Programming Infinite Machines


For infinite machines that are free from the classical Thomson’s lamp paradox, we show that they are not free from its inverted-in-time version. We provide a program for infinite machines and an infinite mechanism that demonstrate 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 machines (Davies in Br J Philos Sci 52(4):671–682, 2001), our examples are free from infinite masses, infinite velocities, infinite forces, etc. Only infinite divisibility of space and time is assumed. Thus, the infinite devices considered are possible in a Newtonian Universe and they do not conflict with Newtonian mechanics. Note that the classical Thomson’s lamp paradox leads to infinite velocities which may not be producible in acceptable models of Newtonian mechanics. Finally, it is shown that the “paradox of predictability” is similar to the inverted Thomson’s lamp paradox.

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This work is supported by the Russian Science Foundation (RSF) Project 18-11-00032. This paper is also a contribution to the project M3 of the Collaborative Research Centre TRR 181 “Energy Transfer in Atmosphere and Ocean” funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Project Number 274762653. I would like to thank Prof. Dr. Marcel Oliver (Jacobs University), Dr. Ryan North (Hamburg University), the editors of Erkenntnis, and anonymous reviewers, for their valuable comments and very useful discussions.

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Correspondence to Anton A. Kutsenko.

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Kutsenko, A.A. Programming Infinite Machines. Erkenn (2019) doi:10.1007/s10670-019-00190-7

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