Physics Is All About Analogies

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...

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Mass on a spring: The chicken of physics. Even gravity tastes a bit like harmonic oscillator.

I do think analogy is hugely important for thinking, but I'm unconvinced that approximation and analogy are that related. When we reduce systems to harmonic oscillators, we can often get a pretty good quantitative sense for what we're throwing away. I don't see anything similar going on with natural language analogies, and I think that's the reason for the complaint (I'm unfamiliar with the particular example cited.) I think people rarely object to good analogies, but the trouble is that for a lot of things coming up with good analogies is very hard, and we don't really have any rigorous way of telling how good an analogy is.

I'd go further -- I'd say the primary way humans learn and think and talk in general is by analogies. When you attempt to describe something to someone else, it's nearly always by analogy: "big as a house" or "serious as a heart attack" or "my love is like a red red rose" or "this band is like a cross between Elvis and Iron Maiden" or whatever. It's built into the structure of language. The etymologies of words themselves often turn out to be rooted in analogy. "Hippopotamous" means "river horse" right?

Anyone trying to figure out how something works is going to inevitably compare it to things they already understand. "Electronic mail" is an analogy to the postal system. A "car" is something like a railroad car which is also something like a carriage.

If you start trying to assemble a machine you do it with a bunch of analogies in your head -- this is probably a switch like a light switch -- this is probably a drive chain like a bicycle chain -- this is probably a heating element like a stove burner... If you have never see a bicycle or a stove or a light switch before, you're going to have a hard time assembling anything in your workshop. (And how do we understand bicyles etc in the first place? We talk about the gears having "teeth" and the chain "driving" the wheels, a word that used to describe a human marching behind a herd of animals...)

Really it makes no sense to me to think about trying to explain anything, much less physics, without analogies. Why do we even talk about electromagnetic "waves"?

The question is simply how far do you try to extend those analogies. It can be a mistake to insist too much. You don't want to give people the impression that electromagnetic waves are exactly like water waves, even though they have some important features in common. Electromagnetic waves don't splash, and don't need a medium to sustain them, so its wise to put in some disclaimers now and then when you're using that analogy.

But I'd say that formal physics education needs more analogies, rather than that pop science needs less. It's easy to fool yourself into thinking you understand something when all you really know is how to manipulate symbols in a formal system according to a rule set -- a computer can do that, but it doesn't understand what it's doing. It's a cop out when classes teach you the math but don't give you the mental pictures to go with it.

I got really frustrated with E&M, which was taught to me more as a formal system, an exercise in vector calculus, than a physical phenomenon. So I bought a book with some of Maxwell's early papers, and found him writing about electric fields as being like a nest of fluid filled tubes, with the fluid flowing in different directions with different pressures at different points in space...

Nice post, and fair points. I definitely didn't mean to make "the implication that making sophisticated concepts comprehensible is not worth doing" -- that's not what I think "trying too hard" means. Rather, I mean that there's clearly a lot of effort going into it, but the effort seems misplaced. Even in cases where I understood both sides of the analogies she was making, I had a hard time seeing which aspects of the things were supposed to be similar. I just didn't have the impression that they would work very well for a lay reader. Maybe I'm wrong, though.

I think of physics analogies a bit like translated poetry: some translations attempt to create a vague impression of the original, and some attempt to make something independently beautiful, but neither approach can really bridge the language gap. Ultimately, physics is spoken in the language of mathematics, and translation is at best only a rough approximation.

i was told as an undergrad that 90% of physics is the harmonic oscillator, and the other half is the particle in a box.

One more point: When you linearize some equations and then use your knowledge of the harmonic oscillator to solve these equations, I donât think you are using analogies. The systems described by the linear equations are not necessarily analogous to oscillators, in any sense in which the word âanalogousâ is used. Iâd say that when you learn harmonic oscillator, you are learning the basic language of your profession, which you can then use to express various different ideas.

I also think that you misunderstand the AdS/CFT correspondence which you refer to. The two sides there are not supposed to be analogous (i.e, share certain properties, but differ in others). They are supposed to be exactly identical, two different descriptions of one and the same object. How is that possible, despite the two descriptions looking so different, is what makes this so interesting.

The systems described by the linear equations are not necessarily analogous to oscillators

Except that they are, because the equations have exactly the same mathematical form as the equations for oscillators. Only the constants in the equation change.

For example, this is how Maxwell predicted that light was an electromagnetic wave. He considered his eponymous equations for the case of no external sources. He showed that you could derive something that looks exactly like the wave equation, with an implied wave speed of 1/sqrt(ε_0 * μ_0), which just happens to be c. (In Maxwell's day the agreement was within the precision to which ε_0 and c were known; today, both c and μ_0 are defined, constituting a de facto definition of ε_0.) This is a case of an analogy taken too far, because it led to people postulating the existence of an ether (all other known waves require a medium in which to propagate, so this was a natural assumption until experimentally disproved), but we still call light an electromagnetic wave.

By Eric Lund (not verified) on 05 Nov 2010 #permalink

I guess we differ in our intuition on how much similarity you need between systems for them to be "analogous". I'd say that certain type of differential equations are part of the language of physics (and not only physics), and different systems that are (partially) described by the same equations are like different novels that use the same alphabet. In fact, similar equation are used e.g in economics, would you say that the stock market or some bacterial population are analogous to a gravitational wave, because they both use the same piece of mathematics as a small part of their description?

I think at least in part, an important part of what makes an analogy is reduction to the familiar. In case you deal with things that are very much removed from daily experience of most people, that is not necessarily a good explanatory strategy.

I recommend: Similarities in Physics, by John N Shive & Robert L Weber, 1982, Wiley-Interscience, ISBN 0-471-89785-7

Thinking in analogies is just a method we can use to make the transference that gives insight, and which then leads us to further discovery and problem solving. It is a way of modeling a concept in familiar terms, adding a new perspective and toying with it. Most of us will do this as naturally as kids will fiddle with unfamiliar objects (which is where scientists get started). To teach or explain using analogy is certainly valid if it increases understanding, because that's what it is all about.

What exactly would this anti-analogy commenter propose we use as a substitute for analogies in his gloomy analogy-free world?

Similes? Possibly, but wouldn't they result in a different form of confusion due to their very lack of vagueness?