on rotation

Oh space, how do I move through thee? Let me count the ways. I travel east or west, north or south, up or down; I pitch, I roll, I yaw. Six degrees of freedom: three of translation, three of rotation. It seems simple enough to consider these six degrees on equal footing.

After all, I am a bumbling, clumsy animal. I move by swinging my legs, rotating them about my hips back and forth, so that I may creep forward, step by step. When driving a car, I control the angles of my shoulders, rotating a steering wheel, turning the wheels of the car, which are themselves spinning. All so I may move in a certain direction. I do not know how to translate without rotating, so in intuition I hardly even separate the two.

But rotation is different, and in a beautiful way. Rotation is cyclic, elegant, elusive, cyclic. One does not move straight in one direction and arrive at where one comes from. But one does spin three hundred sixty degrees (ta-da!) and find themself facing the same area they were before. Earth's rotation around Sun and about its own axis bestow upon us yearly seasonal cheer and the daily dichotomy of light and night. Galaxies spiral, creating shocks that condense matter, coercing it to form stars and planets, each rotating about themselves and about each other in a celestial dance of inconceivable scale.

Rotation is beautiful, so it is intriguing. One rotates an object about some central axis. Is this not odd? One does not translate an object about an axis; one translates an object in a direction. There are an infinity of ways to rotate an object (say) anticlockwise, but only one way to move it to the left.

Perhaps I fuss over nothing, and pointing out quirks in a phenomenon so well-understood is a folly akin to reinventing the wheel. But, dear reader, have you really pondered the wheel? Are you not amazed at the efficiency in which it uses rotation for the purpose of translation? Have you considered that the bottom of a car's wheel has zero velocity (for it is always adhered to the ground), and as a result the top of the wheel has twice the velocity of the car? Is this not intriguing?

Of course, when I speak of velocities in such a scenario I speak of them relative to the ground. Not relative to the car, not relative to a passerby on a bike, not relative to the clouds. But is talking about velocity relative to the clouds any less valid than talking about it relative to the ground? Surely not. A pilot does exactly that when referring to airspeed. There is thus no superior frame to measure translational velocity in; a train receding from one person may be approaching another, and completely still to a passenger. And a blindfolded passenger on a sufficiently quiet train moving at a constant velocity has no way of knowing they are not sitting perfectly still.

Ernst Mach would like you to imagine yourself on a grassy field under starlit skies. Now hold your arms limp at your sides and pirouette. Didn't you notice your arms try to move outwards? Couldn't you feel yourself twirling? And at the same time, didn't you see the stars spinning above you?

Mach now asks: why is it that your arms move up from their sides exactly when you see the stars spinning above you? Put another way, why is it that you can sense yourself twirling in a field, but you can't sense yourself moving forward on a train?

Rotation is intriguing, so it is special. While in the translational world I can say that all reference frames moving at different constant speeds are equally valid, the connection between the stars being still above me and my hands resting limp by my sides kills any hope of claiming that frames rotating at different speeds are equally valid. I can scarcely avoid concluding that, unlike translational velocities, rotational velocities aren’t ambiguous. The frame where my arms hang down and the stars are still provides a zero-point of rotational velocity in a way unparalleled to translational relativity. Put me in a box in space and I have no idea if I'm moving, but you bet I can tell if I'm spinning.

There are other unique qualities to rotation. The figure skater picks up a burst of speed mid-spin as they pull their arms tight towards them, decreasing their rotational inertia. But short of decreasing one's own mass, there is no way to shed translational inertia. The child on the merry-go-round experiences a constant centripetal force yet maintains a constant speed, whereas without rotation any constant force eventually leads to an ever-increasing speed. Cyclones on Earth rotate anticlockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere, due to the Coriolis effect—an inexplicable phenomenon if the rotation of Earth is ignored.

Even more mystically, undetectably small subatomic particles such as electrons are known to possess angular momentum (“spin”) just as a figure skater might. These particles are so small that for all intents and purposes they are mere points in space, and yet we know they spin. How can a point spin? Somehow, in some sense, it happens—but it is beyond me. One day I hope to develop a seamless intuition for the behavior of spinning objects, to be so familiar with rotation that I find all these quirks not perplexing and fascinating but obvious and boring. Until then I will twirl my pen in awe. Rotation is special, so it is beautiful.