Nostr notes by PensionDan

So you’re saying AI can do time travel now

2026-09-08T21:24:44Z

In reply to nevent1q…xqu5
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So you’re saying AI can do time travel now

The Birkhoff polytope \(\Omega_{n}\) has \(n!\) vertices which ...

2026-09-05T21:28:39Z

In reply to nevent1q…snnh
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The Birkhoff polytope \(\Omega_{n}\) has \(n!\) vertices which are the \(n\times n\) permutation matrices; I.e., (0,1) matrices that have exactly one 1 in each row and column. It has dimension \( (n-1)^{2}\), with \n^{2}\) facets, given by \(a_{i,j} = 0\) for each position in the matrix.

I’ve actually been looking into these! The 4-demicube is a 4-d ...

2026-09-05T14:33:06Z

In reply to nevent1q…809h
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I’ve actually been looking into these! The 4-demicube is a 4-d cross polytope ( a regular polytope).
I encountered these by looking into even & odd tridiagonal Birkhoff polytopes. That is, polytopes whose vertices are just the even permutations making up the tridiagonal Birkhoff vertices (or just the odd). (These are Birkhoff non-faces.)
Demicubes show up as faces of even (but not odd) tridiagonal Birkhoff polytopes with lots of vertices that are a power of 2.

And maybe tally their Crackpot Index score. ...

2026-05-01T18:02:42Z

In reply to nevent1q…mknl
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And maybe tally their Crackpot Index score.
https://math.ucr.edu/home/baez/crackpot.html

I think you need to specify the limit on the amount of train ...

2025-10-04T19:32:19Z

In reply to nevent1q…ejzx
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I think you need to specify the limit on the amount of train track. If it’s something like total length <= k, then the solution would depend on k.

Edinburgh Edification?

2025-09-26T14:15:34Z

In reply to nevent1q…5cqh
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Edinburgh Edification?

I happened to be familiar with this particular Schlegel diagram, ...

2025-02-06T20:56:17Z

In reply to nevent1q…576u
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I happened to be familiar with this particular Schlegel diagram, so I drew it in Paint.
https://en.wikipedia.org/wiki/Schlegel_diagram

Another way to visualize this four dimensional shape is with a ...

2025-02-06T19:04:14Z

In reply to nevent1q…5mmj
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Another way to visualize this four dimensional shape is with a Schlegel diagram. If you stare at the diagram, you'll see six triangular prisms, three with red triangle ends and three with turquoise triangle ends. The Schlegel diagram just shows how the facets fit together, not the 4-dimensional interior. And, there is distortion. Also, the "inside" of the outer triangular prism is the outside, with a containing sphere shrunk to a point.

I recall reading that Feynman thought of himself as not as ...

2024-12-03T20:13:16Z

In reply to nevent1q…hsdm
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I recall reading that Feynman thought of himself as not as brilliant as some other physicists, but able to contribute because he thought differently.

I gotta read more carefully... I overlooked the word ...

2024-10-24T19:23:37Z

In reply to nevent1q…3nmx
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I gotta read more carefully...

I overlooked the word 'least' in your first sentence.