Consider curved spaces.

from Blind spot card with no picture yet Consider curved spaces.

In a plane of zero curvature or a higher dimensional space, if it is finite, it has an edge, and to eliminate the edge, it must extend to infinity. If you want a finite space, but do not want it to have an edge, you can use a sphere or a torus.

A plane of zero curvature or a higher dimensional space has an edge if it is finite, and to eliminate the edge, it must extend to infinity. However, infinitely wide objects are difficult for computers to handle, so we want to make them finite. If we do not want to have edges, a solution is to use a sphere or a torus. The fragment “Output Dimensions” illustrates the idea of embedding a higher dimensional space in two dimensions to make it more human observable. This is related to the solution for “making planes of zero curvature and higher dimensional spaces finite” mentioned in the note. The idea of using a sphere or torus as a solution to a finite higher dimensional space is one way to transform information into a human understandable form. However, this is only one solution, and other possibilities exist. While the use of a sphere or torus is one possible solution for making higher dimensional spaces finite, other methods may exist.” Title: “Finite Higher Dimensional Spaces: Beyond Spheres and Toruses

BELOW_IS_AI_GENERATED

曲がった空間を考える

2023-09-05 00:46

Summary of notes

. A plane of zero curvature or a higher dimensional space would have an edge if it were finite, and it would need to extend infinitely to eliminate the edge. However, infinitely wide objects are difficult for computers to handle, so we want to make them finite. If we do not want to have edges, a solution is to use a sphere or a torus.

Relation to Fragment

. The fragment “Output Dimensions” illustrates the idea of embedding a higher dimensional space in two dimensions to make it more human observable. This is related to the solution for “making planes of zero curvature and higher dimensional spaces finite” mentioned in the note.

deep thinking

The idea of using a sphere or torus as a solution to a finite higher dimensional space is one way to transform information into a human understandable form. However, this is only one solution, and other possibilities exist.

summary of thoughts and title

. While the use of a sphere or torus is one possible solution for making higher dimensional spaces finite, other methods may exist.” Title: “Finite Higher Dimensional Spaces: Beyond Spheres and Toruses

extra info

titles: ["Blind spot card without picture yet"], "Dimensions of output", "Relationship between Stable Diffusion seed and prompt", "Hatena2008-03-31", "Nada2021 question", "Area fudge"] generated: 2023-09-05 00:46

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