John Carlos Baez
My cousin Joan is 84, but she's still got it going on. Here's how she kicked off the first episode of John Mulaney's comedy talk show.
(I think someone had asked her about Martin Luther King's sense of humor.)
https://www.thedailybeast.com/joan-baez-derails-john-mulaneys-live-show-to-attack-trump/
John Carlos Baez
If you have a valid visa to be in the US, be very careful. The Trump gang is starting to deport, detain, and perhaps even torture people in your situation! Here are some examples:
Dr. Rasha Alawieh is a kidney specialist working at Brown University. After visiting family in Lebanon, she was returning to the U.S. on an H-1B visa - a temporary visa that lets foreign professionals work in the US - when customs officials detained her at the airport in Boston. A federal court order was issued to stop her deportation. But she was deported anyway, sent off on a plane to Lebanon!
(1/n)
John Carlos Baez
Fabian Schmidt is a lawful permanent resident of the US, but he too was detained by immigration officers at the same airport in Boston - Logan Airport. He had been visiting Luxembourg, and flew back to the U.S. on Friday. His partner had gone to pick him up at Logan Airport, and waited four hours before calling authorities.
His mother says Schmidt was “violently interrogated” for hours at the airport, stripped naked, put in a cold shower by two officials, and being put back onto a chair.
She said Schmidt told her immigration agents pressured him to give up his green card. She said he was placed on a mat in a bright room with other people at the airport, with little food or water, suffered sleep deprivation, and was denied access to his medication for anxiety and depression.
“He hardly got anything to drink. And then he wasn’t feeling very well and he collapsed,” said Senior.
He was transported by ambulance to Mass General Hospital. Then he was transported to the regional headquarters for ICE in Burlington, Massachusetts, and then transferred to the Wyatt detention facility in Boston. Lawyers are attempting to get him out.
(2/n)
John Carlos Baez
This is a somewhat different case. Tourists from Germany can generally visit the US for up to 90 days without a visa. But this one, Lucas Sielaff, made the mistake of driving to Tijuana, Mexico with his partner to get medical treatment for her dog. When they came back, he had trouble understanding the border control officer questioning him. He gave a muddled answer and got taken to an interrogation room.
After more than an hour of questioning, he was denied re-entry to the U.S. and was chained to a bench along with other travelers.
Outside, his partner was trying to get answers from officials. In response, she says, they searched her car. When she raised objections, two ICE officers detained her and took her to a separate room, where she was subjected to a humiliating body search.
“For the first time in my life, I’m in handcuffs,” she said. “As they’re walking me into a building, they’re twisting my arms.”
After the body search, she, too, was chained to a bench for a time before being released.
Lucas Sielaff was held at the border post for two more days, sleeping on a bench under a Mylar blanket, and then transferred to the Otay Mesa Detention Center. For two weeks, he shared a cell with eight other people. Eventually he was deported on a flight that cost him $2,744.
Something similar happened to another German tourist to the US, Jessica Brösche. She too made the mistake of going to Mexico and trying to get back into the US. She was held for 46 days.
(3/n)
John Carlos Baez
And then there are hundreds of Venezuelans who were sent to the "Terrorism Confinement Center", a massive prison in El Salvador - even though a federal judge ordered that the planes reverse course and return the detainees to the United States!
The right-wing president of El Salvador, Nayib Bukele, made a joke of it on social media: “Oopsie … Too late.” And his post was recirculated by the White House communications director, Steven Cheung. So they are completely mocking the judicial system.
“This sure looks like contempt of court to me,” said David Super, a law professor at Georgetown University. “You can turn around a plane if you want to.”
Paywalled: https://www.nytimes.com/2025/03/16/us/constitutional-crisis.html
Free to read here: https://archive.is/2lXvG
(4/n)
John Carlos Baez
Another case - I'm not keeping up with all of them:
Becky Burke, from Wales, was halfway through a backpacking trip across North America when ICE grabbed her and detained her for 19 days. She is now back in Wales. Her parents haven't asked her for many details yet, but they say she was "taken in leg chains, waist chains and handcuffs".
ICE says she violated "the terms and conditions of her admission". Her parents guess maybe it was because she was on a tourist visa and she'd been getting free lodging from people on her trip in exchange for helping them around the house... thus violating her tourist visa, which doesn't allow employment???
It raises lots of questions.
https://www.bbc.com/news/articles/cly67j35y99o
(4/n)
John Carlos Baez
Want to leave the US? Stockholm University is hiring PhD students in Computational Mathematics and Mathematics, and these positions are open with people with any nationality:
https://su.varbi.com/en/what:job/jobID:807359/where:4/
https://su.varbi.com/en/what:job/jobID:803014/where:4/
Application deadline: April 22
Please help spread the word to students who are interested in doing a PhD on type theory, HoTT, computer formalization of CS and math, constructive mathematics, etc. Note that PhD students here are employed with a salary and that the position comes with benefits. There are also no tuition fees.
