Regular commenter onymous left a comment to my review of Warped Passages that struck me as a little odd:

The extended analogy between the renormalization group and a bureaucracy convinced me that she was trying way too hard to make sophisticated concepts comprehensible. Also, I’m not really sure that analogies are the best way to explain concepts to people without using mathematics.

I’m not talking about the implication that making sophisticated concepts comprehensible is not worth doing, but rather the negativity toward analogies. It’s odd because, if you think about it, a huge chunk of modern physics relies on the making of analogies.

I’ve got a little speech about this that I give when I talk about simple harmonic oscillators in the intro mechanics class, that I started giving because I got sick of the students giving me pitying looks when I went on about masses on springs. Because, really, who gives a damn about masses on springs?

Of course, any physicist knows that the reason we spend time talking about masses on springs is not because masses on springs are inherently fascinating, but because so many systems that *are* interesting can be made to look like masses on springs. That is, there is an analogy to be made between the behavior of a really simple system that we can solve exactly (the mass-on-a-spring problem) and much more complicated systems that we would really like to be able to solve exactly.

The correspondence between a mass on a spring and some more interesting system is everywhere in physics. It’s how we understand the motion of a pendulum, or the vibration of an extended object. It’s the basis for the simplest model of the propagation of sound and heat through a solid. It’s the starting point for models of vibrating molecules. Even our theory of light as a quantum field comes from making the electromagnetic field look, mathematically, like a mass on a spring.

The mass-on-a-spring problem is probably the single most important analogy in physics, but the basic technique is everywhere. Interactions of two-level systems are inevitably described in language derived from looking at spins in a magnetic field. The greatest success to come out of string theory is the much-hyped correspondence between a strongly interacting gas and a higher-dimensional gravitational system, which is, at its core, just a complicated analogy. And, of course, string theory itself comes from the correspondence between the behavior of mathematical objects describing particles and the mathematical description of a vibrating string. Which is, itself, a variant of a mass on a spring.

So it strikes me as odd to say that analogies are not the best tool for making complex ideas comprehensible, because that’s most of what we do in physics. Our primary tool for understanding complex physical phenomena is the analogy– we find a way to map a new and interesting system onto a simpler system that we already understand, and that analogy guides everything that comes afterwards.

Now, you can argue that the analogies we use in physics are *mathematical* analogies, and thus do not suffer from the same crippling flaws as analogies aimed at the laity. And there’s something to that– the sort of mathematical correspondences that form the basis of most analogies within physics are much more quantitative and rigorous than the sort of thing that pop-science book writers engage in.

This isn’t a perfect counterargument, though, because most of the analogies we use in physics do break down. In fact, that’s the origin of a lot of the hard work in physics– if a vibrating molecule really was exactly like a mass on a spring, molecular physics and chemistry would be really, really easy. It’s not, though, because treating a vibrating molecule as a mass on a spring is only the starting approximation that we use to make the basic behavior comprehensible. The real work in physics comes from figuring out where the analogies fail, and finding ways to patch or extend the simple models to cover situations where the analogy is less than perfect. Which, in turn, usually involves finding new analogies.

So, I’m not sold on the notion that there’s something wrong with using analogies to explain physics concepts to non-physicists, because analogies are the main tool we use to explain physics to other physicists. I’ll agree that bad analogies can cause problems, but that’s due to the badness of the analogies, not an inherent weakness in the method of explaining complex things by comparing them to simpler and more familiar things.

But then, I have a lot of time and effort invested in making an analogy between teaching quantum mechanics and talking to my dog, so I *would* say that…