Slightly related, but I've always wondered if there are similar (preferably successful) explorations in maths. "Mainstream" notations are clearly optimized for handwriting, but there's just so much room with current tech for optimizing for e.g. visual intuitiveness. And let's not even talk about all the historical burden that's made these notations the convoluted mess they are today.

(Uncreative, probably very bad) examples: Replace brackets with boxes, use colors (think syntax highlighting), icons, or even basic text-like formatting. And that's still being very conservative in relation to what could be done, as exemplified by the OP.

Any pointers/ideas?

I have always wondered how professional mathematicians work day to day. It depends on their field of course, but I guess most still use pen and paper (or a digital version, i.e iPad Pro + Apple Pencil / Wacom). I have at least never seen any tools for "explorative" manipulation of symbolic expressions. TeX etc works great for final type setting, but when going from mind to _something_ I guess that something is still paper, or an equivalent. Would be really interesting to see the equivalent of an IDE / good text editor for math, perhaps with pen input for speed.

I'm a Ph.D. student in a pure math field, and just coming from personal experience, the overall relationship with TeX is a pretty strained one. The overwhelming majority of working out is done by hand on paper or a chalk board.

That said, as an experiment, I did about half of my Master's thesis work in TeX. Without quick feedback on the rendered formulae, I had a much harder time reasoning through things, so having a comfortable text editing environment seems crucial.

That said, I wouldn't recommend using TeX as a scratchpad. It just doesn't map well to the sets of tools that we tend to use: mini diagrams, arrows between parts of the page, strikeout and circling text, etc.

What might work is something like e-paper that renders a handwritten document into text. Ideally, we could turn letters into Unicode and diagrams into vector graphics, providing tools to edit and embellish the rendered versions if desired.

It's extremely common to edit equations and diagrams on the fly, so I would probably feel friction with anything other that doesn't seem to just magically "prettify" whatever I handwrite at it. Seems like a really tall order though.

Mathematicians play around with new notation all the time. But yes, mostly hand-written.

The standard notation is mostly for communicating with other people mediated via papers. But we don't actually use that many brackets in math---that's more of a programming thing. (Because programmers can't really use visual structure all that much, and mostly rely on linearization of their syntax trees. Languages with significant whitespace like Haskell (and to a lesser extent Python) see less parens and braces.)

There's the Penrose Graphical Notation[0] for linear algebra, and (much more generally) string diagrams[1] for representing and manipulating morphisms in n-categories.

[0] https://en.m.wikipedia.org/wiki/Penrose_graphical_notation

[1] https://en.m.wikipedia.org/wiki/String_diagram

3Blue1Brown has a YouTube video called the "Triangle of Power" which uses a clever bit of notation to unify exponents and logarithms:

https://www.youtube.com/watch?v=sULa9Lc4pck

A bit lowbrow, perhaps (you'd want Penrose notation or such things in that case).

Some alternative/experimental music notation systems look very impressive, and even beautiful, on paper, but with some of them I wonder if that's due to the system itself, or the complexity of particular piece being rendered.

In the coding world, we have "Hello World" and Fizzbuzz. It would be nice if alternative music notation systems had something similar: A simple, familiar melody (candidates that come to mind are "Happy Birthday to You," and "Twinkle, Twinkle, Little Star") that, by rendering it in the new notation system, demonstrated the fundamental features of that system, and could be easily understood by someone knowledgeable in the traditional system.

It would be nice if people on HN didn't try to turn everything into a coding analogy.

But it's fairly fitting since musical notation is /supposed/ to be instructions for making a machine behave in a certain way. It's an early example of write-once-run-everywhere since the sheet music is relatively unchanged from instrument to instrument.

Sheet music contains instructions for making human musicians behave a certain way. There is no sense in which it's a complete description of a musical performance. Timing variations and dynamics are all controlled by the player.

If the score is figured bass, the player will improvise/create a complete accompaniment from a sketch of the bass line and some hints about the harmony.

And it's not necessarily unchanged. The layout of a piano score and a transposed brass line are only distantly related. The notation will be common, more or less, with the limitation that a horn line is monophonic while a piano can play chords.

But the key won't be the same, which means the pitches won't be the same. And many of the expressive markings will be different too.

If anyone is interested by this topic, feel free to check on the software I'm working on : a visual notation for art & multimedia installations which embeds traditional programming constructs (conditions, loops) but at the temporal level. The software is called Ossia Score (https://ossia.io).

Is this in anyway based on the Tiled Media papers? (Tuiles Musicales)

not really, but I did my thesis in the same lab than one of the authors (David Janin (ping Simon si tu passes par là!)) so there has been a lot of discussions about the various models for representing musical time :p

I'm sorry if my layman's perspective is off here, but notation that impedes the musician's ability to actually perform a piece, and be it only for visual pleasure, seems like not a very useful idea to me. It kind of reminds me of this: https://imgur.com/gallery/XOT47

Not everything in art has to be useful

A few of these are really beautiful! I really love the dice example.

But, synaesthesia.

Snowforms by R Murray Schafer: https://goo.gl/images/1FHHXo

I performed this in France with my treble choir in 1990. Schafer sat in the audience looking grumpy. It’s a beautiful piece, and Schafer is odd.

If you find yourself inspired by wild notations I recommend this coffee table book: "Notations 21" by Theresa Sauer.

Requisite link to my product Soundslice: https://www.soundslice.com/

We make web-based interactive music notation. Nothing “experimental” as in the original link, but it may be interesting to the HN crowd as a boundary-pushing web app.