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> Because computers operate on the rational numbers instead of the real numbers, Computers are just devices that perform computations. It's perfectly possible
by cowboysauce 6y ago
> Because computers operate on the rational numbers instead of the real numbers,
Computers are just devices that perform computations. It's perfectly possible to construct computers that operate on values that are continuous and not discrete. In fact, such computers have been constructed before. They are know as analog computers and were used for things like numerically solving differential equations.
- karmakaze 6y agoThis is not even true. We have symbolic processing that can manipulate and formulate with non-rational expressions. This article is so worthless.
- ogogmad 6y agoYou 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.
- caymanjim 6y agoIt seems likely that absolutely nothing is analog. The best theories about physics are all quantized. The only things that we don't have strong quantum theories about are things we barely understand, like time and gravity. And that's just because we haven't found the quanta yet.