Thanks! With the caveat that I profoundly lack depth on both, and am a bit artsy craftsy in my intuitions, I did buy the Maths module precisely because it was an analog computer.
The intent was to create some generative music, and seeing if I could use it to create 1/f noise, and exploring self-similarity using a musical ear instead of in code. Still working on it.
When you look at what you can do with magnets hooked to a synth with a ferrofluid, e.g. https://youtu.be/Q3oItpVa9fs , the sound and your ear helps to develop an sense for what kinds of waves can be used to yield physical effects. If you can functionally suspend and maipulate a ferrofluid with waves, there are likely analogies to laser pulses and electrons for quantum computing. Waves gonna wave, etc.
The other piece that grabbed me recently was "analog fractals," (https://hackaday.com/tag/analog-fractals/ + that rabbit hole) where if you can get those artifacts instantaneously as the effect of physical feedback instead of rendering them computationally, there are likely faster functional approaches to a lot of other problems, only a subset of which we use ASICs and FPGAs to implement today.
It's speculative based on laughably incomplete understandings on my part, but that's hacking.