I'm a data scientist and physicist who likes dabbling with new ideas for #artificialintelligence 🤖 and #quantumgravity Ψ. Occasionally, I join programming game competitions 🚀 . I am curious about mathematical concepts or novel ideas in general.
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2026-08-20T19:00:12Z Event JSON
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Last Notes npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk You are right. You have not implied what I wrote and maybe strictly speaking the articles haven't either if one reads them carefully. But reading the first lines made it very likely to me that after reading the article many readers will think that "Anthropic is trying to 'burn' as many unique books as possible so that we cannot read them". npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Maybe it would be good to critically evaluate that against some more neutral reports. These sources have many signs of populist scaremongering. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Not sure if I had made my question clear enough, but now I've posted a clearer version on https://physics.stackexchange.com/questions/848885/why-do-spinor-bilinear-covariants-satisfy-this-simple-identity .. unfortunately without an answer. The question is about bilinear covariants and Clifford algebras. Interestingly, the AI gave a partial answer to it. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I don't see it explicitely mentioned, but I wish they had told us in physics class, that all of Maxwell's relations follow from $dT dS=dp dV$ https://en.wikipedia.org/wiki/Maxwell_relations#Derivation_based_on_Jacobians npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I've watched quite a few hours of lecture on the standard model and also representation theory. Not a full course, bit still quite a bit. For me - from the learners point of view - it would impossible to understand which set of matrices (3,1,-2/3) stands for and why exactly these matrices represent those 3 precise numbers and not others. I could probably parrot some buzz words I heard in lectures, but even the most basic university-style test question on an actual calculation would make me stumble. I could only pretend like a chatbot. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Great to see a lecture about the standard model from you! Looking forward to the next videos. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I haven't thought about it much, but here is some algebra from the book: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Ah right. Thanks! npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I can confirm that the Moufang laws work for bioctonions, but my instinct is that any law the works for octonions would work for bioctonions? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Oh, how disappointing. It's a general equality which would work for any bioctonion replacing x*? I forgot. I actually knew about the associator last time I was investigating octonions for new identities with brute computer force. I couldn't find any. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk yes npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk But here is a little amendment equation, which I believe holds: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Here is my way to put it as someone who implemented C-D rather than thinking deeply about the math: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Oh right. Sorry that I missed that. My C-D worked before, but after introducing a new conjugate I made a mistake. Apparently there is a 3rd type of conjugation that is needed: conjugate only the complex numbers. It's quite insightful to implement that to see how the math works. Here is the fixed result. Is that as expected? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I've changed the conjugation the following way: the explicit conjugation affects the complex numbers, the conjugation in the C-D construction does not. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Hmm. 1) seems to indicate that I have the same construction, but I believe it's not alternative (in any way; except for the one equation I mentioned). Please let me know if you can confirm. But I had the impression that @npub1nf4…nqe4 wrote it should be alternative?! npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk To understand the convention and check my code, could you please tell me: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk What is the conjugate of i e1? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I'm not using pairs. I just put complex numbers at the beginning of CD. But these complex numbers would also be conjugated according to CD. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I've implemented C-D and I conjugate the complex numbers, but you and the AIs tell me that bioctonions are alternative, but my code doesn't show that. Are they really alternative? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Hmm, given that my code does not produce alternative bioctonions, I guess the question is: what is the complex structure? does your conjugate also conjugate the complex numbers? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Is it a non-trivial statement that defining npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Ah, sorry! I had a typo in my variables (I had y=x). I'm afraid I have to inform you, the equation does not hold: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk To me it looks like bioctonions are just octonions with complex numbers as coefficients? In that case one could just implement the C-D construction and see if the equations works? npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk That's interesting, too. Thanks! npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk If you decide to talk about SU(5) or Spin(10), it would be great if there is a way to do some part down to the very basics so that an undergrad without much knowledge about representations can verify. For example writing something down concretely with matrices. I'd imagine the must be a way to demonstrate things concretely with matrices. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I'd like to learn anything which gets as close as possible to what I describe. Since I don't know about it yet, I wasn't able to describe it better. Sorry if it was vague. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Most interesting would be: Successful simplifications of the Standard model of particle physics. Therefore, any attempt which would be able to reproduce some(?) predictions of the SM, but with more concise/elegant math. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk I've found a way to put it more concretely: npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk It plays a similar role to the Fierz aggregate \(Z\), except that \(A\) is from the real CA and contains all grades. Being based on the bilinears, it's rather quadratic in dependence. Squaring to 1 may have been a confusing statement. Squaring to a scalar (grade 0) is more what I meant. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk Thanks, I'd appreciate that a lot! I read Lounesto and was surprised that I found an alternative way to derive the Fierz identities. npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk **How spinors square to 1** npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk **Beyond complex numbers, quaternions and octonions** npub1689zsw6dyvd8te26mnn2ft0qrqndlu53q3j4g7337slzlgjhfqpsxfnwtu Gerenuk That's the causation the wrong way round. Non-physics inspiring breakthroughs in physics, would be physics. But physics inspiring breakthroughs in non-physics is not physics. Or should spin networks win the Nobel prize then? Neural networks have not produced anything meaningful for physics yet, apart from findings without any interest for physicists.
