Weyl's tile argument

In philosophy, the Weyl's tile argument (named after Hermann Weyl) is an argument against the idea of a physical discrete space (where all the distances are multiples of some constant minimum value), by questioning its concept of distance. It says that it is impossible to define a distance function satisfying Pythagoras' theorem (or even, satisfying it only approximately) on a discrete space, and that since it has been verified that the theorem is at least approximately true in nature, physical space can not be discrete.[1][2][3][4] Solutions to Weyl's argument (i.e. arguing that a discrete physical space is not impossible) have already been proposed in the literature.[5]

References

  1. ↑ Amit Hagar (2014). Discrete or Continuous?: The Quest for Fundamental Length in Modern Physics. Cambridge University Press. ISBN 978-1107062801.
  2. ↑ S. Marc Cohen. "Atomism". Faculty.washington.edu. Retrieved 2015-05-02.
  3. ↑ Tobias Fritz. "Turning Weyl’s tile argument into a no-go theorem" (PDF). Perimeterinstitute.ca. Retrieved 2015-05-03.
  4. ↑ K. McDaniel. "Distance and discrete Space" (PDF). Krmcdani.mysite.syr.edu. Retrieved 2015-05-03.
  5. ↑ "Finitism in Geometry (Stanford Encyclopedia of Philosophy)". plato.stanford.edu. Retrieved 2015-05-02.


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