What are the right proportions for Plato’s line?

In my Introduction to Philosophy class, students looked online for representations of Plato’s line, a model of his metaphysical and epistemological system. In the Wikipedia article on the line, for instance,the line is represented in this way:


Screen shot of the line representation at http://en.wikipedia.org/wiki/Analogy_of_the_divided_line.

This surprised me because I had always pictured the part of the line that corresponds to the visible world to be longer than the part of the line that represents the intelligible world. This is how C. D. C. Reeve sees it. In a footnote on page 205 of his student translation of Plato’s Republic, he draws the line as follows: a total of 6 units of length are apportioned to the visible world, with 3 units apportioned to the intelligible; In the visible world, 4 units are apportioned to images of things, and 2 to perceptions of the things themselves. The 2:1 ratio is preserved in the part of the line representing the intelligible world. Two units are apportioned to geometry and other sciences, and 1 unit to knowledge of Forms. So the entire line reflects this 2:1 ratio: the visible world is given twice as much length as the intelligible, and in each major division of the line, the subdivisions have a 2:1 to one another.

There is clear textual support for this arrangement in the Reeve text (p. 206). Socrates says the following.

Would you also be willing to say, then, that, as regards truth and untruth, the division is in this ratio: what is believed is to what is known, so the likeness is to the thing it is like.

There are presumably more untruths than truths, and more belief than knowledge, and more ways in which a thing appears to be than it really is. This suggests that the part of the line representing the visible world should be longer than the part of the line representing the intelligible world.

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