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VI of Hearts: The Cantor Ternary Set Cantor Ternary Set


It’s self-referential! It’s self-similar! It would give Jonathan Coulton nightmares! It’s the Cantor Ternary Set Cantor Ternary Set: a representation of six steps in the construction of the Cantor ternary set using sped-up and slowed-down samples of Jonathan Coulton singing ‘Cantor ternary set’ in his song Mandelbrot Set, in which he professes to fear said set. I suppose you could say Jonathan Coulton is the cantor, but would it make him turn a reset?

Six of Hearts on a Jonathan Coulton Mandelbrot Floyd shirtI added a Wilhelm scream to the end, because that seemed appropriate. Here’s the audio-only version.

The Cantor ternary set is what you get if you take a line (technically a line segment, but we’ll call it a line), cut out the middle third, then cut out the middle third of the lines that remain, then cut out the middle thirds of those, and so on. If you continue doing this forever, you end up with just as many points as you started with (isn’t infinity grand?) but they’re nowhere near each other. I made the ‘lines’ at each stage out of clips of Jonathan singing ‘Cantor ternary set’ at different speeds; first at one 27th normal speed, then at one ninth, then one third, then normal speed, then three, nine, and 27 times normal speed. Then I put all the lines (i.e. audio clips) from the different steps on top of each other, positioned according to where each line came from in the original line, to make the full canticle (cantorcle?) You can see how it works in the video. To make it easier to differentiate the different layers, I put the second and fifth layers (counting from the slowest one at the bottom) toward the left ear and the third and sixth toward the right, leaving the other three (1/27-speed, original-speed, and 27-times speed) in the centre.

This didn’t take very long to make, in the end, but there were a lot of false starts. A long time ago I decided to make some kind of song about mathemusician Vi Hart using snippets of the various source tracks I have of Jonathan Coulton songs — a Hart-shaped box, on the table, and far too late you see the one inside the box is Vi Hart, who’s not a real heart but is a real bad-ass mathematician… that kind of thing. I realised some time ago that it would have to be the six of hearts, because in Roman numerals that’s the vi of Hearts. But that didn’t stop me from putting off starting it till about a week after the last minute. It’s a good thing I set my own deadlines.

A couple of days ago I finally started to actually work on this. I cut some sounds together (‘my heart’ and a ‘v’ sound from When You Go) to make Jonathan sing Vi Hart’s name, and collected relevant phrases from other songs. But I needed some kind of musical background track to tie it all together (like the Mr. Fancy Pants choir I used in my ‘Code Monkey Like…’ thingy.) I had considered using Vi’s piano music that she played on JoCo Cruise Crazy 2, but in the moment I didn’t feel like looking for it, and also didn’t feel like I could do it justice; I’ve just recently started listening to a basic and hilariously over-dramatic audio course on music theory, but most of what little I know about music, I learnt from Douglas HofstadterLeonhard Euler, Leon Harkleroad, and Vi Hart herself. While I’m okay with the mathematical side of things, I don’t think I remember enough to make a fitting musical tribute. So I asked myself, as I often do, what would Vi Hart do? Probably something symmetrical, mathematical, brilliant. So I hit on the idea of making a Cantor ternary set of Jonathan Coulton singing Vi Hart’s name, and using that as a backing track for the song.

Well, that was interesting, but it sounded terrible. The gap in the middle (the middle middle, not all the other gaps in middles which make the Cantor set what it is) sounded like a lawnmower, most of the rest sounded like a bad choir being massacred by a possessed lawnmower, and the 3x-speed ‘Vi Harts’ were more prominent and understandable than the ones at the original speed. I fiddled with levels for a while, and tried to make the lawnmower sound better by adding more words from other songs, but no dice. The fact was, using a Cantor ternary set of Vi Hart’s name (sung in that particular way) as a backing track was a terrible idea. And now that I think of it, I seem to recall that Hofstadter mentioned experimenting with fractal music and finding it didn’t work very well. That’s fine, though; I’m no musician, so I figured I could make it work to my low standards eventually. But just to take a break, on a whim I decided to try making a Cantor ternary set out of Jonathan singing ‘Cantor ternary set’.

