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Last Notes

2026-09-11 09:48:00 UTC

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I remember reading about Peter Scholze saying something like: he no longer thought proving theorems was interesting, and instead he was mostly concerned about finding good new definitions. So that's maybe even a step further than the old description of problem solvers vs theory builders.

2026-09-08 20:11:52 UTC

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It sounds like Sam Altman has a friend in Minsk who has a friend in Pinsk ;)

2026-09-04 20:56:40 UTC

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I can hardly wait for the Straumli Blight, a reference to the terrific hard-SF novel "A Fire Upon The Deep". A hyperintelligent computer virus tries to take over the galaxy is one way to put it, but it's much more than that.

2026-08-29 07:58:02 UTC

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"attractive central force" in the first sentence should probably say "attractive central force field". I did notice the ugly kerning in the title but kept looking for some other error.

2026-01-29 02:33:33 UTC

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nice! For something that's "out there", try larips.com (spiral spelled backwards). A big analysis claiming (dubiously) that J.S. Bach used a specific non-equal-tempered tuning system. I've listened to some recordings made in that tuning and they do sound different.

2026-01-27 07:51:16 UTC

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Women's tennis, and maybe of more relevance women's chess, both feature the total absence of men, so that's a big confounder.

2026-01-13 21:20:24 UTC

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I just started watching, it looks good so far! Are you taking random somewhat tangential QM questions? Particularly about entanglement, which i guess is something of a clickbait subject.

2026-01-11 08:56:03 UTC

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I seem to remember Gauss also proposing testing for space curvature via astronomical observations. Spivak mentions this in vol 2 of his differential geometry series iirc. That series is way too advanced for me but it was fun to look at.

2026-01-02 09:09:08 UTC

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Laderman's 1975 paper about the 3x3 case in 23 multiplications is nice: https://www.ams.org/journals/bull/1976-82-01/S0002-9904-1976-13988-2/S0002-9904-1976-13988-2.pdf
It explains how he reached it by solving some huge algebraic system by hand. A lot of fancy algebra went into the later improvements. I haven't looked at Bläser's result but it sounds like 19 is a lower bound rather than an upper one? Anyway https://en.wikipedia.org/wiki/Computational_complexity_of_matrix_multiplication goes into this, and it's informative.

2026-01-02 08:52:17 UTC

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the noncommutativity lets you apply it recursively to large matrices right? So you can multiply two 3n*3n matrices as 23 n*n matrix mutiplications and so on. So the total # of operations for an n*n matrix mult is \( O(n^{\log_3 23} \) (about \( n^{2.85} \). Of course you can do better (2x2 matrix mult in 7 multiplications gives \( \log_2 7 \approx 2.81 \) as the exponent. Best known exponent is around 2.37 for completely impractical matrix sizes. Huge open question in complexity theory is whether \( O(n^2) \) or maybe \( O(n^{2+\varepsilon} \) is possible.

2025-12-23 06:27:34 UTC

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Arxix used to be entirely inside Cornell and this influence sounds like a consequence of taking US govt funding. Maybe it needs to be independently funded again. I'd send in a few bucks.

2025-12-21 00:07:31 UTC

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ah thanks. well i still wonder the amount of power. i mean if it's less than a few KW someone could drive out to home depot and get another generator...

2025-12-20 22:13:49 UTC

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I wonder how much power it takes to keep one of those fancy clocks running. Is battery or generator backup such a difficult thing? Every hospital, bio lab with a cryo freezer, etc. has something like that.

2025-12-10 16:47:52 UTC

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I haven't finished watching this (or started the 2nd one) but I like it a lot so far.

2025-12-10 16:35:10 UTC

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instead of an English version maybe they'd reach more global readers by requiring Chinese or Hindi versions.

2025-12-10 16:21:07 UTC

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Wow I wonder if the US government had something to do with this. Readers can drop preprints into machine translation if they want. Maybe Arxiv could even do that automatically. But it's obnoxious to require it if submitters who already meet the requirements for posting stuff.

