2026-06-28T01:25:39+02:00 https://nostr.ae Refurio Anachro https://nostr.ae/npub17lwktvf6fa9mlehaafftx3a78ge47js4pxd25qvm0wdl80dqtn7sde5ctv https://media.mathstodon.xyz/accounts/avatars/000/000/341/original/989540505d7029f1.png https://media.mathstodon.xyz/accounts/avatars/000/000/341/original/989540505d7029f1.png https://nostr.ae/nevent1qqsryafaxlzsk87ylj72m0cur5ykzyexd2h9kx6vrawlprqf2dq7tyqzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06g2pdhs In reply to <a href='/nevent1qqsq88957kpjancfxl7mmxscee3z5tswgy0ljepsr74jxqe5rrmy2achcv447'>nevent1q…v447</a><br/>_________________________<br/><br/>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&#39;s so much to see!<br/><br/>Uhm. I guess it&#39;s a bit simpler with relativity. But still: we get new features when we add new dimensions?<br/><br/>1+1 either no mass or no metric<br/>1+2 no curvature without mass<br/>1+3 in other words: gravitational waves!<br/>1+4 ?<br/><br/>I shouldn&#39;t be surprised, but what are they?<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1fayw49zkgcklpwmvdsplpmxgdd3xm4vdkg45vgf9ff4nzxgvr42s00s7kh" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Gerard Westendorp</span> (<span class="italic">npub1fay…s7kh</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1zz2mah7y6j4nld7dwedl7eh0yph4swkkv88spuvh0urq32xgz3ws459mhx" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Paul Schwahn</span> (<span class="italic">npub1zz2…9mhx</span>)</a></span> 2026-07-09T14:15:46+02:00 https://nostr.ae/nevent1qqs29hnmq8xfp4zsp78fqduha2wjvmxuqzn2m3x4jyd55r7d7gvgj5qzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06nqv5hx In reply to <a href='/nevent1qqszn7sxx7s5wrwm6z9c8czjlkpy9j2dvuw79dxxv5q4mcqumfu046crhafkq'>nevent1q…afkq</a><br/>_________________________<br/><br/>said:<br/>&gt; but we can only notice the effect of a discrete group being gauged if spacetime is non-simply-connected.<br/><br/>By &#34;spacetime&#34; you really mean some field? Like the electron field that can feel a solenoid? But we can&#39;t measure that because no-one knows how to make a solenoid from nuclear matter?<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1d60hhaertjrlmhefe54s00hfyga38wangrqthcu3zdnnnfm3myase5mhwm" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>theHigherGeometer</span> (<span class="italic">npub1d60…mhwm</span>)</a></span> 2026-06-27T19:02:57+02:00 https://nostr.ae/nevent1qqs976r30tarflmfe5wgpvncfxzap758dat5920t7jacxj7wjpupgvszyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06ga32az In reply to <a href='/nevent1qqspq2se7k46q609y7ymurru057rqh6jq8wxnqcswrq7ldc02c7xxzs99ljeh'>nevent1q…ljeh</a><br/>_________________________<br/><br/>&gt; grade -1<br/><br/>Is this an instance of negative thinking?<br/><br/><a href="https://ncatlab.org/nlab/show/negative%2Bthinking">https://ncatlab.org/nlab/show/negative%2Bthinking</a><br/><br/>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.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2026-06-25T17:57:19+02:00 https://nostr.ae/nevent1qqsqz8c35xmjg4a80j8l37n6nc5h57klaxyzsnlzl3ut68304arcckszyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06dzjp8p In reply to <a href='/nevent1qqs05r4jkp07mqvjpx47t5ndw7gyyfc7v095vgfvdex5vck99gfd95gfxepz8'>nevent1q…epz8</a><br/>_________________________<br/><br/>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.<br/><br/>Thanks, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span>! 2026-05-28T15:48:15+02:00 https://nostr.ae/nevent1qqs05r4jkp07mqvjpx47t5ndw7gyyfc7v095vgfvdex5vck99gfd95gzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06lur4hk In reply to <a href='/nevent1qqsxt9kascgvckka2gwfx48stgj4tgxafys6jh36w7tjcnvzc9d29fgy7qcnv'>nevent1q…qcnv</a><br/>_________________________<br/><br/>I keep getting surprised how good matrices are for counting things. It&#39;s sort of silly, as it just means I haven&#39;t absorbed _what matrices are_ in some sense. First time was when I learned how to make Fibonacci numbers using matrix generators.