The title seems like a weird way to describe the phenomenon, given that the robot exists within our real space, which is essentially flat at the scales and velo

The title seems like a weird way to describe the phenomenon, given that the robot exists within our real space, which is essentially flat at the scales and velocities involved (specifically, non-relativistic ones). Is constraining motion to take place within a spherical slice of Euclidean 3-D space really equivalent to motion in an actually spherical space? Unless I'm missing something, it's fairly easy to understand why it works. The horizontal weights use Newton's 3rd law to rotate the bar in the opposite direction from their own motion. The vertical weights are used to alter the robot's moment of inertia relative to the constrained axis of rotation. (You could replace these weights with a single weight that slides along the radial bar toward and away from the center axis.) The moment of inertia determines how much the robot as a whole moves then the horizontal weights move, so if you move the weights one way, then change the moment of inertia and move the weights back the other way, you get a net change in position. This is why it doesn't work with a cylinder: because when the vertical weights are constrained to a cylindrical space, moving them doesn't change the robot's moment of inertia. I guess the point is that in a true spherical (or otherwise non-flat) space, any robot with the appropriate moving parts can do this "swimming" just by moving its parts in the right way in space without pushing on anything, essentially "pushing" against the curvature of the space itself. Now that I think about it, there's a conceptually simpler way to demonstrate the same thing. Imagine a "robot" made of two parts: a "gun" and a "bullet". The gun starts on the "equator" of a spherical space and fires the bullet due west. By Newton's 3rd law, the gun begins moving east. After some time, the bullet flies all the way around the equator and impacts the gun from the east. The gun catches it and its velocity once again becomes zero, but in the time between firing the bullet and catching it, the gun has progressed some distance to the east, and now the combined gun and bullet system that we started with has changed its position. The gun can reload and fire the bullet west again, repeating the process as many times as necessary to continue progressing around the equator.