Rajeev’s Almanack

Part 1
To understand the origin of this non-commutativity, let us again consider the example of a hurricane. It is an extended object, whose radius is of the order of 100 km. It wouldn’t make sense to have two such objects within a 100 km of each other: the two hurricanes will interact strongly with each other and combine into a single one. (This phenomenon of a `reverse cascade’ can been seen clearly in some simulations.) Thus there is a limit to the resolution of the co-ordinates of a hurricane, given by the area of a hurricane. This is reminiscent of the uncertainty principle of quantum mechanics, except that there it is the co-ordinates of phase space that is fuzzy: the analogue of the area is Plank’s constant.
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Introduction to Talk at SIAM DS07 Conference Snowbird Utah May 28th-June 1

The equations of motion of a fluid are obtained by averaging over the equations of motion of the large number of molecules that occupy even a small volume: we are not for the most part interested in the details of the motion of individual molecules. The equations of a fluid so obtained ( Euler or Navier-Stokes) are quite different from those of particle mechanics, being partial differential equations. Nevertheless the fundamental symmetries (translation and rotation invariance) of particle mechanics are preserved in this reformulation.
The conservation laws (energy, momentum,angular momentum) are preserved for ideal flow (Euler). In the next approximation, the effect of the transport of these conserved quantities to molecular scales are incorporated (viscosity). Even higher order corrections from molecular scales can be incorporated ( Chapman and Enskog) but are rarely needed.
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It is difficult to know when it is time to drop what you are doing and start something new. Jerry Seinfeld, the comedian was an exception. At the height of his fame he was willing to walk away from a deal worth a million dollars an episode, because he knew his show had lost its originality. But so few in the political world seem to know when it is time to quit. Some linger on, braving daily insults and votes of no confidence, in the mistaken belief that it shows strength of character.
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Terrence Tao has made some deep observations on why the regularity of three dimensional Navier-Stokes is such a hard problem. Although he has gone on to many other equally interesting topics, I remain fascinated by his main point there: that Navier-Stokes is supercritical. The nonlinearities become stronger at small distance scales, making it impossible to know (using present techniques) whether solutions remain smooth for all time. Thus, it is crucial to understand the scale dependence of non-linearities in fluid mechanics.
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I must confess I never quite got what the phrase `compassionate conservatism’ means. So it was interesting to listen to a three hour long `In Depth’ interview on C-SPAN with a Marvin Olasky. He is the inventor of the idea.
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Tammany Hall was the nickname given to the Executive Committee of the Democratic party that controlled New York throughout the nineteenth century. Although it suffered a few setbacks, Tammany remained a force until the middle of the twentieth century. The base of its strength were the new immigrants, for a time mostly Irish, that flocked to the United States through Ellis Island during this time. The tough unemployed youth were the enforcers of party discipline. More established immigrants contributed money and votes. The bosses had much patronage to hand out as rewards to the faithful. If you do a good job all your life as a precinct captain, maybe your nephew would get a plum job as a bridge inspector. That is, if he agreed to pass along part of his income to the party.
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