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Optics and the Line in Plato's Republic

Published online by Cambridge University Press:  11 February 2009

Sarah. B. Pomeroy
Sarah. B. Pomeroy
Affiliation:
Hunter College,City University of New York
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Extract

Socrates, in the Republic (509 d–511 e), uses the symbol of a divided line to illustrate the distinction between the Visible and Intelligible Worlds, and between the kinds of perception appropriate to each. This paper will present a new hypothesis: that the proportions of the line are derived from optical theory.

The construction of the Divided Line is described as follows: Socrates asks his interlocutors to represent the Visible and Intelligible Worlds by a line divided into two unequal segments. (See Diagram I, below, where line AA' is divided at C.) The ratio in which the division is to be made is not specified, and it seems that any ratio is acceptable provided that one segment is longer than the other. Socrates then tells them to cut each part again according to the same ratio as the original division. (In Diagram I, below, AC is divided at F, and CA' is divided at F'.) After describing the division of the line thus into four parts, Socrates goes on to explain the philosophical significance of each part. For the purposes of this paper the following brief identification of each segment of the line will suffice.

Type
Research Article
Information
The Classical Quarterly , Volume 21 , Issue 2 , December 1971 , pp. 389 - 392
Copyright
Copyright © The Classical Association 1971

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References

page 389 note 1 I wish to express my thanks to Professor Martin Ostwald of Swarthmore College for his invaluable suggestions during the writing of this paper.

page 389 note 2 for detailed discussions on the actual contents of the line see Stocks, J. L., ‘The Divided Line’, CQ v (1911), 72–88Google Scholar; Ferguson, A. S., ‘Plato's Simile of Light’, CQ xv (1921), 131–53CrossRefGoogle Scholar,andxvi (1922), 15–28; Ferguson, A. S., ‘Plato's Simile of Light Again’, CQ xxviii (1934), 190–210CrossRefGoogle Scholar; Raven, J. E., ‘Sun, Divided Line, and Cave’, CQ n.s. iii (1953), 22–32CrossRefGoogle Scholar; Ferguson, J., ‘Sun, Line, and Cave Again’, CQ n.s. xii (1963), 188–93;CrossRefGoogle Scholar and Tanner, R. G., CQ.N.S. xx (1970),Google Scholar

page 389 note 3 According to Proems 289. 21 είkών is used elsewhere by Plato with many connotations, but the meaning is limited here to those images which appear by means of the power of light. See J. L. Stocks, loc. cit. 88.

page 390 note 1 See Brumbaugh, R., Plato's Mathematical Imagination (Bloomington, 1954), 279 n. 23.Google Scholar

page 390 note 2 Above, p. 389 n. 2.

page 390 note 3 Brumbaugh, op. cit. 3–7.

page 390 note 4 The stem

page 391 note 1 The phenomena observed by Plato exist irrespective of his theory of the mechanics of vision involving the emanation of rays from the observer and the object observed.

page 391 note 2 For an analysis of early work on optics see Sir Heath, Thomas L., A History of Greek Mathematics (Oxford, 1921), ii. 3, 200–3 et passim.Google Scholar

page 391 note 3 See Heath, T. L., ‘The fragment of Anthemius on burning mirrors and the "Fragmentum mathematicum Bobiense” ’, Bibliotheca Mathematica, Ser. 3, vii (1906–7), 225–33Google Scholar; especially 232–3.

page 391 note 4 For a discussion of ancient magnifying glasses, including nine from the sixth to fourth centuries B.c. which were displayed in the Lavigerie Museum in Carthage, see Beck, H. G., ‘Early Magnifying Glasses’, Antiquaries Journal vii (1928), 327–30CrossRefGoogle Scholar. Beck observes that in antiquity magnifying glasses were probably used commonly for such precision work as gem cutting and die sinking. It is likely that such glasses were far more abundant than archaeological evidence would indicate, but, owing to the fragility of glass, they have not survived.