Greg Egan

I am a science fiction writer and computer programmer.
Latest novel: SCALE.
Latest collection: INSTANTIATION.
Web site: gregegan.net

Public Key

npub1qqm7nu2qf25xd3mw6y6cyp4v2wr7ktf43ymp5wqz4u8jvz76ymtsjj5nhv

NIP-05 Address

gregeganSF_at_mathstodon.xyz@mostr.pub

Profile Code

nprofile1qqsqqdlf79qy42rxcahdzdvzq6k98plt956cjds68qp27rexp0dzd4cpzemhxue69uhhyetvv9ujumn0wd68ytnzv9hxgrrp3qc

Publishing to

relay.nostr.band

Author Public Key

npub1qqm7nu2qf25xd3mw6y6cyp4v2wr7ktf43ymp5wqz4u8jvz76ymtsjj5nhv

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Last Notes

2024-11-02 06:06:02

A friend emails: Yes, let’s a catch a movie, will confirm details later today or tomorrow morning.
Siri: “Found an Event!!! Tomorrow at 1:00 AM!!!”
I guess if you start dumb enough, people will praise Apple Intelligence as if it’s a personal assistant with a PhD in everything.

2024-10-05 22:23:26

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@npub1knz…c73p Yes, and specifically I say in the post that we’re measuring things in the reference frame of a tidally locked body that always points towards the central mass, so we know exactly how fast it’s rotating around its own axis.
Of course you could work this out in any frame you like, but I find it intuitively easier to linearise the central force after choosing a specific frame, and it’s one whose test-particle trajectories I studied very closely when I was looking at the Newtonian, Kerr and Schwarzschild metric versions for “Incandescence.”
And in this case we also have the advantage that the triangle the spacecraft form lies on a circle that is fixed in the “tidally locked hollow asteroid” frame.

2024-09-12 11:52:29

Does anyone really watch foreign-language programs dubbed into English, when subtitles are available? I hadn't been hit with the old lips vs dialogue mismatch for about 50 years, but suddenly I’m seeing Apple TV promos as hilarious as those dubbed spaghetti Westerns from the 70s.

2024-08-26 14:19:04

An interview with Laurie Anderson, soon to release a new album about Amelia Earhart.
https://www.thelineofbestfit.com/features/interviews/laurie-anderson-flying-into-the-sun

2024-08-26 04:22:07

After upgrading to MacOS Sonoma, my keyboard was possessed by an evil force that seemed to want to poke its idiotic nose into every damned thing I was trying to write … so thanks to “cree8er” who posted the solution here.
https://discussions.apple.com/thread/255649815

2024-08-25 12:43:28

The home screen of ABC Australia’s Listen App used to show a list of the latest episodes of the programs you’d chosen to follow. Perfect.
So of course they’ve now “upgraded” it to show, instead, “personalised suggestions based on your interests”: i.e. things you did not choose.

2024-08-25 08:37:50

Flipping through my 1973 Norton’s Star Atlas, I saw the trajectory of the asteroid Eros during its Jan/Feb 1975 opposition sketched in pencil.
I had completely forgotten that I observed this! It moved from 48°N to the celestial equator over 6 weeks.
https://en.wikipedia.org/wiki/433_Eros

2024-08-20 12:31:36

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@npub19g8…9445 I’ve only watched the first two episodes.

2024-08-20 11:08:35

“Scavengers Reign” is something else — it’s as if Miyazaki decided to remake Tarkovsky’s “Solaris”. I have absolutely no idea what’s going on, but as a gloriously hallucinatory xenobiological dream, I’m happy to just sit and stare at all the strange creatures chittering around.

2024-08-20 06:43:20

“Many of the accounts' posts showed clear signs of the involvement of a large language model (LLM) similar to ChatGPT in the construction of sentences and grammar. Some posts cut off mid-sentence suggesting little human oversight.”
https://www.abc.net.au/news/2024-08-20/linda-reynolds-brittany-higgins-x-ai-bot-network/104247616

2024-08-20 03:24:23

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In contrast, on the same day: the harried person who took my blood for some tests was forced to waste time (re)typing details from a paper form, which had been printed using data typed earlier by the referring doctor. Made even sillier by both people working for the same company.

2024-08-20 01:58:26

Australians who send parcels overseas: you can now pre-fill the customs declaration form online with Australia Post.
So what used to take 5 minutes in the post office, with harried counter staff typing every detail from the paper form into their computer, now takes 30 seconds.

2024-08-18 09:44:06

TIL about TMAO, a molecule that protects proteins in fish from the distorting effects of pressure:
https://en.wikipedia.org/wiki/Trimethylamine_N-oxide
Its maximum concentration before reverse osmosis would set in seems to impose a depth limit on fish:
https://www.pnas.org/doi/full/10.1073/pnas.1322003111
H/T: https://www.bbc.co.uk/programmes/w3ct5rhf

2024-08-14 12:56:08

Candidatus Thiomargarita magnifica: a bacterium visible to the naked eye with half a million copies of a very large genome.
https://www.science.org/doi/10.1126/science.abb3634

2024-08-13 08:43:28

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@npub1ztm…t758 Regardless, my priority for the next 10 billion years is now to prevent anyone from using the word “Milkomeda” ever again.

