Ask Lemmy

Non-linear equations have entered the chat.

Chaos and non-linear dynamics were treated as a toy or curiosity for a pretty long time, probably in no small part due to the complexity involved. It's almost certainly no accident that the first serious explorations of it after Poincare happen after the advent of computers.

So, one place where non-linear dynamics ended up having applications was in medicine. As I recall it from James Gleick's book Chaos, inspired by recent discussion of Chaotic behavior in non-linear systems, medical doctors came up with the idea of electrical defibrillation- a way to reset the heart to a ground state and silence chaotic activity in lethal dysrhythmias that prevented the heart from functioning correctly.

Fractals also inspired some file compression algorithms, as I recall, and they also provide a useful means of estimating the perimeters of irregular shapes.

Also, there's always work being done on turbulence, especially in the field of nuclear fusion as plasma turbulence seems to have a non-trivial impact on how efficiently a reactor can fuse plasma.

I've read that all modern cryptography is based on an area (number theory?) that was once only considered "useful" for party tricks.

Not math but the discovery of Thermus aquaticus was seemingly useless but later had profound applications in medicine. There's a good Veritasium video on it

Donuts were basis of the math that would enable a planned economy to be more efficient than a market economy (which is a very hard linear algebra problem).

Basically using that, your smart phone is powerful enough to run a planned economy with 30 million unique products and services. An average desktop computer would be powerful enough to run a planned economy with 400 million unique products and services.

Odd that knowledge about it has been actively suppressed since it was discovered in the 1970s but actively used mega-corporations ever since…