4 ms·
The Burau representation of the braid group is faithful for n = 4
- wglb 2mo agoAlso https://www.yahoo.com/news/science/articles/99-old-mathematician-unraveled-century-111500867.html https://www.yahoo.com/news/science/articles/99-old-mathemati.... Someone who has been at this problem for 60 years.
- slwvx 2mo agoShe has a wikipedia page: https://en.wikipedia.org/wiki/Joan_Birman https://en.wikipedia.org/wiki/Joan_Birman
- axus 2mo agoNice! Her experience getting a "bionic ear" at age 80 was very interesting: https://www.math.columbia.edu/~jb/my-bionic-ear.pdf https://www.math.columbia.edu/~jb/my-bionic-ear.pdf
- marysminefnuf 2mo agoBirman 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 2mo ago99, according to Wikipedia, but yeah
- vlovich123 2mo agoWhat are the ramifications?
- marysminefnuf 2mo ago??? 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 2mo agoInterestingly, 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-david-wengrow-the-dawn-of-everything#toc77 https://theanarchistlibrary.org/library/david-graeber-and-da...
- scuppernong 2mo agonot necessarily disputing any of his conclusions, but I find his style of argument frustratingly slippery, always generalizing broadly from weak evidence
- culi 2mo agoHe 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 https://www.youtube.com/watch?v=Hn78MhPmbCc
- globnomulous 2mo agoThis essay: https://thebaffler.com/salvos/whats-the-point-if-we-cant-have-fun 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."
- killjoywashere 2mo agoHave a look at hyperbolic crochet as well https://en.wikipedia.org/wiki/Daina_Taimi%C5%86a https://en.wikipedia.org/wiki/Daina_Taimi%C5%86a https://pi.math.cornell.edu/~dtaimina/crochet/hplane.htm https://pi.math.cornell.edu/~dtaimina/crochet/hplane.htm https://www.routledge.com/Crocheting-Adventures-with-Hyperbolic-Planes-Tactile-Mathematics-Art-and-Craft-for-all-to-Explore-Second-Edition/Taimina/p/book/9780367375072 https://www.routledge.com/Crocheting-Adventures-with-Hyperbo...
- jlev1 2mo agoThere was an excellent Dance Your PhD video about representations of braid groups and faithfulness in 2017: https://www.youtube.com/watch?v=MASNukczu5A 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 2mo agoAm I going crazy or are the timestamps of the comments here wrong (after being merged?)?
- fragmede 2mo agosecond chance pool messes up timestamps https://news.ycombinator.com/item?id=26998309 https://news.ycombinator.com/item?id=26998309