About: Weyl's tile argument

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In philosophy, the 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. 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. Academic debate on the topic continues, with counterarguments proposed in the literature.

Attributes	Values
rdfs:label	Weyl's tile argument (en)
rdfs:comment	In philosophy, the 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. 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. Academic debate on the topic continues, with counterarguments proposed in the literature. (en)
foaf:depiction
dcterms:subject	Discrete geometry Spacetime Philosophy of physics Philosophy of mathematics
Wikipage page ID	46586008 (xsd:integer)
Wikipage revision ID	1111625214 (xsd:integer)
Link from a Wikipage to another Wikipage	Pythagoras' theorem Cubical complex Discrete geometry Spacetime Causal sets Digital physics Discrete calculus Tessellation Hermann Weyl Philosophy of physics Philosophy of mathematics Philosophy Poisson point process Taxicab metric
sameAs	Weyl's tile argument Weyl's tile argument Weyl's tile argument
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thumbnail	wiki-commons:Special:FilePath/Approximate_the_diagonal_with_vertical_and_horizontal_edges.png?width=300
has abstract	In philosophy, the 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. 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. Academic debate on the topic continues, with counterarguments proposed in the literature. A demonstration of Weyl's argument proceeds by constructing a square tiling of the plane representing a discrete space. A discretized triangle, n units tall and n units long, can be constructed on the tiling. The hypotenuse of the resulting triangle will be n tiles long. However, by the Pythagorean theorem, a corresponding triangle in a continuous space—a triangle whose height and length are n—will have a hypotenuse measuring units long. To show that the former result does not converge to the latter for arbitrary values of n, one can examine the percent difference between the two results: Since n cancels out, the two results never converge, even in the limit of large n. The argument can be constructed for more general triangles, but, in each case, the result is the same. Thus, a discrete space does not even approximate the Pythagorean theorem. 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. Thus, we might have reason not to accept the size thesis for discrete spaces. (en)
gold:hypernym	Argument
prov:wasDerivedFrom	wikipedia-en:Weyl's_tile_argument?oldid=1111625214&ns=0
page length (characters) of wiki page	4177 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Weyl's_tile_argument
is Link from a Wikipage to another Wikipage of	Digital physics Zeno's paradoxes List of things named after Hermann Weyl Weyl tile argument
is Wikipage redirect of	Weyl tile argument
is foaf:primaryTopic of	wikipedia-en:Weyl's_tile_argument

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