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...

postulate Weyl's theorem on complete reducibility Weyl's tile argument Weyl–Titchmarsh–Kodaira theory Weyl's tube formula Weyl's unitary trick Weyl (crater)...

mathematics vs mathematical analysis Smooth function Digital physics Weyl's tile argument Stanford Encyclopedia of Philosophy: "Continuity and Infinitesimals"...

Mathematical universe hypothesis It from bit Simulation hypothesis Weyl's tile argument Natura non facit saltus Schmidhuber, Jürgen (1997), Freksa, Christian;...

In philosophy, the Rietdijk–Putnam argument, named after C. Wim Rietdijk [nl] and Hilary Putnam, uses 20th-century findings in physics – specifically in...

affine Weyl group of An (the affine symmetric group). For n = 2, this can be pictured as a subgroup of the symmetry group of the standard tiling of the...

to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "tile argument" or "distance...

The Penrose–Lucas argument is a logical argument partially based on a theory developed by mathematician and logician Kurt Gödel. In 1931, he proved that...

discovery of Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold...

pattern on the tile we have p2 (more symmetry of the pattern on the tile does not change that, because of the arrangement of the tiles). The rectangle...

product. It is not necessarily symmetric and is linear only in the first argument. The rank of a root system Φ is the dimension of E. Two root systems may...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

which exactly cover the sphere. Spherical tilings provide two infinite additional sets of regular tilings, the hosohedra, {2,n} with 2 vertices at the...

uncountability proof, which differs from the more familiar proof using his diagonal argument. Cantor introduced fundamental constructions in set theory, such as the...

singularity theorems Riemannian Penrose inequality Penrose process Penrose tiling Penrose triangle Penrose stairs Penrose graphical notation Penrose transform...

example, an element of the (2,3,7) triangle group acts on a triangular tiling of the hyperbolic plane by permuting the triangles. By a group action, the...

semiconductor wafer inspection, polymerization process monitoring, acoustic tiling, free-space communications and computer-generated imagery. Particle-particle...

painted on wood panel, they exist in other media, such as mosaics, painted tile, and cloth. Ernst Kitzinger distinguished two types: "Either they are images...