nostr:npub1lqe2qhsfqlrufyhtg8fczy9h6y2rg0r5666yq790urr3j0a80fcsyvguw8 - I could never penetrate far into Finnegan's Wake - particle physics is easier for me - though I've read and enjoyed Ulysses several times.
I'm glad my explanations made sense! That's what I'm aiming at.
nostr:npub1gzyqeta7fyv98m6gf4tqxmwa3p0atzc04hxrrvz84tjvnuexpu3qqatpxv - maybe that's it!
I also like this new unicode symbol, for Bigfoot:
nostr:npub1mrvtrws4n55we6rtty8suxnkmd699ys50ar4g0grl5sdt0f4t9kstvjc8k - hi! I agree with you. I think if we want to model the real world in ways that capture the subtle web of relationships between things, category theory will be a helpful tool. But mainly we have to really want to work on it. There's certainly no way we can just "throw category theory at it".
nostr:npub1uas3xsp68gzt092ktx49x908xc88r03ewhyupqrw2d9ts3jxhlqqum9cm9 - the "sudden demand for logicians on Wall Street" article was just a joke, not serious.
On the other hand category theory is really getting lots of funding now; see for example this:
https://johncarlosbaez.wordpress.com/2025/02/08/category-theorists-in-ai/
nostr:npub16dwy5q9ps06ph5z4s0uj7gxj3lnw84yn2xls3qf2pfp8le5slr3sfwkdp2 - nostr:npub1dmafnnylf892u4mza4van8775yuv8hetk8q4p0325g984m29yzes5fdk8m says an equals sign with an infinity symbol *below* it is already used in chess. I don't know how.
nostr:npub1r0695e2t8qjlkslfpg6s7ya90zmg9dn33v5xufkf62m0n2smu7tsq70u6g - my main advice is to write several essays, each tackling fewer subjects than this one here. This one tackles Buddhism, the history of category theory and how it's been used, the question of whether you need to develop category theory within set theory, the recent history of what people are doing in "applied category theory", the role of mathematics in a capitalist society, and a few other things. Too much for one essay!
nostr:npub1hyzn5m04499l6khlgfglt4yfn3me04mx6w34fqqprrftx0k9zjyswtq2c8 - it's tough, but he didn't get a chaired profess of the Harvard astronomy department, etc., by being a crackpot. He's more or less a crackpot when it comes to aliens, but this new paper of his looks serious to me.
New unicode math symbol just dropped!
It means "equal apart from errors that could be, like, infinite".
nostr:npub16vlumeuw8z34jxyxklpszd9gtd09ml9ullstupcdjspwsp794ars96enl5 - I'd need to read a paper that's more about the basic theory to understand how a pulse of laser light affects the wavefunction of an electron. I know plenty of physics, but "ponderomotive potential" is not in my vocabulary. This paper says
"Consider the paraxial wave function of an electron
travelling at a relativistic velocity v along the axial z-
direction, ฯ(r, t) = exp(iฮณm(v_zโc^2t)/โ)ฯ_โฅ(x, y, t), with m
the electron mass, ฮณ = 1/sqrt(1 โ v^2/c2) the relativistic
factor and ฯ_โฅ the transverse electron wave shape. The
electron shall be illuminated by a short laser pulse of
moderate intensity, described by a vector potential A(r, t)
with a temporal profile extending over 100 optical
periods. Following [53] and neglecting the transverse
electron motion, the light-induced velocity modulation, as
well as electron-positron mixing, we can approximate
the interaction by an effective scattering phase...."
So I would need to read [53]:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.123901
Fabio Pacucci and Abraham Loeb claim that the most common little red dots, found at redshift z = 5, are explained as galaxies formed in the lowest โผ1% of the halo spin distribution. This naturally reproduces both their observed abundance (โผ1% of standard galaxies) and their compact sizes (effective radius < 300 parsecs).
They aren't making any claims about the precise structure of little red dots. They may be black holes, they may not, etc.
They claim this theory fits some of the statistics of little red dots.
(2/2)
I want to learn more about 'little red dots'. In March last year, astronomers were shocked to find these objects in the very early universe, just 600 million years after the Big Bang. That seemed too soon for galaxies to form.
