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The Square Cat

We present a simple, two dimensional example of a "cat" -- a body with zero angular momentum that can rotate itself with no external forces. This model is used to explain why this problem is known to be a gauge theory and to illustrate the importance of non-commutative operators. We will also show a comparison between the free-space "cat" in Newtonian mechanics and the same problem in Aristotelian mechanics at low Reynolds number; this simple example shows the analogy between (angular) momentum in Newtonian mechanics and (torque) force in Aristotelian mechanics. We will end by pointing out a topological invariant common to our model in free space and at low Reynolds number.