{"title":"Wormholes, Superfast Computations, and Selivanov’s Theorem","authors":"O. Kosheleva, V. Kreinovich","doi":"10.1134/s1055134424020020","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> While modern computers are fast, there are still many practical problems that require\neven faster computers. It turns out that on the fundamental level, one of the main factors limiting\ncomputation speed is the fact that, according to modern physics, the speed of all processes is\nlimited by the speed of light. Good news is that while the corresponding limitation is very severe\nin Euclidean geometry, it can be more relaxed in (at least some) non-Euclidean spaces, and,\naccording to modern physics, the physical space is not Euclidean. The differences from Euclidean\ncharacter are especially large on micro-level, where quantum effects need to be taken into account.\nTo analyze how we can speed up computations, it is desirable to reconstruct the actual distance\nvalues – corresponding to all possible paths – from the values that we actually measure – which\ncorrespond only to macro-paths and thus, provide only the upper bound for the distance. In our\nprevious papers – including our joint paper with Victor Selivanov – we provided an explicit\nformula for such a reconstruction. But for this formula to be useful, we need to analyze how\nalgorithmic is this reconstructions. In this paper, we show that while in general, no reconstruction\nalgorithm is possible, an algorithm <i>is</i> possible if we\nimpose a lower limit on the distances between steps in a path. So, hopefully, this can help to\neventually come up with faster computations.\n</p>","PeriodicalId":39997,"journal":{"name":"Siberian Advances in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Advances in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1055134424020020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
While modern computers are fast, there are still many practical problems that require
even faster computers. It turns out that on the fundamental level, one of the main factors limiting
computation speed is the fact that, according to modern physics, the speed of all processes is
limited by the speed of light. Good news is that while the corresponding limitation is very severe
in 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 Euclidean
character 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 distance
values – corresponding to all possible paths – from the values that we actually measure – which
correspond only to macro-paths and thus, provide only the upper bound for the distance. In our
previous papers – including our joint paper with Victor Selivanov – we provided an explicit
formula for such a reconstruction. But for this formula to be useful, we need to analyze how
algorithmic is this reconstructions. In this paper, we show that while in general, no reconstruction
algorithm is possible, an algorithm is possible if we
impose a lower limit on the distances between steps in a path. So, hopefully, this can help to
eventually come up with faster computations.
期刊介绍：
Siberian Advances in Mathematics is a journal that publishes articles on fundamental and applied mathematics. It covers a broad spectrum of subjects: algebra and logic, real and complex analysis, functional analysis, differential equations, mathematical physics, geometry and topology, probability and mathematical statistics, mathematical cybernetics, mathematical economics, mathematical problems of geophysics and tomography, numerical methods, and optimization theory.
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