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2026-05-28T15:33:51+02:00 https://nostr.ae/nevent1qqs88dcuedfvc2dny37famk2uh755qjn58u6ermdeqx56n2l6sce2dgzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06r6hdh0 In reply to <a href='/nevent1qqspe48aqd9vt39dc57c96g4a4e3zsx9dn5ldwp39rmxd76tkfx77vqlj9grw'>nevent1q…9grw</a><br/>_________________________<br/><br/>Oh wow, that&#39;s much closer to what pops out when you overlay wave trains aligned along the edges of a pentagon, than I would have expected!<br/><br/><a href="https://www.shadertoy.com/view/4cXBz2">https://www.shadertoy.com/view/4cXBz2</a><br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span><br/> <img src="https://media.mathstodon.xyz/media_attachments/files/116/562/804/002/338/024/original/51943e9050647b5f.jpg"> <br/> 2026-05-12T19:36:12+02:00 https://nostr.ae/nevent1qqsw5x5lx2a6g4h7fg5vxaygvzrm0szqhx8et39ttekt0wr2l74mg0szyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06l5ca35 In reply to <a href='/nevent1qqs2vlq24lsyt42p7ft7krz3vfche9n5ljp8vqkdq52gl3wxdgf8dfqas9uxu'>nevent1q…9uxu</a><br/>_________________________<br/><br/>The last couple of weeks? Learning is what drives me, a week is quite a long time!<br/><br/>There are two things I learned from your posts: Donella Meadows&#39; nine leverage points were quite engaging. Didn&#39;t talk about it much on-line, because there&#39;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!<br/><br/>The other is that I now have a picture of the 600-cell! I always felt, nah, that&#39;s too complicated, let&#39;s stick to the smaller ones. And then your explanation of <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1mcusen3wt7qsl24xutmzw7dzx9jmyne5yxtyhv9dcnghh53x67jq3gg2al" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Entropy</span> (<span class="italic">npub1mcu…g2al</span>)</a></span> happened, and <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub10zcfmh333hf5phqzjwn2avyueg2aly69rauj2c5utdg5y6fggv9svdtds5" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Henry Segerman</span> (<span class="italic">npub10zc…tds5</span>)</a></span> showed off his models. That&#39;s so cool, now what do I do with it?<br/><br/>It&#39;s sort of on-topic for me, because I have been eyeing little facts about rendering hyperbolic spaces for a while. Since [@Number_Cruncher](<a href="https://mathstodon.xyz/@Number_Cruncher">https://mathstodon.xyz/@Number_Cruncher</a> ) 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...<br/><br/>For one, I have now practical experience optimizing compressed data size by rewriting the uncompressed source. That&#39;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.<br/><br/>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&#39;t dare to use, thanks [@JacquesC2](<a href="https://types.pl/@JacquesC2">https://types.pl/@JacquesC2</a> ) for writing about it years ago!<br/><br/>You see, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span>, you&#39;re still important to me, and I miss our conversations! 2026-05-07T15:57:09+02:00 https://nostr.ae/nevent1qqs03rsfxqm9vgc8qcv4kzhjyrm6y3vgfxndz8yfwktp2yq3vykjfwqzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw062pp8sl In reply to <a href='/nevent1qqs8l48qx5z004c4ewzgwt8t8c02dkmnyur7j66ap6rk3ua8frprxwcqk9yef'>nevent1q…9yef</a><br/>_________________________<br/><br/>Gorgeous! DrFlopine just did something physalis related in #revision2026 live coding semifinals on a bonzomatic.