2025-11-22 01:19:35 UTC

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OMG

2025-11-19 20:18:49 UTC

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It occurs to me that the dotcom bubble merely set a lot of good money on fire, while e.g. the subprime mortage crisis had lots of bad money too, an AI financing is looking like the latter. I haven't been saving links but here's a tweet from today: https://x.com/HedgieMarkets/status/1990530634960478584

2025-11-19 08:20:37 UTC

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Here are some graphs https://i.redd.it/hjvpic1za32g1.png

2025-11-19 06:00:14 UTC

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LLM bubble (as opposed to AI bubble) is an interesting turn of phrase. Yes there might be a local collapse, like the dotcom bubble of the late 1990s / early 2000s. but online industry has grown stupendously since then despite the setback. main difference is AI may lead to a dystopia where humans are obsolete :(.
I see current LLM stuff as being like spark gap radiotelegraphy, the earliest wireless communications. it took megawatts of power to communicate from a transmission platform to a ship at sea. but now you can do it (even without satellites) with a tiny little radio. AI technology will also evolve like that. probably a bad thing, sort of like the manhattan project a-bomb being optimized into a pocket sized one. :(

2025-11-12 04:56:12 UTC

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I've watched about half of this so far, had to pause temporarily but will finish later. But, I think the math level of the middle part (introducing complex numbers) isn't that well matched to the first two videos. Maybe it an intro to basic QM could have worked better? Getting from complex numbers to QM is one thing, but from there to QFT and from that to the SM seems like a lot of ground to cover.

2025-11-08 21:24:34 UTC

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The discovery of all those exoplanets makes it less seemingly likely that we're along in the universe. Unfortunately it may also indicate that lots of other civilizations have self-destructed, i.e. maybe we're next. :(
https://www.livescience.com/milky-way-alien-life-map.html

2025-11-08 21:13:48 UTC

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That link goes to your interesting post about the Gaia space telescope. Did you intend a different link?

2025-11-07 21:36:43 UTC

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Hmm I'll give that one some thought. But I remember a well known problem from class, where you shoot a rocket in the general direction of the moon but not straight at it. So if the rocket moves in a straight line, it will miss the moon by some distance. Since the moon's gravity will curve the trajectory, the rocket will come closer, but by how much? That turns out to be easy to calculate by conservation of L. I remember thinking "you can *do* that?!". Yet there is no rigid coupling to keep the torque constant.
Anyway I watched a youtube vid recently that demystified the Lagrangian which had always puzzled me before, so now I feel like I have some hope of understanding Noether's theorem, and I want to attempt it at some point.

2025-11-07 21:24:48 UTC

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Angular momentum conservation is a separate issue from computing centripetal acceleration. I don't personally know why L is conserved. It's just something I was taught in high school physics class, and it allows calculating lots of stuff easily. But to derive it from F=ma would likely go through Noether's theorem or something related (stationary action principle maybe). That's higher up there in abstraction and I don't know how to prove it. Someday.
Relativity shouldn't come into the everyday case of this btw. Lots of orbital mechanics was developed long before relativity.

2025-11-07 19:53:12 UTC

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Aha, hmm, ok, I'll give it some thought. But it may be difficult. It was historically hard to convince people that heavy and light objects don't fall at the same speed, or that the earth was round.

2025-11-06 22:24:17 UTC

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Centripetal acceleration is 𝑟ω² by dimension analysis and also by differentiation, is there more to it than that? Conservation of L is another matter of course.

2025-11-04 02:57:58 UTC

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I thought "QED and the men who made it" by Sylvan S. Schweber was great, though as the title says it is mostly about QED's development from 1946 to 1951 or so, by Tomonaga, Schwinger, Feynman, and Dyson. It gets pretty detailed and I didn't understand the very technical parts, one reason I'm trying to catch up a bit, though I probably still won't get there. It's part history, part biography, part physics. Other than there are some biographies of Dirac and Einstein that I liked, though they were less about the physics.

