Publication Date
3-1-2025
Abstract
Everyone talks about the need for Explainable AI -- when, to supplement a long difficult-to-understand sequence of computational steps leading to AI's decision, we are looking for a shorter and understandable more-informal explanation for this decision. In this paper, we argue that this need is a particular case of what we call Explainable Mathematics -- when we want to supplement a long sequence of arguments and/or computations with a shorter and understandable more-informal explanation. Important instances of Explainable Mathematics are Yuri Gurevich's Quizani dialogs that help explain complex results from theoretical computer science and physicists' more-informal explanations of complex physical phenomena. We explain that in the physics' case, since -- according to most physicists -- all physical theories are approximate, the use of approximate more-informal methods often makes more sense that the use of rigorous methods that implicitly assume that the current theories are absolute correct. We then apply this argument to one of the common uses of physics in theory of computation -- that limitation by the speed of light limits the computation speed. Specifically, we show that quantum space-time ideas potentially allow computations at the micro-level speed of light which can be higher than its usual macro-level value. This potential increase in possible communication speed can speed up computations.
Comments
Technical Report: UTEP-CS-25-8