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Rashomon


Total Posts: 215
Joined: Mar 2011
 
Posted: 2020-10-28 18:01
I came back and somehow saw this term in the zombified corpse of what was once a decent place. I finally was able to understand Spivak, so I want to record my thoughts about this and see if anyone real reacts.

Differential geometry is fundamentally about explaining curl. Curl should and does annoy people mathematically—this includes every undergrad who asks if the universe is handed (I forget which way). The exterior product answers this question and ties curl into something else surprising, det.

Det as you know is used in Cramer’s Rule and therefore excavates small bits of every matrix you ever see. (If you think I’m exaggerating the importance or complexity of Cramer, it showed near the end of MacLane/Birkhoff’s algebra.)


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Then, there is a way to do functional division. Not *the* way, a way. It’s not commutative. People who take “information” in a spiritual or mystical direction then want to integrate against it, involve yokes/tensors, or other things …… which are considerably less principled than, for example, deriving curl and det from wedge.

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Also notice that statisticians never distinguish between even-dimensional and odd-dimensional data, whereas wedge does this (thankfully!) as part of explaining curl.


That’s my take. Any reactions?

nikol


Total Posts: 1235
Joined: Jun 2005
 
Posted: 2020-10-28 19:19
Let me insert my bit.
I like invariants/symmetry. Topological.

gax


Total Posts: 25
Joined: Apr 2011
 
Posted: 2020-10-28 23:32
I don't know, I got lost at the plus-minus alpha connections.
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