Five minutes later, I discovered that the greater variety in syllables and pitches makes this sound quite interesting even without added lyrics, and you can fairly easily hear the words at several different speeds, so you can tell what’s happening well enough for it to be a demonstration of the Cantor ternary set in itself rather than just a backing track. Plus it’s a Cantor ternary set made up of the words ‘Cantor ternary set’. Why on Earth did I not think of that in the first place? Sorry Vi Hart; you’ll get your tribute song some day, and hopefully from someone better at music than I am.

On the subject of Vi Hart, last weekend I was at my physicist friend Aidan‘s place and noticed he had made some pretty neat things with Geomag, so I asked him to explain it all on video. He did mention Vi at one point. Here’s the video, in which we talk about RF cavities, conservation of angular momentum, triangles, and various kinds of pole, among other things:

Aidan also makes a lot of videos explaining particle physics; you should check them out.

Also on the subject of physics, and cool people I’ve met on JoCo Cruise Crazy (Vi Hart being one of them) here’s an LHC-related comic that Randall Munroe from xkcd drew for me on JoCo Cruise Crazy 3.

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Three of Diamonds: The Family Tradition


One plus one makes three? (of diamonds)Your father, his father, and his before that,
Your mother, her mother, and all the way back
Have kept a tradition by chance or by will
To each have a baby (or several) until
The flame’s passed to you, but now you have a choice
So don’t join the choir till you find your own voice.
Creating a person’s a huge thing to try;
You can if you want, but first think about why:

Not to continue this age-old tradition
Not to be sure that your life has a mission
Not for a god or a country or norm, oh
Not for a lark, or the whim of a hormone
Not for a vague or instinctive desire
Not just to copy the folks you admire
Not out of fear you’ll leave nothing behind
(Not that your DNA outdoes your mind)
Not ’cause you’re bright so you should spread your genes
Not ’cause you’re dim and don’t know what that means
Not to rebel against Mum and Dad’s view
Not because they want their vengeance on you
Not as a snake oil to quiet your fears
That you might feel a twinge of regret in ten years
Not when your body clock’s ticking through dates
And you’re always a sucker for ‘Buy now! Don’t wait!’s
Not because well-behaved babes tug your heart
Not so your parents can relive that part
Not ’cause your partner would like to have some
Not ’cause you’re grateful that Dad convinced Mum
Not ’cause you’ve thought of a name you must give
Or things you’d do better if you could relive
Not when a thoughtless mistake involved sex
Not ’cause you’re married and that’s what comes next
Not because all of your friends ask why not
Not because they’re doing well with their lot
Not ’cause you’re told that it’s selfish to live
without making a beggar to whom you can give
Not because parents say nothing else matters
Not to add glue to a romance in tatters
Not because children learn more tricks than cats
Not to prove your kids would never be brats
Not so your welfare amount will be goin’ up
Not ’cause you think it’ll make you a grownup
Not so they’ll pay for your food in old age
(for pyramid schemes have to collapse at some stage)
Not to fulfil a perceived need for love
Not if you’re not sure, when push comes to shove
Not ’cause you read this and thought, ‘This’ll show ’em!’
Not for the sentiment closing this poem.

But only because you adore helping youth
and can’t think of life without living that truth.
You know that their life-long love’s not guaranteed
and you’re yearning to face unconditional need
of a boy, girl or intersexed, well, sick or crippled
dunce, saint or murderer, one, twins or tripled.
You’re deeply concerned the resources you borrow
may add to the hardship of grandkids tomorrow
and realise your efforts to curb your consumption
are more than undone if you make the assumption
that your kids survive and continue to breed
and their kids spawn ever more hungers to feed.
If raising a person is your lifelong dream,
and not just a gesture to race with the team
then go ahead, try to conceive, but know this:
it’s not just a baby that’s made in all this.
You remake yourself as you start your new quest,
as parent first up, and then some of the rest.
From baby’s perspective you’ve made the whole world;
you’ve led them from nowhere to cosmos unfurled.
So enjoy your big bang and enjoy your inflation,
And cherish your well-informed act of creation.

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