@f26421da - I don't think people route their Nobel prize through an institution. Grants, yes - because you apply *through* the university, and the university forces you to give them a cut.
"The typical Nobel Prize winner is no slouch — he or she has probably already got a good job at a prestigious university — but while winners make an honest dollar, wealthy they are not. Most laureates spend their prize money (about $1.4 million) in mundane ways: to pay the mortgage, buy a car or save for rainier days. MIT's Wolfgang Ketterle, one of three scientists to win the 2001 Nobel Prize in Physics 2001, said, "I used the Nobel money to buy a house and for the education of my children." Others, meanwhile, such as the late Franco Modigliani, an MIT professor who won the Nobel Memorial Prize in Economics in 1985, buy a sailboat. In the following pages: how a smattering of other Nobel laureates spent their winnings."
@0269c0e4https://content.time.com/time/specials/packages/article/0,28804,1848817_1848816_1848803,00.html
@5fff00cf - no, that's incredibly rare. People can fail to get tenure, but they're not "demoted" to adjuncts; that would be against the rules at my university. So I would like to understand in more detail what happened here.
The University of Pennsylvani is acting proud of Katalin Karikó now that she's won a Nobel Prize. But they kicked her out of her tenure track job when she insisted on doing the work that won her that prize:
"She recalls spending one Christmas and New Year’s Eve conducting experiments and writing grant applications. But many other scientists were turning away from the field, and her bosses at UPenn felt mRNA had shown itself to be impractical and she was wasting her time. They issued an ultimatum, if she wanted to continue working with mRNA she would lose her prestigious faculty position, and face a substantial pay cut.
”It was particularly horrible as that same week, I had just been diagnosed with cancer,” said Karikó. “I was facing two operations, and my husband, who had gone back to Hungary to pick up his green card, had got stranded there because of some visa issue, meaning he couldn’t come back for six months. I was really struggling, and then they told me this."
"While undergoing surgery, Karikó assessed her options. She decided to stay, accept the humiliation of being demoted, and continue to doggedly pursue the problem. This led to a chance meeting which would both change the course of her career, and that of science."
Elsewhere she recalled:
“I thought of going somewhere else, or doing something else. I also thought maybe I’m not good enough, not smart enough."
She's now an adjunct in UPenn's neurosurgery department. Will they make her tenure-track now? Luckily she also has a good job at BioNTech.
Both quotes here come from interesting stories. The first is from here:
https://www.wired.co.uk/article/mrna-coronavirus-vaccine-pfizer-biontech
The second is from here:
https://billypenn.com/2020/12/29/university-pennsylvania-covid-vaccine-mrna-kariko-demoted-biontech-pfizer/https://media.mathstodon.xyz/media_attachments/files/111/167/287/127/975/745/original/2bccdf1795f16e02.jpg
I’m speaking Edinburgh Category Theory Seminar this Wednesday, October 4th, at noon UK time. It won't be recorded, but if you whisper a request in my ear I can give you a Zoom link. Also, you can read my lecture notes here:
https://golem.ph.utexas.edu/category/2023/10/the_free_2rig_on_one_object.html
Schur Functors
The representation theory of the symmetric groups is clarified by thinking of all representations of all these groups as objects of a single category: the category of Schur functors. These play a universal role in representation theory, since Schur functors act on the category of representations of any group. We can understand this as an example of categorification. A ‘rig’ is a ‘ring without negatives’, and the free rig on one generator is ℕ[x], the rig of polynomials with natural number coefficients. Categorifying the concept of commutative rig we obtain the concept of ‘symmetric 2-rig’, and it turns out that the category of Schur functors is the free symmetric 2-rig on one generator. Thus, in a certain sense, Schur functors are the next step after polynomials.
@00797bc6 wrote:
"The problem is bigger - junior people who work in different areas at the same time are viewed with suspicion, or worse, by hiring committees."
Yes. There's a limit to how much one can pretend to be something one is not, but I try to tell my grad students that they should pick one thing to be the world's expert on, and let other things take a background role. Joe is the world's expert on the monoidal Grothendieck construction. That work has been used in at least two software projects involving multiple people: one when he was a grad student, and another now: I'm using that math to help design software for modeling infectious disease. But there are also lots of other papers citing Joe's work on this! If he explains those in his research statement, he'll look like what he truly is: the world's expert on some pure math that has lots of different applications.
