Spare me the math
Part of what scuttled my blogging during the past couple years was the fact that every post took me such a long time to write. Crafting a careful, conceptually clear, and readable blog post takes (me) a lot of work: I would estimate that the average physics-related post took me 12 (non-consecutive) hours to write. As a consequence, my blogging became infrequent, and I was often too daunted to try and delve into some interesting scientific topic.
In this second time around, I’m going to try and fix that a little bit. I’ve decided to confront my fear of writing sloppy or incomplete posts by, in short, writing sloppy and incomplete posts. I’m hoping that the increased breadth of material will compensate, to at least some of my readers, for the potentially decreased quality.
I’ve also resolved to have less trepidation about delving into more “hard core” topics from condensed matter physics, which is my own subfield. These topics aren’t conceptually more difficult than, say, the second law of thermodynamics or the double-slit experiment; in fact they’re usually simpler. It’s just that they are generally discussed only by a more professional audience, and so they can seem daunting to someone who is uninitiated. But it seems to me that for many of these topics there is a real dearth of qualitative discussion. And a lot of them are really pretty cool.
In light of these two resolutions, I’ve decided to institute a new series of posts here at G&L, called “Spare me the math” (SMTM). The idea of SMTM is to look at some topic from “advanced” physics in a brief and very conceptual way, with the goal of bringing some “feel” for a physical phenomenon that can be hard to get from typical textbooks or Wikipedia articles. Where possible, I will try to include just enough equations to codify the most important physical relations at work. If I do my job well, then there should be enough information to put together a schematic derivation of the primary results, at least to within numerical factors. As usual, I use math as a tool for remembering and reasoning with basic dependencies, and not as a series of exact statements.
So in that sense, Spare Me The Math will not actually be “math-free”, in the sense that you can still expect to see very basic equations. But it should be “hard math-free,” or at least “formality-free.” Or in other words, the focus will be on big picture ideas, with a little algebra (and maybe a little calculus) to piece them together and help you keep track of them.
It has been my experience, by the way, that such simple derivations are much more useful for scientific thinking than more formal ones; so it’s unfortunate that textbooks (and academic papers) are almost always dominated by the latter. I am always pleasantly surprised by how much easier it is to talk science one-on-one with someone than it is read their papers. That’s because in a one-on-one conversation a scientist will talk to you in the language that s/he uses to think about the problem, whereas when writing a paper everyone gets paranoid that they’ll say something incorrect and be called out for it. But as my undergraduate advisor used to say, “what’s a factor of between friends?”
I should, of course, reiterate the caveat that my explanations may be unsatisfying, incomplete, or just plain wrong. They represent only the best way I have to think about the problem. If something sounds rotten to you, please say so in the comments.