If you are a student interested in doing a PhD with Anders Mörtberg, who works on higher inductive types using cubical type theory:
https://staff.math.su.se/anders.mortberg/
you are welcome to apply to both positions above; just make sure you apply to the one in Computational Mathematics as that is the division he formally belongs to. Please also specify clearly that you want him as an advisor in your application (e.g. in your cover letter).
(1/2)
John Carlos Baez
The arXiv is where we keep papers on math, physics, etc. It's run by Cornell University.
It seems unlikely that the US government would demand that Cornell destroy the arXiv. But the many copies of the arXiv around the world were shut down on September 15, 2024, and it seems that now all the data resides in the US.
If anyone wants to back up the arXiv, they should go here:
https://info.arxiv.org/help/bulk_data_s3.html
The complete arXiv was 2.7 terabytes in March 2023, and growing at about 100 gigabytes a month.
Also read this, if you want to keep your backup up to date:
John Carlos Baez
You also can't trust AI when it comes to n-categories!
In reality a 1-category is a category, a 0-category is a set, and James Dolan discovered that a (-1)-category is a truth value and a (-2)-category is a true truth value (of which there is only one: "true").
But my friend Allen Knutson asked Gemini and got this garbage. Clearly it's Russian propaganda.
(2/2)
John Carlos Baez
A test shows that all the leading AI chatbots have been infected by Russian propaganda created by an organization called the "Pravda network".
According to the American Sunlight Project, a failed attempt to protect democracy in the USA, the Pravda network put 3.6 million articles online in 2024. In a strategy called "LLM grooming", this network seems designed to manipulate AI models rather than directly influence people. It's mainly focused on spreading lies connected to the Ukraine war:
https://www.newsguardrealitycheck.com/p/a-well-funded-moscow-based-global
But on a lighter note...
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John Carlos Baez
Resistance to autocrats has often come from university students. That's why in 2022 Curtis Yarvin said that if an authoritarian president were to take office in January 2025, he couldn't allow Harvard to exist after the start of April. And that's why Trump has suddenly and illegally tried to cancel $400 million of government contracts with Columbia University... and threatened to do the same with
Harvard
George Washington University
Johns Hopkins University
New York University
Northwestern University
UC Los Angeles
UC Berkeley
University of Minnesota
University of Southern California
The pretext is that these universities allowed "illegal protests" of Israel's invasion of Gaza and didn't do enough to stop anti-Semitism. However you feel about those issues, I don't believe that's the point of what's happening now. Trump is always self-serving: for him "anti-Semitism" only matters if he can use it as a cudgel against his enemies. I see other motives:
• He's trying to scare university administrators into not allowing protests against *his* forthcoming activities. By listing universities that will be looked into, he seeks preemptive compliance. There will be more congressional hearings where university presidents are pressured to suppress demonstrations, etc.
• He wants to attack elite universities because his right-wing base will applaud this. Academics, students and educated people tend to not go along with the xenophobic, racist and sexist "othering" which provides the emotional fuel for the fires of fascism. So they, too, are "others".
https://www.nytimes.com/2025/03/08/us/columbia-trump-colleges-antisemitism.html
You can read this NY Times article for free here:
(1/2)
John Carlos Baez
The Trump gang, in their quest to kill off diversity, equity and inclusion, has flagged over 26,000 items on the Defense Department's website, marking them for deletion.
One is a photo of the plane that dropped the atomic bomb on Hiroshima. Why?
Because it's called the Enola Gay. 🥴
But there's really serious stuff going on, like an attempted total erasure of trans people:
January 20th - Trump signs an executive order declaring the federal government will no longer recognize transgender people by defining sex as strictly male or female based on characteristics at birth.
January 23rd - State Department freezes trans passport applications.
January 27th - Trump signs an executive order barring transgender people from enlisting in the military.
January 28th - Trump signs an executive order ending federal support for gender-affirming care for people under 19 by directing federally-run insurance programs like TRICARE and Medicaid to exclude coverage for such care.
January 29th - Trump signs an executive order barring federally-funded schools from allowing transgender students to use names, pronouns, bathrooms, locker rooms, and sports teams that align with their gender identity. (It's not clear he has the power to do these things by executive order, but he's trying!)
January 31st - The Social Security Administration directs field offices to put an immediate halt to all sex identification changes in its Numerical Identification System.
John Carlos Baez
This is the color of infinite hotness.
This is the color something gets in the limit where its temperature approaches infinity. Of course you’d instantly be fried by gamma rays of arbitrarily high frequency, but this would be its spectrum in the visible range.