Now Avi Loeb has a theory to explain them.
Aliens!
Just kidding. It's amazing how he's managed to discredit himself so thoroughly. But he's had some good ideas and may continue to do so. This new work was done with Fabio Pacucci at Harvard.
Their theory is that little red dots formed from the collapse of dark matter clouds that happened to have low angular momentum. Most of the dark matter clouds spin around too fast to collapse quickly. They collapse more slowly - and pull visible matter along with them, creating the galaxies we see.
(That at least is the standard theory. We need dark matter to explain galaxy formation and many other things.)
(1/2)
nostr:npub1gyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqsejr6gc wrote: "But how do we proceed from there - how do we decide which of these constructions is the best/most interesting/most promising for physics?"
Nobody has a fucking clue, which is why particle physics has been completely stuck since 1980, except for the experimental revelation that neutrinos have mass.
Well, "completely stuck" is a bit of an exaggeration. People are trying lots of things, none of them have worked, but we are still perhaps learning things in this frustrating process. Different approaches succeed to different extents, and the full answer to your question would outline all of what's been done - too long for a post here!
I am trying to follow a particular approach now, which may be wrong but deserves to be tried. Namely, to take the octonions, exceptional Jordan algebra, and so on seriously. This means, for example, taking seriously the fact that a Euclidean Jordan algebra serves as both an algebra of observables and a kind of "spacetime", with a lightcone structure. The consequences of this fact are well-understood for ๐ฅโ(โ): we get the connection between qubits, spinors, the Riemann sphere, and Minkowski spacetime, some of which is nicely explained in Penrose and Rindler's books.
Maybe we should think about how all this works for ๐ฅโ(๐).
The fact that the Standard Model gauge group arises from the interplay of ๐ฅโ(๐) and ๐ฅโ(โ) feels incredibly suggestive to me.
But I hadn't known where to go with it.
nostr:npub1gyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqsejr6gc wrote: "Also, now I'm curious what these new avenues are!"
In physics we use the Higgs mechanism to explain spontaneous symmetry breaking. Most notably, the electroweak group SU(2) ร U(1) breaks down to the subgroup observed at low energies, U(1), via the Higgs field. Here's how: the Higgs field takes values in โยฒ, and SU(2) ร U(1) acts on โยฒ in a certain way, and the subgroup fixing a nonzero vector in โยฒ is the relevant U(1).
I should look at how a similar mechanism can break the automorphism group of the exceptional Jordan algebra down to the Standard Model gauge group.
Also, I know a lot about how the fermions (i.e., matter) form a representation of SU(5) and how the Standard Model gauge group is the subgroup S(U(3) ร U(2)) - see below. I should transfer this knowledge to think about how the fermions show up in the exceptional Jordan algebra approach.
nostr:npub1gyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqsejr6gc wrote: "But how do we proceed from there - how do we decide which of these constructions is the best/most interesting/most promising for physics?"
Nobody has a fucking clue, which is why particle physics has been completely stuck since 1980, except for the experimental revelation that neutrinos have mass.
Well, "completely stuck" is a bit of an exaggeration. People are trying lots of things, none of them have worked, but we are still perhaps learning things in this frustrating process. Different approaches succeed to different extents, and the full answer to your question would outline all of what's been done - too long for a post here!
I am trying to follow a particular approach now, which may be wrong but deserves to be tried. Namely, to take the octonions, exceptional Jordan algebra, and so on seriously. This means, for example, taking seriously the fact that a Euclidean Jordan algebra serves as both an algebra of observables and a kind of "spacetime", with a lightcone structure. The consequences of this fact are well-understood for ๐ฅโ(โ): we get the connection between qubits, spinors, the Riemann sphere, and Minkowski spacetime, some of which is nicely explained in Penrose and Rindler's books.
Maybe we should think about how all this works for ๐ฅโ(๐).
The fact that the Standard Model gauge group arises from the interplay of ๐ฅโ(๐) and ๐ฅโ(โ) feels incredibly suggestive to me.
