Psychological symmetry or the cold really creeps into your bones

Last weekend, my wife and I attended the play at the Arena Stage in Washington. It was a one-man show, a monologue called “R. Buckminster Fuller: The History (and Mystery) of the Universe.” Now I’m not usually a great fan of one-man monologues, although as an academic I’m typically perfectly happy sitting all day in lectures at a conference if the topics are interesting. But I thought that Fuller was a thinker and his musings might be interesting. Well, I was right. The text was basically taken straight from Fuller’s writings, but it was implemented in a very dynamic way using videocameras and projection in interesting ways – showing different angles of what we were watching and supplementing it with images so it was theatrically fun as well. And the character (actor Rick Foucheux) even used some interactive pedagogy that I have been trying to use in my classroom. He sometimes turned up the lights and asked the audience questions, insisting on responses. I quite enjoyed it.

Interestingly enough, I found myself agreeing with many aspects of Fuller’s philosophy, much more than I expected. But there was one place where I strongly disagreed with what he said. At one point he said something like, “The wind doesn’t blow, different places on the earth suck!” This got a good laugh from the audience, but it wrinkled my brow. That didn’t feel right to me and I’ve been thinking about why I had that reaction.

When we describe phenomena in physics (or in any science) we typically choose a level at which to make our description. If we’re talking about the wind, we talk about the density of the air and its velocity – macroscopic concepts that we can see, measure and feel. If we’re talking about hot and cold we talk about temperature and heat flow. If we’re talking about electric currents, we talk about the electric potential difference and the current – volts and amps. We can’t see or feel those (Well – actually we can, in terms of the hair on our skin rising or feeling shocks, but we don’t have a lot of experience with that and we don’t tend to interpret those feelings quantitatively the way we do wind speed or heat and cold.) but we can measure them directly with devices we can hold in our hand.

It’s a question of ontology. Wikipedia current defines that as the philosophical study of the nature of being and the categories of being. I like to think of ontology as answering the question, “What kinds of things are there?” – or perhaps better, “What kind of concepts should I use to describe a particular phenomenon?” If we are discussing the motion of the air, the thing we are talking about is “air” – a substance that we consider has the properties that it is continuous (no gaps), is everywhere, has a variable mass density (any volume of it has mass but the same volume can have different masses in different places) and it can move. If we want to describe the causes of its motion, it is natural to try to apply Newton’s laws, which give the general principles that successfully describe the motion of essentially all classical objects. This description relies on our being able to identify forces – pushes and pulls.

Fuller’s statement about the wind makes clear that, if we are talking only at the macroscopic ontological level, there is a possible symmetry in our description: we can say that there are forces in the air that push it from place to place, or there are forces in the air that pull it from place to place. We can describe the motion in terms of repulsive (pushing) forces or attractive (pulling) ones. Newton’s synthesis of the laws of motion tells us that forces on objects are caused by other objects, so we have to identify who is doing the pulling or pushing, but that’s not a big deal. It could be the air acting on itself or it could be bits of the earth pulling or pushing on the air (Fuller’s “some places suck!”).

Another example of this kind of symmetry is heat and cold. When I am teaching about thermodynamics I ask my students to place their hand first on the cloth part of their chair and then on the metal part of their chair. They all respond that the metal feels colder than the cloth, even though we have just had a discussion that concluded when things are left to stand together for a long time they tend to come to the same temperature. We resolve this by deciding that it is the rate at which they come to the same temperature that matters in what we feel. The temperature of your hand is higher than the temperature of the chair in my classroom, so when you touch either the cloth or the metal heat energy will tend to flow out of your hand into the chair. It flows into the metal faster so it feels colder.

In temperate climates, we tend to see the “hot” as the active agent that moves. But I suspect that if we lived in a climate that was extremely cold most of the time we would see the “cold” as the active agent. When you go out in a temperature of 40 below, you might feel that “the cold is sucking the heat right out of you” or that “the cold just seeps right into your bones.” This is an ontological symmetry: we could describe things equally well in terms of the motion of “heat” (better: “heat energy”) or of “cold”. We would just reverse the direction of the flow if we switched our description from heat flow to cold flow. Everything else would look the same and it would work fine. In my classes some student often makes this suggestion.

In physics, symmetries are of great importance. If we decide that we are going to create a theory in which the placement of the origin of our coordinates doesn’t matter, then the theory we create will necessarily conserve momentum. If we decide that our theory should not depend on the orientation of our coordinate system, then the theory we create will necessarily conserve angular momentum.

But the symmetries I’m discussing here are different. They’re not really physical symmetries; rather, they’re psychological symmetries. It’s a question of how we look at the system we’re describing. Whereas physical symmetries are about what we think we are able to explain with our theories. [Aristotle made no attempt to create a theory of gravity. The result of the earth’s gravity was imposed on the theory without physical explanation. The center of the earth was the center of the universe where everything tended to go. There was a “special point” in the theory, so theory was not independent of coordinate system and momentum did not emerge as a relevant concept.]

Another nice psychological symmetry is in the construction of Newton’s laws and contact forces. For a physicist or an engineer looking at a bowling ball being hit by a hammer it seems natural to look at the changing motion of the ball as responding to the forces it feels. But for a biologist looking at an active organism, it looks like it’s the intent of the organism that causes its motion to change. If you are riding a scooter and push your foot on the ground, your backward push is what sends you forward. Since Newton’s third law says that for every force that one object exerts on another, the other objects exerts an equal and opposite force backward on the first, we could write Newton’s second law to say that an object responds negatively to all the forces it exerts instead of positively to all the forces it feels. Since mostly in physics we are talking more about inanimate objects we tend to prefer the traditional choice. [This is discussed in detail in my paper with Rachel Scherr, Newton's zeroth law: Learning from listening to our students, The Physics Teacher, 43, pp. 41-45 (2005).]

So if these psychological symmetries are really symmetries and it doesn’t matter which way we look at it, why was I uncomfortable with Fuller’s statement?

The reason is that the current paradigm of science is to relate things across levels. Up until the 19th century, most of science was about learning to describe the regularities in the world as we saw it. But when, at the end of the 19th century, we began to understand the structure of matter in terms of atoms and molecules, another level became available. We could now describe the properties of matter we had observed phenomenologically in terms of the structure of matter and what is happening to its molecules. The flow of the air is naturally understood in terms of pressure – the air pushing on itself – and that pressure can now be interpreted in terms of the average momentum and the number density of the molecules moving around. The temperature of matter that controls heat flow can now be interpreted in terms of the average kinetic energy of a molecule. At the molecular level, the ideas of pressure and heat flow have natural and simple explanations; the concepts of “sucking” and “cold flow” do not. It’s not always useful or necessary to think down to the molecular level. An electrician can be perfectly competent thinking about volts and amps without ever considering electrons. But crossing levels changes the ontology of how we think about matter and enriches our view of what’s happening. And it provides a “psychological symmetry breaking” that chooses which of our symmetrical descriptions are more appropriate.

Now when I’m teaching these physical concepts I think not just about the entire package that I have learned through my many years of studying physics. I also think about what I can expect my students to know and what might appear natural to them that appears bizarre to me. For many of my university science students, although they know perfectly well about atoms and molecules, they don’t necessarily have the idea that their observations at the everyday level should in fact be consistent with what we know about the structure of matter. This has lots of implications that I will discuss in other posts.