Refurio Anachro

I like to learn and popularize higher maths. I'm not a pro, but I can stomach corrections!

InfoSec: Refurio Anachro (npub1gh7…60cw)
Home Account: [@[email protected]](https://toot.cat/@RefurioAnachro )

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Last Notes

2026-07-09 14:15:46 CEST

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With dynamical systems you get new features with every dimension you add. Or rather, it gets much more complicated. I suppose these things are good at exhausting what certain topologies have to offer. I have spent a lot of time trying to get mental pictures of this stuff. There's so much to see!
Uhm. I guess it's a bit simpler with relativity. But still: we get new features when we add new dimensions?
1+1 either no mass or no metric
1+2 no curvature without mass
1+3 in other words: gravitational waves!
1+4 ?
I shouldn't be surprised, but what are they?
@npub1nf4…nqe4 @npub1fay…s7kh @npub1zz2…9mhx

2026-06-27 19:02:57 CEST

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said:
> but we can only notice the effect of a discrete group being gauged if spacetime is non-simply-connected.
By "spacetime" you really mean some field? Like the electron field that can feel a solenoid? But we can't measure that because no-one knows how to make a solenoid from nuclear matter?
@npub1d60…mhwm

2026-06-25 17:57:19 CEST

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> grade -1
Is this an instance of negative thinking?
https://ncatlab.org/nlab/show/negative%2Bthinking
I actually ran into this a few times recently. Once, coming from looking at color spaces with n channels, while thinking about homotopy groups, and later again, when I found myself holding n-groupoids.
@npub1nf4…nqe4

2026-05-28 15:48:15 CEST

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That was a fun and easy afternoon coffee read. I especially enjoyed the notation for vertices and edges on the topograph. Feels pretty much Conway.
Thanks, @npub1nf4…nqe4!

2026-05-28 15:33:51 CEST

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I keep getting surprised how good matrices are for counting things. It's sort of silly, as it just means I haven't absorbed _what matrices are_ in some sense. First time was when I learned how to make Fibonacci numbers using matrix generators.
@npub1nf4…nqe4

2026-05-12 19:36:12 CEST

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Oh wow, that's much closer to what pops out when you overlay wave trains aligned along the edges of a pentagon, than I would have expected!
https://www.shadertoy.com/view/4cXBz2
@npub1nf4…nqe4
https://media.mathstodon.xyz/media_attachments/files/116/562/804/002/338/024/original/51943e9050647b5f.jpg

2026-05-07 15:57:09 CEST

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The last couple of weeks? Learning is what drives me, a week is quite a long time!
There are two things I learned from your posts: Donella Meadows' nine leverage points were quite engaging. Didn't talk about it much on-line, because there's so much to say! I found it to be a hopeful perspective, well worth any dread caused by talking about big problems. People I told about it mostly liked it!
The other is that I now have a picture of the 600-cell! I always felt, nah, that's too complicated, let's stick to the smaller ones. And then your explanation of @npub1mcu…g2al happened, and @npub10zc…tds5 showed off his models. That's so cool, now what do I do with it?
It's sort of on-topic for me, because I have been eyeing little facts about rendering hyperbolic spaces for a while. Since [@Number_Cruncher](https://mathstodon.xyz/@Number_Cruncher ) reignited my interest in Coxeter-Dynkin diagrams, and all that comes with it. I think I owe them a shader for hyperbolic Coxeter groups. Sorry, been busy...
For one, I have now practical experience optimizing compressed data size by rewriting the uncompressed source. That's quite an odd thing to do, but I learned a ton about what my code actually needs to do. Oh and if you ever want to submit a shader you wrote to a demo competition, I might have something for you.
The other obsession that got lots of time was to write an ocaml module for conformal geometric algebra. That alone is a very beautiful subject! I want it to output math kernels for shaders. In the end I learned that typed-tagless-final is the name for the concise style to represent syntax trees I didn't dare to use, thanks [@JacquesC2](https://types.pl/@JacquesC2 ) for writing about it years ago!
You see, @npub1nf4…nqe4, you're still important to me, and I miss our conversations!