But I hadn't known where to go with it.
nostr:npub1gyewnrnvhqg0dlqmn5mfp0wjcvpkgxycjat9527w8cmf0c6cxwqsejr6gc - "Are these descriptions equivalent?" You have to take the theorem below as definitive, not any of these simple-sounding verbal descriptions.
For example, to say "that preserve a choice of โโ๐" or "we take those symmetries which preserve a โโ๐" is sloppy. We're starting with automorphisms of ๐ฅโ(๐) and finding a subgroup of those. But an automorphism of ๐ฅโ(๐) does not act on ๐!
What does make sense is for an automorphism of ๐ฅโ(๐) to preserve a Jordan subalgebra isomorphic to ๐ฅโ(โ).
That's what I was saying, in abbreviated form, on the slide: "choose a subalgebra ๐ฅโ(โ) โ ๐ฅโ(๐)" is my abbreviated way of saying "choose a Jordan subalgebra of ๐ฅโ(๐) isomorphic to ๐ฅโ(โ)."
I need to write a paper, simply to clarify all this.
nostr:npub14lya6peeg26tjvwzz86su0dsexfre6ad5t24lfcy2nfhn4x3gdnqt7wpkh - I've been talking about the octonions and the exceptional Jordan algebra for a long time, but Dubois-Violette and Todorov figured out how the Standard Model gauge group was hiding in these in 2018, so I could only have figured this stuff out after then. Not sure when!
nostr:npub12n42w9z249p9yc8jjla3thn26vm6mtc83eyhnhye40targr5ggxspu8z9u - Cool! "Islamicate"?
China is carrying out the solar revolution at scale. Here panels float on a reservoir in northwest China. This is just one of many massive solar plants. See more here:
https://www.theatlantic.com/photography/archive/2025/07/photos-china-solar-power-energy/683488/
Meanwhile Trump is fighting solar power and pushing coal. These days the Chinese call him ็นๆๆฎ, "Comrade Jianguo". Literally this means "Comrade Building the Nation". It's a joke about "Make America Great Again". It hints that Trump is a comrade building the greatness of China by holding back the US.
Great! A bunch of people here wanted it. Now it exists. ๐
It's a "dark archive" of the arXiv - a non-public backup to save the data in case of attack by hackers or government. The arXiv, I hope you know, is the biggest source of modern math and physics papers.
Who got the job done? The TIB: the Technische Informationsbibliothek, run by the Leibniz Information Centre for Science and Technology, in Hannover, Germany.
They write:
"The TIB has now set up a so-called dark archive for the arXiv content in order to be able to make the backed-up data accessible if the data stored in the USA is lost. The archive functions as a silent reserve: the complete copy of the content is stored decentrally at the TIB, but is not publicly accessible. This means that the data stock โ almost 10 terabytes โ is protected against potential outages and can be activated in an emergency.
The TIB is currently working on processes to keep the archive up to date: new submissions and updated versions must be backed up regularly in order to preserve the state of research as completely as possible.
โBuilding a Dark Archive is an expression of our longstanding commitment for a reliable, international academic provision, and as a partner of arXiv. Even though the Dark Archive today only works in the background, it is a key element in safeguarding digital research contents in the long term, because in case of a crisis, we could open the archive,โ explains Dr Irina Sens, Deputy Director of the TIB."
More details here:
https://blog.tib.eu/2025/05/14/protecting-science-tib-builds-dark-archive-for-arxiv/
nostr:npub1mh35g2n3gx4lgwt24aqhsfpax9u7r0mf9v82vh5mkus64lw8dd8q66mxds nostr:npub1m343wwwdmvare434daq4jpjyc4q4nv56pftgh03jej5l42azs44qwpnjzz nostr:npub1pnrvhdkuc6y8s7dva2rhef589x2uskn7csaed8fyv7dvzsge5uxs0aerkd - indeed, massive fundamental change is coming, of a not very pleasant sort, if we attempt to continue on our present reliance on fossil fuels.
It's *true* that 3-5% of natural gas is used to make ammonia for nitrates in fertilizer. So we should be working on CO2-free ammonia.
https://ammoniaenergy.org/articles/the-cost-of-co2-free-ammonia/