Was a maths lecturer, main research interest general relativity. Now retired, rebooting as a classics under^H^H^H^H^Hpostgrad at Warwick University. Still @RobJLow on Twitter: seeing how that goes.
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2026-08-03T09:16:30Z Event JSON
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Last Notes npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4257 My general experience of the IT helpline (so long ago there was a human being on the other end) was trying not to say 'If that worked, I wouldn't be talking to you' too often. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…ck2y And I thought the taped messages for your survivors in 'Things to Do in Denver When You're Dead' was distasteful... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…tfwq Virtue is its own punishment. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…vhdw @nprofile…udvu Presumably because people's intuition is generally about situations with a finite number of possible outcomes? npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4hp5 Yes - and it's consequently all too easy to write something that inadvertently comes across as dismissive. 😬 On the bright side, I've now been nerd-sniped into trying to understand Lagrangian mechanics a bit better - it's been ages since I thought about it. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4hp5 This time I can definitely agree with 'sure' - and no 'buts' at all :-) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4hp5 I wasn't trying to be slippery, but am trying to work out in my mind what I think about this, and what it means for the notion of force to be fundamental beyond a faint nagging feeling at the back of my mind which makes me not too happy with immediately identifying generalized forces with Newtonian forces. And I'm fairly sure that Newton's third law (each force having an equal and opposite reaction) is closely tied to conservation of momentum. But, since I'm kind of floundering about in my own mind, I should clam up now ans wait until you write the blog article, and then at least I'll know if I still think 'sure - but'. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4hp5 Sure - but the generalized forces are derived notions (and not always easily identifiable as Newtonian forces) rather than the basic ones of Newtonian mechanics, and the conserved quantities arise from symmetries that are not intrinsic to the Lagrangian framework, so the action/reaction thing must be a consequence of symmetries imposed on the Lagrangian. I'm not saying it can't be done, just that it looks like significant work is required - which isn't surprising if you haven't already done it! npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4hp5 "I believe this principle is built into the fabric of Lagrangian mechanics" That sounds like a hard thing to make sense of, in that force doesn't seem to have a natural/fundamental place in Lagrangian mechanics. At least, not as I understand it - though that may just be my ignorance speaking. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…pklh There must be some nasty subtleties lying around: for a start, there are uncountably many different initial states, but only countably many Turing machines, so in one sense it's entirely unsurprising that TMs can't capture the behaviour of billiards. (I guess the trick is to show that it can't capture the behaviour in an interesting way.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…pklh @nprofile…8eua Back when I had a web page, I had a list of pet peeves. High on that list was people making nonsense claims in maths or physics based on misunderstandings of Goedel's theorems. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…ztfm Seems very much in the spirit of Linderholm's 'Mathematics made Difficult'. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…9s72 I believe this was the argument Heisenberg presented in his doctorate. I think the difference between that and the current (mainstream) thinking is that the uncertainty is not due to the physical process of locating a particle by its interaction with light (which might potentially be overcome by another measuring process) but is fundamental. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy Feeling a bit cheated.:-( npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy It is - but i can't see anything about it on the YouTube page, just a brief AI summary then the comments. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy That is really very cool. And it might be a good place to point out (a thing that I learned later than maybe I should have) that although the general quintic cannot be solved by purely algebraic means, it can be solved using elliptic functions. (This isn't new, Hermite did it.) I have no idea if there are other methods (inevitably involving transcendental functions) for higher order polynomials. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…00p2 It's hard not to wonder if that's something to do with which people were attracted to move to Bluesky/Mastodon. (Or, of course, which people you choose to follow...) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…pklh @nprofile…8eua Arg. They really shouldn't confuse 'can be represented as a set of 3x3 matrices' with 'lives in 9 dimensions. :-( npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…pklh @nprofile…8eua @nprofile…l4xy @nprofile…4ndu Ah, thanks! npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…l4xy @nprofile…4ndu Grumble. I did take a look at a visualization somebody'd uploaded, but after it zoomed out a few times all I could see was a line. (But since I could see it, it must have been quite think really, I suspect.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy @nprofile…4ndu @nprofile…8eua Any idea how 'fat' it gets during the process? npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy 🤯 npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua Let's go for only 6 in 10 hating it, so that a majority like it :-) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…stct NCC01701-D is Picard's ship. Should have been 'baldly'. