Children of the Cosmos

Presenting a Toy Model of Science with a Supporting Cast of Infinitesimals
  • Sylvia WenmackersEmail author
Part of the The Frontiers Collection book series (FRONTCOLL)


Mathematics may seem unreasonably effective in the natural sciences, in particular in physics. In this essay, I argue that this judgment can be attributed, at least in part, to selection effects. In support of this central claim, I offer four elements. The first element is that we are creatures that evolved within this Universe, and that our pattern finding abilities are selected by this very environment. The second element is that our mathematics—although not fully constrained by the natural world—is strongly inspired by our perception of it. Related to this, the third element finds fault with the usual assessment of the efficiency of mathematics: our focus on the rare successes leaves us blind to the ubiquitous failures (selection bias). The fourth element is that the act of applying mathematics provides many more degrees of freedom than those internal to mathematics. This final element will be illustrated by the usage of ‘infinitesimals’ in the context of mathematics and that of physics. In 1960, Wigner wrote an article on this topic [4] and many (but not all) later authors have echoed his assessment that the success of mathematics in physics is a mystery. At the end of this essay, I will revisit Wigner and three earlier replies that harmonize with my own view. I will also explore some of Einstein’s ideas that are connected to this. But first, I briefly expose my views of science and mathematics, since these form the canvass of my central claim.


Natural Science Mathematical Knowledge Jigsaw Puzzle Hypothetical Structure Imaginative Play 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Science is a multiplayer game. Therefore, I am grateful to Danny E.P. Vanpoucke for his feedback on an earlier version of this essay and to all participants in the discussion on the FQXi forum [42]. However, we do play with real money. This work was financially supported by a Veni-grant from the Dutch Research Organization (NWO project “Inexactness in the exact sciences” 639.031.244). I am grateful to FQXi for organizing the 2015 essay contest “Trick or Truth: the Mysterious Connection Between Physics and Mathematics”, thereby giving me an incentive to write this piece. And, of course, I am very thankful that they awarded me the first prize for it.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.KU Leuven, Centre for Logic and Analytic PhilosophyInstitute of PhilosophyLeuvenBelgium
  2. 2.University of GroningenFaculty of PhilosophyGroningenThe Netherlands

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