RobJLow

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 (npub1dxf…v5xz) on Twitter: seeing how that goes.

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npub1dxfpptm696ejdjun36sl8tpac20hs6z4jv92qp4jp5w7666mmq0ss2v5xz

NIP-05 Address

[email protected]

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nprofile1qqsxnyss4aazavexewfcag0n4s7u98mcdp2exz4qq6eq680ddddas8cprpmhxue69uhhyetvv9ujumt0d4hhxarj9ecxjmntyqk608

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relay.momostr.pink

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npub1dxfpptm696ejdjun36sl8tpac20hs6z4jv92qp4jp5w7666mmq0ss2v5xz

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Last Notes

2026-08-06 09:48:51 GMT

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"A magnetar's magnetic field has an energy density that corresponds to a mass density over 10,000 times that of lead."
This is just mindboggling!

2026-01-07 14:50:12 GMT

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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.

2026-01-07 14:44:38 GMT

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This time I can definitely agree with 'sure' - and no 'buts' at all :-)

2026-01-07 14:29:50 GMT

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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'.

2026-01-07 14:10:03 GMT

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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!

2026-01-07 13:43:48 GMT

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"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.

2025-12-23 12:54:50 GMT

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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.)

2025-12-23 11:25:42 GMT

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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.

2025-12-07 12:15:28 GMT

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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...)

2025-12-05 11:04:42 GMT

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Arg. They really shouldn't confuse 'can be represented as a set of 3x3 matrices' with 'lives in 9 dimensions. :-(

2025-12-04 13:29:33 GMT

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Ah, thanks!

2025-12-04 13:16:33 GMT

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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.)

2025-12-04 11:24:23 GMT

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Any idea how 'fat' it gets during the process?

2025-11-30 16:22:34 GMT

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Let's go for only 6 in 10 hating it, so that a majority like it :-)

2025-11-24 09:28:03 GMT

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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.

2025-11-22 22:20:30 GMT

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Some of us would settle for 'interesting' :-/

2025-11-17 13:26:41 GMT

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"could one day" doing some pretty heavy lifting there.

2025-11-12 10:51:29 GMT

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I'd be careful... I think HP Lovecraft wrote a story about that colour.

2025-11-11 14:26:19 GMT

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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.

2025-11-09 17:06:18 GMT

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Well actually, that was Aristotle, not Einstein.

2025-10-30 11:49:51 GMT

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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.)

2025-10-27 21:44:23 GMT

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This is maybe politer than I deserve for jumping in in the middle of a conversation without checking what's already been said 😳

2025-10-27 21:39:54 GMT

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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

2025-10-15 14:50:09 GMT

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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.

2025-10-09 10:17:21 GMT

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A tsunami of intimidating maths...

2025-10-04 12:37:43 GMT

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Not having an exam looming on the horizon makes a big difference to how much pleasure you can get out of organic chemistry :-)

2025-10-01 09:52:04 GMT

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That would be a very safe bet :-)

2025-10-01 07:19:54 GMT

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Decided to take another bite at this stuff, and hoping to have at least some idea what forcing is before I crash and burn..
https://media.mathstodon.xyz/media_attachments/files/115/297/690/117/960/760/original/ba763e81ec2e41fb.jpg

2025-09-28 19:44:41 GMT

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Argh, I think I was talking nonsense. By the same calculation as in normal Schwarzschild, we must have
\[
\frac{d^2r}{d\tau^2} = -\frac{M}{r^2}
\]
for a radial timelike geodesic, so for negative M the particle is repelled harder and harder the closer it gets to the singularity. After a finite amount of proper time it must reverse and head back out again.
And of course, no orbits, so no precession of perihelion.

2025-09-28 15:22:12 GMT

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I think that infalling radial geodesics should get to the singularity, but others will go near then come out again, a bit like for a point source in Newtonian gravity. (Of course, since exactly infalling ones are very scarce, even if I'm right about this, you can still argue that the central singularity is physically inaccessible.)

