The phrase comes from a joke about theoretical physicists:
- Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer "I have the solution, but it only works in the case of spherical cows in a vacuum."
It is told in many variants, including a spherical horse in a vacuum, from a joke about a physicist who said he could predict the winner of any horse race to multiple decimal points - provided it was a perfectly elastic spherical horse moving through a vacuum.
The point of the joke is that physicists will often reduce a problem to the simplest form they can imagine in order to make calculations more feasible, even though such simplification may hinder the model's application to reality.
In a related joke, the farmer contacts the local university's renowned mathematician and asks for a solution. The mathematician takes notes and returns to the university. The farmer eventually becomes concerned when several weeks pass without any response, and visits the mathematician's office. Finding the office empty but what looks like a feeding schedule on the desk, the farmer borrows the schedule and begins applying it on the farm. When the cows begin producing milk, the farmer calls the mathematician to thank him, only to be told mournfully "oh, but I was never able to complete it — the solution only works in the case when the number of cows is greater than zero, and each cow has a finite mass." This refers to the concept of a mathematical proof, which must demonstrate that a solution to a problem is valid for all possible sets of values, even though some of the sets of values (cows with infinite mass) are physically impossible.
- Episode 1 of the satirical comedy series Brass Eye includes a scene where the presenter, Chris Morris, talks about the unethical production of beef from spherical cows.
- In the sitcom The Big Bang Theory, in Season 1 Episode 9, Leonard Hofstadter cited this joke with slight variation (as "spherical chickens in a vacuum").
- Shelton, Robin; Cliffe, J. Allie. "Spherical Cows" nasa.gov
- Kirkman, T. W. (1996). "Spherical Cow: A Simple Model". Statistics to Use. Retrieved 2007-02-19.
- Hefley, Bill; Hefley, William E.; Murphy, Wendy (1 February 2008). Service science, management and engineering: education for the 21st century. Springer. p. 80. ISBN 978-0-387-76577-8. Retrieved 28 September 2011.
- Birattari, Mauro (15 April 2009). Tuning Metaheuristics: A Machine Learning Perspective. Springer. pp. 183–184. ISBN 978-3-642-00482-7. Retrieved 1 September 2012.
- "Fedora 18 Is Codenamed The Spherical Cow". phoronix.com. 2012. Retrieved 2012-05-11.