@47933d1d -
@00797bc6@47933d1d - I should have been a lot clearer: I wasn't suggesting Joe say anything false in his research statement, I just meant he should not treat it as the place to bare his heart and talk about everything he's interested in doing. He needs to leave out most of that and focus on how his most impactful work has already transformed the landscape of applied category theory. It's much more impressive to talk about that.
"Every time someone asks what I'm currently working on, I'm frozen because immediately I'm confronted with a list of 10+ projects I've unwisely mentally listed as "active"."
If I talked about all the projects I'm working on in a research statement, people would laugh at it: the mathematics of tuning systems and modes, the splitting principle, the moduli space of triangles, the work and life of Hoàng Xuân Sính, separable algebras in Grothendieck's Galois theory.... I would leave all that out and focus on applying category theory to modeling in epidemiology.
Wow! I just learned that Isaac Newton wrote a treatise about music theory, comparing just intonation with equal tempered scales!
This was in 1643, when he was 22: the year he fled Trinity College to avoid the Great Plague, went to the countryside, invented calculus, and discovered a prism can recombine colors of light to make white light.
This great new video about Newton's never-finished treatise is probably the most pleasant way to learn about this stuff.
One reason Newton's work is amazing is that while an equal tempered scale (with notes equally spaced) is standard now, it was very unusual in Newton's time. Much more common was just intonation, where the frequency ratios are simple fractions.
Another reason Newton's work is amazing: he compared just intonation not only to a 12-tone equal tempered scale, but also to equal tempered scales with 15, 19, 20, 24, 25, 29, 36, 41, 51, 53, 59, 100, 120 and 612 notes! He discovered that the 12, 53, 120 and 612 note scales work especially well.
The 53-note equal tempered scale actually goes back to the Chinese music theorist Jing Fang (78–37 BC), who discovered that a series of 53 just fifths is very nearly equal to 31 octaves. Later the same observation was made by Nicholas Mercator. (No, not the guy with the map, another guy: the one who invented natural logarithms.)
I don't know if Newton could have known of Mercator's work, but Newton *was* influenced by Descartes's Compendium Musicae.
To fall deeper into this rabbit-hole, read on!
(1/n)
https://www.youtube.com/watch?v=83ytb6AWRAk
@aa82d4be - cool, I'm glad you're spreading the news about this wonderful set.
Our paper says what people have proved, or at least what we know they've proved:
https://www.ams.org/journals/notices/202309/rnoti-p1495.pdf
It's known that the set of all roots of all polynomials with coefficients ±1 is contained in the annulus
1 ≤ |z| ≤ 2
and that it contains the annulus
2^(-1/4) ≤ |z| ≤ 2^(1/4)
It's also known that this set is connected and locally path-connected! But that's about all.
So given what people have proved so far, in theory the set could fill in the whole annulus 1 ≤ |z| ≤ 2. But from numerical computations I'm completely sure that's not true. So, someone should start proving theorems about this stuff!
@0bacad63 - the sets do converge as the degrees get large (i.e. the degrees plus 1 get large in a multiplicative sense) , but a lot has not been proved about what the limiting set looks like!
It's known that this set is contained in the annulus
1 ≤ |z| ≤ 2
and that it contains the annulus
2^(-1/4) ≤ |z| ≤ 2^(1/4)
It's also known that this set is connected and locally path-connected! But that's about all.
@531868ba - wow, so we were destined to meet! In a way the best source of information on these polynomials is here:
http://math.ucr.edu/home/baez/roots/
since it has lots of pictures and links to everything else I know about.
@0bacad63 - of course they don't look similar for very small degrees, but by what I said the sets of roots converge as the degrees get large in the funny sense I described.
@cd2b7137
@cd2b7137 - a bunch of theorems are known for the set consisting of all roots of Littlewood polynomials of *all* degrees, and we discuss them in our paper, but in our pictures we lazily plotted pictures of roots of Littlewood polynomials of degree 23, so 24 nonzero terms, since any root of a Littlewood polynomial with n nonzero terms is also a root of one with m nonzero terms if n divides m.
At left you see two closeups of the set of all roots of polynomials of some large degree with coefficients ±1. At right you see "dragon sets" - fractals described in a simple way depending on where we do the closeup. They look very similar in character... but not exactly the same. Can you make this precise and prove it?