This is also the color of a typical neutron star. They’re so hot they look the same!
It’s also the color of the very early Universe!
This was worked out by David Madore, and you can find the details at my blog article, including a discussion of whether this is exactly the right color:
https://johncarlosbaez.wordpress.com/2022/01/16/the-color-of-infinite-temperature
Luckily, the alternative someone suggested is so close I can't tell the difference.
For computer screens and cell phones this color is approximately #98b5ff.
Perhaps we should call it "baby blue" - for the early universe.
John Carlos Baez
I'm trying to go from Riverside California up to the Topos Institute in Berkeley for a week, to talk to @epatters about his collaborative web-based modeling software using double categories.
It should be great, but here's the catch: I want to take a train, to reduce carbon emissions a bit.
To go the whole way by train I could:
• leave at 6:40 am and walk from my house to Hunter Park Station in 50 minutes
• take a train from Hunter Park leaving at 7:40 am and arriving at LA Union Station at 9:20 am
• take a train from LA Union station leaving at 9:50 am and arriving in Oakland at 9:06 pm
• walk from the train station to a bus station in 10 minutes
• take a bus leaving 9:27 pm and arriving in Berkeley at 10:03 pm.
• walk to a hotel
The good part: the train ride up the Pacific Coast is beautiful. Some people go all the way up to Seattle! The bad part: it starts brutally early. The really bad part: there's only 30 minutes to make the connection in LA, I've never done it before, and there's not another train that day.
Another plan: I need to visit my aunt near Santa Barbara. I can drive there in 3.5 hours, spend a a few days there, then drive to the train station. I hear they have long-term parking. I leave the car there, then:
• take a train from Santa Barbara leaving at 12:21 and arriving in Oakland at 9:06 pm
• walk from the train station to a bus station in 10 minutes
• take a bus leaving 9:27 pm and arriving in Berkeley at 10:03 pm.
• walk to a hotel
So, the same thing but starting later and avoiding the tight connection! A lot of driving, and if there's no long-term parking available the plan collapses.
Any good ideas? (Yeah, I could just not go.)
John Carlos Baez
On Wednesday, Trump and the Republican party unleashed a tidal wave of disease and death around the world.
....
“People will die,” said Dr. Catherine Kyobutungi, executive director of the African Population and Health Research Center, “but we will never know, because even the programs to count the dead are cut.”
The projects terminated include H.I.V. treatment programs that had served millions of people, the main malaria control programs in the worst-affected African countries and global efforts to wipe out polio.
Here are some of the projects that The New York Times has confirmed have been canceled:
A $131 million grant to UNICEF’s polio immunization program, which paid for planning, logistics and delivery of vaccines to millions of children.
A $90 million contract with the company Chemonics for bed nets, malaria tests and treatments that would have protected 53 million people.
A project run by FHI 360 that supported community health workers’ efforts to go door-to-door seeking malnourished children in Yemen. It recently found that one in five children was critically underweight because of the country’s civil war.
And more....
(1/n)
Free archived version:
John Carlos Baez
More life-saving missions that Trump and his evil minions nuked:
All of the operating costs and 10 percent of the drug budget of the Global Drug Facility, the World Health Organization’s main supply channel for tuberculosis medications, which last year provided tuberculosis treatment to nearly three million people, including 300,000 children.
H.I.V. care and treatment projects run by the Elizabeth Glaser Pediatric AIDS Foundation that were providing lifesaving medication to 350,000 people in Lesotho, Tanzania and Eswatini, including 10,000 children and 10,000 pregnant women who were receiving care so that they would not transmit the virus to their babies at birth.
A project in Uganda to trace contacts of people with Ebola, conduct surveillance and bury those who died from the virus.
A contract to manage and distribute $34 million worth of medical supplies in Kenya, including 2.5 million monthlong H.I.V. treatments, 750,000 H.I.V. tests, 500,000 malaria treatments, 6.5 million malaria tests and 315,000 antimalaria bed nets.
Eighty-seven shelters that took care of 33,000 women who were victims of rape and domestic violence in South Africa.
A project in the Democratic Republic of Congo that operates the only source of water for 250,000 people in camps for displaced people located in the center of the violent conflict in the east of the country.
Pre- and postnatal health services for 3.9 million children and 5.7 million women in Nepal.
(2/n)
John Carlos Baez
The dark litany of disaster continues! Someday, someone will count the hundreds of thousands of victims - the sick, the starved, the crippled, the dead - caused by ending these programs:
.....
A project run by Helen Keller Intl in six countries in West Africa that last year provided more than 35 million people with the medicine to prevent and treat neglected tropical diseases, such as trachoma, lymphatic filariasis, schistosomiasis and onchocerciasis.
