From Classics to Colonialism

Dr Ben Swift

via drum circles

I acknowledge the First Australians on whose traditional lands we meet, and pay respect to the elders past and present.

391 · 578

what’s the biggest number that divides evenly into both?

the Euclidean algorithm

one of the oldest known algorithms (c. 300 B.C.)

first described in Euclid’s Elements, Book VII — and independently found in China and India

granddaddy of all algorithms, because it is the oldest nontrivial algorithm that has survived to the present day

Donald Knuth, TAOCP Vol. 2

in plain English

to find the greatest common divisor of a and b, repeatedly replace the larger by their difference until both are equal

that final number is the GCD

in code

(define (gcd a b)
  (if (= a b)
      a
      (gcd (min a b) (abs (- a b)))))

in code (a bit more efficient)

(define (gcd a b)
  (if (= a 0)
      b
      (gcd (modulo b a) a)))

sounding bodies & Euclidean rhythms

rhythmic notation

three patterns to compare:

0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7

euclid(3, 8)

same basic idea as Euclid, attributed to Bjorklund

0
1
2
3
4
5
6
7

euclid(3, 8) — final

0
5
3
1
6
4
2
7

aka: cuban tresillo

euclid(5, 12) — final

0
7
5
3
10
1
8
6
4
11
2
9

aka: South African Venda, Macedonia, Tool’s Schism, and many more

euclid(5, 8)

0
1
2
3
4
5
6
7

aka: cuban cinquillo

the paper’s kite-flying

a simple algorithm; a laundry list of examples “in the wild”; proofs of some nice properties

…and a leap: that these properties explain the human cultural practices of musicmaking

musician → simple interface → cultural domain

…such rhythmic structures can be fruitfully regarded not only as retentions of African musical and cultural heritage, but also as a way of theorizing the threads of continuity between many disparate musics and cultures that share African roots.

Stewart, J (2010). Articulating the African Diaspora through Rhythm

The commercialisation of the pseudo-African Drum is socially, ethically and legally upheld by our moral framework. It is, however, in violation of the ethic of the ethnic Drum.

Friedberg, L (2003). Drumming for Dollars

youtube.com/watch?v=fn3KWM1kuAw

“Ben said the Euclidean algorithm is racist!”

well, maybe — but that’s not the point

you learned it earlier (I saw you), so you’re implicated

algorithms give us leverage in cultural domains — can we use them safely, at scale?

Machine learning is like money laundering for bias.

Maciej Cegłowski, The Moral Economy of Tech

what did you learn?

Euclid’s algorithm!

repeatedly replace the larger of two numbers by their difference until both are equal — that’s the GCD

yes, it will be on the final exam

questions?

apps.musedlab.org/groovepizza