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Dialogue of Cultures
Translations of the Works of
Great Thinkers:
A Short Excerpt from
Plato's Theaetetus
David Shavin and Susan Kokinda
Autumn, 2002
The Dialogue

Platos Theaetetus dialogue was composed upon the death of Theaetetus, the prized geometer of Plato's Academy. In the 380's and 370's BC, Theaetetus had systematically investigated the five "Platonic solids," their unique characterization of our space, and their internal orientation around the dodecahedron. In 369 BC, Theaetetus died from battle wounds, in a war against the Persian-controlled portions of Greece. The Athenians, after decades without a mission, had mustered for duty in this war on the very grounds of the Academy.

Plato chose to stage the conjunction of the genius and the courage of Theaetetus in a dialogue, set thirty years earlier, in Socrates' last year, 399 BC. The future genius and courage of Theaetetus, Plato suggests, is to be seen as one of the marvelous fruits of Socrates' demonstration of his own unity of courage and genius, facing his immanent trial and execution.

The youthful Theaetetus is said by his teacher, Theodorus, to resemble the elder Socrates, in that his inquisitiveness is dominated, not by the typical egotistical display, but by a search for truth. Socrates wanted Theaetetus to correct an assumption that he had made, by conceiving of a species-idea of knowledge, above individual instances of knowledge. Though momentarily stumped, Theaetetus says that he cannot answer the question directly, but Socrates' challenge impels Theaetetus to relate his recent excitement over his recent mental journey with his teacher over incommensurables. Since his mind is honestly excited over pursuing knowledge, and his mind can re-create that pursuit, Theaetetus is on the right track for his search for the species-idea of knowledge.

This Passage
147D - 148B

In this translation fragment, Plato displays what Socrates sees in Theaetetus' mind and character. The issue in the young student's power to form concepts is nothing less than the same power to order the world, and to bring into being a higher order. English translations that leave matters with "roots" and "squares," bind Plato's scene to the same horror of high school math, where the numbers are the ones that have the magical powers. An honest reader of such a translation would stop reading his Theaetetus, and conclude with something like, "Well, Socrates liked students who were good with words and with making categories. I've known teachers like that. I guess Socrates was a fraud too. I can't imagine why he, or Theaetetus, would stand and fight."

However, Plato structures a large part of the dialogue around the intellectual courage to pursue the most intimate and fragile of one's thoughts, as if one's life, or a civilization's life, depended upon doing so--even if one's most cherished and deeply-held beliefs would, like a miscarriage, be shown to be nothing but "a wind-egg." It is true that Socrates compares his work to that of his mother, who was a midwife, helping pregnant women to give birth. However, commentators, who love this image, overlook the point - Socrates affirms that intellectual midwifery is much more difficult and dangerous.

Socrates died in giving birth to Western civilization. Plato knew this, and also knew what made Theaetetus a courageous genius. So, our translation invites the reader not to enjoy some fresh English prose - which this is not - but to get jarred into the non-academic thinking processes of Plato's Academy.

The Translation Project

The translation of this particular passage arose out of three ongoing and overlapping projects, centered in Leesburg, Virginia:

The first of these, is the reading of Plato's dialogues aloud in a small group, as drama, with various participants playing the roles of the different characters in Plato's play. This process enriches the participants' comprehension of both the paradoxes posed, and the Socratic method itself. Discussion of the historical specificity of the dialogues, of which Plato was very conscious, succeeds in grabbing current events by the throat, and putting into relief, on stage before the very human participants, the audience's own capacity to make history.

The second project is the ongoing class series and pedagogical exercises developed by collaborators of Lyndon H. LaRouche, Jr., focussing on the discoveries and work of Kepler, Kaestner, Gauss, and Riemann, all of whom were intimately familiar with the work of the ancient Greeks. (See the list of articles on the Schiller Institute Pedagogical Articles Page.)

The translation project itself, developed out of the necessity to figure out what was in fact being discussed by Plato!  Political organizers, including David Shavin, Gabriela Carr, Renee Sigerson and Susan Kokinda, who are students in Antony Papert's ancient Greek classes, and who are also involved in the above two projects, were able to decipher Plato's idea, and eliminate the mumbo-jumbo that often passes for "translations."

In 1981, associates of Lyndon LaRouche published an original English translation of Plato's Timaeus, which the Leesburg Plato group recently read aloud, along with other English translations and the original Greek version. Although it is by far superior to other published versions of Timaeus, we are examining it for possible corrections and improvements, for publication online or in print, sometime in the future.

The following is not meant to be a polished English translation, but rather a help to the reader in unfolding the ideas as they unfold in the Greek. (Words in parenthesis are implied by the Greek constructions, but not literally in the text). To make this point more sensuous, the Harold N. Fowler translations (from the Loeb Classical Library, 1921) of Theaetetus's arguments, are placed in italics, for comparison.

Excerpt from
147D - 148B

This is a somewhat literal translation of the passage where Theaetetus excitedly describes his approach, when bumping into something that doesn't fit, the incommensurable. He is happy to tackle a new idea, even if only, initially, to identify something that he doesn't know.

