It is usually pleasing to be frictionless, for I know that makes me desirable in certain problem-solving circles, but sometimes I crave physical contact.
My extent is infinite, and though there is no means of locomotion for a plane to travel itself, I have traveled widely. I just can’t move. Here’s the secret: I mentally fix upon a region of myself, a region that, but for what objects are placed in it and what activities are happening there for the sake of some thought experiment or physics problem or demonstration, would exactly resemble any other region of myself. It’s true: I am sameness. Uniformity. But when I turn my attention to that region, I make maps, pack appropriate clothing, and leave space in my luggage for souvenirs.
A map of a region of an infinite plane doesn’t look like much, unless the map is made at the precise moment the region coincides with a perfect sphere rolling by whose purpose is to demonstrate inertia. And how often does that happen? All the time, you say. But when it comes to infinity, any imprecision in “all the time” can look like never. Nevertheless, every summer and winter (I can at least imagine seasons), I plan a trip in hopes of catching such a spectacle as motion in my midst.
There is always the problem of how to dress for the occasion. Would the idealized sphere, rolling by, disturb the air such that there were a breeze, and I might need a jacket? I had purchased a dazzling purple—if a little flat—coat expressly for the possibility of wind, but I know I will never wear this coat, for I am the kind of plane that buttresses an air of absolutely no resistance. That is specified in every problem in which I appear.
The only souvenir I have ever kept is a point I plucked from my surface—I would say where, but as I was never assigned an origin (0,0), I have only ever traveled east (east being a completely arbitrary fiction, but this sort of thing takes commitment) for fear that changing direction might cause me to double back and repeat territory, which for the wanderlust is death. I can only say that it was a while ago, and it’s hard to say how fast I was traveling—but of course I don’t really move, I only concentrate on areas of myself.
So, I suppose it is more “correct” to say that some time ago (time being relevant to that sphere traveling somewhere on my surface), I perceived what seemed to be a fluctuation of a point—that is, I felt something—contact that must have been with the sphere I am always pursuing. So shattered was I by the sensation, I forgot to pick up my cherished purple coat as I snatched the point of contact and stuffed it in my bag. (Do I ever contradict myself? Very well, then.)
There is an infinite line of contact between the sphere I love and my surface, but there was only one time that I felt the touch of sphere on plane. I carry that souvenir point with me ever east rifling through region after region, chasing the memory of that encounter. To what end? I think the point is to just keep moving.
Subtraction[1]
The first question asks you to treat a trapeze and a performer together as a simple pendulum. But has an aerial apparatus ever become one with its swinger, whether sitting or standing or hanging by her ankles?
The next asks whether one would have more sugar to the pound at the North Pole or the equator, and then asks the same about sugar to the kilogram, which signals to you that one or both of these measuring systems has an odd relationship with the world, or at least that they have an odd relationship with each other. Either way, it is deeply unsettling, and you skip the sugar problem as well.
Next, a rabbit runs across a parking lot where, “strangely enough” (the problem reads), a set of coordinate axes has been drawn. This problem tempts you, but ultimately you decide that it is too self-conscious.
Now: consider both the Earth’s rotation and orbiting (in the same direction), then explain whether a tree moves faster during the day or night. You daydream about moving trees, picturing first a dark forest of imposing bare branches, then swift, fully-foliaged trees skating the earth like towering chess pieces. When you realize the question is really about reference frames, you feel tricked and leave it alone.
It feels like this game is important, that it has actual consequences. You need to find a problem soon. Two identical cars travel at the same speed in opposite directions on an east-west highway. You pause to dutifully imagine these cars but are irritated when asked which car presses harder on the road.
Is it you? Are you being too selective? What are you looking for? Maybe the trapeze and the performer were perfect all along. Consider what it means to treat them as a simple pendulum. Together, they would move as one, and according to the rules of harmonic motion. Oh, but how false the whole thing feels, treating the world as a uniform mob of harmonic oscillators.
You were once an infant, receiving an undifferentiated mass of signals. Then you teased out sight from sound. You untangled. You learned to subtract. This problem space, this summit of subtraction, is where you were always headed.
“Give several examples of bodies that are not in equilibrium, even though the resultant of all the forces acting on them is zero.” It sounds pure, but how can you be sure? Steering wheels and twisting bottle caps? Torque, angular motion? You’re not comfortable here in this world, designed to be cleaner, less plentiful yet somehow more fruitful than the world your body inhabits. This inner world created by formalisms, a product of the human mind—of a collective.
Imagine a table on which a pencil is standing on its end, about to fall.
[1] Some word problems borrowed from Fundamentals of Physics, 4th ed., by David Halliday, Robert Resnick, and Jearl Walker. (Hoboken:Wiley, 1993).