There was a flurry of discussion recently on campus about “critical thinking,” and how we sell that idea to prospective and current students. This was prompted by a recent report arguing for the importance of the humanities and social sciences (which I found really frustrating in ways that are neither surprising nor important for this post). This eventually led to a meeting on Monday this week to discuss this sort of thing, in the course of which one of our Deans mentioned an abandoned project to collect statements about the modes of thinking associated with particular disciplines, which I thought was the most interesting thing to come out of the whole business.

One of the examples she gave was from a mathematician, who described solving problems in math as a process of taking a big problem and breaking it down into smaller and smaller pieces, solving the pieces, then putting them back together. Which is not that different from the quick overview of physics I give students on the first day of intro mechanics, a coincidence that got me to thinking about what it means to think like a physicist.

That math description is probably fairly reasonable for scientific problem-solving in general– the various scientific fields have a lot in common, and a generally reductive approach is one of those things. Scientists in general tend to look at a big problem as a bunch of little problems that can be individually attacked and then combined to provide some answer to the larger issue. This is arguably different from the approach common to some humanities disciplines, where they tend to view things somewhat more holistically, with big problems being intrinsically Big and interconnected in a way that defies attempts to break off pieces.

But I think there are some differences in fundamental approach that set the different fields of science apart from one another, though I find them kind of hard to articulate (thus the rambling equivocation in this thinking-out-loud blog post). At least, I have a sense from teaching tons of majors from other departments and from interactions with colleagues in other sciences that there are real differences between the approach I take and the approach they take, that I suspect are attributable to my background as a physicist.

I think it comes back to that reductive approach, which I suspect is taken to greater lengths in physics than many other sciences. By which I mean that physicists, even more than other scientists, are inclined to abstract things away to get to the simplest and most universal principles. Even when that means that we end up working mostly with idealizations and first-order approximations. There’s a reason why the “Assume a spherical cow” joke is nerd-funny, after all– physicists really are prone to approximating complex objects as spheres, and spheres as points.

Going along with that, though, is the realization that a lot of the time, an approximation is good enough. There’s another terrible science joke I heard once, where a mathematician and a physicist are brought in for a psychology experiment. The mathematician is led into a room containing a bed and a chair, and told to sit in the chair, whereupon an exceedingly attractive individual of the appropriate gender enters, naked and ready for action, as it were, and lies down on the bed. The psychologist then explains the terms of the experiment: after five minutes, the chair will be moved half the distance to the bed. Five minutes later, it will be moved half the remaining distance, and so on.

“What?!?” the mathematician explodes in indignation. “I’ll never get to the bed! That’s outrageous!” The mathematician storms out in a huff. Then the physicist is brought in, and given the same explanation. “Sounds good!” says the physicist. “Let’s get started!”

The surprised psychologist says “You do realize that you’ll never get all the way there, don’t you?” “Oh, sure,” says the physicist. “But I’ll get close enough for all practical purposes!”

(I did say it was a terrible joke, right?)

Like the “spherical cow” joke, that captures something of the physicist mindset. The reason why we treat cows as spheres is that it’s often good enough for practical purposes. By the time you figure in measurement uncertainties and all the rest, the difference between the spherical-cow model and what you actually see probably isn’t too far off. You can see a lot of this in action at Rhet’s awesome Dot Physics blog, where he does a lot of simple calculations making these kinds of approximations, and gets pretty close.

Another variant of this is the “Fermi problem” game– the image above comes from this page of Fermi problems. The basic idea is associated with the great Italian physicist Enrico Fermi, who used to pose seemingly unanswerable questions as a sort of game. The idea is to use general intuition and round numbers to try to find a quantitative answer, which usually turns out to be pretty good. A good Fermi problem answer doesn’t use any exact numbers, but it’s rare to find a situation where an educated guess is off by more than an order of magnitude. Throw a few such guesses together and some are bound to be a little high, others a little low, and you end up in the right general ballpark, sometimes even in the right section and row of seats.

Physicists seem to do a lot more of this kind of back-of-the-envelope estimating than even other scientists. To say nothing of things like dimensional analysis, another of the great no-knowledge-required tricks for arriving at answers– Sean Carroll’s explanation of “effective” field theories is a great example.

The textbook we use for introductory courses has a couple of sections that use these tricks– there’s a bit where they get a value for the speed of sound in a solid from dimensional analysis, and a couple of problems where they estimate things. I try to make a point of presenting these bits (though several of my colleagues just skip them) because I think they’re important illustrations of the physics approach. Students (the vast majority of whom are engineers and chemists) invariably look at me like I’ve sprouted an extra head when I do dimensional analysis tricks, though, and whenever I assign a problem asking for an estimate, I’m all but guaranteed to get answers reported to all the digits that a calculator can muster, which misses the point.

But I’ve also had this happen even with other faculty from science and engineering departments. I’ve had several meetings where I’ve done some back-of-the-envelope toy model to check the plausibility of something or another, and get baffled stares from everybody else. Or arguments about how the round numbers I used weren’t exact (“But we don’t have 600 students in the first-year class. There are only 587 of them…”) It was a real shock the first time that happened, because I’ve always thought of that as a general science trick, but I’m coming around to the idea that it’s really more of a physicist trick. And maybe, if you’re looking for an explanation of what it means to think like a physicist, specifically, that might be the place to look.