Σ(i³) = (Σi)²

Geometry, Physics, Art, Math.

https://scholar.google.com/citations?user=G0JsJQMAAAAJ

https://cmns.umd.edu/news-events/news/SvenGeiermeasurements-matter

Erdős:: 4
Dijkstra:: 5
h-index:: 17

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npub1kglgmj6v32ekpj348tjhh97gs7uexh5tyaygvfej93u9ufwxcpjq3upskh

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svengeier_at_mathstodon.xyz@momostr.pink

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nprofile1qqsty05dedxg4vmqeg6n4etmjlyg0wvnt69jwjyxyuezc7z7yhrvqeqprpmhxue69uhhyetvv9ujumt0d4hhxarj9ecxjmntqyxhwumn8ghj77tpvf6jumt9zzr7qg

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npub1kglgmj6v32ekpj348tjhh97gs7uexh5tyaygvfej93u9ufwxcpjq3upskh

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Last Notes

2026-10-31 21:26:26 UTC

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Some day somebody will have to explain to me why people are so enamored with unitary time evolution.
I mean: I don't need complicated collider experiments or black hole thought experiments or CP violation and such machinery to tell me that the universe 𝑜𝑏𝑣𝑖𝑜𝑢𝑠𝑙𝑦 isn't time symmetric. I just need to look all around me for a second. We can haggle over the "how" and "why" of the time asymmetry all day long, but a mathematical gadget that describes the universe as time symmetric is 𝑜𝑏𝑣𝑖𝑜𝑢𝑠𝑙𝑦 at best an approximation that is missing some fundamental part somewhere. Maybe we'll find a better one some day. Maybe this is as good as we'll ever figure it out. But 𝑜𝑏𝑣𝑖𝑜𝑢𝑠𝑙𝑦 there is no "problem" anywhere with breaking unitarity in any part of physics since it is 𝑜𝑏𝑣𝑖𝑜𝑢𝑠𝑙𝑦 not "strictly true" to begin with.
What am I missing here?

2026-10-22 05:38:16 UTC

For those of you that care about that kind of thing: this Saturday, 10/24/26 (or 24.10.26 for all'y'all in Europe) is the last date of this century that spells a Pythagorean triple.
Celebrate accordingly.

2026-10-14 23:29:40 UTC

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LLMs are a new tool. That's all.
If you're already a skilled woodworker, a new woodworking tool may make your job a lot easier. You still have to learn the new tool, find out the hard points and the brittle ones. But then you can show to others how much easier your work is now.
That does not mean this tool will make anybody into a skilled woodworker. It does not mean someone who watched how easy your job is can now suddenly do that job. If it's the only tool they've ever used, then there's no "woodworking job" there to be "made easier".
You do, absolutely, become better at using LLMs by using them more - Just like any other tool. If nothing else because they're still shifting around a lot and whatever worked yesterday may not work tomorrow any more.

2026-10-12 15:59:18 UTC

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I'm feeling a little embarrassed for not getting what appears to be pretty basic geometry here: the absolute value distributes over the inner product, no?
|<v,w>| = |v|•|w|, right? For v,w unit vectors that would always be =1 in any dimension, no? How does that mesh with the original \(n\) up there?
It feels like there's one small thing that'll make me slap my forehead once I get it ...

2026-10-11 23:10:16 UTC

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I'm probably completely misunderstanding something in your 1st sentence, but for \(n=1\) I can look at \(\mathbb C\) and draw 2 unit vectors (1,0), (-1,0) that lie at the same angle (\(\pi\) to each other. What am I missing here?

2026-10-07 19:28:51 UTC

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As far as my reading on the topic goes¹, proving "a version of" the homotopy hypothesis isn't remarkable - various versions of it were already proven. Coming up with the overarching framework that includes them all seems to be the trick nobody has figured out yet.
¹) Nlab has an entry for "homotopy hypothesis", I don't remember seeing your name there. If you coined the term you should go and claim credit ... ;)

2026-09-30 17:22:21 UTC

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"testing advanced mathematical problems on proprietary models" sounds ... wrong? ... to me?
I would've said "testing proprietary models on advanced mathematical problems".
Typically I wouldn't say a math problem needs to be "tested" - it needs to be 'examined', maybe, or 'considered', or ultimately 'solved'.

