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Aeschylus,Pythagoras, and

Brandon Weislak

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Motivation forResearch

Aeschylus: Poet orPythagorean?

Arguments forAeschylus as aPythagorean

Arguments againstAeschylus as aPythagorean

Conclusion

Number, itsScience, and itsPlace in Society

Pythagoras and thePythagoreans: ACloser Examination

Plato and Pythagoras:The Necessity ofMathematics for theDevelopment of theSoul and Good MoralCharacter

Mathematics: AnEtymology andOverview

Mathematics as theCornerstone ofPlatonic Education

Conclusion

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Aeschylus, Pythagoras, and PlatoA Brief Overview of the Centrality of Mathematics to

Greek Society and Education

Brandon Weislak

February 21, 2008

Brandon Weislak

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Outline

Motivation for Research

Aeschylus: Poet or Pythagorean?Arguments for Aeschylus as a PythagoreanArguments against Aeschylus as a PythagoreanConclusion

Number, its Science, and its Place in SocietyPythagoras and the Pythagoreans: A Closer ExaminationPlato and Pythagoras: The Necessity of Mathematics forthe Development of the Soul and Good Moral CharacterMathematics: An Etymology and OverviewMathematics as the Cornerstone of Platonic Education

Conclusion

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I A curious passage

I In Prometheus’ delineation of the things which he gaveto men, he tells how he found number for man calling itthe, “chiefest of the arts.”1

I Why does Aeschylus have Prometheus make thisdistinction, and why is number the chiefest of thesciences?

1Aeschylus, Prometheus Bound, 459.

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I A curious passage

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I A curious passage

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Aeschylus: Poet or Pythagorean?

I Griffith in his commentary notes that theaforementioned phrase “recalls Pythagorean saying,panton sophotatos ho arithmos (number is the mostlearned of all things).”

I Cicero says, “Aeschylus non poeta solum, sed etiamPythagoreus (Aeschylus was not only a poet, but also aPythagorean).”2

2Cicero, Tusc. Disp., 2.23.

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I Griffith in his commentary notes that theaforementioned phrase “recalls Pythagorean saying,panton sophotatos ho arithmos (number is the mostlearned of all things).”

I Cicero says, “Aeschylus non poeta solum, sed etiamPythagoreus (Aeschylus was not only a poet, but also aPythagorean).”2

2Cicero, Tusc. Disp., 2.23.

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Aeschylus: Poet or Pythagorean?Arguments for Aeschylus as a Pythagorean:

I Thomson not only seats the aforementioned passage inthe tradition of the Pythagoreans, but numerouselements of Orestia as well.

I Bous epi glossei megas (a great ox upon the tongue) isa symbol of the Pythagoreans who advocated silentmeditation3

I Discussion of marrow refers to the soul residing in thecerebral spinal fluid and other Pythagorean doctrinesrelated aging and the spinal marrow4

I Discussion of health refers to the mean, which again isa Pythagorean idea5

I The unwritten incest law in the Eumenides is actually aPythagorean commandment.6

3Aeschylus, The Orestia, ed. George Thomson, Vol. 2, p.12.4Ibid. p.15-17.5Ibid. p.80.6Ibid. p.201.

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Arguments against Aeschylus as a Pythagorean:

I Griffith notes that by Cicero’s time the knowledge ofthe Pythagoreans of the fifth century BC was likelymore limited than our knowledge today.7

I Supposed Pythagorean elements cannot be held to betruly Pythagorean, since those present in Aeschylus arenot unique to the Pythagoreans, e.g. the incest law wasa commonly followed custom

I Also the foremost place of number is characteristic ofits utility to man, not its religious significance8

7M. Griffith, Dionysiaca, p.110.8Ibid. p.110.

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Conclusion:

I Without the quote from Cicero, the “Pythagorean”elements of the plays seem too general to be taken astruly Pythagorean sentiments.

I Sentiments expressed elsewhere in previous authors, andalso sometimes even common customs

I No other explicit Pythagorean statements, aside fromthe “foremost of the sciences” statement, therefore it isthe exception rather than the rule

I Aeschylus was a poet, not a Pythagorean.

I Prometheus stating that he gave number to man, is nota reflection of Aeschylus as a Pythagorean, but rather areflection of the importance and utility of number andmathematics for man, making Prometheus seem all themore tragic for giving such a great gift.

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Number, its Science, and its Place in Society

I Number already seen as the foremost science inAeschylus

I For Pythagoras and the Pythagoreans, number seen asthe most learned of all things

I For the Pythagoreans, number takes on mystical andreligious significance as well

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Pythagoras and the Pythagoreans: A CloserExamination

Pythagoras:

I Historical background provided by post-Aristoteliansources, namely Aristoxenus and Dicaearchus9

I Sources often contradict each other, making theconstruction of any history of Pythagoras difficult

I Traditionally, Pythagoras lived in 6th century BC, fromSamos, associated with Egypt and Orient, active insoutern Italy, namely Croton and Metapontum10

I Discovered relation between notes of octave, namelythe ratio 6:8:9:12, through the use of means11

I HE DID NOT DISCOVER PYTHAGOREANTHEOREM! The result was known to the Babylonianmathematicians working nearly a millenium beforePythagoras.