2025-11-03 20:18:03 UTC

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This was great, I watched the Edinburgh version and the audio didn't bother me. The captions helped though they had a few autotranscription errors. I liked how the different theories were connected. I'm looking forward to the next one, about QM.

2025-11-02 01:51:07 UTC

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after the complex numbers you get the quaternions (take away commutativity), then the octonions (take away associativity too), are there still invariants to remove one by one as you reach the 16-ions (sedenions), 32-ions, etc.? Is there some cool algebra that describes them?

2025-10-28 01:08:16 UTC

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Yes I didn't mind the speculation. I had just hoped to see if it made sense mathematically. I don't have a sense of how far apart math and physics are from each other when it comes to this type of thing.

2025-10-27 23:01:55 UTC

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Cool, thanks. Fwiw I watched the Susskind videos (mostly the first few) hoping that GR would help me understand https://arxiv.org/abs/2509.07831 but after a while realized that at minimum I'd have to study a lot further than those videos went (though they were still great). And that it gets a lot harder, probably beyond my capabilities. Oh well.

2025-10-27 22:28:01 UTC

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Thanks, yeah, by sufficiently large black hole I was figuring SMBH or SDMBH (super duper massive) if that's a thing. I think I understand the idea of classical GR from Susskind's videos but not enough to actually calculate stuff. Is it impossible from the Penrose diagram to travel inside the BH in any direction other than towards the singularity? If yes, I misunderstand the claim by some that we live inside a humongous BH.
I realize that if you and Phil jumped into the BH, made observations, and wrote a joint paper, you wouldn't be able to publish it to observers on the outside. But if there were enough other physicists already on the inside, maybe they could have a journal you could publish in. That assumes everyone can survive long enough to handle such a process.

2025-10-27 09:19:59 UTC

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Another good video. I liked the part where the two of you jump into the BH to observe the singularity but then can't publish your findings.
Question: suppose you go in first and then Phil notices that you forgot your hat, so he jumps in after you with the hat. For sufficiently large BH, can he catch you? He has rockets and stuff of course.

2025-10-27 08:39:32 UTC

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I don't know any QFT but I'm interested in learning some!

2025-10-27 05:14:21 UTC

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Wow, just saw this, will watch part 1 soon (haven't yet). I had been wondering how much QFT I need to grok to have any understanding of the standard model. I guess I'll find out!

2025-10-21 08:15:51 UTC

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would it have been difficult to just code up that octonion multiplication and run some tests, instead of messing with an LLM? I didn't get around to trying that. I wonder if it's already built into sagemath or whatever.

2025-10-10 22:53:07 UTC

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Thanks. I know that the big bang is a mystery but after that I hoped it was just GR. Expanding space removes the invariant Noether's theorem relies on to predict mass conservation, so new mass being created doesn't bother me. I'm still trying to understand about it being infinite though.
The explanation about protons and electrons helps. But the universe starting out finite and becoming infinite sounds like another singularity. Ok I better check your links! I'll stop bothering you for now. Thanks again.

2025-10-10 22:11:08 UTC

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Thanks! I'll try those links. I hope to find out, if the universe is infinite with roughly uniform density, where did all the mass come from? And how does newly created mass decide to be hydrogen atoms, if it does?
If you do videos about the standard model, maybe it could include an intro to Lie groups since I don't know anything about those.
Can't go wrong with visually beautiful math either. I tried to read McMullen's book about the Mandelbrot set in the hope of finding out what renormalization is, but I got nowhere.
Anyway, I'm excited!

2025-10-10 06:32:26 UTC

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I'd like something about cosmology and maybe the size of the universe (not just the observable part). Could it really be infinite? I've watched parts of Lenny Susskind's videos on GR and they are great, there's no need to redo them. But what I'd hoped to learn is what it means for spacetime to expand, such as during inflation. I guess the metric tensor changes, but not the way GR describes in response to mass. So any enlightenment would be appreciated!

2025-10-10 03:08:49 UTC

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it seems to hold up! Main question I think is producing the materials at scale. I also didn't notice at first that one of the laureates is Omar M. Yaghi. He has done a lot of work on water harvesting. So I guess there is something to it!