2026-09-27 18:10:10 UTC

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Super satisfying. This is the combination of simple idea, tight implementation, clean presentation that stands out when you see the result. Many thumbs up!
[@jn3008](https://mastodon.social/@jn3008 )

2026-09-20 17:59:16 UTC

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It is my current perception that the vast majority (90%+) of things people complain about current AI are just problems with our systems and institutions that were always there and that are merely made visible by LLMs.
An educational system that measures "learning" by "getting good scores on some standardized test" leads to someone inventing a tool that lets you get good scores on a standardized test with minimal learning. That's not "a problem with that tool", it's a problem with an educational system that was rewarding the wrong thing.
In the same way, a discipline that motivates work through "reaching this proof" will get disturbed by a machine who's purpose is "reaching this proof very efficiently" - but that's not any fault of the machine, it a problem with the motivating structure inside that discipline.

2026-09-19 17:02:48 UTC

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* "n less than 9" in the 5th paragraph

2026-09-18 20:09:21 UTC

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One thing I find attractive about math and physics is that they're ideas that we can strip of all the human baggage and messiness that birthed them. By being not human, they're connecting us, shared amongst us, ultimately the expression of humanity itself, not any one human or group of humans. And paradoxically, here the group effort has led to something that appears better than any one of us alone - humans are messy, groups of humans are much worse, but humanity as a whole seems to generate something shared, something we can all relate to. It can be "weird" but it's not in the sense that "humans are weird".

2026-09-18 20:08:33 UTC

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I try to separate the ideas generated by people from those people: I'm pretty sure I wouldn've gotten along with Paul Erdős. I find everything I read about Feynman off-putting at best. I have no doubt that I would've hated knowing Newton in person.
Humans are weird!
Put a bunch of them together and you get group dynamics. Put a bunch together that were (self-)selected on being outside the human norm and you get very weird group dynamics - some of it easily recognizable (there will never be a human group where sex is not somewhere on the table) some come out of left field and leave us confounded.
Eight billion ways to be human - and put ten of us into a room and the result will not be nice to look at.

2026-09-11 15:56:52 UTC

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The answer is eleven (11).

2026-09-10 21:44:31 UTC

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In my case, at least, "intimidated" is the closest description - the full text is more "oh, excellent, new post by JCB, this looks really interesting, wow, I understand many of the words and maybe 20% of the topic; I'll definitely want to learn more about this some day, so I can better appreciate what's going on here..."
[@j_bertolotti](https://mathstodon.xyz/@j_bertolotti )

2026-09-05 23:14:04 UTC

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... And if you go "one step back" and cut every other corner of a regular 3d cube you get ... a tetrahedron...

2026-09-03 23:55:38 UTC

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It wasn't really meant as a 'joke' - one of the things I've been slowly catching up with now that I'm retired (← never gets old to say that out loud) has been this convergence of currents in QG, topological field theory and discrete geometry that sort-of steps away from (physical) "space" as a differentiable manifold at the bottom. Lots of variants, LQG, spin foams, 𝑠𝑜𝑚𝑒𝑡h𝑖𝑛𝑔 that emerges from a local topology somehow - causal sets, relational QM, possibly even Connes' non-commutative geometries - there sure is a thread that tries to establish "connectedness" or "neighborhood" (in the Hausdorff sense) somehow through some sort of network of interactions and then tries to emerge smooth Lorentzian space from it. Can a topology 'emerge' a metric 'naturally'?
I 𝑙𝑖𝑘𝑒 many of those ideas, though there's enough hand-waving there to impress a Hindu god to come up with a macroscopic space that 𝑗𝑢𝑠𝑡 𝑠𝑜 h𝑎𝑝𝑝𝑒𝑛𝑠 to obey exact SU(3) gauge symmetry AND Lorentz symmetry.
Triggers my skepticism neurons.
That was my mind-state when I quipped that.
Now I'm seeing at your link a yet-different approach, allowing space to be locally a manifold (but an arbitrary one). I wonder how many people have come up with how many approaches to "hey, what if physical space is not a (globally) metric space?". Has someone classified that zoo?
Have I mentioned that I'm retired? Now that the quality of my understanding doesn't determine my paycheck any more, I'm so looking forward to a couple decades of consuming the wild and wacky ideas of mathematical physicists...

