Notation

I’m a hyperlink maximalist: everything should be a hyperlink, including everything that is hyperlinked by the author, everything that isn’t hyperlinked by the author, and perhaps even the hyperlinks themselves. Words should be hyperlinked, but so should be every interesting phrase, quote, name, proper noun, paragraph, document, and collection of documents I read.

This vision of a knowledge tool with “everything as a link” really appealed to me when I was building myself a new app for my personal notes earlier this year, so I sought out to prototype a basic tool that would try to achieve some of what I speculated on above: begin with basic, conventional text documents, generate links “on the fly” between my ideas, and visualize a map of such links and connections across my knowledge base.

The result is an app that I named Notation.

The representation of a task can radically affect our reasoning abilities and performance. For example, the game of tic-tac-toe (opposing players mark X's and O's in a 3x3 grid) can be equivalently represented as a game of drawing numbered cards with the goal of selecting three that sum to 15. From a computational perspective, these two problems are isomorphic. However, the tic-tac-toe representation is significantly easier to work with because the representational form of the problem makes visible the most relevant constraints implicit in the problem. As Simon writes, in mathematics, "solving a problem simply means representing a problem so as to make the solution transparent"

Lynch puts forward five primitive elements: paths (e.g. streets); edges (e.g. uncrossable rivers); districts; nodes (e.g. street corners); landmarks (e.g. a recognisable building). Each element has an intuitive way to sketch it, as if on the back of a napkin.

...Lynch’s five primitives comprise a notation.

It’s composable. A small number of simple elements can be combined, according to their own grammar, for more complex descriptions. There’s no cap on complexity; this isn’t paint by numbers. The city map can be infinitely large.

Compositions are shareable. And what’s more, they’re degradable: a partial map still functions as a map; one re-drawn from memory on a whiteboard still carries the gist. So shareable, and pragmatically shareable.

Not only are maps in this notation functional for communication, but it’s possible to look at a sketched city map and deconstruct it into its primitive elements (without knowing Lynch’s system) and see how to use those elements to extend or correct the map, or create a whole new one. So the notation is learnable.

We need to get some freedom from context so that we're not stuck repeating a single performance, without ending up so free that we have no idea what the music is supposed to sound like. This is the space where notation comes in.

There are two different vocabularies I like for thinking about this tension. One is Brian Cantwell Smith's idea of "the middle distance" in On the Origin of Objects, which I wrote about here. Useful notation is somewhere in the middle distance between the spectrogram and the cat, not rigidly causally linked and not completely unrelated either.

The other is super obscure. I got it from this paper by Gordon Bearn that I fished up from Google Scholar. Bearn talks about how representations must broach the possibility of meaning, by providing some link at all to the thing they represent (this is what the cat fails at). At the same time they must also breach their context by getting some distance from it (this is what the spectrogram fails at).

This syllabus examines the design of notation. We concern ourselves chiefly with one question: how does working in a particular notational system influence the ways that people think and create in it?

.stave {
    display: grid;
    row-gap: 0;
    grid-template-rows:
        [A5] 0.25em [G5] 0.25em [F5] 0.25em [E5] 0.25em
        [D5] 0.25em [C5] 0.25em [B4] 0.25em [A4] 0.25em
        [G4] 0.25em [F4] 0.25em [E4] 0.25em [D4] 0.25em
        [C4] 0.25em ;

    background-image:    url('/path/to/stave.svg');
    background-repeat:   no-repeat;
    background-size:     100% 2.25em;
    background-position: 0 50%;
}

Too often have I witnessed the improvising musician sweaty-handedly attempting to pinch-zoom an A4 pdf on a tiny mobile screen at the climax of a gig. We need fluid and responsive music rendering for the web!

Back in the days of Roman numerals, basic multiplication was considered this incredibly technical concept that only official mathematicians could handle, but then once Arabic numerals came around, you could actually do arithmetic on paper, and we found that 7-year-olds can understand multiplication.

It's not that multiplication itself was difficult. It was just that the representation of numbers — the interface — was wrong