<br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1t564phwqc6sn2wsqtqy3x63j5hw6xx28ae479mfmq7phedmaaevss8rjx3" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Etienne Jacob</span> (<span class="italic">npub1t56…rjx3</span>)</a></span> 2026-04-04T17:36:47+02:00 https://nostr.ae/nevent1qqsyzj07e3ktdzdl325cz7rplfmcd562c29t7sx2zzu2mxm7mmpc63szyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06ergkyn In reply to <a href='/nevent1qqsy5tdq0eamsgd958fpq90u4qlsetxzzdsjduuka9v52n888xu48rqlmejcd'>nevent1q…ejcd</a><br/>_________________________<br/><br/>I&#39;m talking about the inverse of zeta for the primes 3 and 5 at the critical line. And I&#39;m guessing the idea works for any set of primes.<br/><br/>Of course you knew what it is. I&#39;m just stubbornly sticking to guessing because it&#39;s easier. Don&#39;t mind me %-D<br/><br/>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.<br/><br/>And why am I not seeing any zeros? My fourier approximation has +1 at the end. Have I missed a -1 in ζ? <br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2026-02-20T16:57:05+01:00 https://nostr.ae/nevent1qqsru6rcd7l3kewg8stevqsl49w5ysfl5j7kscgr0nqrhy5uewfx7gqzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06828ntj In reply to <a href='/nevent1qqs8ahhf2uq65unxyqnfm5aktemax348ygax8p407tpd7w9h5nsrj8czc4gh5'>nevent1q…4gh5</a><br/>_________________________<br/><br/>For no good reason, I tried guessing the first few terms of the fourier transform myself.<br/><br/>(cos(x*log(3))/log(3)+cos(x*log(5))/log(5))/2+1<br/><br/>It&#39;s even better when we add<br/><br/>cos(x*log(15)-pi)/log(15)<br/><br/>I&#39;m not sure where the extra phase pi comes from.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1ycrteqr30nchvwx4uk8dxshpqda7gd9kexxjlh5kf9sc3qgk25gq9h856a" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Mike Battaglia</span> (<span class="italic">npub1ycr…856a</span>)</a></span> 2026-02-19T04:05:44+01:00 https://nostr.ae/nevent1qqsr0k5vhmaejuv98j22knarplehadv6g9qv45hkka5a057lyqucu5szyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw064gzjgu In reply to <a href='/nevent1qqs0ahe563x7g3sn3pzpvvha62kt7mnckz0clmgqd6zq47c8dttpshgrhje9a'>nevent1q…je9a</a><br/>_________________________<br/><br/>Here&#39;s Adam Neely about AI in music and the link to fascism.<br/><br/><a href="https://www.youtube.com/watch?v=U8dcFhF0Dlk">https://www.youtube.com/watch?v=U8dcFhF0Dlk</a><br/><br/>As always, somewhat tangential to your thread, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span>. 2026-02-03T03:49:22+01:00 https://nostr.ae/nevent1qqsdndaxjnwguuhsp7taxtyw7tdgf4x86x730qc3ghsnz3eu4ssp4eczyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06mhfs39 In reply to <a href='/nevent1qqswqmh55cu3jm6r3llhhahe8ya5x6u29qnahry3lmvusvrsnqdlp8ga89zq2'>nevent1q…9zq2</a><br/>_________________________<br/><br/>Oh. Sure.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2026-01-28T07:20:36+01:00 https://nostr.ae/nevent1qqsfrn0hqczwx6wwvtl6t5n6gz9jqllme6vuqhz4skz8ywruacyh55qzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06fq46qh In reply to <a href='/nevent1qqsy39004tm2hk2zdgacwqpqxp7284rs085pqk5mglqs0klm7pfg8lqg5rydx'>nevent1q…rydx</a><br/>_________________________<br/><br/>You joke is quite funny. It made me look at your crackpot index once again! It&#39;s oddly specific at places :D<br/><br/><a href="https://math.ucr.edu/home/baez/crackpot.html">https://math.ucr.edu/home/baez/crackpot.html</a><br/><br/>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.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub10sqxqh3prkrezat0vfr2hwqv7076sm33n2ewncw2pu9ls8fe09jshga55p" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Azimuth</span> (<span class="italic">npub10sq…a55p</span>)</a></span> 2026-01-28T06:01:16+01:00 https://nostr.ae/nevent1qqsdrf45cc3x9nkud26dq6gm572plvvveaulzx3svnfl96yxt2zwguszyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06cw6smw In reply to <a href='/nevent1qqsvqde6kfea5hzah66hsnt9hn79uesup2hgn3n2wmrkya8c4xv65wqr0dlxv'>nevent1q…dlxv</a><br/>_________________________<br/><br/>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&#39;s so much tedious work involved with current tools that it&#39;s simply infeasible beyond very small code bases.