Rhythms essential to logical communication

摘要

In the context of quantum theory, recently we distinguished mathematics for expressing evidence from mathematics for explaining evidence. Here this distinction is made in spacetime physics. We offer a system of mathematical thought-or as termed in geodesy a reference system-for evidence, separated out from additional assumptions of a geometry in terms of which to explain that evidence. The offered reference system for evidence, free of any assumption of a particular explanatory geometry, whether Euclidean or general relativistic, amounts to a (theoretical) "assemblage of histories accumulated in the memories of parties to a synchronous communications network." The assemblage of histories gives voice to the known experimental finding, sometimes forgotten by theorists, that any memory device for recording logical symbols must be insensitive to variations in signals in which those symbols are carried. Out of acknowledging this insensitivity comes an appreciation of rhythms essential to the communication of digital symbols and of the need for analog measurements to maintain these rhythms. The separate reference system for evidence reconciles what otherwise is a conflict between the demand in quantum mechanics for repeatable experiments and the lack in spacetime metrics appropriate to the Global Positioning System of any exact symmetry, a lack that rules out an isometry between two spacetime regions for two occurrences of an experiment.