You can see a heuristic explanation here:
https://math.ucr.edu/home/baez/roots/
(Search the page for "dragon".) This has got to be the key to solving the puzzle - but nobody has yet turned this idea into a precise statement and proved it.
If you ever wanted to prove an interesting theorem about fractals, this could be your chance.
(2/2)
https://media.mathstodon.xyz/media_attachments/files/111/153/932/996/109/180/original/dda0c7f75479ad33.jpg
It warms my heart to see so many lighthouses beaming out into the chilly night in the far north of the British Isles, near Orkney and the Shetlands.
But what are those two lighthouses due west of Orkney? I know of no land there. They're well north of the Hebrides.
It's also fun to see there's a lighthouse in the middle of Scotland! I think that one is on Loch Ness. But where, exactly?
Odd that there are none on the west coast of Ireland.
So you can see the details, I'm only showing you the top of this beautiful map made by @49f821b2, The whole thing is here:
https://mathstodon.xyz/@terence@fosstodon.org/111132853426508413https://media.mathstodon.xyz/media_attachments/files/111/150/750/845/670/618/original/da6e83b24a8d9293.png
@b114a88b@e3fc6945 - the thing is, the no-hair theorem is proved using general relativity plus classical Maxwell theory or some other classical theory, so it has nothing to say about black hole evaporation.
@e64f5e94 - Until about 47,000 years after the Big Bang, most of the energy was in the form of radiation - that is, particles moving at the speed of light or close to it, namely photons and neutrinos. This is called the "radiation dominated era". Eventually this radiation was either absorbed by matter or was set free as the cosmic background radiation we see today (stretched out by the expansion of universe, so mostly microwaves now).
But the dominance of matter over antimatter must have started much earlier, because the radiation was only energetic enough to turn into quark-antiquark pairs (and be formed by them) for roughly the first 50 microseconds after the Big Bang. After this, radiation would form (and be formed by) lighter things like electron-positron pairs, etc.
@e64f5e94 - if our galaxy had significant amounts of antimatter in it, we would know that, because occasionally this antimatter would bump into matter and annihilate, releasing gamma rays with specific energies. Physicists have spent a lot of time looking for these gamma rays, and other such evidence, and they haven't found it, so we feel very sure that our galaxy has almost no antimatter in it. Similar studies have ruled out the possibility that clusters of galaxies or even superclusters contain significant amounts of both matter and antimatter. So if the Universe contains more than a tiny bit of antimatter, we would need entire superclusters made of antimatter, besides those made of matter. And it's very hard to come up with a workable theory where, starting from the dense hot gas in the early universe, we wind up with some large regions made of matter and others made of antimatter.
What we actually believe happened is very interesting: originally there was a lot of matter and antimatter all mixed up, but almost all of it annihilated, and there was a tiny excess of matter left. The theories for how we got this tiny excess of matter are connected to the CP violation I discussed, which makes matter slightly different from antimatter. For more:
https://en.wikipedia.org/wiki/Baryogenesis
@e3fc6945 - great question!
"From what I heard, an antimatter blackhole is just a regular blackhole."
Nobody knows for sure. Not only haven't we studied this experimentally, for obvious reasons, the theory is a bit murky. General relativity hints that black holes formed from matter and antimatter are the same. But as you note, this would allow us to violate various conservation laws - for example, we could use black holes and Hawking radiation to convert matter into antimatter in ways that are "illegal" in the Standard Model of particle physics.
The problem is that nobody has combined general relativity and the Standard Model into a single theory that we believe in. Until we do, it's hard to give a definitive answer to your question... and this question shows how challenging this task will be!
Now that it's on your mind: what's the difference between matter and antimatter?
1) Antimatter has the opposite charge. This is true not just for electric charge, but also the subtler kinds of charge that affect the strong and weak nuclear forces.
2) There's a lot more of one than the other! Nobody knows why. But if there were more antimatter, we'd call that one 'matter' - and we'd be just as happy.
3) More subtly, there's a difference in "handedness" between matter and antimatter! For example, a neutrino moving very fast tends to spin *clockwise* around its axis of motion. An antineutrino tends to spin *counterclockwise*.
If you switch matter and antimatter and view what's going on in a mirror, they behave almost the same way. This is called 𝗖𝗣 𝘀𝘆𝗺𝗺𝗲𝘁𝗿𝘆.
