 Nevertheless, in the Divided Line, Socrates posits intelligible entities, abstract but real, as objects of mathematical thought and of dialectical knowledge. Although it treats them only as hypotheses, mathematics reasons about the odd and the even, the various kinds of shapes, and the three kinds of angles. These are entities distinct from their perceptual representation in material diagrams. In turn, dialectic does not treat forms as hypotheses but comes to know what each is. This knowledge comes from grasping their relation to the unhypothetical beginning point, the form of the good (509d-511e). The super-eminence of the knowledge of the good leads to the latter’s becoming an end in itself. When philosophers, after years of study, at last see the good, they would prefer to stay at this level and not go back down into the city to rule. They must be forced, by argument, to undertake the task of applying their knowledge of the forms to the affairs of ruling (519c–520e). So, when this account introduces abstract but real entities as objects of knowledge, Socrates comes close to giving theoretical knowledge a sphere of activity that is distinct from that of practical knowledge.