Nick @internic@qoto.org

@pdsmix @cwebber I agree it's really good. An analogous thread exists over on Bluesky and is getting responses (cordial, last I saw) from some of the developers.

@johncarlosbaez @j_bertolotti I would expect the movie @BartoszMilewski posted elsewhere in this discussion to be pretty accurate, as it was made by @SchnittGetsReal and co. based on simulation.
https://mathstodon.xyz/@BartoszMilewski/113525935025414414

@dougmerritt @davidsuculum @j2kun I had never seen one in real life until Thinkgeek made some years ago and I got one. I knew it was somehow based on logarithms but it took me a little while to puzzle out how to use it. I showed it to some younger engineers I work with, and they were utterly baffled.

I assume there's a bit of an art to organizing larger calculations so that you lose the least precision.

@dougmerritt @davidsuculum @j2kun For more advanced fun the slide rule.

@cwebber This made me literally LOL.

@BartoszMilewski @j_bertolotti @johncarlosbaez No, from the perspective of the second observer the first never disappears. You can see this by taking the above conformal diagram and drawing two timelike world lines that cross the event horizon and end at the singularity. If you then draw a set of outward-pointed light rays (moving up and to the right at 45°) from events on the first world line, you will see they continue to intersect the second. However, also note that the image that the second observer receives just before crossing the event horizon is of light the first observer emitted just before crossing the event horizon.

It's also worth noting that technically even for a stationary observer an in-falling object never disappears, it just appears to gets dimmer, slower, and more redshifted as it approaches the event horizon (until it becomes imperceptibly dim as an effectively frozen image at the event horizon).

@j_bertolotti @BartoszMilewski Right. The situation with your arm is different, and that's where the conformal diagram that @johncarlosbaez posted is helpful. If you imagine an extended object falling into the black hole you can see that light from the left side (closer to the center) will always reach the right side at a later time. If, however, the object stops falling inward while partially over the horizon, light from the portion inside the horizon will never reach the portion outside (correspondingly meaning no causal force law can possibly keep them from tearing apart).

I think that another way to think of it is that near the horizon light is moving outward from the center more and more slowly (in terms of Schwarzschild coordinate distance vs. coordinate time), at the horizon it's standing still, and inside the horizon it's actually falling inward. If you're stationary outside the event horizon, the light from inside never reaches you. If you're falling inward, you will catch up with with the light from stuff further toward the center, because while it is falling toward the singularity, it is doing so more slowly than you (or any massive body).

@BartoszMilewski @johncarlosbaez Incidentally, that video is the work of @SchnittGetsReal

@johncarlosbaez Yeah, but perhaps a sloppy one. Just associating adjoints, duals, and one-forms on a manifold (as a common example of a dual space).

@johncarlosbaez I can only hope that the application for Adjoint School is one form.

@polotek Maybe I don't know enough about the governance of open source projects, but isn't this a fairly common situation? (Which isn't to say it's not a problem.)

@nixCraft A @frameworkcomputer laptop is also a very good alternative.

@johncarlosbaez But presumably @BartoszMilewski's statement that "you'd see the horizon as a black surface coming at you" is true at some level, because what you see in the distance is not only a function of local spacetime (unless you're inside an enclosure, which is the usual conceit of equivalence principle thought experiments).