Born on this day in 1860, Gustav Mahler spent his life searching for the music that could contain everything – joy, grief, nature, eternity. (Berlin Phil)

Harlequinade is a very rare ballet but its variations are frequently seen in ballet competitions. It’s terribly age inappropriate but too often danced by young (and talented) ballerinas. See dancetabs for a very good review “American Ballet Theatre – Harlequinade (premiere) – New York”) Nevertheless, here’s a version by Crystal Huang — her footwork and musicality are impeccable. She portraits a graceful, adorable Columbine. I would generally hope for Columbine to be more flirtful. But Crystal’s version is near perfect: and I think for now the best version on the internet: ...

Interactive walkthrough of the four-step martingale decomposition of an additive functional, with a CLT check.

This was one of my favourite during Empirical Analysis III course. ...

The most famous tango in concert music.

Jazz that behaves like Bach.

The Grant Park Music Festival’s outdoor venue is at the Jay Pritzker Pavilion, sitting in the heart of downtown Chicago around the skyscrapers. Your browser doesn't support the video tag. Tonight’s concert featured the Grant Park Orchestra, Carlos Kalmar and pianist Olga Kern, playing a magnificent program: Sergei Rachmaninov Piano Concerto No. 3 Igor Stravinsky Game of Cards Edward Elgar In the South The outdoor festival is exactly like the Frank Gehry architecture — it pierce through the air and stand firmly among the Chicago skyscrapers. You feel more the shape and less the nuance. Rachmaninoff carries through with Olga Kern’s powerful playing, very metallic, sculptured and sharp. She played the first original cadenza for mvt I written by Rachmaninoff. My pianist friend think it’s the best cadenza ever written and its early appearance even shadows rest of the concerto movements.

The same nocturne, the other temperament.

The Goldbergs returned to the instrument they were written for.

The idea originates in Milton Friedman’s essay “The Methodology of Positive Economics” (1953), the opening chapter of his book Essays in Positive Economics (University of Chicago Press, 1953, pp. 3–43). Basically, Friedman’s central idea is, a theory should be judged by the accuracy of its predictions within its intended domain — not by whether its assumptions are realistic or descriptively accurate. And further — “the more significant the theory, the more unrealistic the assumptions.” So we should use the “as if” method. Model agents as if the assumptions held. Three examples: the expert billiard player (plays as if solving the physics), leaves on a tree (arranged as if maximizing sunlight), the profit-maximizing firm (behaves as if optimizing; competition weeds out those that don’t). Tie-breakers. When theories predict equally well, prefer greater simplicity and fruitfulness (scope, precision, new research). Friedman’s original essay is ambiguous, contested but never settled. I printed it as part of my Price Theory I readings and it now lies with my Bach sonata sheets… ...