2026-09-03 19:06:17 UTC

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How about space?

2026-08-17 21:07:41 UTC

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Ah, but there's a trick: if you decline the axiom of choice then you don't have to pick a small finite set of topics to work on - because you can't. ;)

2026-08-17 15:46:50 UTC

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It hasn't been my impression that the people doing the math are the ones too worried about "what's worth bothering with". Everything is. Duh.
Occasionally a bystander might get a whiff of some part of it and either find it useful for some scientific endeavor or ... well ... not. 🤷🏽‍♂️
Overall, math has been useful often enough that we've kept it around, I guess.

2026-08-17 14:28:29 UTC

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In math, both the problem and the methods used to arrive at solutions are formulated in the most precise language devised by man before computer languages. So obviously math is more amenable to a solution by an entity that knows about anything at all only by reading about it. 🤷🏽‍♂️

2026-08-04 22:16:50 UTC

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There was a previous message?

2026-08-04 21:51:18 UTC

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Well, I've only ever taken the "math for physics students" classes (back in the eighties) so I'm definitely not up to speed on math lingo (though now that I'm retired I'm slowly reading a bit more into the fascinating stuff that I've missed in math in the last bunch of decades).
As far as I understand the terms, "null set" is basically synonymous with "empty set", i.e. the special set with no elements, EXCEPT in measure theory where it means a set of measure zero. Is there some other way to read "null set" as expressly distinct from an empty set? I'm nothing if not eager to learn more math subtleties...

2026-08-04 19:43:58 UTC

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Explicitly distinguishing between an empty set and a Null set implies measure theory in my brain - and the prototypical example of a set of measure zero would be ℚ in ℝ.
(Which ought to make for some fun word play how being entirely rational is considered woke and such.)
It is of course possible to put a tree into a set of measure zero, like the Calkin-Wilf tree that covers ℚ⁺ without ever leaving the rationals. So maybe there's a way to finagle a tree logo that is also a Null set?

2026-08-01 02:19:22 UTC

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By accident I stumbled across this paper
https://www.math.ucla.edu/~totaro/papers/public_html/tate.pdf
which contains what appears to be an entry for the "which of these are most closely linked and might be equivalent":
https://media.mathstodon.xyz/media_attachments/files/117/017/848/280/138/903/original/5086be19a8657294.png

2026-07-29 22:20:52 UTC

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These are not at all mutually exclusive. Obviously I'd like to have all of the above.
No wait, not the traitor one...

2026-07-23 19:36:07 UTC

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In my brain, the Navier-Stokes question always felt like a topology problem ("a solution to the NS equations is a time dependent manifold in phase space", the Clay problem is about uniqueness and non-degenerateness of that manifold) so I'd think the Hodges conjecture would be my guess as to the most likely equivalent. But I wouldn't begin to have a guess how they would be connected...

2026-07-11 22:15:01 UTC

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There's a special place in Hull for the inventor of autocorrect.

2026-07-11 21:32:36 UTC

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That's the real difference between hardware and software: if the hardware manual differs from the hardware, the manual is wrong; if the software manual differs from the software, the software is buggy.

