A. What, will you leave me when you have raised my expectations so high? I had rather, so help me Hercules! be mistaken with Plato, whom I know how much you esteem, and whom I admire myself, from what you say of him, than be in the right with those others.
M. I commend you; for, indeed, I could myself willingly be mistaken in his company. Do we, then, doubt, as we do in other cases (though I think here is very little room for doubt in this case, for the mathematicians prove the facts to us), that the earth is placed in the midst of the world, being, as it were, a sort of point, which they call a κέντρον, surrounded by the whole heavens; and that such is the nature of the four principles which are the generating causes of all things, that they have equally divided among them the constituents of all bodies; moreover, that earthy and humid bodies are carried at equal angles by their own weight and ponderosity into the earth and sea; that the other two parts consist, one of fire, and the other of air?
As the two former are carried by their gravity and weight into the middle region of the world, so these, on the other hand, ascend by right lines into the celestial regions, either because, owing to their intrinsic nature, they are always endeavoring to reach the highest place, or else because lighter bodies are naturally repelled by heavier; and as this is notoriously the case, it must evidently follow that souls, when once they have departed from the body, whether they are animal (by which term I mean capable of breathing) or of the nature of fire, must mount upward.
But if the soul is some number, as some people assert, speaking with more subtlety than clearness, or if it is that fifth nature, for which it would be more correct to say that we have not given a name to than that we do not correctly understand it—still it is too pure and perfect not to go to a great distance from the earth.
Something of this sort, then, we must believe the soul to be, that we may not commit the folly of thinking that so active a principle lies immerged in the heart or brain; or, as Empedocles would have it, in the blood.
Looking for something other than legends about spirits, philosophers attempted to further employ reason in understanding the workings of the world.
Is it possible to interpret our experience using more precise terms, identifying the parts by their very essences? Can the study of mathematics help to provide measure and order to the patterns of nature? It is still the same old sense of wonder, though it also adds a longing for more comprehensive explanations, where evidence and proof give a firmer foundation than a feeling and a hunch.
I do wish I had more of a gift for mathematics, but what I can manage is enough to show me how the relationship in quantities reveals so much about the qualities of the universe we observe. A disciplined consideration of numbers, beginning with clear definitions and proceeding by valid demonstrations, tells me that what may initially seem jumbled and chaotic is actually an expression of profound balance and harmony.
In my case, it was working through Euclid’s Elements on my own that finally made it “click” for me. I had struggled for many years in the usual math classes, and I felt frustrated that many others saw the connections, where I only saw the drudgery of memorization. I suppose I can’t blame my teachers for giving up on me, so I eventually decided I would have to knock myself into better shape. My father told me to go straight to the source, not mess about with watered-down textbooks, though he warned me it might hurt at first.
It did hurt, and I imagine that was a necessary initiation. There came a moment, quite suddenly, where I saw a larger sense of what Euclid was doing, and then all of those definitions, axioms, postulates, and propositions came together. It was something beautiful now, not just a hodgepodge of lines and letters.
I am not qualified to speak about any historical influence the Pythagoreans may have had on the philosophy of Plato, as Cicero here describes, and yet I immediately draw a link in my own thinking between the way an abstract awareness of numbers clears the path to grasping universal concepts and principles about reality.
I cannot see or touch an idea directly, even as my apprehension of an idea ends up being precisely what gives meaning to whatever I see or touch. Once I have risen to the level of the intelligible realm, everything in the sensible realm now looks like a pale imitation. It was in this manner that Euclid helped me to appreciate Plato.
Now once again, the ideas of physics presented here will come across as raw and ridiculous to many moderns; I will not bicker with them, as I believe that they do not quite understand how science is an evolving process, not a fixed set of doctrines. Note simply how a worthy attempt is being made to distinguish between the different elements out of which the world is composed, and to describe how these constitutive parts behave in very distinct ways.
What is heavier appears to descend, and what is lighter appears to ascend, and by extension we can ask whether the soul, as the first principle of life, is more like something with greater or lesser substance. If we are to speak of the soul as breath, or as similar to fire, would it not make more sense to argue that soul will be lifted up into the heavens when freed from the body, instead of being dragged down into the earth?
Such speculation may not even be necessary, however, if the soul is considered to have an immaterial existence, like that of a number or of an idea, or if it is made from a totally different type of matter, one which is not directly evident to our senses. Then it would not be subject to the forces of the other elements at all, and it would also not be bound to this one point in space and time.
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