2026-04-04 17:36:47 CEST

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Gorgeous! DrFlopine just did something physalis related in #revision2026 live coding semifinals on a bonzomatic.
@npub1t56…rjx3

2026-02-20 16:57:05 CET

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I'm talking about the inverse of zeta for the primes 3 and 5 at the critical line. And I'm guessing the idea works for any set of primes.
Of course you knew what it is. I'm just stubbornly sticking to guessing because it's easier. Don't mind me %-D
I just wish I knew more about why the critical line is interesting. Your posts suggest one very hands-on idea, but I feel I might want to know about some of the countless other ideas.
And why am I not seeing any zeros? My fourier approximation has +1 at the end. Have I missed a -1 in ζ?
@npub1nf4…nqe4

2026-02-19 04:05:44 CET

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For no good reason, I tried guessing the first few terms of the fourier transform myself.
(cos(x*log(3))/log(3)+cos(x*log(5))/log(5))/2+1
It's even better when we add
cos(x*log(15)-pi)/log(15)
I'm not sure where the extra phase pi comes from.
@npub1nf4…nqe4 @npub1ycr…856a

2026-02-03 03:49:22 CET

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Here's Adam Neely about AI in music and the link to fascism.
https://www.youtube.com/watch?v=U8dcFhF0Dlk
As always, somewhat tangential to your thread, @npub1nf4…nqe4.

2026-01-28 07:20:36 CET

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Oh. Sure.
@npub1nf4…nqe4

2026-01-28 06:01:16 CET

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You joke is quite funny. It made me look at your crackpot index once again! It's oddly specific at places :D
https://math.ucr.edu/home/baez/crackpot.html
How did you manage to come up with that python code? Looks fine to me. However, the indentation on azimuth looks broken in my browser.
@npub10sq…a55p

2025-12-07 23:34:18 CET

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Software verification is a big one. I believe that we will eventually need verified software everywhere to help solve fundamental security issues we have today. And indeed, there's so much tedious work involved with current tools that it's simply infeasible beyond very small code bases.
I love Terry Tao's approach! It strikes right at the heart and effectively makes weaseling much harder. I enjoy reading his finds a lot. It's good to see he gets support by a community.
Research, teaching and engineering are intertwined. At least to Archimedes' times they were, he was a carpenter and architect. Of late, the engineers seem to have been incing away a little. Maybe to catch some new fish. If you had an oracle, you would use it, wouldn't you?
@npub1nf4…nqe4 @npub1fp0…s4sx

2025-11-21 22:41:39 CET

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Yes, the placement is probably due to the algo avoiding one edge crossing in each row. That can probably be turned off. I'll have a look later if I can find out how.
@npub1nf4…nqe4

2025-10-28 17:12:15 CET

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>> The existence of a naked singularity implies a failure of global hyperbolicity.
Hyperbolic in the sense of a Minkowski manifold, which basically means we cannot rotate (boost) an inertial frame to point outside its future light cone. Global means that I can't get outside my future lightcone even by topological means allowing me to travel back in time.
https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold
They have definitions with funny mames:
> M is non-totally vicious if there is at least one point such that no closed timelike curve passes through it.
Or:
> M is non-total imprisoning if no inextendible causal curve is contained in a compact set. This property implies causality.
And an old acquaintance, the Cauchy horizon:
> A Cauchy surface for M is a closed achronal set whose domain of dependence is M.
That is a place where the future development is not sufficiently determined by the laws of physics!
Your link makes it very easy to spend my afternoon reading your paper, instead of following my day-job. Very tempting indeed!
@npub1nf4…nqe4 @npub100e…c8sg

2025-10-28 15:39:29 CET

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> Hawking proposed the cosmic censorship conjecture that no naked singularities form in GR given realistic starting conditions. There is evidence from numerical simulations that this is false.
What?! I didn't notice this happened! Has the community already turned away from the cosmic censorship conjecture? Or are there good reasons to mistrust these numerical simulations? Is this a recent result?
On my todo list I have that I want to make a shadertoy with relativistic raymarching. I suppose I now want to illustrate a fall into a white hole! Colliding things is a bit harder, not just because the computation is more inolved, but also because the shader language was made to render textures, so it's not up to iterating over a large chunk of data.
Anyways, thank you very much for that information, so exciting!
@npub100e…c8sg @npub1nf4…nqe4

2025-10-27 21:58:49 CET

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> might have [met]
Apparently not. Nevermind, @npub100e…c8sg :D While we're at collecting questions, what happens when a white hole and a black hole collide? Looking at the Penrose diagram it seems like they can't merge?
@npub1nf4…nqe4

2025-10-23 19:00:20 CEST

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Yeah, I noticed you guys having fun juggling Jordan algebras, you even got me to fresh up my memory about them! I have no connection to them, so I guess I have some catching-up to do. Sometimes, my understanding gets better when I don't look at something for a while, but I need some sort of intuition for that to work, and I don't have much for Jordan algebras. Is there a geometric interpretation for them?
@npub1nf4…nqe4 @npub1zz2…9mhx

