Notices by Greg Egan (gregegansf@mathstodon.xyz)

While the FCC has approved a test satellite from Reflect Orbital (which wants to illuminate solar farms at night), the basic physics here seems decisive — on the side of “No, this can’t possibly be a practical thing to do.”

From the linked analysis by Michael Brown and Matthew Kenworthy:

[Reflect Orbital’s plan is “simple satellites in the right constellation shining on existing solar farms”. And their goal is only 200 watts per square metre – 20% of the midday Sun.

Can smaller satellites deliver? If a single 54 metre satellite is 15,000 times fainter than the midday Sun, you would need 3,000 of them to achieve 20% of the midday Sun. That’s a lot of satellites to illuminate one region.

Another issue: satellites at a 625km altitude move at 7.5 kilometres per second. So a satellite will be within 1,000km of a given location for no more than 3.5 minutes.

This means 3,000 satellites would give you a few minutes of illumination. To provide even an hour, you’d need thousands more.

Reflect Orbital isn’t lacking ambition. In one interview, Nowack suggested 250,000 satellites in 600km high orbits. That’s more than all the currently catalogued satellites and large pieces of space junk put together.

And yet, that vast constellation would deliver only 20% of the midday Sun to no more than 80 locations at once, based on our calculations above. In practice, even fewer locations would be illuminated due to cloudy weather.]

https://theconversation.com/a-us-startup-plans-to-deliver-sunlight-on-demand-after-dark-can-it-work-and-would-we-want-it-to-264323

https://ca.pcmag.com/news/16760/fcc-approves-reflect-orbitals-giant-mirror-satellite-that-astronomers-hate

“Mathematician Laurence Sigler had made it his mission to translate [Fibonacci’s Liber Abaci], rushing to complete the task right before he died of lymphocytic leukemia in 1997. But his editor moved on, and the manuscript languished on floppy disks for years. For a while Sigler’s widow Judith Sigler Fell, fearing the project would be killed, took the extraordinary step of impersonating her husband in communiqués.

By the time Fell found a new publisher, Springer Verlag (now part of the same publisher as Nature), floppy disks had been superseded and she had to hire a hacker to extract the files. Fell then discovered that Springer only accepted submissions in TEX format, the technical standard for physics and mathematics texts. She learned it and spent six months retyping the text. Fibonacci’s Liber Abaci was finally published in 2002 — the 800th anniversary of the book’s first appearance.”

https://blogs.nature.com/aviewfromthebridge/2017/04/20/fibonaccis-mathematical-legacy/

Lots of regrettable silliness here: two papers by Max Planck (!) have been retracted, probably by some automated process that based the decision on the same material appearing in another journal (which was far more common at the time, and even Einstein did it) and a rebuttal to a work being published under the same title (but not author) as the thing being rebutted.

But the funniest line in the article is:

“Springer Nature is nevertheless still selling the empty PDF for $39.95.”

https://www.science.org/content/article/why-have-papers-one-history-s-most-famous-physicists-been-retracted

I saw the movie “Backrooms” [not having seen the web series] and though the ideas and visuals were interesting at first, overall it felt very thin. Maybe the original form was a better fit, with an open-ended accretion of lore rather than expectations of a self-contained plot.

“I’d created 2000 free-text responses and labelled them ‘UK’. Then I copied and pasted the exact same 2000 responses but labelled these ‘US’. Finally, I combined them to create a dataset of 4000 total responses, and jumbled them up.

Despite the responses being identical for the UK and US, Copilot produced a rich, detailed summary of how US and UK respondents differed.”

https://kucharski.substack.com/p/real-signals-or-artificial-stereotypes

H/T @sinalana.eurosky.social

@dtl

This is Ray Kurzweil, who told New Scientist that he aspired to “resurrect” his dead father from the man’s (conventionally buried) remains and a few home videos.

The Onion, gloriously on target as ever.

https://theonion.com/the-onions-exclusive-interview-with-sam-altman/

“AI-powered writing tools are increasingly integrated into our e-mails and phones. Now a new study finds biased AI suggestions can sway users’ beliefs”

“We told people before, and after, to be careful, that the AI is going to be (or was) biased, and nothing helped,” Naaman said. “Their attitudes about the issues still shifted.”

https://www.scientificamerican.com/article/ai-autocomplete-doesnt-just-change-how-you-write-it-changes-how-you-think/

Doctor: I’m not sure what’s going on.
Me: So, time to send Olivia Wilde and Kal Penn to break into my house to search for drugs, toxins and mould, while gossiping about their colleagues’ sex lives?
Doctor: Nah. I think we’ll do a bone marrow biopsy.
Me: It was worth a try.

