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.
Isn’t it more common to assume that the cow is a point mass at its COM?
Or are you worried about its MOI?
To answer your question, I can’t draw a point-like cow that looks like a cow. And I think the technical answer to that question is yes.
The falling cow’s shape can be fundamentally important. If the vacuum is isotropic you get Einstein’s elevator. If the vacuum contains a chiral pseudoscalar background you still get Einstein’s elevator – except if you drop a pair of shoes. Opposite shoes fit on a left foot differently. Put on two identical left shoes, close your eyes, and try to walk a straight line.
Theory predicts what it is told to predict. Safe experiments validate agreement, important experiments seek divergence. Before Christmas Day 1956 Yang and Lee were upstarts and fools. Orthodox theory demanded it! On New Year’s Day 1957 things had changed, as did orthodox theory.
Gravitation does not quantize and then testably predict. Somebody should drop a pair of shoes (pdf) and look for a naughty footnote. (The cow is chiral via L-configuration protein amino acids. That is not chiral enough.)
Welcome to the Physics blog-o-sphere! I’m a high school physics teacher…fyi…and have enjoyed your first posts. Love this blog on the spherical cow and especially the cartoon! Can I use it in class? We, of course, are always doing similar things to reduce the mathematical complexity to something the students can handle. This would be a nice tie-in with how ‘real’ Physicists also do simplifications of complex motion.
Hi Michelle:
You are free to use the cow in class. I’m glad you like the cartoon too.
I don’t know if cows are like cats, by our cats would clearly like to be spherical someday. (Judging by their eating habits.)
The physics joke that I know along these lines actually involves a spherical horse: “Assume the track is frictionless and the horse is a perfect sphere…” But somehow a spherical cow, or cows in general, are more innately humorous than horses. Anyone who watched the new show Fringe last night may note that they brought in a cow; I am pretty sure that the cow served no scientific purpose, and was merely there for humor value. 🙂
Hi David!
Welcome to the blog-o-sphere! Got referred to your site from Mark over at Cosmic Variance. I’m looking forward to your posts, and may your blog enjoy a long and lively life!
Very interesting blog. Retired physics teacher and presently online tutor (tutor.com).
You got me thinking about spherical milk and spherical MacDonald’s burgers. Or should it be dimensionless milk and burgers? Would dimensionless burgers have less cholesterol or just spherical cholesterol? Or is it just an isotropic pseudoscalar chiral cholesterol? See what dilemmas you create?
Cholesterol has 8 chiral centers and thus 256 stereoisomers. Take a precursor achiral linear polyolefin, ball it up in mostly aqueous medium, initiate a cationic zipper. The first chiral center formed locks all the others. Two stereoisomers emerge.
One stereoisomer obtains biologically. How did biology become homochiral – chiral protein L-amino acids and chiral D-sugars? (Looking glass milk is not good to drink.) Scholarly posits are thermodynamic faery dust,
Mendeleev Commun. 13(3) 129 (2003)
Angew. Chem. Int. Ed. 41(24) 4618 (2002)
Vacuum chiral in the massed sector originates a spherical cow you can eat. String theory and SUSY could fall in an Eötvös balance. Somebody should look (pdf). A homogeneous isotropic solid sphere is crypto-chiral. Hey man… have a cow!
Hi Todd:
Do you know if spherical cats bounce better than regular cats?
At our university, some of us undergraduates joke that for certain problems (perhaps those that are highly nonlinear), we may have to make the inverse approximation, where we approximate spheres as cattle instead.
David wrote:
Do you know if spherical cats bounce better than regular cats?
Sadly, the more spherical they become, the less bouncy they are. 🙂
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Some addition information blogged here for consideration in concert with what David offers within this entry.
AS a lay person, I am interested how this approximation is done.
Best,