<br/><br/>I love Terry Tao&#39;s approach! It strikes right at the heart and effectively makes weaseling much harder. I enjoy reading his finds a lot. It&#39;s good to see he gets support by a community.<br/><br/>Research, teaching and engineering are intertwined. At least to Archimedes&#39; 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&#39;t you? <br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1fp0024ns6k99e42eet6esd3c3n7rh6p2u0snkmdtcxm48rmmwrcsgvs4sx" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Morgan Arnold</span> (<span class="italic">npub1fp0…s4sx</span>)</a></span> 2025-12-07T23:34:18+01:00 https://nostr.ae/nevent1qqs0caxy5zqtt2tr6ny62jkrsnxfwgtvwurx70zsc0eszl068nx8s5qzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06lj6xeh In reply to <a href='/nevent1qqsgusnszgkjjf7a202999msuncsdxpup9fp0htq8ecxd8763rpc0esqyvdgw'>nevent1q…vdgw</a><br/>_________________________<br/><br/>Yes, the placement is probably due to the algo avoiding one edge crossing in each row. That can probably be turned off. I&#39;ll have a look later if I can find out how.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-11-21T22:41:39+01:00 https://nostr.ae/nevent1qqsvt23w740jkcfplzdrjwm40dgt70nahlhktsw60t96n8vrd6tjdhgzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw066k9wkj In reply to <a href='/nevent1qqswcudhuqu2stysnzrf40x56m0askh0e3xdhc2y0gm97e7uxp7jn5q5gllc2'>nevent1q…llc2</a><br/>_________________________<br/><br/>&gt;&gt; The existence of a naked singularity implies a failure of global hyperbolicity.<br/><br/>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&#39;t get outside my future lightcone even by topological means allowing me to travel back in time.<br/><br/><a href="https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold">https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold</a><br/><br/>They have definitions with funny mames:<br/><br/>&gt; M is non-totally vicious if there is at least one point such that no closed timelike curve passes through it.<br/><br/>Or:<br/><br/>&gt; M is non-total imprisoning if no inextendible causal curve is contained in a compact set. This property implies causality.<br/><br/>And an old acquaintance, the Cauchy horizon:<br/><br/>&gt; A Cauchy surface for M is a closed achronal set whose domain of dependence is M.<br/><br/>That is a place where the future development is not sufficiently determined by the laws of physics!<br/><br/>Your link makes it very easy to spend my afternoon reading your paper, instead of following my day-job. Very tempting indeed!<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub100eaq390lh64gdggf9un8nq86xchu35e2etl3p6kglrjlg5fsvnqmcc8sg" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Phil Gibbs</span> (<span class="italic">npub100e…c8sg</span>)</a></span> 2025-10-28T17:12:15+01:00 https://nostr.ae/nevent1qqsf6e8xcm76g4aq5n0f90kfxxe4z3pprdjuz3q44tmu98enwew94ngzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06z05j62 In reply to <a href='/nevent1qqsw2sg8gwu60hla5fl8ukkkuefcwpnp46ak38s4egr2ydrcq0xlffct099kp'>nevent1q…99kp</a><br/>_________________________<br/><br/>&gt; 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.<br/><br/>What?! I didn&#39;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?<br/><br/>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&#39;s not up to iterating over a large chunk of data.<br/><br/>Anyways, thank you very much for that information, so exciting!