make people more useful to themselves, and more wide
awake; and again in measurements of things which have length, and
breadth, and depth, they free us from that natural ignorance of all
these things which is so ludicrous and disgraceful.

CLEINIAS: What kind of ignorance do you mean?

ATHENIAN: O my dear Cleinias, I, like yourself, have late in life heard
with amazement of our ignorance in these matters; to me we appear to be
more like pigs than men, and I am quite ashamed, not only of myself, but
of all Hellenes.

CLEINIAS: About what? Say, Stranger, what you mean.

ATHENIAN: I will; or rather I will show you my meaning by a question,
and do you please to answer me: You know, I suppose, what length is?

CLEINIAS: Certainly.

ATHENIAN: And what breadth is?

CLEINIAS: To be sure.

ATHENIAN: And you know that these are two distinct things, and that
there is a third thing called depth?

CLEINIAS: Of course.

ATHENIAN: And do not all these seem to you to be commensurable with
themselves?

CLEINIAS: Yes.

ATHENIAN: That is to say, length is naturally commensurable with length,
and breadth with breadth, and depth in like manner with depth?

CLEINIAS: Undoubtedly.

ATHENIAN: But if some things are commensurable and others wholly
incommensurable, and you think that all things are commensurable, what
is your position in regard to them?

CLEINIAS: Clearly, far from good.

ATHENIAN: Concerning length and breadth when compared with depth, or
breadth and length when compared with one another, are not all the
Hellenes agreed that these are commensurable with one another in some
way?

CLEINIAS: Quite true.

ATHENIAN: But if they are absolutely incommensurable, and yet all of us
regard them as commensurable, have we not reason to be ashamed of our
compatriots; and might we not say to them: O ye best of Hellenes, is not
this one of the things of which we were saying that not to know them
is disgraceful, and of which to have a bare knowledge only is no great
distinction?

CLEINIAS: Certainly.

ATHENIAN: And there are other things akin to these, in which there
spring up other errors of the same family.

CLEINIAS: What are they?

ATHENIAN: The natures of commensurable and incommensurable quantities in
their relation to one another. A man who is good for anything ought
to be able, when he thinks, to distinguish them; and different persons
should compete with one another in asking questions, which will be a fa