2026-07-10 18:33:14 UTC

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oh,no! not the re-twist! what is the world coming to...? ;)

2026-07-09 14:44:05 UTC

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I may have to apologize that my little throwaway comment is stirring up so much commotion. No, it wasn't "contributing to the discussion", but then there wasn't a whole lot of "discussion" going on there - Alice posted about paying (or not) for compilers and such and I wanted to comment that you pay for programming in more than just the price of tools. (And a point could be made that we pay in more than time as well, as it sure costs me a chunk of sanity every time I spend an evening trying to hunt down some stupid bug somewhere).
When compilers were expensive, did people pay for them? Yes. They didn't just hand-type assembly op codes into a hex editor (well, some of us did). Because the compiler saved uncounted amounts of time compared to that. Which people valued enough to pay for. "Here's a new tool that allows you to code much more by taking care of many fiddly under-the-hood details, for a price" is a value proposition - it's up to us to choose, but it's not a foregone decision. 🤷
@npub1s4h…qs84 @npub13ps…gm9l

2026-07-09 05:00:10 UTC

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Programming is only "free" if your time is worthless.

2026-07-07 16:42:06 UTC

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Did you ... type that alt text?

2026-06-27 17:33:36 UTC

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Just so you don't forget what weather in NICE places is like...
https://media.mathstodon.xyz/media_attachments/files/116/823/268/806/197/734/original/d3147ca7ca941354.jpg

2026-06-19 17:24:54 UTC

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There's been a bit of a rash of recent publications of people using all sorts of technologies not normally suited for terrain mapping for this kind of archaeology work. (Lidar mostly will give you canopy; its ability to see the ground underneath is more-or-less an accidental byproduct). I think this is driven by NISAR's launch, whos dual-band SAR is directly geared for ground feature mapping (at 2-5cm resolution from orbit) looking through foliage and similar obstructions. I think there's a bunch of people who've been sitting on data sets who are feeling pressure to publish now before NISAR publishes its global map products - which are not at all intended to be used for ancient temples, but will undoubtedly find all sorts of ancient, overgrown structures too large to notice when you're walking on the ground and too obscured to be visible from survey airplanes...
@npub18qx…9a9r @npub12cu…d38p

2026-06-19 17:09:32 UTC

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This is how paper beats rock

2026-06-03 23:01:47 UTC

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Accurate visualization of my ~50 remaining brain cells trying to make sense of the world...

2026-05-31 05:38:22 UTC

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[Converts to PST, finds 730am on a Sunday morning] uh, maybe next time...
@npub1zz2…9mhx

2026-05-10 16:36:26 UTC

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My local library has a section that is Lit A-F ...

2026-05-08 06:33:39 UTC

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https://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/

2026-04-19 05:47:48 UTC

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It's allowed in Scrabble:
https://scrabble.merriam.com/finder/ruth

2026-04-14 22:41:13 UTC

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There appears to be a view that tuning isn't so much about the ratios of the notes, but their overtones: https://youtu.be/tCsl6ZcY9ag

2026-04-14 01:27:48 UTC

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This looks ǰ̴̡̥̆̌ų̷̡̢̩̰̭͖̟̠̪̩̯̥̳̣̓̃͋͌̀̈́͒͜͝͝ş̶̧͖̱͈͖̦̤̠̬̞̠̂̅̀̽̆̾̈́̃̒̄͛̐͗̀̇͘͝t̵̨̡̛̛̤̝̦̫̼̑̒̆̔̍̃͊́̑̅̌͐͒͝͝ ̶̢͕́̉̇̋̀̇̏̚͝f̵̛̛̖̝̦͇̦̀͐̓͗̔̂̓͋̇̌́ͅi̵̢̨͙̙͈͚̲̭̭̞͐̈́̊̓̍͜n̷̨̡̪̠̻̬͙̗̰̞̺̓̎̉͐͆̃̚͝ê̵̡̡̖͍͔̹̣̤̥͍͓̼̹̜̈́́̍̈̓̃͊̃͆͜͝ͅ to me ...

2026-03-29 19:33:21 UTC

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It is my "intuition" that YouTube clicks now constitute her paycheck. With all that implies.

2026-03-10 01:33:54 UTC

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I think using the same word "law" for the way the universe actually fundamentally functions and also for random rules monkeys invent for themselves is worse...

