[HN Gopher] The Arithmetic of Braids (2022)
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       The Arithmetic of Braids (2022)
        
       Author : marysminefnuf
       Score  : 24 points
       Date   : 2025-11-24 06:44 UTC (16 hours ago)
        
 (HTM) web link (mathcenter.oxford.emory.edu)
 (TXT) w3m dump (mathcenter.oxford.emory.edu)
        
       | MarkusQ wrote:
       | Nice presentation. I would probably have written it as an
       | additive group (and then shown that the two strand braid was
       | isomorphic with Z) as a further bidirectional intuition anchor
       | (both "look, this new thing relates to something you are familiar
       | with" and "this thing you are familiar with generalizes in
       | unexpected ways").
       | 
       | Definitely liked the exploration of how theorems arise from
       | speculation, and don't spring fully formed straight from Zeus's
       | forehead.
        
         | geordiew wrote:
         | the problem with additive notation is that the braid group
         | isn't commutative when number of strands is > 2.
        
           | MarkusQ wrote:
           | Excellent point. I tend to enjoy "garden path" pedagogy,
           | leading the students to surprising twists and having them
           | explore -- but it's important to lead and not mislead. So
           | yeah, multiplicative notation is probably better.
        
       | fsckboy wrote:
       | this is pretty interesting but i don't think i can justify
       | dropping everything to study it. but it did remind me of an
       | adjacent "field", that guy who explores all the ways to lace
       | shoes
       | 
       | (i think this is the one, but whereas old search engines would
       | find it right away, now the results are full of "i made this" or
       | me-too spam)
       | 
       | https://www.fieggen.com/shoelace/lacingmethods.htm
        
         | marysminefnuf wrote:
         | What i do is keep a list of 3 things every day i learn about
         | braids and it just kinda adds up after a little bit.
        
         | srean wrote:
         | I was expecting Mathologer's book when you mentioned shoelaces.
         | Thanks for the link
         | 
         | https://www.ams.org/books/mawrld/024/mawrld024-endmatter.pdf
         | 
         | > whereas old search engines would find it right away
         | 
         | One of my pet peeves is how Google makes it hard to get at the
         | url to share directly from the search results. Yes there's the
         | share link but that does not link to the original.
        
       | srean wrote:
       | Very nicely explained. I find the mathematics of weaving,
       | knitting, braiding very dopamine squirt inducing.
       | 
       | It seems this interest is shared by many here on HN because there
       | have been many threads on them. @dang had once compiled a list.
       | 
       | Let me repost one of mine where Richeson explores Maypole dancing
       | through the lens of Braids.
       | 
       | https://news.ycombinator.com/item?id=44225324
        
       | max002 wrote:
       | Im bad at mathematics, but this looks great. Gonna use it in my
       | app to make 'braidy' connections :) thank you very much!
        
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       (page generated 2025-11-24 23:01 UTC)