Episode 32: Maya Alapin on Mathematical Structures in Plato’s Republic

For several episodes we have been circling around the idea that Plato may have been doing something even more tricky than usual in his structuring of the Republic. In this episode we seek expert help in getting to the bottom of the matter. Maya Alapin worked at Oxford on the question of mathematical structures embedded in the text of the Republic, and is now developing this work at doctoral level. In this discussion we look at some of the previous work relevant to this subject, and at Maya’s own contributions, including the application of a custom-built software solution to the problem of number-crunching the text of the Republic.

The conversation ranges from the heights of Plato’s metaphysics to the depths of mundane syllable-counting, and everywhere in between. In the process we get not only a very plausible map of the harmonic structuring of Plato’s masterwork, but also, more importantly, address the possible philosophical purpose behind such an approach to philosophic writing, and address the all-important question: ‘But is it esoteric?’

Among many topics touched upon are:

  • The work of John Bremer, whose work on ‘counting’ the Republic set the stage for our guest’s, and the later work of Jay Kennedy, who has more recently propounded the idea of a harmonic structure in the dialogues.
  • The problem of ancient composition: in a world without paper, how did books get written? To what degree should we be thinking about oral composition and oral reception?
  • The possible (conjectural, of course) ways in which Plato might have measured out his Republic. We consider the klepsydra (water-clock), stichometry (counting lines), and the counting of syllables.
  • Some of the implications for the measuring of the dialogue on textual questions, such as whether the Republic was composed as we have it today (it was, it turns out!).
  • The musical ratios involved in Alapin’s (and Bremer’s) reading of the Republic, namely 1:2 (the octave), and 6:8 :: 9:12.
  • The narrative parallels which occur at these ratios (you’ll have to listen to the episode to understand how these ratios are present in the text). There is definitely interpretation here, but there are nevertheless some striking chiastic parallels in the text at the ratios mentioned, organised around the ‘octave’ of the central passage, including the discussion off the tripartite soul twinned with the divided line at the 3:4 ratio (get it?).
  • We get into a discussion of what it means to call Plato’s mathematical riddles ‘esoteric’.
  • Maya presents us with a refeshingly non-elitist reading of Plato’s Republic, in which we discuss the central axis of the dialogue, the ‘octave’, where Socrates begins the discussion anew, introducing the so-called ‘third wave’ of the dialogue.
  • Everyone’s mind is blown by the genius of Plato.

Works Discussed in this Episode:

  • Adam, J., 1985. The Nuptial Number of Plato. Kairos, Wellingborough.
  • Bremer, J. (2000). ‘Some Arithmetical Patterns in Plato’s “Republic”‘, Hermathena : 69-97.
  • Brann, E., with Kalkavage, P. and Salem, E., 2011. The Music of the Republic: Essays on Socrates’ Conversations and Plato’s Writings. Paul Dry Books, Philadelphia, PA.
  • Bremer, J., 1984. On Plato’s Polity. Institute of Philosophy, Houston, TX.
  • Gregory, A. (2012). ‘Kennedy and Stichometry: Some Methodological Considerations’, Apeiron 45 : 157-79.
  • Kennedy, J. (2010). ‘Plato’s Forms, Pythagorean Mathematics, and Stichometry’, Apeiron 43 : 1-32.
  • Kennedy, J., 2012. The Musical Structure of Plato’s Dialogues. Acumen, Durham.
  • Strauss, L. (1986). ‘Exoteric Teaching’, Interpretation 14 : 51-59.
  • Strauss, L., 1988. Persecution and the Art of Writing. University of Chicago Press, Chicago, IL.

Recommended Further Reading:

  • Barker, A. (1978). ‘Symphonoi Arithmoi: A Note on Republic 531c1-4’, Classical Philology 73 : 338-44.
  • Barker, A., 1984. Greek Musical Writings. Cambridge University Press, Cambridge.
  • Barker, A. (1994). ‘Ptolemey’s Pythagoreans, Archytas, and Plato’s Conception of Mathematics’, Phronesis 39 : 113-25.
  • Barker, A., 2007. The Science of Harmonics in Classical Greece. Cambridge University Press, Cambridge.
  • Brann, E., with Kalkavage, P. and Salem, E., 2011. The Music of the Republic: Essays on Socrates’ Conversations and Plato’s Writings. Paul Dry Books, Philadelphia, PA.
  • Csapo, E. (2004). ‘The Politics of the New Music’. In: Murray, P. & Wilson, P. (Ed.), Music and the Muses, Oxford University Press, Oxford.
  • Douglas, M., 2007. Thinking in Circles: An Essay on Ring Composition. Yale University Press, New Haven, CT/London. A cool essay on chiastic structure which, unfortunately, doesn’t mention Plato.
  • Gregory, A. (2012). ‘Kennedy and Stichometry: Some Methodological Considerations’, Apeiron 45 : 157-79.
  • Kennedy, J. (2010). ‘Plato’s Forms, Pythagorean Mathematics, and Stichometry’, Apeiron 43 : 1-32.
  • Kennedy, J., 2012. The Musical Structure of Plato’s Dialogues. Acumen, Durham.
  • McClain, E. (1974). ‘Musical ‘Marriages’ in Plato’s Republic’, Journal of Musical Theory 18 : 242-72.
  • McClain, E., 1978. The Pythagorean Plato: Prelude to the Song Itself. Nicolas-Hays, York Beach, MN.
  • Mckay, J. Z. and Rehding, A. (2011). ‘The Structure of Plato’s Dialogues and Greek Music Theory: A Response to J. B. Kennedy’, Apeiron 44.
  • Mountford, J. (1923). ‘The Musical Scales of Plato’s Republic’, Classical Quarterly 17 : 125-36.
  • Ohly, K., 1928. Stichometrische Untersuchungen. Otto Harrassowitz, Leipzig.
  • Schofield, M. (2010). ‘Music All Pow’rful’. In: McPherran, M. (Ed.), Plato’s Republic: A Critical Guide, Cambridge University Press.

Useful works on the subject of the oral and the written in Plato:

  • Birt, T., 1882. Das antike Buchwesen in seinem Verhältnis zur Literatur. Hertz, Berlin.
  • Havelock, E. A., 1963. Preface to Plato. Harvard University Press, Cambridge, MA.
  • Havelock, E. A., 1986. The Muse Learns to Write. Yale University Press, New Haven, CT.

Themes

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