# The Use of Sound in Mathematics

I asked this question on Mathematics Stack Exchange first. It was well-received, but put on hold as off-topic. This site seems more appropriate. Here it is verbatim.

I'm not sure that this question is appropriate here. There's a good chance it's too opinion-based. If that's the case, I'm sorry.

I was sat in a research seminar recently and wondered whether it'd be tacky if the speaker made the mathematics in his presentation somehow audible (in a non-trivial sense).

I've been tempted to write a programme or something ever since, that'd attach all the bells & whistles to a given symbol-heavy proof. I picture something like a beamer presentation where each relevant slide makes a noise once it's called, so that any patterns in the equations (or whatever) really leap out at the audience. If used sparingly and with taste, I suppose it could be quite effective.

$\color{red}{\text{The }}\color{green}{\text{use }}\color{blue}{\text{of }}\color{magenta}{\text{colour }}$, $\Large{\text{font sizes}}$, italics, etc., are certainly effective on me, so why not sound?

In studying Mathematics alone, too, especially with dry, dense proofs, I have tried making small noises. It is a bit silly, yeah, but the odd "pop" for certain substitutions can be really handy. If anything, it makes things less dry . . .

So here's my question:

How best does one use sound in the study and/or presentation of Mathematics?

Again, I'm sorry if this is too opinion-based.

NB: I suppose what I'm looking for is suggestions for its use, ideally drawing upon experience and research. I don't know (yet) how to decide which answer (if any) would be considered the best. I'm sorry.

• Just curious: how would someone prove that their suggestion is the best use of sound? Do you really mean "how best does one use sound" or are you just looking for suggestions, experiences, etc.? It might help people to know what you are thinking would be an appropriate answer to this question. I don't think asking about sound is opinion based, it just depends on what you're asking for. Perhaps you could ask for "experiences using sound to teach mathematics?" – JPBurke Sep 24 '14 at 16:23
• Also: welcome to the site. I've worked on projects researching multimodal approaches to teaching math, and sound is very interesting. – JPBurke Sep 24 '14 at 16:24
• @JPBurke That's a good point. I don't know. Perhaps I'm looking for reasonable suggestions on its use in teaching and/or learning Mathematics, ideally drawing upon experience and research. And thank you :) – Shaun Sep 24 '14 at 16:28
• Cool question, and welcome to the site! – Chris Cunningham Sep 25 '14 at 1:25
• Interesting question. "The use of colour, font sizes, italics, etc., are certainly effective on me, so why not sound?" A difference between sounds and colors/fonts is that colors and fonts are used to contrast with regular color/fonts settings. It seems to me difficult to have this effect with sounds. Another difference is that color/fonts (or any visual trick) is a spatial way of representing information, whereas sounds are temporal (one sound after the other). – Taladris Sep 25 '14 at 7:10

Sound effects!

I substituted once for a friend in her ODE class. A week later I met her in the Department's lounge and she complained with a smile in her face that I had ruined her class because the students wanted the "bloop" professor back. My task had been to illustrate exponential growth, which I did with reference to a bacterium in a Petri dish. After 20 minutes, it goes "bloop" and you have 2 bacteria; after 20 more minutes they go "bloop, bloop" and you have 4...

The idea is to add a layer of realism to your gesturing, making the concept more palpable. Alberto Verjovsy has a wonderful explanation of how geodesics look in a torus. You see... (he says) you have this torus (he pretends to hold one) and it has a geodesic with rational angle, so it goes around a few times (fingertip flies around) and comes back to the original point, so the geodesic closes. But if the angle turns irrational..... (he wiggles his fingers around the whole surface of the torus) the geodesic never closes and is in fact dense. Sounds nice, BUT while wiggling his fingers, he gently blows air on his fingers, making a rustling noise between his teeth, and it sounds exactly as when you blow the pages of a book to separate them. The effect is really spectacular, and completes the visual presentation.

My classrooms have whiteboards, which I hate because the markers are always dry. Nevertheless, the squeak that you get when removing the cap is quite useful :) Say I try to explain how a simple linear transformation stretches things differently in different directions. I take the marker in my hand with thumb and index holding the cap; then, as I slowly open my arms wide to represent the stretching, I twist the cap to get as much squeak as I can. It really sounds as if poor $\mathbb{R}^2$ is stretching and is about to rip.

In my classes, things go 'bloop' and 'ping' and 'boom'. It helps students, and I could not stop it even if required; it is already second nature.

This is not a direct answer to your interesting question, but rather just one instance where I found it useful to use sound to convey aspects of an algorithm's operation. The algorithm walks through the space of polygonizations of a point set, and I used the polygon perimeter to control the pitch of a "Crystal" MIDI instrument.

If your browser enables Quicktime movies, you can see/hear it at this link:

The paper and video were well-received when I presented at a conference.