2026-02-17 18:13:12 UTC

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You haven't mentioned it, but surely you've read https://cbaberle.com/Blog/The+Music+of+the+Primes
Right?

2026-02-17 04:24:37 UTC

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I would guess that one could hand that zeta function to something like Wolfram Alpha and it might just give you an analytic expression for the Fourier terms so you don't have to guess what frequencies have what power in them (?)

2026-02-13 03:50:09 UTC

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I guess I'll leave the "whitespace is significant" to the Python programmers...

2026-02-13 02:51:53 UTC

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These two sure 𝑙𝑜𝑜𝑘 like mirror images to me...
https://media.mathstodon.xyz/media_attachments/files/116/061/048/930/845/079/original/3a55261484e27430.png

2026-01-26 17:54:47 UTC

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The suggestion that there could possibly be anything treasonous happening at Alpha Complex (the Happiest Place on Earthᵀᴹ) is itself treasonous thought and has been reported to the nearest troubleshooter team.
It was nice making your acquaintance, human.

2026-01-21 01:52:12 UTC

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Ohhh ... I had almost forgotten about those. I guess there was a phase when the Internet shunted many of these into easily ignored silos (phys.org and such) and their onslaught got fairly light(?). Or maybe it's that I spent a couple decades in instrumentation, which isn't as amenable to random flights of fancy and so I became a less desirable target? These days I seem to be mostly a target of "we want you to submit to this journal" or "come to this conference" spam; it must've been several years since I last got an individual crackpot solicitation...

2026-01-15 02:19:10 UTC

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What's a couple dimensions more or less amongst theoreticians?

2026-01-14 15:59:33 UTC

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”Thinking about the early arthropods in the Cambrian seas"
As one does...
"[...] there isn't anything exactly like these early simple brains."
I'd like to draw your attention to the right end of the political spectrum...

2026-01-11 19:17:21 UTC

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Somehow I expected more katana fights in abandoned malls and less arguing with robots over what exactly constitutes a traffic sign...

2026-01-09 20:47:32 UTC

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https://earth.gsfc.nasa.gov/sites/default/files/lab_cryo/data/polar_ice_altimetry/antarctic_ice_velocity_maps/antds_on_rignot_log.jpg

2025-12-25 17:34:23 UTC

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Oh, I see. I'd never taken the entire list to account for each individual day, i.e to add up to 12 partridges total. That's a lot of pear trees...

2025-12-25 16:44:06 UTC

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I don't think that's right. Day 3 for example (3 French hens, 2 turtle doves and 1 partridge in a pear tree) comes to 6, maybe 7 if the pear tree counts extra.
But 3x4x5/6 is 10 (=1+3+6).
I think you got triangles and pyramids mixed up somewhere...

2025-12-10 16:13:11 UTC

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Not *quite* what you're asking, but pretty close might be 'Dexter' (a blood splatter expert who doesn't just solve murders, but commits a whole lot of them)
@npub1x78…xn0m @npub1qf9…r5tc

2025-11-23 16:29:06 UTC

Grant Sanderson has something to say about category theory... https://youtube.com/shorts/vMHUkrMLM6E

2025-11-21 05:30:11 UTC

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Came here for these exact two questions...
@npub1nf4…nqe4

2025-11-01 01:17:13 UTC

18:14 PST: it is the last minute of the first quarter of the first hour of the last quarter of the last day of the first month of the last quarter of the last year of the first quarter of the 21st century.

