A spherical cow is usually a parable to describe how physicists tend to have an oversimplified view of the world. On the other hand it is a great metaphor for how we actually go about solving problems. Between us physicists, we have other words to describe these spherical cows. The name spherical cow for some reason just does not sound respectable…
Let me give you an example of how spherical cows might be put to some use. Assume that a cow is falling from a cliff onto a body of water like a lake (we don’t want the cow to get hurt after all, we are not cruel). A physics question you might ask is how long does the cow take to fall. This is controlled by gravity and the height of the cliff. One of the things we know is that the shape of the cow does not really change the result much. Sure, there is some air resistance, etc, etc, but these effects are small. Saying an effect is small is stating that you only need an approximate answer and not an exact one. For these situations, given that you don’t have the information of the exact shape of the cow and that you don’t need it, it might as well be spherical. Now, a spherical cow falling on water would be a comical sight. Don’t you think? Well, you might also consider that a lot of flailing legs and a panicked look on the face of a cow is funny.
On the other hand, without making simplifying assumptions, physics problems tend to be so hard that nobody can solve them. One might hope that the assumptions one has made capture the essence of what the physical system is doing.
Now let me guide you through some of the terms that we use in technical papers to describe a spherical cow with an explanation
- “Toy model”: hopefully this model has something to do with the original problem that I couldn’t do.
- “This is a very rough approximation”: We are calling a spherical cow a spherical cow. If you are lucky the order of magnitude is right.
- “An approximation”: One can probably do better, but this is all I can do now.
- “To zero-th order”: This suggests that there is a systematic way to improve the calculation: these are called first order, second order, etc.
- “An uncontrolled approximation”: Something that seems to work even if I don’t know why.
I’m sure there are more, but this is an approximation to the lingo actually used in papers. (Notice the subtle use of words to describe how much I believe in the above list) . You should also notice that spherical cows can be put to good use by making humorous cartoons, like the one depicted in this post. It is my first cartoon and it is obviously a variation on a theme. Let me deconstruct it for you.
The guy with the hat is supposed to be a farmer or cowboy. You should be able to tell by the clothes. He is also calling by phone the most recognizable physics person name out there. It is the way one hints that the cartoon could be talking about physics for the non-expert in physics humor. It is also funny to imagine that physicists would be in the job of selling cows over the internet. Finally the cow is cute. You can also tell that I can’t draw well, so I had to use computer aids in generating the graphics.
Finally, since I put so much work in it, I must as well put a copyright notice on it: so long as you don’t use my spherical cow for profit, go ahead. Otherwise, I want a piece of the action.
**** Clifford also has something to say about spherical objects in general. Thanks Clifford.