The Cave Analogy - The Perfect Circle

The cave analogy is trying to make, at least with the part of it that's outside the cave. All the objects that the person can see are, for plato, the real objects. So what about these reflections then in the pond? Well, these aren't like as real as the objects that they are reflections of. And this movement from the imperfect things realized in the world around us to the perfect object studied by something like mathematics,. It's that movement up towards perfection that plato thinks is so crucial about the study of mathematics. A lot of mathematicians deal with their blackboards through extensive mathematical training. You remember everythings just one little footnote and you say 'O' O