Weyl's tile argument

In philosophy, Weyl's tile argument, introduced by Hermann Weyl in 1949, is an argument against the notion that physical space is "discrete", as if composed of a number of finite sized units or tiles.

[1] The argument purports to show a distance function approximating Pythagoras' theorem on a discrete space cannot be defined and, since the Pythagorean theorem has been confirmed to be approximately true in nature, physical space is not discrete.

[2][3][4] Academic debate on the topic continues, with counterarguments proposed in the literature.

[1]A demonstration of Weyl's argument proceeds by constructing a square tiling of the plane representing a discrete space.

In response, Kris McDaniel has argued the Weyl tile argument depends on accepting a "size thesis" which posits that the distance between two points is given by the number of tiles between the two points.

However, as McDaniel points out, the size thesis is not accepted for continuous spaces.