Today in the supermarket I scanned 2 packs of flour … and one of them was listed on the receipt as frozen raspberries. So that must have been a genuine barcode misread, rather than just incorrect data in a product database. The barcodes looked fine, so maybe the reader glitched.

@Infoseepage

The barcodes on the two packs of flour that I scanned look completely identical to me. Not only is there no sign of tampering, there are no tears or stains etc. that might have confused the scanner.

Right now I have no idea what the frozen berries barcode number was, because I only noticed the error when I got home, but I should check next time I’m in the supermarket, to see how many digits were misread.

@Infoseepage They were paper packages that might as well have been rectangular cardboard cartons. There was no wrinkling or curvature or physical distortion of any kind.

“Can a time capsule outlast geology?

A ridiculous but instructive thought experiment involving deep time, plate tectonics, erosion and the slow death of the sun”

This is hugely enjoyable! The subheading is exactly right: don’t take the premise seriously, just go along for the ride.

https://www.scientificamerican.com/article/can-a-buried-time-capsule-beat-earths-geology-and-deep-time/

For crying out loud, ABC news, never send a line graph to do a bar chart’s job.

Link: https://www.abc.net.au/news/2026-01-21/midnight-oil-rob-hirst-pancreatic-cancer-death/106252876

A few days ago, I saw a nice approximation to the arcsine function by @eniko

asin(x) ≈ a(x) = x + (π/2-x)(1-√[1-x^2])^2

I won’t bother plotting a(x) against asin(x), because the two curves are indistinguishable to the eye, but the proportional error is plotted below.

I spent some time trying to figure out if there’s an underlying *geometric* reason why this works so well ... in the same sense that there is for, say:

asin(x) ≈ chord(x) = √[2(1-√[1-x^2])]

the length of the chord that subtends the angle asin(x).

There are some obvious nice features built into a(x): it clearly must agree with asin at x=0 and 1, and less obviously it will match derivatives at those points as well.

But surely there had to be some special geometric relationship too, to make it work so well?

If so, I never did find it. Maybe someone else will (or already has). But I found another approximation, roughly as simple and roughly as good:

asin(x) ≈ b(x) = ½(π-4)x^2 + x + 1 - √[1-x^2]

which also matches values and derivatives with asin(x) at x=0 and 1, and whose proportional error is the gold curve in the plot below. [Note that it matches values with asin exactly at an additional, intermediate point, asin(1/√2) = b(1/√2) = π/4.]

That partly cured me of my conviction that there had to be a nice geometrical account for any approximation this good. Maybe all that’s really needed is a low-degree polynomial and one function, √[1-x^2], with an infinite derivative at x=1 the same as asin(x).

Who could have guessed that the end product of a fearless, intellectually rigorous research program whose sole aim was to produce an LLM with the most reliable, objective and trustworthy responses possible would sound so much like a sycophantic courtier flattering a demented, narcissistic monarch?

Google’s “AI overview”, pointlessly appended to their usual weather forecast for my suburb:

“The weather in XXX is currently sunny with a temperature of about 17° C ... ”

The forecast already states the current temperature, but no, it is not “currently sunny” as it’s 10:23 pm.

The forecast by itself is perfectly understandable. It does not need a summary, an overview, an interpretation, a Reader’s Digest Condensed Version.

FFS, Google, is this what you’re building new data centres and buying billions of dollars worth of GPUs to do?

Most people know how to draw an ellipse by pinning two ends of a string to a board and sweeping a pencil around inside the string, keeping it taut.

But what about the 3D equivalent?

Start with an ellipse (blue) and a hyperbola (green) in orthogonal planes, with each curve’s vertices (extreme points) being the other’s foci.

Pin one end of a string (red and black) to one focus of the hyperbola, and the other to the opposite focus of the ellipse, and then pull the string taut, while also requiring it to pass through whatever point on each curve minimises the distance. The point the string reaches in between will trace out an ellipsoid!

This construction was found in the late 1800s by the German mathematician Staude (Wikipedia says the famous physicist Maxwell also made a start on the problem a bit earlier). I haven’t read Staude’s proof, but you can read a modern treatment here:

https://arxiv.org/abs/1707.01233v1

“About 2:00pm on Saturday, mine workers found the object burning near a remote access road and alerted emergency services.

Police said it may be "a composite-overwrapped pressure vessel or rocket tank", from a space vessel.”

https://www.abc.net.au/news/2025-10-19/wa-space-debris-reentry-investigation/105909612

An astonishing result, beautifully described in @QuantaMagazine — the mathematics linking scattering amplitudes in particle physics to a geometric object called the amplituhedron can be better understood by also mapping the amplituhedron to the mathematics of origami.

https://www.quantamagazine.org/origami-patterns-solve-a-major-physics-riddle-20251006/