An Even Bigger Problem in Plato

This I discovered today and burst into laughter. I am sure you will see why it is problematic.

"Now the oligarch in turn was third from the king, if we identify the king and the aristocrat.--Third he is.

So the dictator is three times three times removed from true pleasure.--So it appears.

The image of dictatorial pleasure, according to the number of its dimensions, is a plane. By squaring and cubing this number it will become clear how large is the distance between the dictator and the king.--Clear at any rate to a mathematician.

Turning this around, if one wants to know how far the king is superior to the dictator in the truth of his pleasure, he will find, if he completes his multiplication, that the king lives seven hundred and twenty-nine times more pleasantly than the dictator, and that dictator is the same number of times more miserable.

You have brought up an extraordinary calculation, he said, of the difference between the two men, the just and the unjust, as regards pleasure and pain.

Yet it is a true one, I said, and a number appropriate to human life, if days and nights and months and years are appropriate to them.--They surely are."

--Republic, 587d-588a