2025-09-28 11:56:25 GMT

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I haven't though about it enough yet either, but it seems pretty plausible that (in the usual spherical polar coordinates) since the connection coefficients are algebraically just the same as before, but there's no Schwarzschild surface event horizon at which t and r swap over which is spacelike and which is timelike, we have a timelike naked curvature singularity at r=0 that things can fall into, surrounded by an asymptotically flat space-time. So if you're reasonably far away from the singularity, gravity behaves pretty much like Schwarzschild, but with some sign changes (orbital precession, angle of light deflection) but if you're close in things are rather different in ways I don't propose to work out before sending this.
And of course, now there's no Cauchy surface or well-defined initial value problem, so a lot of stuff must fly out of the window.

2025-09-27 12:36:22 GMT

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I seem to recall that it's got undesirable global properties - in particular, it's not globally hyperbolic, and has a naked singularity. There's more detail than I've chased through in
https://arxiv.org/pdf/2001.11376

2025-09-25 07:40:51 GMT

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"True is top is ⊤ because truth implies anything; false is bottom is ⊥ because anything. "
I think something went astray between brain and typing fingers there.

2025-09-21 11:45:45 GMT

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I sometimes feel like there's a tiny Platonist living on my shoulder whispering 'But *really*...' in my ear. Maybe I need to cultivate a formalist on my other shoulder.

2025-09-21 10:42:38 GMT

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I kind of know this: I'm just also kind of uncomfortable with the notion that a very large cardinal might be "really" countable. I know just enough model theory to get myself into (self-inflicted) trouble. I suspect it's a matter of getting used to it (as von Neumann said :-))

2025-09-21 09:59:52 GMT

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Here is where my head explodes (or possibly implodes). The cardinal has to be really, really large - but the Skolem-Lowenheim theorem tells us that it can still be (externally) countable. I suspect I'm just not cut out to understand logic and set theory (though I would like to).

2025-09-21 09:02:47 GMT

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A tiny bit of information in
https://en.wikipedia.org/wiki/Axis_of_evil_(cosmology)
As far as I know (which is not very far) there's no compelling evidence for cosmological anisotropy, where by 'compelling' I mean 'generally accepted'.

2025-09-19 15:35:36 GMT

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I've only come across 'bottom' for ⊥ and 'top' for ⊤. (I'm pretty sure this is standard in logic/Boolean algebra, but then I haven't seen them in other contexts.)
Also, the LaTeX commands are \bot and \top respectively, so that should be enough reason for everybody to stop calling them up/down and down/up rather than bottom and top.

2025-09-19 10:04:23 GMT

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I remember trying to read Segal's cosmology book years ago, and failing to make sense of it. Is it (has it ever been) a serious competitor to the standard cosmology? (I ask because of him being your doctoral supervisor---and I may have asked you this before, but can't remember.)

2025-09-18 09:02:07 GMT

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Oops. I wasn't actually *trying* to make a claim that was wrong in as many different ways as possible, but if I had been trying, it would have been a good attempt.

2025-09-18 06:08:11 GMT

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We have to have some faith in humanity, or at least that segment of it that might see that little bit of whimsy. (Though on twitter I'm sure I'd have at least one person yelling that I'm a complete idiot and explaining why it's wrong.)

2025-09-17 10:00:55 GMT

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"In 2017, the magnetic fields near its event horizon were spiraling around one way. By 2018 they settled down. But by 2021, they were spiraling in the opposite direction! "
The galaxy must have crossed the universe's equator...

2025-09-14 07:46:22 GMT

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What I've found on Bluesky is that when I follow people I see a lot more political content than I'm interested in, so I tend to use feeds more (eg #Mathsky for maths stuff).
Also I usually don't follow people on Bluesky if they're posting just the same stuff I see in other places, and I doubt I'm alone in that.

2025-06-20 10:32:32 GMT

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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.)

2025-06-20 10:23:30 GMT

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I think It's all Clairault's theorem, really.

2025-06-05 15:55:32 GMT

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As any fule know, they're doing dismal science.
https://en.wikipedia.org/wiki/The_dismal_science

2025-06-05 12:42:08 GMT

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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.

2025-06-04 06:40:23 GMT

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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.

2025-06-01 13:27:03 GMT

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Yes, what I meant was that their mistake was writing total nonsense instead of abstract nonsense.

2025-06-01 13:23:22 GMT

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A small mistake: it should have been abstract nonsense, not total nonsense.