Theaetetus: "Concerning powers [1], Theodorus [2] drew for us somehow (like this), showing the powers of [3] both the three-foot and the five-foot, with respect to length, are not commensurate with the foot; and, thus, selecting out each one, up to (the power) of seventeen. And, in this way, more or less, he had it.

"Then, it came to us, in some such way - since the powers appeared to be an unbounded multitude (or number) - to try to conceptualize (them) into one, in which way we would address all these powers."

[Fowler. Theaetetus: Theodorus here was drawing some figures for us in illustration of roots, showing that squares containing three square feet and five square feet are not commensurable in length with the unit of the foot, and so, selecting each one in its turn up to the square containing seventeen square feet; and at that he stopped. Now it occurred to us, since the number of roots appeared to be infinite, to try to collect them under one name, by which we could henceforth call all the roots.]

Socrates: "Indeed, and did you discover some such thing?"

Theaetetus: "To me, we seem (to have). But even you, examine."

Socrates: "Tell."

Theaetetus: "We divided all number into two. The one able to become (or to grow) equal equally, we - likening the shape to a tetragon [4] - called (it) both tetragonal and equilateral."

[Fowler. Theaetetus: We divided all number into two classes. The one, the numbers which can be formed by multiplying equal factors, we represented by the shape of the square and called square or equilateral numbers.]

Socrates: "And well done!"

Theaetetus: "Accordingly, the (other) one amongst this (class of) number - of which are both three and five, and all (numbers) that are unable to become (or to grow) equal equally, but become (or grow) either by less folds of a greater, or by more folds of a lesser, and always greater and lesser sides encompass it - so in turn, we, likening (it) to an elongated shape, name (it) an oblong number."

[Fowler. Theaetetus: The numbers between these, such asthree and five and all numbers which cannot be formed by multiplying equal factors, but only by multiplying a greater by a less or a less by a greater, and are therefore always contained in unequal sides, we represented by the shape of the oblong rectangle and called oblong numbers.]

Socrates: "Most beautiful! But what is next?"

Theaetetus: "Which lines tetragonize the equilateral and planar number, we call length; and which (tetragonize) the mixed-length (number), (we call) powers - since in length they are not commensurate with each (other length) , but (are commensurate) with the planar (numbers) which they have the power (to form).

And concerning the solids, (there is) another (explanation) such as this."

[Fowler. Theaetetus: All the lines which form the four sides of the equilateral or square numbers we called lengths, and those which form oblong numbers we called surds, because they are not commensurable with the others in length, but only in the areas of the planes which they have the power to form. And similarly in the case of solids.]


1. "Powers" is the Greek word, "dunamai" - and, hence, is the potential or the capability to bring something about. The 'modern' translation of "roots" (as in square roots) does capture the idea that the square-shape somehow originates from the 'root'; however, it seems to be designed to bury the substantial issue, instead of focusing the mind on how higher actions and powers are mastered. (back).

2. Theodorus is said to have been a teacher of Plato, and is one of the two most likely candidates to have introduced Plato to Archytas, during Plato's "missing years" of 399-388 BC. (Eudoxus, diplomat in Egypt, geometer, and likely teacher of Archytas, is the other one.)(back).

3. "Powers of" is not "the square of" but "the power to create or form" the three-foot or the five-foot shape (back).

4. The word "square" does not appear. "Tetragonal and equilateral" is the description of what happens when the power forms equal equally. Power that acts fully symmetrically is qualitatively different from power that acts dissymmetrically. The shapes, oblongs and squares, are the products of distinguishable species of action (back).

See also Lyndon LaRouche's introduction to In Defense of Common Sense, where, even without reference to a Greek text in prison, LaRouche knew that translator Robin Waterford's grasp of Plato's "tegragonal and equilateral" was a conceptual illiteracy

Translators' Notes:

Now, just in case Fowler had not sufficiently "Eulerized" the translation, he provides the following footnote:

"A simple form of the first statement would be: The square roots of 3, 5, etc., are irrational numbers or surds. The word "dynamis" has not the meaning which we give in English to "power," namely the result of multiplication of a number by itself, but that which we give to "root," ie, the number which, when multiplied by itself, produces a given result. Here Theaetetus is speaking of square roots only; and when we speaks of numbers of of equal factors he evidently things of rational whole numbers only, not of irrational number or fractions. ... The modern reader may be somewhat confused because Theaetetus seems to speak of arithmetical facts in geometrical terms."

And, this is not the worst. See Lyndon LaRouche's introduction to "In Defense of Common Sense," for an even more outrageous translator's footnote to this passage.

See also Pedagogical Discussion: Plato's Dynamis vs. Artistotle's Energeia

Related Articles:

Pedagogical Exercises

On Reading Plato

The Life of Socrates

Humboldt's Essays on the Greeks

Preface to The Sophist

Part I - Sections 1 to 22

Part II- Sections 23 to 40

Part III- Sections 41 to 52 (end)

Excerpt from Plato's Phaedon

Translations Page:

Works of Friedrich Schiller

Table of Contents of Fidelio Magazine Issues


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Dialogue of Cultures

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