2025-10-22 23:15:33 CEST

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Getting to read mathstodon from my phone again should make a difference. I hesitated to move because I've had enough of political social media. That other account of mine will have to sleep a little longer, I suppose. Can't live without the maths, though.
And haven't, really. There's Fractal Chats on Discord, @npub1kr6…lhf0's HyperRogue Lounge has a nice hyperbolic geometry channel. Noticed I forgot how to compute cohomology...
I'm also making interactive maths in 60 frames per seconds on shadertoy.com. Even released a 4k intro at the Evoke demoscene party. That got me in touch with some video artists who keep imploring me to put up visuals at parties. Makes me feel old and young at the same time.
@npub1nf4…nqe4

2025-09-10 23:50:13 CEST

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Ah, the good old exponential \king^\queen.
@npub196u…kntt @npub1qhm…qhxt @npub1nf4…nqe4

2025-03-23 05:15:28 CET

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Abdelaziz Nait Merzouk made gorgeous renderings! They are really something to aspire to. I would really like to make similar ones in shadertoy. First get a Newton root finder implemented and then see what I can do with that. Another inspiration is to try and get something like [@KangarooPhysics](https://cornerof.world/users/KangarooPhysics )'s Seifert-like surfaces for knots.
Another project idea is to write a relativistic raymarcher, to render black holes and some other, more weird 4d stuff.
I'm kind of obliged to something along these lines, because I promised some guys to show off with them at the next Evoke demo party in Cologne. That means I have about half a year to get it done, which should be plenty. Should...
@npub1nf4…nqe4

2025-03-23 05:07:39 CET

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I finally managed to watch your talk, @npub1nf4…nqe4! Those were good times, and I really enjoyed going through your visual insights again, looking at all those nice pictures and remembering the things I learned. Or more like rediscovering them.
You said that you'd like to have another, better look at that spheroid. Well, perfect spheres are rather boring. I've attached an animation I captured from my shadertoy implementation. The point where it gets quite symmetric is close to what a sphere looks like. The browser version allows you to change its parameters to perfectly spherical by clicking onto it. Left/right changes the spheroid's shape, up/down the position of the light source.
This version doesn't behave well in more extreme configurations, black means numerical instability, red means it's too chaotic for anti-aliasing to work. The color changes from orange to blue and back every other iteration. If I'm not mistaken the orange parts are odd, and the blue parts have undergone an even number of reflections. Deep blue means the light source wasn't hit after 50 iterations.
All parameters can be changed either at the top of the file, or down in the MainImage1 function. If you want to animate the angle you need to remove "//" from line 151, and add "//" to line 158, so the animated parameter isn't overwritten by the mouse cursor.
That external ray pattern shows the slope of the spheroid in the picture plane, I added this for debugging purposes. It all looks right, but I'm not entirely sure I made no mistakes. I'll certainly have to spend some more time to improve on the black parts and to investigate the strange pictures for more extreme parameter settings.
https://www.shadertoy.com/view/43fcRs
https://media.mathstodon.xyz/media_attachments/files/114/209/728/803/583/882/original/2d0e4b0d13a11c20.mp4

2025-03-15 15:05:03 CET

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That looks like a lot of fun. I aimed for it, but couldn't make it yesterday. I'm looking forward to see the recording!
@npub1nf4…nqe4

2024-11-20 02:30:24 CET

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This paper has much more to offer than estimates on supernova kicks! They implemented reaction networks to model nucleosynthesis! This is fun! They even show pictures of this most extreme stellar process, so folks, go look at it! The scales are indeed mind-boggling.
> Natal
Aww ❤️
So, The kick flips it over, and then the binary partner winds it up? Or how does it happen that the magnetic and rotational poles diverge?
Anyways, neat find! Thanks! You're right, I should not shy away from searching for papers. My clock is broken, the time it shows isn't plausible.
@npub1nf4…nqe4 @npub1gex…rjyz

2024-11-19 22:45:02 CET

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Supernovae are violent processes where most of the star's mass gets ejected at more than escape velocity. This can happen in an asymmetric way, such that the remnant itself can get whipped away at high speed. I find it highly plausible that the star might pick up angular momentum. I'd like to support this hypothesis with papers, but I'm not used to finding them, and I'm feeling lazy.
Another idea is that, often, the magnetic and rotational poles of a pulsar don't match. The lighthouse beaming follows the magnetic poles, sometimes there are even more than two! Anyways, that's how we get pulsars, if these were always aligned, there would be no blinking!
@npub1nf4…nqe4 @npub1gex…rjyz

2024-09-14 01:43:45 CEST

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Those were the days, @npub1nf4…nqe4! I really enjoyed working on this one! And now it's there for everyone to play with, and I don't have to make variations for other people anymore... I'm free :D