Learning How to Fly from Ancient Greece
Look at Raphael’s fresco and go to the middle of the image. The middle is the vanishing point from visual perspective, and you see two figures walking. On the left is Plato. On the right, we have Aristotle. Rather than a painting on canvas, this painting was done on plaster. It resides in one of four walls in the Stanza, located in the Vatican in Rome. The link in the figure caption goes to a web page where there is a numbered map depicting many philosophers. The philosophers include Plato and Aristotle. You can see many others such as Zeno, Pythagoras, Socrates, and Ptolemy.
Plato is pointing upward. Aristotle is pointing downward. This may seem like a weird idea, but in this juxtaposition of directions, we find many questions, answers, and problems that help us relate to today’s societal issues and disciplines. I’ll generalize, probably beyond what Raphael intended. Plato is saying if you want to understand a thing, to acquire knowledge, you need to abstract and pay attention to what he called “the forms.” A good understanding of the nature of forms can be found in Plato’s Republic where there the allegory of the cave. Aristotle is saying if you want to understand a thing, look to the physical world as made clear to us through our senses. You might interpret Plato’s gesture as one relating to religion, and this is one interpretation. You might also interpret him as celebrating the power of conceptual thinking. This aspect appeals to me: that for Plato, knowledge is mainly in concepts, not in particulars and examples. However, Aristotle’s gesture is equally as valid: one cannot understand a form, a concept, an abstraction without observation, and what today we call science.
I like to think of Raphael’s brilliant art as describing ways of knowing our world. Sometimes, you need to think abstractly and conceptually. Other times, you need a specific skill, or you need to pay attention to what the world is telling you through your eyes, ears, and skin. Think of the painting, and the idea of two ends of a spectrum (looking up vs. looking down) as a metaphor for life and learning. On any subject that tickles your fancy, pull out a copy of this painting and use it as an artistically inspired slide rule. If you look, for example at immigration issues in the United States — currently a hot topic as of January 2018 — what does looking down and looking up mean?
For immigration, we can play Aristotle first. What are the ground truths, the data, the observations? What are the concrete examples of migration, emigration, and immigration? These examples can be found in abundance by starting with the news. But now, let’s become Plato for a moment. What are the abstractions of immigration? There is a concept we call government, the concept of citizen, and so forth. This exercise is very useful if done alone or in a group, getting diverse opinions from friends and colleagues. What will you focus on — the ideas and abstract things, the concepts? Or will you cite specific opinions, or display plots and data visualizations?
Doing this exercise is like learning how to fly. It’s true that we need to walk and observe (Aristotle). It is also true that humans regard abstract thinking as one of the defining characteristics of homo sapiens (our species). Sapiens is Latin for wise. But how can we know a thing only conceptually? We need examples. For example, if I want to talk about the concept of number, it may help if I show one apple, one tree, and one book. So, we need to fly but not have our heads permanently in the clouds. I think we can best know things by walking on the ground but also by flying high with stops along the way.
If you try to tie Plato and Aristotle to what we learn in school, mathematics is most like flying all of the time. This is because mathematics can be seen as being either the science of pattern or, somewhat equivalently, the science of abstraction. If you want to conceptualize something, and you fly high enough, you will enter the mathematical realm. There are many subjects that have sprouted from mathematics, such as statistics and computer science, so all of these subjects provide additional conceptual structures. Plato’s forms. Attach your wings and fly with me.
