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Honestly I’ve never considered an analog computer, and I’m a physicist but not a lattice expert. While an analog computer would let you use real numbers, you’d
by atty 4y ago
Honestly I’ve never considered an analog computer, and I’m a physicist but not a lattice expert. While an analog computer would let you use real numbers, you’d still need a way to store state at every point in space, which would lead to the infinite memory problem (and you’d need infinite compute to operate on the infinite memory). Perhaps there’s a clever way to get around that, but my suspicion is that if it were possible someone would have done it already.
- MacsHeadroom 4y agoThe complex plane does have infinite memory. A Turing machine can perform all discrete computations with a single bit. An idealized analog computer can compute anything with a "single" complex plane. Our (mis)conception of there being an "infinite memory problem" when the complex plane is infinite is analogous to flatlanders getting hung up about a "discrete bit memory problem."