9Walter Burkert, Lore and Science in Ancient Pythagoreanism, p.10910Ibid. p.112.11George Thomson, Aeschylus and Athens, p.200.

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Pythagoras:I Historical background provided by post-Aristotelian

sources, namely Aristoxenus and Dicaearchus9

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Tenants and Practices:

I Transmigration of souls, reincarnation

I Vegetarianism, except beans, namely lentils

I Mathematical studies as moral basis for life, supposedly“all is number”12

I Numerology:

I Odd number is male, even femaleI First ten numbers assigned special meaning, ten holiest,

represented number of universe, two first female, threefirst male, five marriage because two plus three

I Seventeen abhorred because it fell between sixteen andeighteen, a perfect square, and the double of a perfectsquare respectively.

I Initiation process

12Carl Boyer, A History of Mathematics, 2nd ed., p.56-57.

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I Numerology:

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I Numerology:

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I Numerology:

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I Numerology:I Odd number is male, even female

I First ten numbers assigned special meaning, ten holiest,represented number of universe, two first female, threefirst male, five marriage because two plus three

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I Numerology:I Odd number is male, even femaleI First ten numbers assigned special meaning, ten holiest,

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Plato and Pythagoras

I As seen, for Pythagoras mathematics and study ofnumber necessary for moral life

I Use of the adjective mathematike to describe that areaof study credited to Pythagoras

I Later, mathematics becomes a cornerstone of educationwith Plato

I What exactly was mathematics for a Greek?

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Mathematics: An Etymology and Overview

Mathematics:

I From ta mathemata meaning “learning, knowledge, orthings which are learnt”13

I Not a singular subject or area of study, but rathercomposed of subdisciplines:

I For Plato there are tria mathemata : arithmetic,astronomy, and measurement of length, level, andheight, or geometry.14

I For Pythagoras and his followers only arithmetic andgeometry are mathematike .15

I Others, such as Archytas, a later Pythagorean, includemusic.

13Liddell and Scott, Greek-English Lexicon.14Plato, Laws, 7.817e.15Thomas Heath, Greek Mathematics, Vol. I, p.11.

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Mathematics:

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I Arithmetic separate from calculation (arithmon kailogismon) 16

I Arithmon for Greeks is closer to modern number theory,whereas logismon is closer to modern arithmetic

I Geometry also often considered only abstractly, e.g. inhis Elements, Euclid does not assign any numericalvalue to a side or angle in a geometric figure

16Heath p.13.

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Mathematics as the Cornerstone of PlatonicEducation

I In the Republic, the guardians are given instruction incalculation, geometry, solid geometry, astronomy, andfinally music.17

I Music to ears as astronomy to eyes, says Socrates toGlaucon citing the Pythagoreans.18

I Pythagoras loved for educational legacy, and followersare still present in Plato’s day19

I Republic intended to be used as manual for orderingsoul and living well, thus mathematics central to theformation of the person

I The legacy of this educational philosophy can be seentoday in the modern liberal arts education espoused bymany universities (math is a requirement).

17Plato, Republic, 521c-531d.18Ibid. 530d.19Ibid. 600b.

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I Passage in Aeschylus begs question of whether or nothe was Pythagorean

I Unlikely since most evidence seems too general tosupport the conclusion

I Passage then explained by number being great utility,which makes Prometheus seem more tragic in that he ispunished for giving such a good thing to man

I While Pythagoreans were cultic religion, the idea of thecentrality of mathematics in education was picked up byPlato, and made a cornerstone of his personal formativephilosophy, which has a lasting legacy even today.

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Aeschylus. The Orestia. ed. George Thomson. Vol. 2.Amsterdam: Adolf M. Hakkert, 1966.

Aeschylus. Prometheus Bound. ed. Mark Griffith. NewYork: Cambridge University Press, 1983.

Boyer, Carl. A History of Mathematics. 2nd ed. NewYork: John Wiley and Sons, 1989.

Burkert, Walter. Lore and Science in AncientPythagoreanism. trans. Edwin L. Minar Jr. Cambridge,Massachusetts: Harvard University Press, 1972.

Griffith, Mark. Aeschylus, Sicily and Prometheus. inDionysiaca. Cambridge: Cambridge University Press,1978.

Heath, Thomas. Greek Mathematics. Oxford: OxfordUniversity Press, 1921.

Plato. Republic. trans. G. M. A. Grube. ed. C. D. C.Reeve. Indianapolis: Hackett Publishing, 1992.

Thomson, George Aeschylus and Athens. London:Lawrence and Wishart, 1966.

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