Hofstadter’s Spherical Chickens

I really love the comedic series “The Big Bang Theory”, however in the episode “The Cooper-Hofstadter Polarization”, Leonard recites a joke that greatly amuses Howard, Raj and even Sheldon. At this point during the episode, I felt my own countenance mirror Penny’s as I was left deeply confused.

“There’s this farmer, and he has these chickens, but they won’t lay any eggs. So, he calls a physicist to help. The physicist then does some calculations, and he says, um, I have a solution, but it only works with spherical chickens in a vacuum.”

The origins of this joke come from the notion of a spherical cow. In theoretical physics, problems are complex and difficult to imagine, and so a spherical cow in a vacuum is used to simplify the problem, even though this simplification may lead to inaccuracies when applying the solution- once found!- to real life. For example, when creating models of motions, certain conditions must be taken into account;
• Air resistance
• Air density and any variations of this
• If the gravitational field is constant, or if gravitational interactions happen due to large objects nearby
• If the object is flexible, inflexible or semi-rigid
• If there are any electromagnetic or electrostatic interactions

Therefore, physicists use the spherical cow in a vacuum. The vacuum means that many of the conditions, such as air resistance, do not have to be considered. This is because there are no particles, including air particles, in vacuums.

The cow is spherical, as spheres have minimal surface areas. This keeps heat transfer- through radiation- minimal. A good biology comparison for this is to consider the small intestine. Molecules of broken down food pass through the small intestine, where absorption takes place; this means the important nutrients in the food- such as glucose- will pass through the walls of the intestine and into the bloodstream where they will be assimilated. The larger the surface area, the more opportunity for absorption. Therefore, the small intestine is lined with villi and microvilli, to increase the surface area and create more opportunity for absorption. On the other hand, physicists want minimal heat loss when calculating theories. The cow is therefore spherical, as there is as little opportunity for heat loss as possible because the surface area to volume ratio is low.

Villi mean that the small intestine has a larger surface area, photo from bbc.co.uk

Therefore, Leonard’s joke implies that he has calculated a theory for the farmer’s chickens not laying eggs, however because he has simplified the problem to make it possible, the solution only works with spherical chickens in a vacuum. Bazinga!

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