4) But CP symmetry isn't perfect. Antimatter viewed in a mirror behaves a tiny bit differently from matter viewed the usual way! This was discovered in 1964 by James Cronin and Val Fitch, who won a Nobel for it.
In the Standard Model of particle physics there are 2 numbers that describe how much things change if you switch matter and antimatter and also view things in a mirror. One is for quarks and it's tiny: about 0.0003. So this effect is very small for quarks.
The other one is for neutrinos and it's bigger: we don't know it precisely, but we know it's less than 0.03.
Nobody knows why these numbers have the values they do! We just measure them experimentally.
The good news is that now you know ALL the ways that matter and antimatter are different... as far as we know. So probably you mainly need to learn more about item 4, which is explained here:
https://en.wikipedia.org/wiki/CP_violation#P-symmetryhttps://media.mathstodon.xyz/media_attachments/files/111/147/947/743/348/532/original/27e12f3e4742164e.jpg
Edward Frenkel is a bigshot mathematician who has worked with Ed Witten. But starting at 2:41:30 here:
https://www.youtube.com/watch?v=n_oPMcvHbAc&t=9690s
he points out the failure of string theory - and worse, how the leaders of string theory have never acknowledged this failure:
He mocks the string theorist Andy Strominger, who now says string theory's original goal of unifying all the forces and particles was "really a small thing."
Frenkel says:
"Remember Moses? He took the Israelites out of Egypt and he told them that he would lead them to the promised land. Imagine that Moses, after 40 years of wandering in the desert, says "You know guys? This idea of a promised land - it's not such a big thing. Look how much we've learned! We've learned about the desert. We've learned so much about the sand. Who cares about the promised land?"
"People call it "moving the goal-posts". This is not moving the goal-posts! This is going to a different stadium and starting to play a different game - like you used to play soccer at one stadium, and you move to a different stadium and start playing baseball, but you say you're still playing soccer".
@f15ef1f3@cf713a4e - I said the anti-Higgs mediates the mass of antiparticles and then said the anti-Higgs is the Higgs. I was not trying to lecture this person on quantum field theory, vacuum condensates, Weyl and Dirac spinors, etc. I was just pointing out that the Higgs field is just as responsible for the mass of antiparticles as it is for partices - which is unsurprising, since the Higgs particle we've detected in the lab is its own antiparticle.
@cf713a4e - most things work exactly the same if you stick antiparticles in where you had particles. So yes: the anti-Higgs boson mediates the mass of antiparticles just like the Higgs mediates the mass of particles.
BUT: the Higgs boson is its own antiparticle! In this respect it's like the photon.
As far as we know, the only thing that changes when you replace particles by antiparticles are a few *numbers* describing how *strongly* the Higgs interacts with them. This makes antimatter behave in a very subtly different way than matter.
@f604b7a1 wrote: "is gravity some kind of emergent property of LOTS of particles?"
No. I think our theories of gravity work too well to be some completely wrong as this.
@f604b7a1 - again the answer is obvious from the laws of physics: yes, antimatter makes gravity. But again, testing it will be major nuisance. The lightest object whose gravity we've deteted is a 90-milligram gold sphere:
https://arstechnica.com/science/2023/09/antimatter-falls-downward-not-upward-just-like-regular-matter/
But it was shaken back and forth, not easy to do with antimatter! And antimatter currently costs about $60 billion per microgram, which would be $5.4 quadrillion for 90 micrograms. Even worse, that quoted price is for antiprotons, which wouldn't work: antihydrogen would cost even more!
https://en.wikipedia.org/wiki/Antimatter_weapon
@a344ae77@9f023162 - luckily this is one of those rare cases where a 3-word headline correctly summarizes a new experimental result in particle physics!
@e5c46634 - I think if you want degrowth to actually occur you'll need to use some of those more amicable options. I just think it won't catch on with that name - except with a limited audience of people, those of a contrarian ilk.
For example, "Black Lives Matter" says what it means, it's a reasonably hard phrase to hard to coopt, and indeed, it's un-sugar-coated enough that a lot of people actually out against it.
@31b3bda5
@4c681c0c - Great chart. The one object that does not exist is "instanton". More precisely instantons exist but there is not an object called an instanton whose Schwarzschild radius equals its Compton wavelength.
@4799d2d4 - I hope your paper actually *said* "hole point was to recast an existing construction using low-tech tools and show how far one could get." Then at least the referee would know that's what you're doing, and if they don't like that, well, submit it to another journal.
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