2025-10-17 15:30:07 UTC

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As an old-style overclocker (you'd be surprised how fast a 486dx-33 can go) I'm considering "silica melting ruffian" an honorific...
@npub1nf4…nqe4

2025-10-13 02:35:11 UTC

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Why the subjunctive for "If we had right-handed neutrinos"? I thought neutrino oscillations had largely answered that? Or is there some loophole in relativity that I'm missing?
@npub12cu…d38p

2025-10-06 16:03:55 UTC

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According to Scott McCloud, making environments very complex makes them "other", allowing us to perceive their weight and presence, while keeping characters simple and stylized allows us to identify with them (McCloud, "understanding comics", 1993)

2025-10-05 01:26:42 UTC

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Since there are only countably infinite pieces of track, I would figure there can only be countably infinite many gaps between them(?)
[@Chip_Unicorn](https://im-in.space/@Chip_Unicorn )

2025-10-04 20:16:09 UTC

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I think the mathematically correct answer is that ℚ² is sparse in ℂ, therefore I can cover all the rational points in the square with an arbitrarily small amount of track in countably infinite many pieces of track of length zero each, consuming no total track length at all. But since ℚ² is also dense in ℂ, can get from any point in the square to a track in zero seconds of foot travel and I can get from any point on the tracks to any other point on the tracks by only touching points that have tracks on them. So the optimal track layout is the characteristic function of ℚ².

2025-09-27 18:55:28 UTC

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I think you're last line needs ay instead of an x somewhere...
[@g_merzon](https://mathstodon.xyz/@g_merzon )

2025-09-22 16:36:29 UTC

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I read that in the early eighties (I was a teenager and consumed anything vaguely sci-fi) and yes, in hindsight I have no doubt that this book resulted from the confluence of people knowing math and taking LSD...

2025-09-16 23:32:10 UTC

#TilingTuesday again, huh?
https://media.mathstodon.xyz/media_attachments/files/115/216/582/419/285/544/original/456d7dec6b62d124.jpg

2025-09-11 21:20:58 UTC

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For what it's worth, there's also a "mathstodon" app for Android (with over 100 downloads in the Google Play store) which also renders LaTeX correctly (I'm using it right now)

2025-09-03 19:20:25 UTC

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Whoa - so my pick (purely on intuition, nothing about maps or anything) was right. I'm actually starting to develop a functional geometric intuition in my older age...

2025-08-19 14:12:49 UTC

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I fear you're not the first one to try that - after my defense I showed that whole thing to my wife who immediately came up with the same idea. But I'm not counting it if people don't find it themselves...
@npub1fp9…5xuu

2025-08-18 14:30:18 UTC

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Not just papers. My PhD thesis has a (nowhere referenced) citation to an article in Playboy magazine in its bibliography. Nobody's ever called me on it 🤷🏽‍♂️
(I also had an unreferenced footnote in the first appendix that promised a bottle of wine to the first person that mentions this footnote to me, because I wanted to know which of the members of my PhD committee made it there first. Again, I never had to pay up. 🤷🏽‍♂️)
@npub1fp9…5xuu

2025-08-16 18:41:07 UTC

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Maybe the prop was made for The Big Bang Theory and some random non-physicist set designer just saw it as "this is the kind of stuff young people wear these days" and re-used it?

2025-08-12 16:15:51 UTC

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Mom is from mom-tana, but I'm from Me-vada...

2025-07-09 19:29:15 UTC

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... Of course anything discovered in the last 200 years is usually just a rediscovery of something Euler did in some obscure manuscript...

2025-07-05 18:07:13 UTC

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The C gates are colocated with the B gates but you have to go in the opposite direction to get there...

2025-06-24 16:24:34 UTC

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I'm one of the people who thinks he's intelligent. I'm definitely not thinking that I'm "intelligent enough".
There's really two use areas I am thinking of
- at the very limits of my intelligence I think there's a lot more stuff I could figure out, understand, broken things I could fix, amazing new things I could create, if I were "more intelligent" (I don't actually know how to quantify intelligence but what I just wrote is what I would consider the definition of intelligence: the ability to get intelligent things done)
- much more frequently, however, I operate at a much lower level than my limits: places where I don't have to think hard and can solve some problem with relative ease. And in that realm I figure if my limit was doubled, so would be the ease with which I can handle those "simpler cases". Being able to move the majority of my life from the "requires a little thought" to "can be done without effort at all" would free up a whole lot of space (or, really, time) to actually use that expanded limit. To do whatever strikes me as interesting, (including doubling my income if I thought that interesting.)

