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A thread in 15 parts
(0/15)
Recall that a quasigroup (Q,*) is a set Q with a binary operation * such that for each a,b in Q, the equations a*x=b and y*a=b have unique solutions x,y. Groups are quasigroups and this property is usually one of the first things proved in elementary group theory.
(1/15)
Note that we don't assume associativity of *!
A loop is a quasigroup with an identity element. The story of why they are called loops is an interesting one and may even be true, but I will save it for another day. I am going to focus on loops in this thread.
(2/15)
Natural examples of nonassociative loops:
- The nonzero octonions under multiplication
- The sphere S^7 under octonion multiplication
- I have discussed other examples
Rethinking Vector Addition
— Michael Kinyon (@ProfKinyon) December 1, 2020
or
How I Learned to Stop Worrying and Love Nonassociativity
A thread in 29 tweets
(0/28)
For each x in a loop Q, define the left & right translations L_x, R_x : Q->Q by L_x(y)=xy and R_x(y)=yx. These mappings are permutations of Q. The composition L_x L_y of two left translations is not necessarily a left translation because Q is not necessarily associative.
(4/15)

First and foremost, do not tag law enforcement agencies on Twitter as a way of reporting ANYTHING. It doesnât work. Also, tweeting or RT-ing a screenshot is not an effective means of alerting law enforcement.

If you want to tip federal law enforcement, you have a couple of options. If it relates to the J6 Capitol events, thereâs a website where you can upload photos and video. (Thereâs also a toll free number if your uploads exceed the limit.)
https://t.co/eEviPTZYfM

If you have a tip thatâs not related to the J6 events, you have other options. You can call the FBI, and give your tip by phone, with or without your name.
https://t.co/WGEgksBgbp

Or you can use the FBI website to submit it online (again, with or without your name). Hereâs the landing page. https://t.co/X7Tl2I6sbm

Yep, and the parallels to Nazi Germany, where the same kinds of people supported the Nazi party, are hard to miss. Equating people who didn't finish college with the "working class" is missing the picture. By that defintion, Sean Hannity is working class. https://t.co/abu6RXTqb4
— Amanda Marcotte (@AmandaMarcotte) January 10, 2021
If you are trying to start a restaurant, and a black or latino, or god forbid, female AND black or latino city worker comes to inspect and finds a small problem, or the government is telling you what the minimum wage must be, or the ADA is requiring a ramp when you've (ct'd)
never had a customer even once come in in a wheelchair can feel like the government is solely in the business of making you fail. And then charging you for it in the form of your tax bill.
The most vitriolic pushback I get is when I speak out about preserving the estate tax, even though 99.8% of estates owe no tax at all. That is because the people swearing at me online are thinking that I am trying to take away the imaginary money they aspire to make.
I am pissing on the dream of them being my Uncle Walt going from rags to riches in the American Dream. Because the dream is so real to the people who hold it, but so unreal in practical life, the disconnect between how great it sounds and the likelihood of it ever happening ct'd
We have tried that path multiple times already.
It does not work.
Rep. Jordan does not see!..
(thread)
Rep. Jordan on potential Trump impeachment: \u2018I do not see how that unifies the country\u2019 https://t.co/GiiQtKTqvv @SundayFutures @FoxNews @Jim_Jordan
— Maria Bartiromo (@MariaBartiromo) January 10, 2021
Of course not. It is imperative that he not see.
Here is how it works...The way you and your team always put up a concrete wall when it comes to the relatively petty crimes some people do. They need to learn the lesson by suffering the consequences of their choices.
Consequences you absolve those who actually do deep and structural damage to the country from. At least until it cannot be ignored any longer, and you need a "sacrificial lamb".
Looking forward to seeing which 'lambs' will be offered up for this monumental moment.
Eventually
Eventually when the lesser 'lambs' are insufficient to the crime, sometimes, the responsibility finally lands on the leader, the head perp, the mob boss goes to prison after all. Or like Spiro Agnew, allowed to resign quietly... (one of the lucky ones).
Trump has the option to
Trump has the option to resign. The quick (and cowardly) way out. It won't heal the nation as well as a deep investigation would.
However, regardless of how these next few days play out, that investigation that has been called for before Jan6 still needs to happen.
So there
What about medical culture and who is not policed on professionalism that allowed him to get so far?
Has a single physician caused more damage to the public health than British gastroenterologist Andrew Wakefield? https://t.co/W3k21Ais6F
— Harry Thomas (@DrHarryThomas) June 10, 2020
When I look at Wakefield, I see the same kind of lack of ethics evident in #Medbikini study
but Wakefield was far further down the spectrum
because he was doing invasive GI procedures on children for his study, funded by a lawyer
First: consent matters
Informed consent matters

What incentives exist in healthcare & academia that shaped his mindset & behaviors?
What was Wakefield rewarded for throughout his career?
Where did he NOT get questioned?
Look as this patent he had filed to compete vs MMR
Gibberish
+
His đ€incentive
https://t.co/NRqXvBCGvB

Please note in his patent application Wakefield used those 12 samples that he cited in his @TheLancet study. He was not the only author. There were reviewers. There were editors. He was not alone in a cave. He was bullying his staff too
This was NOT âone manâ
And lots of silence

âJokingâ about kids crying & vomiting? Sounds like a massive jerk.
Erased/changed data
I have a hard time believing no one found him problematic before
Were people afraid to report?
When held accountable, he catastrophized, claiming he was being âpersecutedâ
Sound familiar?

TL;DR Absolutely nothing has changed in the civil service, apart from the identities of a few very senior office holders (1/20)
Significant - congratulations (if that is the right word for a reappointment; given the last 12 months I guess it is) to Tom Scholar. The survivor of the s**t list and HMT leadership recognised https://t.co/68FP1QGQ5c
— Alex Thomas (@AlexGAThomas) January 6, 2021
Firstly, the âwarâ does genuinely seem to be over. Congrats to Tom Scholar on his reappointment, kudos to the PM & Chancellor for a wise decision, and to Simon Case for whatever heâs done to bring these pointless hostilities to an end at such an important time (2/20)
But itâs worth asking: what has this latest attempt, accompanied as it has been by ferocious (if mostly anonymously briefed) rhetoric, actually involved?
The answer is, by historical standards, virtually nothing at all. There have been two discernible strands of activity (3/20)
First, thereâs been the defenestration of about half a dozen very senior officials, including, most unusually, the cabinet secretary.
But the replacements have been career insiders, cut from the same cloth. Sometimes theyâve been a good bit younger, but not always. (4/20)