2024-08-09 06:54:17

Me: Is there anything stupider than nominating a day as “Book Lovers Day”?
ABC News [Australia]: “With Book Lovers Day falling on Friday, August 9, ABC News has compiled a list of TV shows and movies you can watch at home that are based on books.”

2024-08-08 13:48:51

“A feature documentary about two out of work actors attempting the impossible task of mounting a full production of Hamlet inside the ultra violent world of Grand Theft Auto Shot entirely in game.”
https://www.undiscoveredcountryfilm.com

2024-08-08 09:51:22

“All that’s zapped is not killed”
Your microwave oven has its own microbiome.
https://www.nature.com/articles/d41586-024-02553-9

2024-08-07 11:59:56

“The Decameron” was fun, all the more so for the relentless anachronisms and random accents, and there was a lot that felt genuinely Covid-era poignant between the romps. Mystified as to why its soundtrack was from my youth, but no complaints on that score.

2024-08-07 07:17:12

Things we’ll now check at compile time:
“The new IPC Template Type defined 21 input parameter fields, but the integration code that invoked the Content Interpreter with Channel File 291’s Template Instances supplied only 20 input values to match against.”
https://www.crowdstrike.com/wp-content/uploads/2024/08/Channel-File-291-Incident-Root-Cause-Analysis-08.06.2024.pdf

2024-08-06 13:14:19

I wanted to send copies of some of my print-on-demand books to Korea ... but Amazon refuses to ship to Korea unless I supply details of the recipient’s passport for customs purposes!
How bizarre. I’ll have them sent to me, then mail them myself, and it will all take much longer.

2024-08-05 06:57:42

The Seiun Award for “Solidity” just arrived in the mail! Thanks again to my wonderful translator Makoto Yamagishi.
The Seiun’s trophies are always very cool, but I hope this one doesn’t wake up in the night and tap me on the shoulder. It’s a replica of:
https://en.wikipedia.org/wiki/Masked_Goddess
https://media.mathstodon.xyz/media_attachments/files/112/908/109/313/603/900/original/d623e86635d5abb7.jpg

2024-08-01 11:09:31

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@npub1knz…c73p Thanks! It’s going to take me a while to digest all this.

2024-08-01 08:44:30

I don’t mind that “efflorescence” *also* means “the formation of a powdery deposit on the surface of brickwork as a result of loss of moisture on exposure to air” but that the mini OED on my computer lists this *before* anything about flowers, or cultures, in bloom is depressing.

2024-07-29 21:55:21

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@npub1c9m…9xjd This is what happens when you go hiking in the Garden of Forking Paths.

2024-07-27 13:48:36

Trying to imagine the pitch meeting for “Greta”:
“It’s a stalker movie! With *all* the clichés!”
“So … it’s a tongue-in-cheek metafictional parody, like ‘Cabin in the Woods’?”
“No.”
“A fresh take, with an astonishing new angle?”
“No.”
“Um, OK. Here’s a budget and some stars.”

2024-07-27 04:23:15

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@npub16tg…rfyq Thanks!

2024-07-26 22:36:45

Quantum effects might make it impossible to form black holes by immensely concentrating light, because photon collisions create particle-antiparticle pairs that the electromagnetic field accelerates to escape the collapse.
https://physics.aps.org/articles/v17/119

2024-07-23 13:33:44

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@npub1zad…szcu Luckily I’ve now managed to find a sensible one like that, which I will give as the gift instead of the terrible one.

2024-07-23 07:12:02

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@npub1pal…cy7v Yes!

2024-07-23 04:38:11

Some product designers are idiots. I bought a 2-hotplate induction unit as a gift, then realised you can’t turn off hotplates individually, and removing one pan makes it beep for a minute. Keeping this for myself for when my old stove dies, but would never inflict on anyone else.

2024-07-21 09:52:20

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@npub1pst…gnrd Yeah, I should have stated that I’m talking about wholly synthetic running shoes, not leather shoes. I’ll edit the post to add that.

2024-07-21 06:13:00

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@npub1kva…xqsq No, these were fine for the same walk, dozens of times, back when they were the shoes I wore most of the time.

2024-07-21 06:07:09

How much does “wearing in” shoes involve (A) the shoe becoming less stiff & deforming, vs (B) the wearer’s gait adapting & their foot callousing at rub points?
Just walked 16km in shoes I hadn’t worn for 18 months (much used & comfortable back then) and ... ouch, seems mostly B.

