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I am indeed scared about the habit you mention, but I am still more alarmed about the people who take up these very sciences for study, and do so badly.1 Complete and absolute ignorance of them is never alarming, nor is it a very great evil; much more mischievous is a wide variety of knowledge and learning combined with bad training.Clinias
That is true.Athenian
One ought to declare, then, that the freeborn children should learn as much of these subjects as the innumerable crowd of children in Egypt2 learn along with their letters. [819b] First, as regards counting, lessons have been invented for the merest infants to learn, by way of play and fun,—modes of dividing up apples and chaplets, so that the same totals are adjusted to larger and smaller groups, and modes of sorting out boxers and wrestlers, in byes and pairs, taking them alternately or consecutively, in their natural order. Moreover, by way of play, the teachers mix together bowls made of gold, bronze, [819c] silver and the like, and others distribute them, as I said, by groups of a single kind, adapting the rules of elementary arithmetic to play; and thus they are of service to the pupils for their future tasks of drilling, leading and marching armies, or of household management, and they render them both more helpful in every way to themselves and more alert. [819d] The next step of the teachers is to clear away, by lessons in weights and measures, a certain kind of ignorance, both absurd and disgraceful, which is naturally inherent in all men touching lines, surfaces and solids.Clinias
What ignorance do you mean, and of what kind is it?Athenian
My dear Clinias, when I was told quite lately of our condition in regard to this matter, I was utterly astounded myself: it seemed to me to be the condition of guzzling swine rather than of human beings, and I was ashamed, not only of myself, but of all the Greek world.3 [819e] Clinias
Why? Tell us what you mean, Stranger.Athenian
I am doing so. But I can explain it better by putting a question. Answer me briefly: you know what a line is?Clinias
And do you know that these are two things, and that the third thing, next to these, is the solid?Clinias
Do you not, then, believe that all these are commensurable one with another?Clinias
And you believe, I suppose, that line is really commensurable with line, surface with surface,
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