In mathematics there is an operation known as the Fourier Transform. Using it one can take a function of time (represented by f(x)) and 'decompose' it into an equivalent function of frequency (represented by f(ω)). The two functions will express exactly the same information, just in different terms. Similarly the operation can be performed on a function of space (represented by f(x) and expresses it as function of what is known as reciprocal space f(k'). This has many interesting applications. For example the wave pattern of a light beam after being shone through a hole (providing the distance from the hole at which you observe it is a lot bigger than the radius of the hole; too close to the hole and quadratic terms in the equation dominate) is the Fourier transform of the wave as it passes through the hole.

The Heisenberg Uncertainty Principle is concept in quantum physics which states that sets a limit on degree of accuracy which you can measure certain pairs of properties of a particle. Most young physicists will first come across this concept in regards to position and momentum. The product of uncertainties in a particle's position and momentum most be greater or equal to the reduced Planck's constant divided by two. Therefore the more accurately you can measure momentum of a particle, the less accurately is possible to measure the position. This isn't due to limitations in measuring equipment. It's a fundamental law of the universe!

These two concepts are linked in the field of optical physics. A pulse of light can be represented as a function of time, f(t). A Fourier transform can be performed on this to express it as a function of frequency, f(ω). The interesting result is that the shorter and sharper the expression in t is, the longer and duller the expression in ω is, and vice versa. Since the width of a pulse is equivalent to the uncertainty in that value, this shows that as the uncertainty in in t decreases, the uncertainty in ω increases. It just so happens that t and ω are two values that are linked by the Uncertainty Principle! A simple mathematical operation performed on a function corresponds to a physical law in the universe!


I was revising Fourier optics while listening to this yesterday (for an exam I sat this morning, which went ok, thanks for asking, although I opted out of the question about this topic and instead answered one about Fabry-Perot interferometers) and the point is that The Complete On the Corner Sessions is like a Fourier transform has been applied to On the Corner. The latter is the short sharp function. Over the course of a single LP Miles lays down a short intense blast of his new style of post-modern funky sound-collage jazz. He reaches incredible heights in a small space of time, and it's wonderful. The former album (this one) is the long, dull function. I don't mean dull in the sense of boring though. This is anything but. What I mean is that this is a sprawled out version of On the Corner, and even though it contains a lot of the same material it is prevented from reaching the same giddy heights purely because of how much the material is spread over a such a wide span. Its just as good as On the Corner (the two functions express the same thing after all), just in a different terms. Mathematical mumbo jumbo aside some of the funky jams presented here without all the crazy editing sound really good.