2025-06-17 19:22:35 UTC

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I don't think your alt-texts are accurate: the white little balls attached to the carbon atoms are almost certainly Hydrogen, not Oxygen...

2025-06-14 21:43:10 UTC

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Last I checked the whole reason ANITA existed was to look for the radio signatures of neutrinos penetrating the earth. That's why there's downward-looking horn antennas on that balloon (or at least that's how it was sold ~20+ years back when I first heard of it. We had a prototype/demonstrator for the experiment as a secondary payload on a different instrument I was flying down there in 03/04)

2025-05-21 21:01:21 UTC

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Yeah - and the Lagrangian version is baked directly into the formalism itself: \[ \frac{\partial \mathcal{L}}{\partial \mathrm{q}} - \frac{\mathrm{d}}{\mathrm{d}t}\frac{\partial\mathcal{L}}{\partial \mathrm{\dot q} } =0\] If your Lagangian is not expressly dependent on some generalized coordinate q then the first partial derivative is zero, which means the second term is also zero, which is just the change with time of the second partial derivative (of \(\mathcal{L}\) with respect to the associated generalized momentum). So that's conserved. No extra "theorems" needed.
I'm having a hard time imagining what a formalism might look like that doesn't have some mechanism like this somewhere under the hood. 🤔

2025-05-21 20:45:38 UTC

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That feels like almost a philosophical question - or maybe a linguistic one. "symmetry" means that there's something I can change about a system and nothing about it changes. But "nothing changes" implies "conserved". I having trouble even expressing this in English because it's so close to the very meaning of words like "symmetry" and "conserved".
Is there an example of a theory that has symmetries but does not implicitly have "something conserved"? I'm having a hard time imagining such a thing...

2025-05-17 17:35:31 UTC

Hey, @npub1nf4…nqe4 : Rob Miles is trying to put you out of a job...
https://media.mathstodon.xyz/media_attachments/files/114/524/369/668/235/138/original/66a9c28c5b768043.png

2025-05-13 00:16:43 UTC

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When the original (random) bit of torque rotates the sphere by a bit, some portion of its surfaces moves "out of sight" of the electron source (presumably a cathode at the top). The electrons are still attached there, but at the symmetrically opposing side (which has just rotated "into view" of the source) electrons haven't had time to attach yet. So the torque persists. Rotating the "heavier" side (that has accumulated electrons for longer) away from the cathode and bringing more "fresh" (uncharged) territory into view.
I guess this would work if the electrons stay attached long enough after they're out of view to exert torque, but then fall of fairly quickly before they reach the bottom.
In my brain this sort-of hangs together.
Question becomes - shouldn't this exactly work with a sphere out in the rain? The side that has more water attached to it drags down in the gravitational field, pulling drier material to the upside. As the water-logged side travels to the underside, water droplets fall off, so the upward moving side becomes lighter - exactly maintaining the ongoing torque. No?

2025-05-06 21:06:46 UTC

Driveway in Highland Park, CA
#TilingTuesday
https://media.mathstodon.xyz/media_attachments/files/114/462/922/386/261/233/original/c6dd5becaf5e70e7.jpg

2025-03-12 16:26:01 UTC

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...and JUST when you thought you recognized the pattern ...

2025-03-12 16:11:55 UTC

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"didn't fail" -> "failed"?

2025-03-08 17:07:32 UTC

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This is an aside, but apropos Google search going to the dogs: I wonder if there's venture capital to be milked right now for starting a new search website that does vanilla page rank with no further embellishments/ai/recommendations/advertising/etc...

2025-02-28 00:14:43 UTC

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> Do you know any others?
Lie's third theorem?

2025-02-26 16:22:26 UTC

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There may be a lot of red herring going on here. The whole stuff with N people and then letting N go to ∞ feels like a misdirection. Surely the majority of the N people will be on whatever half of the [0,1] interval that Alice is not. And by symmetry that's the same probability "larger than 0.5" or "smaller than 0.5", so we can ignore one case and just look at the other.
So the whole question is really asking
If \(A\in \{0,0.5\} \) and \(B\in\{0,1\}\) what is the probability that \(B\gt A\)?
(It's 1/2 chance that B>0.5 and then another 1/2 of the remaining probability space that B>A if B<0.5)

2025-02-20 01:22:37 UTC

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Boo!
(I'm rooting for the asteroid!)