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…stct And you thought they had a post-capitalism society... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…l4xy Add salt? https://youtu.be/TyJWa6SwUmk?si=VqhRkFiIZmoDpogC npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…ztfm You just reminded me of the time a colleague told me about going to a talk promising an 'elementary proof of the prime number theorem'. "At last" he'd thought "a chance to understand that." He left thoroughly traumatised. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua Some of us would settle for 'interesting' :-/ npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…u6hy I'm watching from home too (though not helping). npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…pklh @nprofile…8eua "could one day" doing some pretty heavy lifting there. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…578r @nprofile…u6hy I see a lot of 'you just boiled off a small lake' posts, but surely the energy requirements are heavily loaded on to the training period. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua I'd be careful... I think HP Lovecraft wrote a story about that colour. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…zzyf A very interesting book. I remember reading it (well, looking at the words in it) when I was trying to get to grips with quantum logic. Not exactly light reading though, or at least, not for me. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…9s72 Once you have enough bits, you can (at least sometimes) get help from the etymology: neu = new (easy if you already speak a Germanic language) gierig = greedy (eager is cognate), so neugierig=greedy for new things = curious. I find this kind of thing helps more than making some kind of mnemonic out of syllables. When it helps at all, that is... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…4x5t @nprofile…8eua Cool, thanks! npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua Maybe also a kind of reductionist assumption that everything (interesting?) can be broken down into a combination of binary operations, so it's all implicit. (Which might a bit like saying that chemistry is implicit in quantum mechanics - sort of true, but not usefully so.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…y4cv This is maybe politer than I deserve for jumping in in the middle of a conversation without checking what's already been said 😳 npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…8eua @nprofile…y4cv But couldn't you also just invert the usual stellar collapse (on account of the laws of physics being time reversible)? Then you'd have a white hole that spews out matter with empty space to its future, and no black hole. i.e. turn this upside down. https://media.mathstodon.xyz/media_attachments/files/115/448/272/780/156/792/original/e63b91294acdeb4b.jpg npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…00p2 @nprofile…5gem Real men use ed. (Disclaimer: not a real man.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…pklh @nprofile…9s72 I heard it claimed (and it sounds reasonable) that the absurdly high prices on some second hand books are because they're being used in a money laundering scheme. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k A tsunami of intimidating maths... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k Not having an exam looming on the horizon makes a big difference to how much pleasure you can get out of organic chemistry :-) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…5k3r You could take a look at Bernard Schutz's 'Geometrical methods of mathematical physics'. It's on the archive at https://archive.org/details/Schutz_Geometrical-Methods-in-Mathematical-Physics_1980/mode/2up so you can try before you buy. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hr6z They should also open a night club called Meson Scene. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…saev @nprofile…hr6z What they should have done is kept the 1mm markings, but put them farther apart for ease of reading. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…5k3r A lot of stuff is made difficult by the fact that almost all our surviving literature from the ancient world is from precisely those people with a very atypical education. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…5k3r I thought I might have a pdf of it squirrelled away somewhere, but I've checked the place it would be and it wasn't. Sorry :-( npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…5k3r In GR (assuming global hyperbolicity) the configuration space is the space of all three-geometries on a Cauchy surface, which is far from finite dimensional (and phase space is, of course, bigger). This, of course, doesn't necessarily mean that there can't be a return, only that the Poincare recurrence theorem won't guarantee it. But in fact Tipler showed (back in 1980) that there is no Poincare recurrence in a universe with compact hypersurface: https://www.sciencedirect.com/science/article/abs/pii/B9780126913804500095 npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hszg Giving your AI generated assignment to the teacher's AI to mark is now pandemic at all levels. Why am I not even surprised? Kind of feel that hidden text should be an automatic 'reject' from any journal worth publishing in. (Though I bet some authors will claim they were only doing a Sokal.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…saev Seems to work fine on my Android device. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x Sure - I just find it interesting that you can (kind of) do cosmology on a surface of revolution, and there it's essentially Clairault. (OK, you have to use the right metric, and trig functions become hyperbolic ones, but if you squint hard enough it makes sense.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x I think It's all Clairault's theorem, really. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…saev Sometimes the fates are kind :-) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…saev @nprofile…mqrg Oh, very good! (Since x^y doesn't have a well-defined limit as x and y tend to 0 through positive reals. Just to prove I was paying attention.