered by man, and that any attempt to search out what the gods had not chosen to reveal must be displeasing to them. He said that he who meddles with these matters runs the risk of losing his sanity as completely as Anaxagoras, who took an insane pride in his explanation of the divine machinery… When [Anaxagoras] pronounced the sun to be a red-hot stone, he ignored the fact that a stone in fire neither glows nor lasts long, whereas the sun-god shines with unequalled brilliance forever.”
- 32.
Plutarch, “Nicias,” 23, 2–3. Quoted in: Ioannis Liritzis and Alexandra Coucouzeli, “Ancient Greek helicoentric views hidden from prevailing beliefs,” Journal of Astronomical History and Heritage, 11, 1 (2008), 39–49:43.
- 33.
Plutarch, “On the Face in the Orb of the Moon,” 6, 923a.
- 34.
E. A. Burtt, The Metaphysical Foundations of Modern Science. Garden City, NY: Doubleday, 1954, p. 37.
- 35.
Pannekoek, History of Astronomy, p. 123.
- 36.
Jo Marchant, lecture to the Royal Institution in London, quoted in: “Antikythera clockwork computer may be even older than thought,” Guardian science blog, July 29, 2009.
- 37.
An excellent account is: Jo Marchant, Decoding the Heavens: the mystery of the world’s first computer. London: William Heinemann, 2009.
- 38.
See: M.T. Wright. Epicyclic gearing and the Antikythera Mechanism, Part I. Antiquarian Horology, 27 (2003), 270–279 and Part II, 29 (2005), 52–63. Also: M.T. Wright. The Antikythera Mechanism and the early history of the moon-phase display. Antiquarian Horology, 29 (2006), 319–329. The Antikythera mechanism was used to calculate the 4-year cycle of the Olympiads and its associated pan-Hellenic games and contains a dial, arranged as a five-turn spiral, that is a 19-year calendar based on the Metonic cycle, while the lower dial is a Saros eclipse-prediction dial, arranged as a four-turn spiral of 223 lunar months, with glyphs indicating eclipse predictions. See: T. Freeth, A. Jones, J.M. Steele and Y. Bitsakis, Calendars with Olympiad display and eclipse prediction on the Antikythera Mechanism. Nature, 454, 7204 (July 31, 2008), 614–617.
- 39.
Owen Gingerich to William Sheehan; personal communication, December 26, 2006.
- 40.
Owen Gingerich, The Eye of Heaven. New York: American Institute of Physics, 1993, p. 55.
- 41.
In a conversation with Janos Plesch, a Hungarian doctor who had been Einstein’s personal physician in Berlin until 1933 and maintained a friendship with him over the years, a few days before Einstein’s death. Quoted in: Janos Plesch and Peter H. Plesch, “Some reminiscences of Albert Einstein,” Notes and Records of the Royal Society of London, 49:2 (1995), 303–328:317.
- 42.
Quoted in Peter Woit, Not even Wrong: the failure of string theory and the search for unity in physical law. New York: Basic Books, 2006, p. 262.
- 43.
Woit, Not even Wrong, p. 262.
- 44.
Quoted in Gingerich, The Eye of Heaven, p. 4.
- 45.
Pannekoek, History of Astronomy, p. 161.
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Sheehan, W. (2010). Pure Ambrosia. In: A Passion for the Planets. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5971-3_5
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