illuminating science

1/3/2005

Back of the envelope

Filed under: — Joel @ 6:23 am

Perhaps the most universally useful thing I’ve learned through studying physics is how to do “back of the envelope” calculations, so called because all the maths and diagrams needed to solve the problem are fit onto the back of an envelope. At the extreme end are “Fermi problems”, named after the famous physicist, where all you want is an “order of magnitude” answer for a problem that is just too hard to do exactly. For instance, how many blades of grass are there in your backyard? Seems almost impossible to guess, doesn’t it? Well, say there is one blade to every square centimetre of lawn - then there’ll be 10,000 to every square metre. Estimate your yard size (let’s say a small yard of 5×5m = 25 square metres), and there’s your answer - 250,000 blades of grass! (Thanks to Brett for pointing that out - a quarter of a million blades of grass is a lot more impressive that 25,000!) I’ve done similar calculations to find the g-force on roller coasters, the force required to smash a wooden board with your fist (not much!) and even the best way to make three pieces of toast and keep them hot.

While these problems are just a bit of fun, I’ve been talking to an awful lot of people lately who say that these problem solving skills make physicists highly valued in a wide range of jobs beyond just research. You’re taught to focus on the important issues and variables, and how to make reasonable assumptions that simplify the problem to something you can do, but which still gives roughly the right solution. A major field where physicists are becoming vital is engineering. Engineering degrees these days apparently focus less on the understanding and the problem solving side of things than they did 30 years ago, instead teaching how to do things. These skills are obviously important, but it also gives physicists an important role in engineering firms. The engineering managers and leaders I’ve been speaking to recently are very emphatic that a PhD in physics is a highly sought after quality in an employee!

And it seems that universities are picking up on this too - certainly at UQ our first year physics courses are focussing more and more on the technique of approaching problems and using the basic knowledge we’ve learned of physics to solve them. Students are still learning the physics, but the way it’s taught and the type of problems and exams is evolving. I think this is excellent, as it not only produces better physicists but is an incentive for people who don’t necessarily want to be physicists to study at least a little physics.

So, I strongly recommend that if you’re going into a degree, study a little physics: it might just get you a job! And you never know, you might enjoy it and go back for more.

Brett Witty Says:

Here here! This idea also applies equally to mathematics, though you need to be careful: some people learn the facts of maths rather than the skills, and it’s hard for some to tell the difference.

I’d add a gentle maths v physics jab, but I’ll just politely mention that 10,000 blades of grass per square metre times 25 square metres is 250,000 blades of grass. I’m sure it’s just a typo :)

 
Brett Witty Says:

Forgot to mention: I’ve found a lot of the problem solving skills I learnt in university were learnt in physics rather than maths. So even if you are a major in something else, I’d second Joel’s advice and recommend you do a little bit of physics.

 
Jen Dodd Says:

Aside from the importance of acquiring job skills, this kind of problem solving is a valuable part of coursework because it feels real — you have to make sensible approximations and decide what variables are most important, and test your answers by trying the problem from several different angles.

For this reason, my most stimulating first year course was an astronomy course whose lecturers went to great lengths to include such fun calculations as assignments and as part of the lectures. Astronomy turns out to be very well-suited to this approach, because the questions can be about really important stuff. My favorite example is calculating how much more likely a collision is between two galaxies than between two stars (even during a galaxy collision).

 
Joel Says:

Good point, Brett. (For those who don’t know) I did an honours degree in mathematics, with a lot of physics thrown in, but I learned a lot of valuable skills from that, particularly how to be rigorous with my proofs, and this is something that has really helped my physics. I’ve been doing some collaborating recently where my overly-pedantic maths brain has really helped to clarify some technical details, and even earned me a place on the author list! :)

This is of course quite aside from the practical benefits of mathematics that I mentioned recently!

 

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