Wormholes, Superfast Computations, and Selivanov’s Theorem

While modern computers are fast, there are still many practical problems that requireeven faster computers. It turns out that on the fundamental level, one of the main factors limitingcomputation speed is the fact that, according to modern physics, the speed of all processes islimited by the speed of light. Good news is that while the corresponding limitation is very severein Euclidean geometry, it can be more relaxed in (at least some) non-Euclidean spaces, and,according to modern physics, the physical space is not Euclidean. The differences from Euclideancharacter are especially large on micro-level, where quantum effects need to be taken into account.To analyze how we can speed up computations, it is desirable to reconstruct the actual distancevalues – corresponding to all possible paths – from the values that we actually measure – whichcorrespond only to macro-paths and thus, provide only the upper bound for the distance. In ourprevious papers – including our joint paper with Victor Selivanov – we provided an explicitformula for such a reconstruction. But for this formula to be useful, we need to analyze howalgorithmic is this reconstructions. In this paper, we show that while in general, no reconstructionalgorithm is possible, an algorithm is possible if weimpose a lower limit on the distances between steps in a path. So, hopefully, this can help toeventually come up with faster computations.