TL;DR
This paper explores infinite machines that avoid classical paradoxes but reveal inverted versions, demonstrating undefined behaviors in infinite computational models within a continuous Newtonian universe.
Contribution
It introduces programs and mechanisms for infinite machines that exhibit paradoxical behaviors without requiring infinite physical quantities, aligning with continuous Newtonian mechanics.
Findings
Infinite machines can simulate paradoxes without infinite forces or masses.
They exhibit undefined behaviors unlike finite analogs.
Applications to Navier-Stokes equations are discussed.
Abstract
For infinite machines which are free from the classical Thompson's lamp paradox we show that they are not free from its inverted version. We provide a program for infinite machines and an infinite mechanism which simulate this paradox. While their finite analogs work predictably, the program and the infinite mechanism demonstrate an undefined behavior. As in the case of infinite Davies's machines, our examples are free from infinite masses, infinite velocities, infinite forces, etc. Only infinite divisibility of space and timeis assumed. Thus, the considered infinite devices are possible in a continuous Newtonian Universe and they do not conflict with continuous Newtonian mechanics. Some possible applications to the analysis of the Navier-Stokes equations are discussed.
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