All we have from Socrates, Plato and Aristotle are writings, but they must have used diagrams of some sort. What would they have done given access to modern computer graphics?
The images [click on them for larger versions] are from a presentation I gave at the Philosophy Club here in The Villages, FL today. You can download the narrated PowerPoint slide show, click on: Part 1 and Part 2.
Here is a brief summary:
Plato's Analogy of the Divided Line
In The Republic, Book VI, Plato divides a line unequally. The first section is analogized to the Physical World and the second to the Intelligible World. Then, by the same proportions, he sub-divides each section. He analogizes the first segment, AB, to Shadows and Reflections of physical things; BC to the Physical Things themselves, CD to Mathematical Resoning, and DE to Philosophical Reasoning. Although Plato does not mention it, later commentators noticed that, by the given construction, it turns out that segment BC (Physical Things) is exactly the same length as CD (Mathematical Reasoning). What could that imply? I go into greater detail in the PowerPoint presentation.
Plato's Allegory of the Cave
Plato, in The Republic, Book VII, see first image above, imagines prisoners who spend their entire lives in a cave, looking at two-dimensional shadows on a wall. The prisoners give names to the shadows, learn to predict sequences, and speculate on their origin and meanings. They come up with the equivalent of religions, sciences and philosophies. Then, one prisoner is released into the real three-dimensional world and learns about physical reality. She returns to the cave but is unable to convince the prisoners of the reality she knows as truth. They make fun of her as a crazy philosopher.
Putting the Analogy of the Divided Line and the Allegory of the Cave together, the prisoners represent a low level of knowledge and understanding, represented as line segment AB. The prisoner released from the cave is at level BC, like ourselves. Those of us who have learned mathematical reasoning are not only out of the cave, but are at a higher level, CD. Finally, the philosophers among us, who understand the Idea of Forms and the Good and so on, are at level DE.
My question is, "Are WE really out of the cave yet?" Perhaps, if, as string theory postulates, there are actually 10 or 11 dimensions, those of us who perceive 3D + time are only about 10% better off than the prisoners in the cave, limited to 2D + time! In the PowerPoint presentation, I speculate on the possible equivalence of time and space.
Aristotle's Five Elements
Aristotle, like most of the ancients, believed there were only five elements: Aether, Fire, Air, Water, and Earth. Indeed, according to him, (see his Meteorology, Book I and his Physics, Book I) there is really only the Aether, the quintessence, the All. Fire, Air, Earth, and Water exist potentially in each other, and all can be resolved into the Aether. This is not far from Spinoza's belief that there is only the Universal Substance, and all things that seem as different as material and spirit are merely different aspects of that Universal.
How ridiculous is this? Well, not so ridiculous as the PowerPoint Show explains.
The names of Fire, Air, Water, and Earth in the image are ambigrams, which read the same right-side-up and upside-down. They are featured in the famous book and movie, Angels and Demons.
Read more detail about Aristotle's Five Elements at my Google Knol.