Author Archives: ejlflop
Implicit coordinate transforms are weird
There’s a wide class of coordinate transforms that are typically given backwards. Witness spherical polar coordinates: Typically we already know what our cartesian coordinates are, and we want to express them in this fancy new coordinate system . That is, … Continue reading
What’s the deal with tautological 1-forms?
Epistemic status: All pretty standard derivations, except the last section on mechanics which is a bit hand-wavy. When formulating mechanics on cotangent bundles, one comes across an object called the ‘tautological 1-form’ (often denoted ) which is supposedly key to … Continue reading
Volume forms on the mass-shell
The setting for dynamics is the cotangent bundle of a manifold with pseudo-Riemannian metric ; relevant observables can be functions of both position and momentum. For example, the distribution function , which is the number density of particles in phase … Continue reading
Composing array masks
Let’s say you have an array , containing (~millions) points . Perhaps it’s the output of an n-body simulation or something more complicated. Anyway, suppose you also have several other arrays of size , each listing some quantity that is … Continue reading
From notated music to audible sounds
This is the second post in a series devoted to music from a mathematical point of view. The first post dealt with written intervals and notes; the moral of that post was that there is some structure (a vector space) … Continue reading
Cheap & Easy differential forms
There’s a way of motivating the notions of tangent vectors and covectors that’s hinted at but generally glossed over – at least in the physics courses that I take. This post is a quick overview, serving mostly as a reminder … Continue reading
Algebraic structure of musical intervals and pitches
Here’s the first in what will hopefully be a series of related posts about one particular (limited) aspect of the interaction between music and mathematics. In my mind, I’ll be explaining things to a hypothetical musically uneducated mathematician, who should … Continue reading
Piping from GNU Screen to GNU Emacs
I’m continually discovering nifty new features of GNU Screen, and I’ve taken advantage of one of them to fix one of my long-standing annoyances with what’s otherwise a nearly-perfect piece of software – the rather awkward scroll-back buffer. Here’s a … Continue reading
Scientific Notation 