Approximations

The post Assume a Spherical Physicist at The First Excited State brings back happy memories of when I was in school. I never mastered thermogoddamics, but I was a whiz at rapid approximations.

• It’s on the order of…

This is the jargon that physicists use when we are doing really rough estimates. Often, you don’t care what the actual numerical value of something is, you just want to know whether it’s about a meter, a nanometer, or a kilometer. This gives us free license to be sloppy. Pi is equal to 3, or 1 if we really feel like it. We don’t have to remember whether the equation has a factor of 2 in it, or the exact values of constants, and we can feel free to make any of the other approximations as we see fit. These calculations are sometimes called “back of the envelope calculations,” since we might work them out on any scrap of paper lying around, as the answer will not be quite worth saving. This is not to say that the answer is unimportant, however, as the calculation can give us a conceptual understanding of how the system in question behaves.

The new blog Shores of the Dirac Sea has a nice list of how such approximations are called in the jargon of technical papers:

• “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.

One of my profs used to say, “The most important thing is physics is to make an even number of sign errors, so that you are right about whether the result is positive or negative.”