Plato, Statesman, section 266b

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[266b]

Stranger
Is the nature which our human race possesses related to walking in any other way than as the diameter which is the square root of two feet?¹

Younger Socrates
No.

Stranger
And the nature of the remaining species, again, considered from the point of view of the square root, is the diameter of the square of our root, if it is the nature of twice two feet.²

Younger Socrates
Of course; and now I think I almost understand what you wish to make plain.

Stranger
Socrates, do we see that besides this something else has turned up

1 There is here a play upon words. Man, being a two-footed (δίπους) animal, is compared to the diagonal of the unit square (√2,διάμετρος δίπους).

2 i.e. the remaining species is four-footed. Our diameter is √2, and four is the area of the square constructed on the diagonal of the square which has √2 as its side. All this satirizes the tendency of contemporary thinkers to play with numbers.

Plato. Plato in Twelve Volumes, Vol. 12 translated by Harold N. Fowler. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1921.

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