2025-01-08 07:42:48 UTC

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It's not just Palisades - the Eastern half of Pasadena is currently either in evacuation warning (down south) or currently being evacuated. Jet Propulsion Lab declared tomorrow mandatory telework day. 3600 people are without power.
I've lived in Pasadena since 2001, I've never seen fire move so fast...

2025-01-03 15:30:21 UTC

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My favorite gimmick about
\( 45 \times 45 = 2025\)
is that you can increase every digit in there by one and the equation still holds...

2024-12-28 18:31:52 UTC

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This isn't helping but in the introductory plasma physics class I took in grad school (which I kinda liked) the hand-waving worked like this: You use Maxwell's equations in their regular form, don't worry about relativistic effects because all the particles we encounter in our MHD are "slow" and you'll usually get to look at your results at the end and say which terms you can drop because they're not significant. If and when your plasma flows get into the realm where relativistic effects would matter, you're probably in the accretion disk around a black hole or some such environment and puny Lorentz transforms won't help you and you'd need a full GR treatment anyways. 🤷‍♂️

2024-12-13 03:07:33 UTC

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https://media.mathstodon.xyz/media_attachments/files/113/643/307/092/692/110/original/e13a30e51ed36b59.jpg

2024-12-01 02:29:31 UTC

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Did you know that people at the Scott-Amundsen South Pole Station have their own local ad-hoc'ish coordinate system for telling someone how to get from one building, telescope, or installation to another one? It's largely just a square'ish grid covering the whole area because things like "West" and "North" get a little squishy the closer you get to the pole itself. They're perfectly well-defined (outside of the pole itself) but trying to communicate the relationships between locations with them is headache-inducing and there's really no good reason why local navigation cannot just follow a grid that has been patched over the the usual lon/lat grid that just doesn't work very well at the south pole proper.
I am reminded of this every time I see people writing about black holes in (r,t) coordinates. Not that they're not perfectly well-defined (outside of the singularity itself) they just don't work very well to describe the relationships between events around an event horizon.

2024-11-26 00:28:35 UTC

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In toot (2/n) you are using the phrase "at that very moment" and I believe you and the other 99 captains have a bit of work to do to define what that phrase actually refers to...

2024-11-05 16:49:48 UTC

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What I'd love to see more of is the NISAR type of collaborative project. I spent much of 2023 in Bangalore to integrate the instrument with the bus and put it all through shake&bake and the ISRO facilities are clean and modern, the people are capable and friendly (and the food is excellent). Both sides get to slap their back for a job well done and national pride blah-blah and it establishes the kind of international collaboration that (hopefully) brings nations together. They learned a few things form us and we learned a few things from them (always carefully avoiding ITAR limits) and in the end I'm sure we got a lot of sheer manpower for very little money. Win-win from where I'm sitting.

2024-10-22 21:17:20 UTC

Most people seem to think of "tiling" as happening with roughly ~equal-sized tiles. Which makes me feel a bit like an outsider when I post these fractal structures for #TilingTuesday
https://media.mathstodon.xyz/media_attachments/files/113/353/143/077/449/949/original/c2dc581007404759.jpg

2024-10-10 16:14:02 UTC

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More importantly: Not all physicists work in the "foundations of physics", looking for "new physics", etc (which is currently sort-of synonymous with particle physics but could be anything). Not all physicists are pursuing a theory of everything or trying to resolve the problems of cosmology or such.

2024-09-20 23:01:07 UTC

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In case you hadn't checked them out yet: Lynden-Bell has a whole pile of excellent papers about gravitational behaviours of galactic structures - his paper with Pringle (from the 40ies, I think) is the best intro to accretion processes I've ever encountered. All of them super accessible.