Wednesday, February 27, 2013

Fundamental Inequalities

Equality is a cornerstone of the law, but it's not at all a feature of natural law.

Consider Heisenberg's famous Uncertainty Principle (but not in any deeper sense than the nature of the symbols):


On the left, Δχ and Δρ (position and momentum) are physical variables; on the right is a fixed valuei.e., half of ħ, the imponderable Planck constant.

Equations are like sentences with the equal sign being like the verb "to be;" they represent either equality or the more subtle notion of equivalency. Inequalities are also familiar from algebra but an inequality also expresses—more or less—an important direction of inequality. In this case, the observables are greater than or equal to the constants.

Bell's Theorem has been called "the most profound [theorem] in science" and it too reduces to an inequality. There's another: the Clausius Inequality, which embodies the Second Law of Thermodynamics, and which expresses changes in entropy against a value of zero. Comparing all three—without even understanding them—it strikes me that they all specifically pit observables against abstract constants. Is this general?

Sunday, February 17, 2013

Samba Per Voi

Deborah linked an older Santana instrumental song called Samba pa' ti (Samba for you):

This was originally from their second vinyl LP called Abraxas (1970), but Carlos Santana carried it forward through the years, reincarnating the song, as the word Abraxas might have hinted at the time.

Thursday, February 14, 2013

Sole Sacrifice

Carlos Santana practically invented "Latin Rock" in the 1960's. He had started out as a blues and jazz influenced musician, but in San Francisco he met Latino and African drummers who beat different rhythms. Hanging around the developing hippie scene in San Francisco, he and his band noticed that girls would spontaneously dance in new and interesting ways to the exotic sounding rhythms--usually with much more hip gyration. He and the band liked this from a stage's eye view, and so the fusion stuck.

The band Santana made its national stage debut at Woodstock in 1969. Three successful albums later, the band had begun to fray, with Carlos wanting to move more towards jazz. Caravanserai (1972) was the last Santana album that I liked. Half the band left him afterwards and later formed the core of the band Journey.

A favorite track from Caravanserai, called Waves Within:

My Funny Valentine

Saturday, February 9, 2013

What I Like About You

Pretty unusual for a drummer to sing lead:

Thursday, February 7, 2013

Bleak House

A bleak song for a bleak season which will end.