Have you noticed that the tact filter applies to not just verbal behavior but also physical behavior? They’re installed in opposite directions in New York and Tokyo—except at Tsukijishijo (築地市場) perhaps? The most obvious example of a physical tact filter is the mouth mask that sick Japanese people wear in public, ostensibly to avoid infecting others.

The Suica is addictive. It’s like Cosmo’s access card in Sneakers, except of course the Suica charges you, and I bet Cosmo’s card doesn’t open his locker at the gym.

The leftover container problem is to partition a partial order into as few total orders as possible.

Pat Hanrahan wrote that “The BRDF is, in general, anisotropic” (on page 29 of “Rendering concepts”, chapter 2 of Radiosity and Realistic Image Synthesis by Cohen and Wallace, 1993). This sentence is the negation of “The BRDF is, in general, isotropic”! If “in general” in both sentences means “without exception” (which it does not in the true reading of “Primes are odd in general”), then the fact that these two sentences are the negation of each other is reminiscent of sentences such as “Hanna sucht kein Buch”, “Ze mogen geen eenhoorn zoeken”, and “You don’t need to bring any dessert” (Jacobs 1980, Theoretical Linguistics 7:121–136; de Swart 2000, in Reference and anaphoric relations, 118–142; inter alia). However, the sentences “The BRDF is always anisotropic” and “The BRDF is always isotropic” are not the negation of each other.

One of Olivier Danvy’s great examples of program transformation and continuation passing is to test in linear time whether a Calder mobile is balanced. For a mobile to be balanced is for each submobile to locate its center of mass right at its root. Real mobiles are of course never exactly balanced, yet the rods stay roughly horizontal—because even the rigid rods are not straight! Below is a program that rotates the submobiles of a two-dimensional mobile so that each submobile locates its center of mass right below its root. (Exercises left to the reader include handling higher-dimensional mobiles and using continuations to avoid repeatedly constructing and taking apart pairs.)

module Calder where
import Complex

data Mobile a = Point a | Rigid [(Complex a, Mobile a)]

balance :: RealFloat a => Mobile a -> (a, Mobile a)
balance (Point a) = (a, Point a)
balance (Rigid zms) = (sum as, Rigid zms') where
  (as, azs, zm's) = unzip3 [ (a, (a :+ 0) * z, (z, m'))
                           | (z, m) <- zms
                           , let (a, m') = balance m ]
  center = sum azs
  zms' | center == 0 = zm's
       | otherwise = [ (z / signum center, m') | (z, m') <- zm's ]

“Hendrik Lenstra claims that he can no more suggest to his students what problems they should work on than who they should marry.” (Update 2008-06-10: Vladimir Arnol’d said in 1995: “I never assign a thesis topic to my students. This is like assigning them a spouse.”)

Has anyone started designing the all-important logo for a joint Hillary-Obama/Obama-Hillary campaign?

What symbol(s) for disjoint union do you use—one of “+|∐⊔⊍⊎⊕” or something else? Do you use a different symbol for the presupposed disjoint union (which is undefined when applied to {{}} and {{}}) than for the tagged disjoint union (which yields a two-element set when applied to {{}} and {{}})? Those who work with sets up to isomorphism, such as topologists, are exempt from answering the latter question.

Update: the symbol ∪ with D inside was sighted in the wild. “I think it was the presupposition version”, reported correspondent Dylan Thurston.

It is interesting to read “Nationalität: Jude” on the cover of the August 2007 AMS Notices. Inside the issue is more information about the cover and about Lipman Bers’s immigration.