Final Form Teaser:

Have you ever wondered what probability distributions sound like?

Probably not. You probably have better things to do.

But maybe you’re curious now. I coded up some audio demos of probability distributions, and heard things you’ve never heard before.

Look, we’re all used to seeing probability distributions. The bold and audacious curves of the the normal distribution. Or perhaps the timeless beauty of the exponential distribution.

If you’ve taken a stats class, these are old friends. Except you’ve never heard them. Let’s change that.

more here

Problem Statement

Develop a framework that enables the sonification of mathematical and statistical concepts. This could be educational and even increase accessibility for those with visual impairments.

Key Requirements

  • Generate audible representations of probability distributions with controllable parameters
  • Create interactive tools / web app for real-time manipulation of distribution parameters
  • Implement convolution and other mathematical operations with clear auditory feedback
  • Build a library of standard mathematical functions and their sonic representations
  • Create documentation and educational materials for both human and AI understanding

Background

Context

Mathematical concepts are traditionally taught and understood through visual and symbolic representations. However, the human auditory system is highly sophisticated and can detect subtle patterns in sound that might be difficult to visualize. This project explores using sound as a medium for understanding mathematical concepts, particularly probability distributions.

Initial Proof of Concept

The initial exploration demonstrated several key concepts:

  • Normal distributions rendered as audio with varying parameters (μ=440Hz, σ=20Hz and σ=100Hz)
  • Auditory demonstration of standard deviation’s effect on sound clarity
  • Convolution of distributions producing beat frequencies

Key Challenges

  • Mapping mathematical properties to perceptually meaningful sound parameters
  • Creating intuitive controls for real-time manipulation
  • Developing consistent standards for mathematical sound representation
  • Balancing accuracy with aesthetic quality

Success Criteria

  • Library of standard distributions with configurable audio representations
  • Interactive web-based interface for exploration
  • Documentation of mapping between mathematical properties and sound parameters
  • Validation studies showing improved understanding of mathematical concepts

Code and Tools

  • https://github.com/rhelmot/sound-machine
  • my own code from the original blog post:
  • I understand that there is a framework called react that would maybe build a web app (?)

Development Considerations

  • Focus on clear / meaningful mappings between mathematical properties and sound parameters
  • Consider both time-domain and frequency-domain representations
  • Build modular components that can be combined for complex concepts
  • Include metadata about mathematical properties in audio files

Potential Pitfalls

  • Avoid confusing or misleading audio representations
  • Maintain consistent scaling across different mathematical operations
  • Don’t make too many paperclips

Changelog

  • 2017-12-15: Initial concept and code
  • 2024-11-18: Initial draft aidea