The Burau representation of the braid group is faithful for n = 4

Posted by wglb 13 hours ago

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Comment by culi 10 hours ago

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...

Comment by Xmd5a 36 minutes ago

> 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

Comment by ashivkum 9 hours ago

not necessarily disputing any of his conclusions, but I find his style of argument frustratingly slippery, always generalizing broadly from weak evidence

Comment by culi 7 hours ago

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

Comment by globnomulous 3 hours ago

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."

Comment by wglb 13 hours ago

Also https://www.yahoo.com/news/science/articles/99-old-mathemati.... Someone who has been at this problem for 60 years.

Comment by slwvx 12 hours ago

Comment by axus 11 hours ago

Nice! Her experience getting a "bionic ear" at age 80 was very interesting: https://www.math.columbia.edu/~jb/my-bionic-ear.pdf

Comment by marysminefnuf 12 hours ago

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.

Comment by vlovich123 10 hours ago

What are the ramifications?

Comment by marysminefnuf 6 hours 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.

Comment by WorkerBee28474 12 hours ago

99, according to Wikipedia, but yeah