ICFP 2018 Keynote Address: Conveying the Power of Abstraction

Conveying the Power of Abstraction, presented by Eugenia Cheng

[aeiousupremacy]

> teaches mathematics

35:00

> rich white male

and there it is. Social justice at it's finest.

[nick]

as @stevenspencer592 said
"Expensive gibberish" (c)

[wtb]

This lecture would be hilarious if given in Beijing.

[jonaskoelker]

8:00 "with art students I've found that what most motivates them are questions of social justice"

BWAHAHA. If the thing that most motivates them is not _art_ then what the fuck are they doing in art school?

For the visual arts, surely the geometry of perspective drawing can inform artistic technique?

In case of music, if you start at any key and go up or down by some fixed interval until you hit that key again, the only way to visit _all_ other keys is via a chromatic scale or the circle of fifths, because {1, 5, 7, 11} are the only numbers (mod 12) which are coprime with 12. Also I think music forms a semiring where addition is parallel performance of two voices (e.g. two instruments playing simultaneously) and product is sequential composition of two fragments (e.g. verse and then chorus). This is true because it's true of the underlying sound waves. (I don't know that there are many interesting equations you can derive from this, but at least it gives you more vocabulary and a new perspective for thinking about your art form.)

Hey, when you double the frequency of a note the human ear and brain says "although they have some differences they're also equivalent in some ways" (see "octave equivalence"). When an instrument plays a tone with frequency f it typically also emits sounds at frequency 2f, 3f, ..., n*f at lower amplitudes. (The amplitude profile differentiates e.g. pianos from saxophones playing the same note.) It would be real nice, because music theory believes in this only-approximate truth, if repeated jumps from f to 3f could align with repeated jumps from f to 2f, i.e. if 2^n = 3^k for some natural numbers n and k.

But that requires log_2(3) to be a rational number, which it isn't. But the continued fractions expansion of log_2(3) tells us how many notes to put into an octave to get a good approximation of this. For example, 12 is a good choice. We probably chose 12 before knowing about continued fractions. This means you want to go from f to 2f in 12 steps, each then being the 12th root of 2. You would love it if (2^(1/12))^7 = 1.5; in reality it's 1.49830707 which is pretty close. You could choose a set of non-uniform steps when you build your instrument, which makes a transposition from C major to D major sound more different than merely higher by two semitones.

I could go on.