Programming infinite machines. (arXiv:1802.01910v1 [cs.LO])

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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