A project in Nigeria providing 5.6 million children and 1.7 million women with treatment for severe and acute malnutrition. The termination means 77 health facilities have completely stopped treating children with severe acute malnutrition, putting 60,000 children under the age of 5 at immediate risk of death.
A project in Sudan that runs the only operational health clinics in one of the biggest areas of the Kordofan region, cutting off all health services.
A project serving more than 144,000 people in Bangladesh that provided food for malnourished pregnant women and vitamin A to children.
A program run by the aid agency PATH, called REACH Malaria, which protected more than 20 million people from the disease. It provided malaria drugs to children at the start of the rainy season in 10 countries in Africa.
A project run by Plan International that provided drugs and other medical supplies, health care, treatment of malnutrition programming, and water and sanitation for 115,000 displaced or affected by the conflict in northern Ethiopia.
More than $80 million for UNAIDS, the United Nations agency, which funded work to help countries improve H.I.V. treatment.
(3/n)
John Carlos Baez
Not content with spreading disease and starvation that will kill hundreds of thousands worldwide, this week Trump and his henchmen did their best to destroy the National Weather Service.
That's the US agency whose work underlies all weather forecasting in the US - stuff like predicting the paths of hurricanes, and so on.
So, more death and destruction. And it's just starting. This will end only when we stop him. He is mad, don't you see? He will destroy us if we let him.
....
"NWS has fired meteorologists as a direct result of upper-level heads telling them to do so," said Ethan Clark, a meteorologist for the city of Raleigh and an intern for WRAL, in a post to X. "Let me be clear, people will die because of this. Absolutely insane... I have no words for it. I’ve spent all day I mean all day in meetings with both republicans and democrats fighting."
UCLA climate scientist Daniel Swain had a similarly grim assessment, in a post to Bluesky.
"Despite widespread discussion to the contrary, the fact of the matter is that the private sector, as it presently exists, simply cannot quickly spin up to fill any void left by substantial dismantling of NOAA and/or the NWS," wrote Swain. "I work extensively with weather and climate scientists who work in the private sector — all of whom do good and important work that I greatly respect — yet even in the private sector there is near unanimous agreement that NOAA and NWS are indispensable."
In fact, he noted, virtually all private-sector weather reporting right down to your local news meteorologist rely on data from these agencies and "could simply not exist" without them.
(4/n, n = 4)
John Carlos Baez
Watch the oligarchs move into their new roles. Jeff Bezos started out selling books. Now he's a multi-billionaire. He bought one of the best newspapers in the US: the Washington Post. But Trump publicly threatened his business, and Bezos is willing to suck up to Trump to stay out of trouble. So now he has decreed that the opinion section of the Post can only publish opinions in support of "free markets" and "personal liberties".
But he's not really in favor of free markets: Amazon is a monopoly and exploits that power to the hilt.
And he's not really in favor of personal liberties: for example, Amazon forced their drivers to urinate in bottles and defecate in bags:
Bezos' notion of personal liberty is "freedom for me to be an oligarch... accountable only to the authoritarian boss." He acted liberal only when it didn't hurt his bottom line.
We cancelled our Washington Post subscription today.
John Carlos Baez
HARDCORE MATH POST
I knew a guy named John McKay who had a crazy good ability to perceive patterns in math. He came up with amazing results, but also some even more amazing conjectures which turned out to be true. One was recently proved by Britta Späth and Marc Cabanes. It took 20 years of hard work, and in the process they fell in love and started a family. Their proof is massive and requires studying lots of special cases. I hope it's correct! It's way too hard for me to understand.
But I understand the statement.
If you have a finite group G whose cardinality |G| is divisible by p, there's a largest power of p that divides |G|, say pᵏ, and G is guaranteed to have a subgroup of cardinality pᵏ. This is called a 'Sylow p-subgroup' of G. There may be more than one, but they're all conjugate - so they all look alike in a very strong sense.
McKay made a conjecture about this. Understanding it requires knowing a bit more stuff, which I'll happily explain if you ask.
Here's what it says:
For any finite group K, let n(K) be the number of irreducible complex representations of K whose dimension is not divisible by p. Let G be any finite group, and let N be the normalizer of a Sylow p-subgroup of G. Then n(G) = n(N).
(Here I count isomorphic representations as the same.)
Now the sensible way to prove this would be to set up a recipe to turn any irreducible complex representation of G whose dimension isn't divisible by p into one for N, and vice versa. But nobody knows how to do that, in general! So the only known proof requires separately studying tons of cases... which is really scary.
So: mysteries remain here.
I'm a mathematical physicist who likes explaining stuff. Sometimes I work at the Topos Institute. Check out my blog! I'm also a member of the n-Category Café, a group blog on math with an emphasis on category theory. I also have a YouTube channel, full of talks about math, physics and the future.
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