It makes some sense to handle self-discovered real numbers of infinite precision using analog methods, though I’m curious about how they handle noise, since in the real world and unlike the mathematical world all storage, transmission and calculations have some error.

That said, my experience way back with a project I did at Uni with Neural Networks in their early days, is that they’ll even make up for implementation bugs (we managed about 85% rate of number recognition with a buggy implementation) so maybe that kind of thing is quite robust in the face of analog error.