Notices by Greg Egan (gregegansf@mathstodon.xyz)

Breaking: DOGE team has barricaded the Sistine Chapel, refusing to release the cardinals until they agree to replace the PopeMobile with a CyberTruck.

[Serious documentary voice]: “Observers will be paying close attention to the colour of the smoke emerging from the Sistine Chapel next week, as the conclave follows a time-honoured tradition: blue smoke means the new Pope will be a boy, while pink smoke indicates a girl.”

Curious to see what ads Netflix shows me now that they know I was born in 1900.

Extreme UV lithography for microchips is wild.

“Getting to EUV light with a wavelength of 13.5 nm requires a source ... around 200,000 °C.”

This turns out to involve laser-zapping tin droplets into exploding bursts of plasma, creating shock waves similar to those of supernovae.

https://spectrum.ieee.org/euv-light-source

This is a fun list of unsolved mathematical problems, described by professional mathematicians who are working on them, ranging from the easily understood (are there any odd perfect numbers?) to some arcane questions in number theory and topology.

[One peculiar typo, at least at the time I’m posting this: y^2 = x^5 – x + 1 is obviously *not* solved by x=0, y=0. I guess they meant x=0, ±1, y=±1.]

https://www.scientificamerican.com/article/9-unsolved-mysteries-in-mathematics/

This is ingenious: astronomers have identified 138 new asteroids just a few tens of metres across by re-analysing JWST images taken for other purposes, shifting and recombining the images to mimic tracking the asteroids and synthesise an effective longer-term exposure.

https://badastronomy.beehiiv.com/p/hundreds-of-small-asteroids-found-in-the-main-belt-using-jwst

Apropos of nothing:

∅

U+2205

https://en.wikipedia.org/wiki/Empty_set

A rigid ring or sphere surrounding a single massive body will not be stable, but in the “restricted 3-body problem” where the ring/sphere is infinitesimally light, and one massive body is orbiting another, there can be some stable configurations.

For example, if the lighter of the two bodies is less than 1/9 the mass of the heavier one, a rigid sphere enclosing the lighter body can be stable.

H/T Shubhendu Trivedi

https://academic.oup.com/mnras/article/537/2/1249/7989465

Samples from asteroid Bennu contain A, G, C, T & U nucleotide bases, and 14 of 20 amino acids used by life — but while we use only left-handed versions of these molecules, Bennu has a roughly equal L/R mixture, puncturing theories that the bias on Earth came from an initial cosmic seeding.

https://www.nature.com/articles/d41586-025-00264-3

This analysis of the highly non-uniform distribution of 4-digit PINs has no big surprises, but it’s still sobering to see it spelled out in detail.

https://www.abc.net.au/news/2025-01-28/almost-one-in-ten-people-use-the-same-four-digit-pin/103946842

@Infoseepage

I saw “Killers of the Flower Moon” at the cinema, which probably helps; it’s easier to commit the time, and focus, if there are no distractions [assuming fellow audience members aren’t arseholes, which is the gamble there].

It was pretty satisfying, though I might have enjoyed it just as much as a limited series on streaming, when it could have been twice as long!

Me making plans: “Over the New Year break, I *will* find 3½ hours when I’m rested and focused enough to watch Scorsese’s ‘The Irishman’ in one sitting.”

Me in reality: “Ooh, a new ‘Wallace and Gromit’ movie from Nick Park! With ‘Cape Fear’ [and ‘Aliens’] references! Cracking!”

What counts as a domestic “robot” right now:

“Hashme told me that he expects the first release of Alfie to handle only about 20% of tasks on his own. The rest will be assisted by a Prosper team of “remote assistants,” at least some of them based in the Philippines, who will have the ability to remotely control Alfie’s movements.”

Also:

“We don’t want you to have to place as much trust in the company or the people the company hires. We’d rather you place trust in the device, and the device is the robot, and the robot is making sure the company doesn’t do something they’re not supposed to do.”

No thanks.

https://www.technologyreview.com/2024/12/23/1108466/general-purpose-robots-humanoids-ai-remote-assistants/

TIL that in 2018 Angélique Kidjo recorded an entire album covering every track of Talking Heads’ “Remain In Light”!

I haven’t heard the whole thing, but the samples here sound good.

https://www.abc.net.au/listen/programs/musicshow/vikingur-olafsson-bach-goldberg-variations-maurizio-pollini/104462508

@mpesce Not mirror life, but an alternative chemistry for the DNA bases. (People really have synthesised those alternative bases, but as with mirror DNA, they’re a long, long way from being able to build a whole organism that uses them.)

https://en.wikipedia.org/wiki/Xeno_nucleic_acid

Headlines for news articles too long for you to read in your busy day?

Why not have an LLM probabilistically “summarise” them into something even shorter that’s easier to take in at a glance, and … might or might not say the same thing as the original.

https://www.bbc.com/news/articles/cd0elzk24dno

In some previous posts, I’ve been chipping away at the question of how two objects falling into a black hole appear from each other’s vantage, and now I’ve put all the pieces together to answer a question @johncarlosbaez posed on his blog:

If a fleet of spaceships all fall into a black hole from different starting points along the same radial line, how would the other ships appear to one in the middle of the fleet?

https://johncarlosbaez.wordpress.com/2024/11/30/black-hole-puzzle/

The plot here shows the “apparent distance” of the other ships (as determined by the angle each ship subtends, if you know its size, or by its parallax if you view it from slightly different positions). It also shows where the ships were located, when the light now being received from them was emitted.

The details are quite different depending on whether we’re seeing a ship that is closer to the black hole than us, by means of “outgoing light” — light moving away from the hole — versus a ship further from the hole that we see by “incoming light”.

Because the event horizon itself is formed by the paths through spacetime traced by outgoing light rays, we see all the ships closer to the hole than us cross the event horizon just as we cross it ourself.

But the incoming light from ships that are further from the hole than us reaches us later, for any given r coordinate where it was emitted, and we hit the singularity at the centre of the hole before we see any light emitted from those ships when they crossed the horizon.

I guess the idea of “checks and balances” is that your Space Czar works towards the goal of a human settlement on Mars, while your Health Czar does his best to ensure that it will swiftly succumb to the measles.

First it was my neighbours’ airconditioner showing up in my WiFi lists, now it’s their “55-inch Samsung The Frame QLED 4K TV” showing up in my Bluetooth. No wonder would-be burglars drive around with Bluetooth scanners looking for things to steal.

Breaking: leading AI moguls have predicted that by 2029, their bots will not only be indistinguishable from humans, they will be able to prove the Riemann Hypothesis with all three-and-a-half legs tied behind their backs.