2025-10-09 03:18:26 UTC

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wow! I heard about MOFs in the context of Atmospheric Water Harvesting, what I used to call moisture farming back on Tatooine (j/k). Providing drinking water for dry areas takes much less scale of operation than decarbonizing the atmosphere.
https://www.sciencedirect.com/science/article/abs/pii/S138589472205135X
was a quick search hit and there are tons of others.

2025-09-18 00:05:51 UTC

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academia.edu always looked like a grift to me. I couldn't understand why anyone allowed their stuff there. scribd is another thing like that.

2025-09-13 19:01:14 UTC

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Yeah I think a lot of "obvious" math is so ridiculously hard that we don't bother thinking about it. Like no one knows whether \(e+\pi\) is rational, iirc. Or I think turbulent flow in physics is supposed to be a thing like that.
Meanwhile (idea by Leonid Levin), if you flip a coin a million times to get a random bit string X, it's near impossible that X can be compressed to half its length. But that fact (for that specific X) is necessarily unprovable because Kolmogorov complexity is not computible. BB(n) hits a similar issue, maybe even for n=6.
But, maybe it's possible to conditionally prove BB(6)=whatever, conditional on assuming that some antihydra sequences don't terminate, and justifying that with probabilistic arguments.

2025-09-13 06:32:21 UTC

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The Collatz conjecture is possibly a lot harder. It's a \(\Pi^0_2\) proposition (forall n, exists k such that n's Collatz sequence reaches 1 after k steps) and it's one of a family of problems the general case of which is \(\Pi^0_2\) complete. This antihydra example has a basic resemblance but it's only \(\Pi^0_1\) (forall n, the number of odds seen is < 2x the number of evens seen).
The antihydra never terminating is very plausible since imagine that the odd-even sequence is replaced by random fair coin flips. Imagine that after some (large) N of flips, there have been 2x as many heads as tails. View the flips as a sequence of 1's and 0's, so 2/3 of the sequence is 1's. From the binomial distribution this gets extremely unlikely very fast. Or using Shannon entropy you could notice that the string must be compressible to about 92% of its original length, again putting it into a very rarefied subset of such possible strings (at most \(2^{-.08N}\) of them).
How to prove that the antihydra sequence acts like enough like a random sequence to transfer something like the above argument? No idea, but I'd like to hope it's not as hard as the Collatz conjecture.

2025-09-10 13:39:55 UTC

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Oh I expected both were jokes. Uh oh.

2025-09-09 01:14:54 UTC

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Lolwut? I guess it will follow set theory into the bottomless Wall Street maw.
http://science.slashdot.org/story/10/05/27/0258245/Sudden-Demand-For-Logicians-On-Wall-Street

2025-09-02 23:53:25 UTC

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dunno about cool but this is scary: https://www.theguardian.com/environment/2025/aug/19/a-climate-of-unparalleled-malevolence-are-we-on-our-way-to-the-sixth-major-mass-extinction . It claims that the end-Permian extinction was mostly due to hot magna setting underground fossil fuel deposits on fire and upsetting the planet's carbon balance, kind of like now. The underground fires weren't mentioned here: https://www.cnn.com/2025/07/02/climate/great-dying-extinction-tipping-point-tropical-forests
OTOH I saw something a few days ago saying the extinctions were not so severe on land: https://www.newscientist.com/article/2481371-theres-growing-evidence-the-big-five-mass-extinctions-never-happened/

2025-08-31 09:13:42 UTC

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I thought TREE(n) was computable and therefore eventually smaller than BB(n). You can evaluate BB(n) with a TM equipped with a halting oracle aka \(\Pi_1\) oracle though. And you can surpass BB(n) with, let's call it, \(BB_1(n)\), the longest time to halt of one of those \(\Pi_1\) oracle machines with n states. And that in turn can be surpassed by \(BB_2, BB_3,\) and so on, using higher and higher oracles. A well known essay by Scott Aaronson discusses these: https://www.scottaaronson.com/writings/bignumbers.html