You don't need analog computation. The theory of Computable Real Analysis still assumes a digital computer: https://en.wikipedia.org/wiki/Computable_analysis ht

You don't need analog computation. The theory of Computable Real Analysis still assumes a digital computer: https://en.wikipedia.org/wiki/Computable_analysis https://en.wikipedia.org/wiki/Computable_analysis See here for a concrete application of the theory: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Another application is the Android calculator, which computes over exact real numbers in the sense described by Computable Analysis. Finally, it's debatable whether analog computation achieves true computation over the real numbers. The presence of physical noise, and the fact that many physical quantities (like electrical charge) are ultimately discrete at the quantum level, implies that it doesn't really work AFAICT.