<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub100eaq390lh64gdggf9un8nq86xchu35e2etl3p6kglrjlg5fsvnqmcc8sg" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Phil Gibbs</span> (<span class="italic">npub100e…c8sg</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-10-28T15:39:29+01:00 https://nostr.ae/nevent1qqs2v0qqxsrsfu6gmz8cy7lwun2h7xjqzlq2zvn3e7hjfh2pcquzr2szyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06tpvru4 In reply to <a href='/nevent1qqsz0gpmhh57cemyv2e767jg0p30hp0j3rlp69qznmsnud76u032ldg4qf7ku'>nevent1q…f7ku</a><br/>_________________________<br/><br/>&gt; might have [met]<br/><br/>Apparently not. Nevermind, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub100eaq390lh64gdggf9un8nq86xchu35e2etl3p6kglrjlg5fsvnqmcc8sg" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Phil Gibbs</span> (<span class="italic">npub100e…c8sg</span>)</a></span> :D While we&#39;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&#39;t merge?<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-10-27T21:58:49+01:00 https://nostr.ae/nevent1qqsfspayrp0ygjlzy4gazyznd7wgj5urh8wa3r82mf0yfex9236k6nczyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06nrygn5 In reply to <a href='/nevent1qqs8v9qexqqtpzk430pks679y7hxh26yts5fxrrj3gl949nazlufeyq56x89r'>nevent1q…x89r</a><br/>_________________________<br/><br/>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&#39;t look at something for a while, but I need some sort of intuition for that to work, and I don&#39;t have much for Jordan algebras. Is there a geometric interpretation for them?<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1zz2mah7y6j4nld7dwedl7eh0yph4swkkv88spuvh0urq32xgz3ws459mhx" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Paul Schwahn</span> (<span class="italic">npub1zz2…9mhx</span>)</a></span> 2025-10-23T19:00:20+02:00 https://nostr.ae/nevent1qqsymwztwczj3ez20vhj06d0z7vuz7mz03fvs7yr8ehkrx00jl6t42czyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw064zvmp3 In reply to <a href='/nevent1qqswpk7ymju7m7n5u5m99u9tv4lvc569ltfr5f9ac4y30z96nu0s0qggytd4c'>nevent1q…td4c</a><br/>_________________________<br/><br/>Getting to read mathstodon from my phone again should make a difference. I hesitated to move because I&#39;ve had enough of political social media. That other account of mine will have to sleep a little longer, I suppose. Can&#39;t live without the maths, though.<br/><br/>And haven&#39;t, really. There&#39;s Fractal Chats on Discord, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1kr6ary4kxp5hcffa27038ts7vqv3fyhkwwsdfealknj6e2wf5resadlhf0" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Zeno Rogue</span> (<span class="italic">npub1kr6…lhf0</span>)</a></span>&#39;s HyperRogue Lounge has a nice hyperbolic geometry channel. Noticed I forgot how to compute cohomology...<br/><br/>I&#39;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.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-10-22T23:15:33+02:00 https://nostr.ae/nevent1qqswpvufs84jyxk69nyhjud33zdkzh2mln0e399m8hal6npqh76qfaczyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06pq4wz7 In reply to <a href='/nevent1qqsxrshfa4k97z6azr9d8gk9yzg34c899cly78v9y6zr2z3r8px4p9st9y2tf'>nevent1q…y2tf</a><br/>_________________________<br/><br/>Ah, the good old exponential \king^\queen.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub196uf0rky2aes0v9ejr994z7h85reg5f9fnxu0eumtm0fue2gjeasn8kntt" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John D. Cook</span> (<span class="italic">npub196u…kntt</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1qhmvul058af20389edx4p2vnuxs68d9cehk544e4hj0l0rkhwuasn3qhxt" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Elias Mårtenson</span> (<span class="italic">npub1qhm…qhxt</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-09-10T23:50:13+02:00 https://nostr.ae/nevent1qqsrk39xd95y2l32gx4pnyqhpljc60wft8050ugdlxkpy6ss6py68hgzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06v4xvgs In reply to <a href='/nevent1qqsr34uuyxhlap8rwsdmhdkexke05fceecy8ur5upp5433mamg4hgms3093lm'>nevent1q…93lm</a><br/>_________________________<br/><br/>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](<a href="https://cornerof.world/users/KangarooPhysics">https://cornerof.world/users/KangarooPhysics</a> )&#39;s Seifert-like surfaces for knots.