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…zkkf As any fule know, they're doing dismal science. https://en.wikipedia.org/wiki/The_dismal_science npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x Yeah, I remember trying to read some of Wald's work in this area some years ago. I think I had an accurate-as-far-as-it-went-but-it-didn't-go-very-far fairly vague idea of what was going on, but never closed in on the detail. That said, the whole endeavour - to extract the equations of motion of an idealised point particle - might be open to criticism along the 'there ain't no such animal' lines. You pays yer money and you takes yer chances. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…m2ru @nprofile…yu7x No, I was saying that as if I were an LLM who had previously said that LLMs were good at literary analysis and been caught out. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x Yes, you're right, I should never have been impressed by the glibness of LLMs. My mistake, and I'll try not to make it again in future. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k Yes, what I meant was that their mistake was writing total nonsense instead of abstract nonsense. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…9wly @nprofile…pmdx A small mistake: it should have been abstract nonsense, not total nonsense. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hr6z ... with enough left over that they can give them back to room service to do the same again next day. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hr6z I didn't realise! I just saw it appear in my timeline. On closer inspection, it's a boost by @nprofile…fqqu, so it's all his fault. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hr6z The Molesworth books are a fond memory from adolescence, and the three-letter truncations are like his semi-phonetic spellings for short words. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…hr6z Shades of Molesworth, somehow. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…dpa9 It looks a bit like earlier stuff of his (which I hadn't initially realized was the same guy), rational trigonometry. It's not that it's wrong, just that it doesn't live up to his claim of being a better way of doing trig. Proof (if proof were needed) that you can be a professional and still be a crank in (at least some aspects of) your own field... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k Hype can make it around the world before informed commentary has got its boots on. (I suspect that these articles are eating and regurgitating each other, without anybody actually looking at his paper.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k Is it nonsense though? I mean, any more than any other strongly finitist approach to maths. I ask because I understand even less about finitism than I've just said, and I said nothing... npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x @nprofile…5k3r I think I actually started to understand tensors a bit when I realised that the 'transformation' rules were actually a very unhelpful way of saying that tensors don't depend on the choice of coordinate system. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…ucsf They should never have told anybody about it. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…y88u This is also a strong hint as to why 'just throw it into the sun' is not a good way to get rid of anything unwanted (from politicians to nuclear waste). npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k I strongly suspect that a poll would show quite a lot of people would prefer a benign dictatorship to a democracy. Of course, that word 'benign' is quite important there. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…saev @nprofile…59k6 This is the flip side (in many senses) of Americans not knowing that Ayn Rand doesn't have worldwide recognition as a major philosopher. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…args Apparently giant ants mine gold in India. I read this in a book, so it must be true. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…3yjd @nprofile…fa4k The big difference between them is that relativity makes sense and QFT doesn't. (This may be biased by my long standing utter failure to understand QFT, of course.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k A lot of the time people believe what they want to be true. I guess these people want to believe that they're victims of a conspiracy. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…n0jg I am confused (not that that's unusual). If you have an isolated (let's say spherically symmetric) object, and classically it sits in a static, asymptotically flat space-time, then don't past and future null infinity have to disagree about the vacuum like they do in a Schwarzschild space, so that it will also radiate (but maybe much more slowly)? (It doesn't help my floundering much that the original calculation is based on a static space-time but concludes that there's no such thing...) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…cnse @nprofile…yu7x Oh no! I'd no idea that had happened, that's terrible. npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…fa4k @nprofile…e5g0 This is why I have problem with the firewall idea. (I've tried to understand the justification, but all I hear is "mumble mumble boundary conditions mumble mumble and then a miracle happens".) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…yu7x @nprofile…cnse @nprofile…fa4k So cool, isn't it! npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @nprofile…cnse @nprofile…fa4k Just to add some quantitative pedantry, the tidal force due to the sun is about half that due to the moon, which is why spring and neap tides are so different. (I still remember how surprised I was when I first did the calculation to see the relative sizes of the effects, so now I take every opportunity to share the information, however marginally relevant it might be.) npub1qku4qwv5aeegp3htdujwpue9jlt89vc068quxrckv8qc272523gqutmrv6 RobJLow @npub1knz…c73p Surely some kind of dinosaur with teeth like a theologian.