Collecting my thoughts about notation and user interfaces

12.34, Thursday 12 Aug 2021

I’m circling something to do with notation and software user interfaces and what connects them. And things aren’t quite cohering for me yet, so this is me just collecting my thoughts…

(I’m designing user-composable interfaces this week, so long term the goal is to figure out some principles.)


A good starting point is pirate maps, those sketched maps with minimal detail that can none-the-less lead you to the X that marks the spot on the right treasure island.

Or to be more specific, urbanist Kevin Lynch’s city maps from his 1960 book The Image of the City. I’ve described his approach here (March 2021) (where I also pick at the possible neurological underpinnings) so to briefly summarise:

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.

The map of Boston (his first example) is immediately recognisable. Ask a person to sketch a city, or a route to a place, and they’ll automatically use something very like Lynch’s system.

So 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.


The idea of composability is worth digging into.

A pirate map is a drawing, and drawings are compositions of dots and lines and textures: A drawing is simply a line going for a walk (Paul Klee). But these would be poor primitives. Why?

A good, composable notation has primitives which are semantic. A line doesn’t mean anything, it’s too abstract – but a path or an edge (in Lynch’s system) refer to qualities of things in the real world. I’m also going to say that a notation must be grammatical, which is to say that there are rules about how primitives can be combined.

There are also not too many primitives. You want a system which is efficiently expressive. Like, you can say complex things with the minimum of vocabulary. Why? Because then the person using the notation can hold it in their head.

Adam Wiggins is the co-founder of Heroku, the prescient cloud-based technology platforms. It was ahead of its time, incredibly simple to use, but powerful – with an almost toy-like interface (I say that as a compliment) the complexity of hosting, scaling and managing servers was almost completely hidden.

Here is Wiggins relating his philosophy:

The value of a product is the number of problems it can solve divided by the amount of complexity the user needs to keep in their head to use it. Consider an iPhone vs a standard TV remote: an iPhone touchscreen can be used for countless different functions, but there’s very little to remember about how it works (tap, drag, swipe, pinch). With a TV remote you have to remember what every button does; the more things you can use the remote for, the more buttons it has. We want to create iPhones, not TV remotes.

(Via Simon Willison who picked out this quote.)

It matters what you can hold in your head because then the notation becomes a tool for the imagination. It is suggestive. Lego is suggestive. If you sit down and compose with the bricks, aimlessly, you will come up with new ideas that you wouldn’t have reached otherwise. The studs on the bricks are a grammar; the shapes are the semantics. You don’t get lost in complexity because the bricks are right there on the floor, so you play and, o ho!, there’s a novel kind of house you can build, you hadn’t thought of that.


At this point I’m slip-sliding between notation and interface, and this is maybe one of the things I’m trying to figure out. Perhaps a notation is always an interface to something?

Think of Feynman diagrams from physics. These are diagrams of particle interactions, like an electron hits a positron and both disappear while emitting a photon. The Wikipedia page shows examples.

But the lines, arrows, and squiggles have a grammar to them. And Feynman diagrams directly map to the fearsomely complex mathematics of quantum field theory. Manipulating the diagram is the same as performing the calculations.

So Feynman diagrams, as a notation, exist on the boundary of two realms; the interface between the scientific model (a representation of physical reality) and the imagination of the physicist.


Software user interfaces: let me try to draw the parallel.

I’ve been reading Steven Sinofsky’s first-person account of the rise of the Microsoft and the PC, which is astounding – it’s technology and strategy and history from someone who was right in the thick of it, at a pivotal time. Sinofsky is serialising the whole story as Hardcore Software: Inside the Rise and Fall of the PC Revolution.

He has this to say about the complexity of Microsoft Office (the first and much successful office software suite), and specifically about the buttons, menus, and commands, and every icon, command name, tooltip, menu string, and keyboard accelerator

One of the most significant differences between Office and most other tools is the sheer breadth and simultaneous depth of features, something that would become even more apparent as web pages came to the forefront. Each application had over 1000 commands (buttons, menus, etc.) with something over 2500 unique commands in Office96.

