Consider a Spherical…

So I went out to get a new kettle a few days ago. I’ve now given up on a rather lovely design by the company Chantal that I’ve been using for many years since on two models in succession (or is it three?) the same flaw has revealed itself – the plastic parts of the Hohner whistling lid began to loosen gradually (probably from too much heat up the sides, which may be my fault) and then you eventually end up with a non-fitting non-whistling lid.

I began to assess other kettle designs, and in doing so found myself thinking idly about a number of physics issues. One of the main ones was energy. If I got a smaller kettle (the one I had before had a capacity of 1.8 quarts, and I was considering ones as big as 2 quarts and ones as small as 1.5 quarts), which I was leaning heavily toward, it would probably encourage me to save energy and not boil so much water. On the other hand, maybe that’s really silly, since I might just be putting the same amount of water into the kettle anyway… I’d never fill either up all the way in any case. But if I put the same amount of water into both kettles, would the smaller one end up using less energy anyway as I don’t have to heat up the extra air in the chamber, or does that not matter…? It’s not that simple since the chamber is not sealed. Hot air (and later, steam) is escaping all the time. Well, this is all complicated by the fact that the smaller kettle has less of its base in contact with flame, so I’d have to turn down the flame, and heat it for longer on a lower flame than with the larger kettle… would that make a difference? Perhaps a smaller chamber at lower flame means slower steam escape velocity, and so a quieter whistle. Not good if you’re prone to forgetting that you’ve put the kettle on during an absorbing computation…downright dangerous, in fact!

This was not an entirely serious discussion, you see, but it’s sort of fun sometimes to find these things floating around in one’s head. Physicists (and I imagine, other scientists) have this sort of thing flit through their heads a lot. The key thing -especially as a Theoretical Physicist- is knowing when to engage with one of these problems, and when to ignore them. Is there are clear route to tackling the problem? Is it worth it? Is there something to be learned from solving this problem that might be useful elsewhere? In fact, I was trying to explain this all to a writer friend of mine recently. We were comparing our our respective fields and daily working routines and, putting aside various similarities and differences that came up (many very interesting that I’ll perhaps talk about some other time), one of the key things I tried to get across about what Physics tries to do -perhaps a defining characteristic of Physics- is figure out what to ignore and what to pay attention to in a system under study. This is really what most Physics training is all about, and the best Physicists I know of are masters at this. The giants in my field that I’ve most admired and had the priveledge (and extraordinary good fortune) to work with and to witness at work, Joe Polchinski and Ed Witten, have this ability as their most prominent -and almost terrifyingly powerful- tool in their arsenal. The real world most often presents us with a mess of things, all mixed up and complicated. Things are rubbing and bumping up against other things, interacting in various ways, there are odd shapes, strange behaviours, and so forth. You could be the world’s greatest mathematical genius and that alone will not help you solve or understand the system. You need to think like a Physicist first. Physics training is all about figuring out which parts of those messy systems are important to the question you’re asking, and which parts are just “noise”.

This methodology is the origin of the caricatures you get of Physics and Physicists. “Consider a spherical cow”, and so forth. One of my favourites (which I related to my friend during the conversation) is the one about the table (usually applied to Pure Mathematicians, but I think it fits Theoretical Physicists maybe even better). Do you know it? I don’t recall it exactly, but the sense of it goes along the lines of: “When presented with the problem understanding the stability of a table, the physicist will rapidly solve the case of the table with no legs, followed by the case of an infinite number of legs. After a while the solution to the case of one leg will present itself, and they will spend the rest of their lives trying to understand the other cases.” I was reminded of this last year when that story – about understanding how to stabilize your rickety restaurant table resting on an uneven surface – was making the rounds in the press based on some scientific studies. (Apparently you just rotate it a bit. See here.)

Physics training is also about knowing which question to ask in the first place. There are many questions that can be asked about a given system. For one question, that stuff that was identified as noise or ignorable clutter (for another question) might now be an essential piece that must be included in whatever solution you find. Also, not all successful Physicists focus on the same questions. It’s a “cultural” thing (in the sense of Physics – your background, training, skill set, personal tastes), all of which adds to the richness and beauty of the field.

Once you’ve found your question, and separated out the noise from the signal (usually by identifying a reliable approximation scheme), then you’re ready to bring out the mathematical tools and solve the problem using brute force and whatever tricks you’ve learned over years of experience. How that process works is another lovely story altogether, perhaps for another time. The last step in the sequence is to step back from the Mathematics and plug everything back into the Physics problem and answer the original question.

This is what it is to understand aspects of a physical system – that identification of what is going on at the core of it all, once you’ve identified and stripped away the noise. One of the remarkable things about Nature is the fact that more often than not, the things learned about understanding one system often show up in what (on the surface) is a completely irrelevant and different system. This is part of the reason why our Physicist-brains are switched on all the time. Even in the silliest of situations, one can sometimes find interesting problems. It is also one of the big reasons that the often heard nonsense that scientifically analyzing something from Nature spoils its beauty is, well, nonsense. If anything, it is a way of seeing even more beauty than meets the eye.

Anyway, I went for the smaller kettle, and yes it was made by Chantal again. They do make such lovely ones, and so I thought I’d give them another chance. It has a brushed stainless steel finish, which some polished steel parts, and that’s all. It’s nice and simple. This is all in line with the look that I like for my kitchen (see, e.g. here), so that was a major deciding factor. Visual aesthetics won out here, and Physics played no role. However, when I got it home and put it down on the stove, I burst out laughing. Look at it! It’s the ultimate theoretical physicist’s kettle – basically a sphere with the other essentials added on! So… Consider a spherical kettle…

-cvj