[HN Gopher] The Burau representation of the braid group is faith...
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The Burau representation of the braid group is faithful for n = 4
Author : wglb
Score : 44 points
Date : 2026-07-27 23:46 UTC (5 days ago)
HTML web link (arxiv.org)
TEXT w3m dump (arxiv.org)
| wglb wrote:
| Also https://www.yahoo.com/news/science/articles/99-old-
| mathemati.... Someone who has been at this problem for 60 years.
| slwvx wrote:
| She has a wikipedia page:
| https://en.wikipedia.org/wiki/Joan_Birman
| axus wrote:
| Nice! Her experience getting a "bionic ear" at age 80 was
| very interesting: https://www.math.columbia.edu/~jb/my-
| bionic-ear.pdf
| marysminefnuf wrote:
| Birman still dropping bangers at 100 is quite something. We knew
| 3 strands is faithful and it was assumed 4 must be true but the
| ramifications of this in the face of quantum computing will be
| really fun going forward.
| WorkerBee28474 wrote:
| 99, according to Wikipedia, but yeah
| vlovich123 wrote:
| What are the ramifications?
| marysminefnuf wrote:
| ??? But it does allow us to better reason about which braids
| are different or the same. and the most promising quantum
| computers use braiding to form logic gates.
| culi wrote:
| Interestingly, David Graeber argued that mathematical thinking
| likely began through initiatives of women. Specifically tied to
| practices like weaving, beadwork, and tracking plant-based
| knowledge.
|
| https://theanarchistlibrary.org/library/david-graeber-and-da...
| scuppernong wrote:
| not necessarily disputing any of his conclusions, but I find
| his style of argument frustratingly slippery, always
| generalizing broadly from weak evidence
| culi wrote:
| He was much more effective at disputing narratives than he
| was at creating alternative ones. But no one can deny his
| ability to captivate and inspire the imagination
|
| This was one of my favorite talks he gave:
| https://www.youtube.com/watch?v=Hn78MhPmbCc
| globnomulous wrote:
| This essay: https://thebaffler.com/salvos/whats-the-point-if-
| we-cant-hav... is so bad, so dogmatic, and so obnoxious,
| verging on something that feels to me like intellectual
| dishonesty, that I ended a friendship with someone who
| praised it as "beautiful."
| ajkjk wrote:
| Don't see what's wrong with it...
| marton78 wrote:
| Found the autist!
| killjoywashere wrote:
| Have a look at hyperbolic crochet as well
|
| https://en.wikipedia.org/wiki/Daina_Taimi%C5%86a
|
| https://pi.math.cornell.edu/~dtaimina/crochet/hplane.htm
|
| https://www.routledge.com/Crocheting-Adventures-with-Hyperbo...
| Xmd5a wrote:
| > Our term 'the state' only came into common usage in the late
| sixteenth century, when it was coined by a French lawyer named
| Jean Bodin, who also wrote, among many other things, an
| influential treatise on witchcraft, werewolves and the history
| of sorcerers. (He is further remembered today for his profound
| hatred of women.)
|
| Damn.
|
| > Now to return to that strange and crude mysticism, which, as
| I have said above, took hold of Empress Alexandra and with
| which she infected her august spouse. In the course of my stay
| in Paris in 1903 I had long talks with Baron Alphonse, the
| septuagenarian head of the Rothschild house. Our conversation
| mostly revolved around the preoccupation with the occult and
| the mystic which had taken root at the Russian Court, this
| being, in the Baron's opinion, a bad symptom. He repeatedly
| returned to this subject. History shows, he pointed out, that
| great events, especially of an internal nature, were always and
| everywhere preceded by the prevalence of a bizarre mysticism at
| the court of the ruler.
|
| The Memoirs of Count Witte
|
| > Whoever has had the opportunity of studying the concealed
| feelings of persons by means of psychoanalysis can also tell
| something new concerning the quality of unconscious motives,
| which express themselves in superstition. Nervous persons
| afflicted with compulsive thinking and compulsive states, who
| are often very intelligent, show very plainly that superstition
| originates from repressed hostile and cruel impulses. The
| greater part of superstition signifies fear of impending evil,
| and he who has frequently wished evil to others, but because of
| a good bringing-up has repressed the same into the unconscious,
| will be particularly apt to expect punishment for such
| unconscious evil in the form of a misfortune threatening him
| from without.
|
| Sigmund Freud, Premonitions and Chance
|
| https://imgur.com/a/gHLhHmy
| jlev1 wrote:
| There was an excellent Dance Your PhD video about representations
| of braid groups and faithfulness in 2017:
| https://www.youtube.com/watch?v=MASNukczu5A
|
| If you look closely, you can find a mention of the n=4 Burau
| representation in it, and the fact that it "remains an open
| problem" to find elements of its kernel, i.e. to determine
| whether it is faithful.
| E-Reverance wrote:
| Am I going crazy or are the timestamps of the comments here wrong
| (after being merged?)?
| fragmede wrote:
| second chance pool messes up timestamps
|
| https://news.ycombinator.com/item?id=26998309
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