The Sacred, Spherical Cows of Physics

Oh, that fearful symmetry

Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surface area scales with their height. But students learn that these numbers are easy to calculate if they assume the cow is a perfect sphere, or in other words, that it has spherical symmetry. The lesson: Hard problems become easier when certain underlying (though approximate) symmetries are enforced.

It’s a very informative post, but it seems to me this introduction has little to do with the symmetry discussions that follow. A spherical cow approximation is less about applying symmetry than about physicists using approximations in an attempt at getting an answer that’s actually solvable and (one hopes) close enough to what nature says it is. An equation describing an actual cow shape would likely be exceedingly difficult to manipulate, for whatever problem you were trying to solve. So you approximate, and hope that whatever information is lost is negligible. That the shape is symmetrical incidental; the important point is that it’s simple — it’s also why we employ frictionless surfaces, perfectly elastic collisions and ignore numbers that are small compared to other numbers in a problem. I think the rest of the piece stands on its own without the spherical cow reference.