That was 25 years ago. I can only imagine that complexity has increased since.

Compare with the Xerox Star (1981) which introduced the desktop interface in the first place, together with the underlying metaphor of objects. Like, you could select a file or a paragraph or a printer and choose what do to with it, and that’s the ancestral idea behind our graphical user interfaces today.

One way to simplify a computer system is to reduce the number of commands. Star achieves simplicity without sacrificing functionality by having a small set of generic commands apply to all types of data: Move, Copy, Open, Delete, Show Properties, and Same (Copy Properties). Dedicated function keys on Star’s keyboard invoke these commands.

As an example of this flexibility:

In Star, users simply Copy to a printer icon whatever they want to print. Similarly, the Move command is used to invoke Send Mail by moving a document to the out-basket.

…which is powerful! But only works because the user can see, on the desktop, the icon of a printer and the icon of an out-basket.


I’m stretching the definition of “notation” now, but let’s say that both Xerox Star and Microsoft Office present the user with a notation to their internals, made out of commands and also graphical components: windows, icons, menus, pointers.

There’s a quality to this “notation” which is suggestive, as with Lego bricks, in that you can experiment with trying different commands.

But I’ll go further as say that there’s a quality which is that the notation is intentional and that is essential to a good notation or a good interface.

That is, you can imagine a goal (being it printing your document or drawing a map of Boston), and you know the available primitives, and you can figure out a sequence or a composition to get from A to B.


Related to all of these points, a notation or an interface must be legible.

It’s no good with a desktop interface, say, if icons are draggable and buttons are clickable, but the user doesn’t know that these operations are possible. So we design icons and buttons with visual affordances: they look as if they are pick-up-able, press-able, and so on.

Legibility, consistency, and affordances: all of these contribute to creating a mental model of the notation system in the mind of the user, and that seems like a prerequisite for many of the other qualities above.


Perhaps HTML is a notation? (Or rather, maybe it was in the early days.)

When I wrote about the original ideas behind files and icons (back in February), it felt important that the file was a boundary object:

Files are meaningful to computers, but they are also meaningful to users, and both can manipulate the same object. The two of you inhabit different worlds, but you’re talking about the same thing.

So HTML, the language for making web pages, is a “notation” on an interesting boundary. It has a small number of primitive elements, and a grammar to compose with them. And it is…

  • Easy to write: the creator can describe something simple or infinitely complex, with the same small set of rules. And given the set of rules is simple, it’s also good to imagine with.
  • Machine-readable: the browser application uses the exact same notation to display the webpage.
  • Obvious to interact with: buttons are clickable, hyperlinks are followable.
  • Good for reading and sharing: a user may View Source with their browser and read the code behind a webpage, and from there they are able to copy, tweak, and learn.

(Those last points were more true in the early days of the web…)

HTML sits on a boundary between the machine, the creator, and the reader.


To summarise those desirable qualities, a good notation is:

  • Composable
  • Shareable
  • Degrabable
  • Learnable
  • Semantic
  • Grammatical
  • Efficiently expressive
  • Suggestive
  • Intentional
  • Legible

I can’t quite tell whether I’m trying to force together two concepts (notation and user interface) which are fundamentally different, or whether there is something fruitful in seeing them as aspects of the same thing.

And I’m still not quite sure whether there are indeed lessons here for designing a composable user interface, or a design system, or whatever it is I’m working on.

But since I’m working on something where

  • engineers are building reusable components (which is the way of modern software and web development)
  • users need to understand how to use, navigate, and achieve tasks with the interface they see
  • and creators will compose these interfaces.

Then it seems like this is the right territory to be exploring.

Any recommended reading is appreciated.

If you enjoyed this post, please consider sharing it by email or on social media. Here’s the link. Thanks, —Matt.

😴