Tag Archives: group theory

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How do I Create the Identity Matrix in R? Also a bit of group theory.

I googled for this once upon a time and nothing came up. Hopefully this saves someone ten minutes of digging about in the documentation. You make identity matrices with the keyword diag, and the number of dimensions in parentheses. > … Continue reading

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Why bicontinuity is the right condition for topological equivalence (homeomorphism): if continuity of the inverse isn’t required, then a circle could be equivalent to a line (.99999 and 0 would be neighbours) — Minute 8 or so. Geometric construction (no … Continue reading

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3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 … modulo 89 An application of group theory to Navy sonar — can you generate a sequence whose 1-differences are … Continue reading

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Talking in Tuples

Mathematics is the *Most* Different Language. In Can we make mathematics intelligible?, R P Boas jokes: There is a test for identifying some of the future professional mathematicians at an early age. These are the students who instantly comprehend a sentence … Continue reading

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In the loop quantum gravity approach, space-time is quantized by a procedure that encodes it in a discretized structure, consisting of spin networks and spin foams. A spin network consists of an oriented embedded graph in a 3-dimensional manifold with … Continue reading

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Vierergruppe

Any four things in order ABCD can be rearranged. You could do ACBD — middle swap — 1324 DBCA — end swap — 4231 BCDA — rotation — 2341 for example. Let’s say the four things are the four corners … Continue reading

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