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.
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.
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)
> 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.
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
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.
the problem with additive notation is that the braid group isn't commutative when number of strands is > 2.
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.
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
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.
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.
Im bad at mathematics, but this looks great. Gonna use it in my app to make 'braidy' connections :) thank you very much!