Ugh! I sure hope the people at CERN have a better grip on astronomy than this sentence.

A "full" moon is no closer than a "new" moon. Only our angle of viewing it makes more light reflect off it. The moon does vary in distance, but not directly related to its fullness.

Sorry, to go off-topic but some things are so wrong they shouldn't be allowed to stand.

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I’m sure you have seen references to the discovery of the Higgs boson particle by physicists working at the Large Hadron Collider in Europe. Today, I read an interesting thing about the super sensitivity of the energies they are trying to work with. The paths of the proton particle streams they send around the 17 miles of collider tunnel to collide with one another must be altered to account for the rising of a full moon. That is the power behind our concept of lunacy, after all.

http://www.msnbc.msn.com/id/47880473#.T_eJrnAmx5Q (see the box on the right side about Stephen Hawking being a bad gambler [topic of another, still more recent, LL post: http://languagelog.ldc.upenn.edu/nll/?p=4059%5D)

[(myl) The effect is not due to the energies that they're working with, as I understand it, but to the size of the accelerator ring. Crustal deformation due to lunar tides changes the effective diameter of the ring. See here for graphs and equations.]

]]>Certainly in the case of graduate school, I found that course overlap with upcoming qualifying exams appeared to be a rather good predictor of course attendance.

]]>[(myl) This sort of argument is always very tricky. It shows that the observed pattern of numbers of students in classes, or viewers in movies, or residents in cities, or whatever, has the form expected if the only thing going on were a Dirichlet Urn Model, in which the rich get randomly richer, with (as you say) "no real a-priori rhyme or reason".

But that's not the same as showing that in fact no such rhyme or reason exists — you might instead have a model in which the a-priori attractiveness of movies or courses is assigned by the same sort of random process, and attendance then stochastically follows attractiveness. Or you could have some sort of mixed model, in which there is one process for distributing intrinsic attractiveness, and then a second one for distributing customers, with the second one dependent both on the product's attractiveness and its popularity.

Such models are generally more plausible in those cases where we have some independent knowledge of the situation — thus the growth of cities is clearly determined in part by geography and politics and so on; enrollment in courses is partly determined by requirements and teaching quality and grading difficulty; and so on.

There's a similar argument to be made about Duncan Watts' "Accidental Influentials" theory: it's true that social network have the statistics you'd expect if they grew by random rich-get-richer accretion — but this doesn't mean that the behavior of the nodes in network has no effect on the process. See Alexy Khrabrov, "Mind Economy: Dynamic Graph Analysis of Communications", Penn PhD thesis 2011, for a demonstration that traditional ideas of "social capital" do apply to the dynamics of social networks.]

]]>Check out England in 1700: just wildly off from Zipf's law. (The second-largest city was about 10 times smaller than it ought to be.) I recall finding a number of cases like this, but the others escape me at the moment.

]]>Of course, we have to leave out the spin-statistics connection, since MYL doesn't share his chair with a spin-down occupant.

]]>[(myl) This doesn't seem consistent with Jason's Dirichlet Urn Model, where the more people choose to view a given movie, the more likely it is that the next viewer will choose that one as well.]

]]>Well, apparently the Bose-Einstein model fits these data. I think you're asking: why might one sensibly *expect* it to fit?

A random partition of indistinguishable objects, imposed upon the students from above, would indeed be an odd model of course selection, but it is not the only way to obtain Bose-Einstein statistics. Here is a more plausible construction in which the students instead act in series:

Suppose that when a student is choosing where to fulfill a CU, she chooses course c with probability proportional to n(c)+1, where n(c) is the number of students *previously* enrolled in c. This so-called Pólya urn model is an oversimplified model but not too crazy. It too yields the observed Bose-Einstein statistics, if I'm not mistaken …

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC432601/

[(myl) Cool! If only Google Scholar had existed in 1995, I might have learned (Wen-Chen Chen, "On the Weak Form of Zipf's Law", Journal of Applied Probability, 17(3) 1980) that when

… we consider more general Dirichlet-multinomial urn models which include the Bose-Einstein models above as special cases and the Maxwell-Boltmann models as limiting cases […] the weak form of Zipf's law still holds […] Parallel results concerning the stronger form of Zipf's law will be reported somewhere else.

But I recall trying to fit a Zipf's-law model to the student registration data, and finding that it fit rather badly. Perhaps I made a mistake — I don't now recall how I did it. Anyhow I didn't know about the relationship between Bose-Einstein statistics and Zipf's Law, and clearly I should have.

Apparently words, citizens, dollars, books, and species are also all bosons? And is this something that sociologists all know about?]

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