How many bus conductors are there in Jerusalem?
An interesting anecdote.
One of the courses I taught last year was "order of magnitude (OoM) physics". In the course, the physics students learn how to think like physicists, that is, boldly (try to) solve questions, especially those without a precise solution, by carrying out estimates, building simple models, doing dimensional analysis, etc.
I wish I could, but I cannot take credit for thinking of such a course. When I was a post-doc at Caltech more than a decade ago, an equivalent course was given by Profs. Goldreich and Phinney. I went to a few of their fabulous lectures and decided to teach it one day.
Anyway, one of the classical questions in OoM estimates is of course Fermi's question of how many piano tuners are there in Chicago. And, the first question I asked the students in their final exam was, "how many bus conductors are there in Jersualem?" (By bus conductor I mean these people that rarely go aboard and check that everyone has a ticket, with no stowaways). Other questions included, among others, calculating the speed with which a soap bubble bursts, estimate the speed of Alfen waves, and how cold is it in the arctic on average given that it develops a 1.7 meter ice sheet in 6 months, that is, the kind of questions physicists should be able to answer, or at least estimate, with a pen and piece of paper (preferably, the back of an envelope).
A curious graduate student of mine decided to estimate the answer, but later he also carried out an actual experiment, or should I say measurement. He asked a driver who tried to count all the conductors he remembered, and counted 10.
A few days ago, I gave a talk in an unrelated venue. A few of the students approached me later, reminded me that they took the OoM course with me. Then one of them said that he asked a bus conductor how many are there in Jerusalem. The answer was 12, but it was followed by a question by the conductor, "Are you also a student of Nir Shaviv?"
Incidentally, the answer to the typical time it takes the soap bubble to burst is
$$ t \sim \sqrt{\Sigma \over \gamma} r ,$$
with $\Sigma$ being the surface density of the bubble, $\gamma$ being the surface tension and $R$ the radius. For a 5cm bubble, one gets ~10ms. (The values of the different constants can be estimated from the fact that a bubble this size will start to significantly deform from its own weight or from a drop of water).
Comments (8)
Hi. I'm sorry that this is not the correct place to post this, but I was wondering if you had heard about the Hadley CRC document leak/what you think about it:
http://digg.com/world_news/ Hadley_CRU_hacked_with_release_of_hundreds_of_docs_and_email
I heard of the CRU hacking (which is not the Hadley Center I think). I personally don't condone hacking and the publication of personal e-mails. Nevertheless, from what I've read in blogsphere, the e-mails did not reveal anything I didn't think was happening anyway (though it may help the general public get a glimpse of that). I also don't think that the scientific battle between the so called skeptics and alarmists should be played on that ground. I personally know that my colleagues and I have valid scientific arguments and it is those which will eventually prevail, irrespective of how dirty people play as we can see.
When you say
"the e-mails did not reveal anything I didn't think was happening anyway"
you mean that you knew all along that the climate scientists were hiding data and conspiring to block skeptic papers from publication and from the IPCC, and skewing the peer review process ?
" the climate scientists were hiding data"
Look at what happened to the data on Mann's ftp site.
"and conspiring to block skeptic papers from publication and from the IPCC, and skewing the peer review process ?"
An editor of one of the more prominent journals wrote a colleague of mine that "any paper which doesn't support the anthropogenic GHG theory is politically motivated, and therefore has to be rejected".
There are many more examples. As I said, these e-mails do not surprise me. They just provide a window to whatever I had thought was happening anyway.
Now the new questions should be: "How many bus drivers in Jerusalem know who Nir Shaviv is?"
I think you mean bus ticket inspectors, not bus conductors.
My first test at university included a question on grass growing in a field with grazing cows in my native Sweden. When will the grass reach 30 cm of height in average was the question. We all failed, as the answer was "never: grass in Sweden never reaches 30 cm of height in average due to the relatively short summer". I still love that teacher, and hope that your students appreciate you as much.
I agree with your teacher's answer 'Never', but a field with grazing cows won't have much grass taller than about 10cm, however long the summer.