2025-05-15 12:17:10 GMT

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I know I'm older than mud, but I kind of like the fact that I can slow down at the hard bits and re-read until it makes sense, if necessary with a kind of spiral approach.
Yes, I know videos can be paused and rewound. It's not the same.

2025-05-05 18:29:31 GMT

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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...

2025-05-05 15:05:36 GMT

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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.)

2025-05-04 15:16:55 GMT

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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...

2025-04-27 13:53:51 GMT

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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.

2025-03-19 10:12:56 GMT

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That's the catch, of course. What people (think they) want and what they get can spectacularly fail to coincide.

2025-03-19 08:13:49 GMT

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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.

2025-01-05 19:29:05 GMT

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I (very) vaguely recall it was something to do with the geometry not having sufficient smoothness properties, so that there is no uniqueness theorem for the time evolution.

2025-01-04 19:32:48 GMT

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I think you're being unnecessarily fair here. But I can't really disagree with any of it.

2025-01-04 15:14:58 GMT

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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.)

2024-12-17 18:42:23 GMT

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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.

2024-12-15 09:16:39 GMT

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I wouldn't be entirely surprised if @npub1wsp…rhgk had a blog post (possibly even more than one) about this he could point us at.

2024-12-06 17:22:46 GMT

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Alas, incompetence prevents me from having a proper opinion.

2024-12-06 17:15:08 GMT

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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...)

2024-12-04 18:30:02 GMT

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"In short, I don't think being a math whiz is just about math being easier for some than others."
This is, I think, an important point. Some people get farther faster for the same effort than others - but if you give up easily then you hit your ceiling sooner. Aptitude and determination both matter.

2024-11-25 08:32:15 GMT

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Kind of weird, because you can see the white hole (but you can't go there) and you can't see the black hole (though you can go there).

2024-11-24 09:19:55 GMT

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Oh no! I'd no idea that had happened, that's terrible.

2024-11-23 21:33:13 GMT

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It's well worth going to Wald after MTW (or some other first GR book). The effort will repay itself. Wald's semi-popular book 'General Relativity from A to B' is (I think) an excellent non-technical approach to give you some kind of orientation for the technical literature, and well worth looking at before gritting your teeth and braving MTW..

2024-11-22 19:38:21 GMT

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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".)

2024-11-21 19:43:58 GMT

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Well, it might not be top of the list of things to worry about:
https://en.wikipedia.org/wiki/Seveneves

2024-11-21 19:24:48 GMT

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So cool, isn't it!

2024-11-21 18:58:58 GMT

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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.)

2024-11-11 21:23:17 GMT

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I'm sure I remember one of my physics lecturers claiming to have seen a paper titled 'Degenerate star has dwarf companion'. But now that it's many years later and google exists, I'm sad to report that I can't find any such thing. Maybe it was just a paper he wanted to write.

2024-09-18 20:11:49 GMT

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Yes, I just took a look. It reminds me of my old suspicion that schoolbooks which insist 'there's no such thing as centrifugal force, it's centripetal force' have a lot to answer for. (To be fair, when you start thinking harder about Newtonian mechanics you realise that the elementary treatments do gloss over quite a lot of hard stuff.)

2024-09-18 19:42:32 GMT

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Just to be contrary: when you're sitting 'still' in the chair, you're accelerating at about 9.8m/s/s, and when you jump off it and are in free fall, you aren't accelerating at all. (Well, a little bit because of drag.)
The difference between the Newtonian and Einsteinian pictures is conceptually huge, even though for almost all practical purposes equivalent.

2023-12-21 20:54:18 GMT

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I tried, but to be honest I found it really hard going. For somebody complaining about other peoples' assertions, he seemed to make an awful lot of his own, and too much of it just came across as crotchety (at best). I have no doubt his computations are correct, it's what he says about them that is really hard to follow. (And the singularity theorem proofs have been looked at by people much more careful than me without anybody pointing out lacunae.)
I'm mostly now waiting for the dust to settle, and trying to to dig myself into any holes about it...

2023-12-21 20:00:39 GMT

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I found it particularly strange that he says in the abstract that Hawking and Penrose just claim that an incomplete geodesic must end in an "actual" singularity, when in fact they are careful to point out specifically that they don't claim the geodesics end at a strong curvature singularity. <shrug>