## Spherical Cow: A Simple Model

My short-hand name for a too-simple model is a "spherical cow" (yes there is even a book with that title [Clemens: QH541.15.M34 1985]). The name comes from a joke that every physicist is required to learn:

Ever lower milk prices were driving a dairy farmer to desperate measures. Two years ago, he tried "Beethoven for Bovines" in his barn and milk production dropped 2%. Last year he signed up for "hex the herd" where Genuine Santa Barbara WitchesTM remotely hexed your herd for health and higher production. (The ad had said its hexes were the cause of California's improved milk production, but it didn't seem to work in Wisconsin.) So this year he drove to town to consult the ultimate power source: a theoretical physicist. The physicist listened to his problem, asked a few questions, and then said he'd take the assignment, and that it would take only a few hours to solve the problem. A few weeks later, the physicist phoned the farmer, "I've got the answer. The solution turned out to be a bit more complicated than I thought and I'm presenting it at this afternoon's Theory Seminar". At the seminar the farmer finds a handful of people drinking tea and munching on cookies---none of whom looks like a farmer. As the talk begins the physicist approaches the blackboard and draws a big circle. "First, we assume a spherical cow..." (Yes that is the punch line)
One hopes (as in this story) that approximations are clearly reported in derivations.
Spherical cows have a long history in science:
I conceive that the chief aim of the physicist in discussing a theoretical problem is to obtain 'insight' --- to see which of the numerous factors are particularly concerned in any effect and how they work together to give it. For this purpose a legitimate approximation is not just an unavoidable evil; it is a discernment that certain factors --- certain complications of the problem --- do not contribute appreciably to the result. We satisfy ourselves that they may be left aside; and the mechanism stands out more clearly freed from these irrelevancies. This discernment is only a continuation of a task begun by the physicist before the mathematical premises of the problem could even be stated; for in any natural problem the actual conditions are of extreme complexity and the first step is to select those which have an essential influence on the result --- in short, to get hold of the right end of the stick.

A. S. Eddington, The Internal Constitution of the Stars, 1926, pp 101-2

As Eddington states above, the real world is filled with an infinity of details which a priori might affect an experimental outcome (e.g., the phase of the Moon). A beginning may be made by striping out as much of that detail as possible ('simple as possible'). If the resulting model behaves ---at least a little bit--- like the real world, we may have a hold on the right end of the stick.