freshwater consumption

I'd like it to be a theme of my writing about teaching that I learn as much as any student in my class when I teach! It certainly is a fact. This semester has been huge for me because I'm teaching a subject I don't know much about (sustainability), and because I am teaching writing, which is a first (yes, in 25 years of teaching, I have never taught writing).

A few weeks ago I gave a (writing) assignment to estimate global freshwater needs by computing your own freshwater needs and extrapolating to the world. Then compare with estimates of global usage. My expectation: That a typical American college kid uses way more water than a typical person on Earth, and this would be a lesson about disparity. I wasn't wrong, but I also wasn't right either:

It turns out that global freshwater use is way larger than any estimate of your own personal water use, extrapolated to the globe! Isn't that odd? It's because global freshwater use is not dominated by household uses like laundry and toilets (which, by the way, don't need freshwater). It is dominated by agriculture. If you add in your own share of agricultural water use, a typical American uses way more than the average human! But it is hard to know or estimate this without significant engineering research.

There was one clue, however, in the essays I got: One student included the amount of water used to water a lemon tree in their dorm room. It was a trivial amount of water, so it was almost a joke. But then if you think about how much food we eat relative to the miniscule annual production of that tiny lemon tree, there is a little window into just how much water we must use for agriculture.

LHC energy and momentum

Problem: The LHC delivers 8 TeV per particle in bunches of 10¹¹ particles. What is the kinetic energy and momentum of a bunch, in SI units and then as compared to (a) a small-caliber bullet and (b) a Major-League baseball pitch?

I get that the bunch has far more kinetic energy than either a bullet or a baseball pitch, but far less momentum. A LHC particle bunch would burn you badly, but it wouldn't knock you down! Of course there are some 10⁹ bunches per second, so you don't want to be hanging out in the beam line when it's running.

teaching physics teachers

I took a break from my no-teaching, all-research sabbatical to make a guest appearance this week in Jhumki Basu's course Recent Advances in Physics in NYU's education program. Her students are building new science units with help and ideas from current researchers. I presented not really my research, but some of my research techniques: estimation and approximation. No surprise there!

I showed on dimensional grounds that cars like the ones we currently drive will never do far better than 30 miles per gallon. 100 maybe. But never 1000. A nice result, with important implications, using only techniques that a high schooler could easily muster.

After I spoke, we discussed, and it was noted by one and all that despite the simplicity of the techniques, in fact estimation and approximation techniques are non-trivial and sophisticated. It is hard to incorporate them incrementally into the existing New York State middle- and high-school curricula. On the other hand, it is my (perhaps optimistic and/or utopian) view that if these things were the focus of quantitative education from day one, they would be easy to have mastered by the end of high school. Of course the teachers I was talking to are going into the system that exists; they can't start from scratch!

Many other interesting things came up, which I hope to blog about at some pont in the future, including students' lack of contact with machinery and hardware and electronics, and the idea (that I hold, but others don't) that education ought to give students skills and tools, rather than knowledge.

mean average rainfall

I dropped in on Sanjoy Mahajan's course 6.055/2.038 Art of approximation in science and engineering at MIT yesterday. We learned about mean average rainfall; you can estimate it pretty well by considering the mean Solar flux, the specific heat of vaporization of water, and the density of water. If you assume all of the Solar flux goes into evaporating the oceans you get 5 m/yr of rainfall, but the true average on the earth is about 1 m/yr; the factor of 5 comes from things like the fact that much of the earth is land, much is covered by clouds, light is reflected, light is absorbed by other processes, and other messy details of the energy budget.

After class, Mahajan and I discussed the size of raindrops, which has a similarly simple calculation: They break up when the stresses exceed the surface tension stress; the main stress is air resistance, which, at terminal velocity, is balancing gravity. I haven't checked the calculation, but Mahajan says this gives you a few mm.

cars and energy

I worked out a page of dimensional analysis and order-of-magnitude estimation to compare automobile energy expenditure in the form of acceleration with energy expenditure in the form of battling air resistance (ram pressure). After putting it together I realized the obvious: The air resistance losses exceed the acceleration/braking losses when the journey is long enough that the car has swept up its own mass of air! This means that for typical US cars, acceleration/braking dominates for journeys much less than 1 km (or city journeys in which there are stops much more frequently than once every km), and battling air resistance dominates for journeys that are uninterrupted by stops for distances much longer than 1 km.

forces and formality

Yesterday in class I worked through the problem of a bouncing ball, concentrating on estimating the magnitude of the force from the floor at bounce. Not a single student was even close to getting the magnitude of that force correct, even after many minutes of discussion, a few minutes of working in small groups, and more discussion. Eventually two students got it and understood after my demonstration in which I prepare to drop a book on a student's hands (comparing with the case in which the student is just holding the book).

Before, during, and after the class, students asked me if the class is going to be more formal soon or ever. I said yes. But what disturbs me is that if we go and do formal problems with vectors and calculus before the class can see even roughly the magnitude of the normal force on a bouncing ball, we are teaching math, not physics. I understand where the students are coming from: They like physics in part because it is formal. But there is no point in calculating forces when you don't understand what forces are.