<br/><br/>Another project idea is to write a relativistic raymarcher, to render black holes and some other, more weird 4d stuff.<br/><br/>I&#39;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...<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-03-23T05:15:28+01:00 https://nostr.ae/nevent1qqstgjneaqtrkpeg7qflycpshyrxw7ypvzlvxny0u35k5g087ywgv7szyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06e24pf0 In reply to <a href='/nevent1qqsry4uzvd70dc4utfettwut4hv659atafx8q43tgz74ey6fz7yy3lqv3apjf'>nevent1q…apjf</a><br/>_________________________<br/><br/>That looks like a lot of fun. I aimed for it, but couldn&#39;t make it yesterday. I&#39;m looking forward to see the recording!<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> 2025-03-15T15:05:03+01:00 https://nostr.ae/nevent1qqs8sygqmjany30uuk9emujh0eqwp49j7k4pnalgxq3267ea7d5rfuczyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06l94g3d In reply to <a href='/nevent1qqs8t9kt7arwt0qauc34fuzkh38p8jekqe2hapa2qa3amtgp3wkg54c9777u0'>nevent1q…77u0</a><br/>_________________________<br/><br/>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.<br/><br/>&gt; Natal<br/><br/>Aww ❤️ <br/><br/>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?<br/><br/>Anyways, neat find! Thanks! You&#39;re right, I should not shy away from searching for papers. My clock is broken, the time it shows isn&#39;t plausible.<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1gex4wa4qve6znh4we06xs7k5us9j8chqavzulydcqvx4wdjyys2qr2rjyz" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Amir Livne Bar-on</span> (<span class="italic">npub1gex…rjyz</span>)</a></span> 2024-11-20T02:30:24+01:00 https://nostr.ae/nevent1qqswt7nvcnnp32sl8ks785jpkkygayg5fmvvjrxw4fkly2h89vldgxczyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06em0zpv In reply to <a href='/nevent1qqst3pf8g3vczqcwunwxlut4sgs9cldws3mryatv9h8easzmg3e80rgv0xp97'>nevent1q…xp97</a><br/>_________________________<br/><br/>Supernovae are violent processes where most of the star&#39;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&#39;d like to support this hypothesis with papers, but I&#39;m not used to finding them, and I&#39;m feeling lazy.<br/><br/>Another idea is that, often, the magnetic and rotational poles of a pulsar don&#39;t match. The lighthouse beaming follows the magnetic poles, sometimes there are even more than two! Anyways, that&#39;s how we get pulsars, if these were always aligned, there would be no blinking!<br/><br/><span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span> <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1gex4wa4qve6znh4we06xs7k5us9j8chqavzulydcqvx4wdjyys2qr2rjyz" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>Amir Livne Bar-on</span> (<span class="italic">npub1gex…rjyz</span>)</a></span> 2024-11-19T22:45:02+01:00 https://nostr.ae/nevent1qqsyer7ey9jm8yyuzamye4yq69hyyc77f46wmn0zc5g750xxv76cr8gzyrma6ed38f85h0lxlh499v68hcarxh62z5ye42spndaehuaa5pw06auww40 In reply to <a href='/nevent1qqsxdku9hnjwcrr98k9qsz9mjq2wz20vl9fwmtph5aywjumc8e2u7tgv8xujz'>nevent1q…xujz</a><br/>_________________________<br/><br/>Those were the days, <span itemprop="mentions" itemscope itemtype="https://schema.org/Person"><a itemprop="url" href="/npub1nf4p4rh06z6n6lsvje4txk7eqs23y3hs8vd7nraq6tgwady5qvsqy3nqe4" class="bg-lavender dark:prose:text-neutral-50 dark:text-neutral-50 dark:bg-garnet px-1"><span>John Carlos Baez</span> (<span class="italic">npub1nf4…nqe4</span>)</a></span>! I really enjoyed working on this one! And now it&#39;s there for everyone to play with, and I don&#39;t have to make variations for other people anymore... I&#39;m free :D 2024-09-14T01:43:45+02:00