2024-07-19 22:19:06

On Guam, they tried to protect nesting boxes for birds from brown tree snakes by placing them on top of smooth, slippery poles.
Snakes: We call this lasso mode.
https://www.youtube.com/watch?v=iRjrawDTFXU
Article in Science:
https://www.science.org/content/article/guam-s-invasive-tree-snakes-loop-themselves-lassos-reach-their-feathered-prey
I heard about this on the wonderful “What the Duck” podcast:
https://www.abc.net.au/listen/programs/what-the-duck/snakes-and-ladders/104010396

2024-07-19 07:23:19

Crowdstrike have advised that the world will be reverted to its last valid backup set, dated 7 Jan 2014, within the next 30 minutes. Please make paper notes of anything important to you from the intervening period, and tape them to your refrigerator door in a prominent position.

2024-07-13 09:26:16

The story of Maurice Hilleman, a wonderfully sweary virologist from Montana responsible for vaccines that currently save 8 million lives a year, “noted by some researchers as having saved more lives than any other scientist in the 20th century”.
https://radiolab.org/podcast/great_vaccinator

2024-07-13 04:03:46

Australian taxpayers: At this time of year, as many as 0.01% of the emails you receive claiming that you have a new message in your myGov inbox can be genuine emails from the Australian Tax Office. Stay alert, to minimise the risk of deleting this 0.01% along with all the scams.

2024-07-12 04:25:01

This was the cringiest thing I’ve heard on the AI front, period. Apart from the fact that all but the crappiest LLMs do a better job at faux-conversation than this, foisting such an obnoxious toy on people in aged care would be a form of torture.
https://www.abc.net.au/listen/programs/radionational-breakfast/robot-developed-to-work-in-aged-care-homes/104089424

2024-07-10 03:54:12

A fascinating and disturbing look at how finite-element engineering simulations, though potentially very accurate, are nonetheless sometimes wildly wrong thanks to old/misused code, and dodgy shortcuts that Gilbert Strang calls “variational crimes”.
https://www.scientificamerican.com/article/how-the-math-of-cracks-can-make-planes-bridges-and-dams-safer/

2024-07-04 09:14:23

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@npub1knz…c73p I’m confused. This seems to be describing an event on August 8, 2023, so why are you saying it’s connected to what happened last night?

2024-06-21 08:33:22

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@npub1knz…c73p
Franklin also totally messed up the QCD colour charges.

2024-06-21 07:24:46

Breaking: Leaked modelling commissioned by the Australian opposition puts a price tag of $1B, over five years, to train a hundred engineering graduates to pronounce the word “nuclear”.

2024-06-19 11:19:22

Apple TV thoughtfully asking my age twice, just in case I’m in a superposition of older and younger selves.
https://media.mathstodon.xyz/media_attachments/files/112/643/002/128/675/505/original/fcf1d1d572cd213c.png

2024-06-15 11:12:28

This is MacOS (13.6.7) content indexing failing.
Two near-identical files, but only the 2nd can be found by content.
I’d be curious to know if the same thing happens for other Mac users, or if it’s specific to my machine (though the bug remains when I rebuild the index.)
https://media.mathstodon.xyz/media_attachments/files/112/620/332/687/665/142/original/1e47164f85d65e42.png

2024-06-14 07:24:24

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@npub1knz…c73p No, I’ve never really got into minimal surfaces.

2024-06-14 06:13:45

“Alice in Wonderland: Simple Tasks Showing Complete Reasoning Breakdown in State-Of-the-Art Large Language Models”
H/T https://x.com/ChombaBupe/status/1801298035802079640
https://arxiv.org/abs/2406.02061

2024-06-12 08:30:33

Here’s a thought, online shoe stores: maybe let the customer enter their shoe size, and filter the choices on offer by whether you have that size in stock, rather than making us check case after case individually?
Either that, or let us send our own SQL queries to your database.

2024-06-07 04:11:23

A complete globe of the world made from a material that can be bent but not stretched or sheared (thus preserving local distances and angles) will be rigid — but if you cut out large enough portions at high latitudes, what remains can be reshaped so the equator becomes an ellipse.
https://media.mathstodon.xyz/media_attachments/files/112/573/380/251/264/238/original/e6b1f2d8870ba611.mp4

2024-06-04 08:45:56

Wow, lucky people in Sydney are seeing a fairly rare kind of soliton cloud known as a “roll cloud”: tubular clouds that appear to be rolling across the sky.
https://www.abc.net.au/news/2024-06-04/nsw-sydney-roll-clouds-explainer/103934424
https://en.wikipedia.org/wiki/Arcus_cloud#Roll_cloud
https://media.mathstodon.xyz/media_attachments/files/112/557/471/530/557/763/original/c9f73f577defe390.png

2024-05-30 10:48:24

Gram negative bacteria have been laughing at us:
https://pubmed.ncbi.nlm.nih.gov/20419407/
but now we might finally have our revenge, with lolamicin:
https://www.nature.com/articles/d41586-024-01566-8

2024-05-27 04:38:18

“exeme” sounds like some new-fangled technical term from the cutting edge of genetics or information theory ... but actually it’s just an archaic Scottish word meaning to release or exempt.
https://en.wiktionary.org/wiki/exeme

2024-05-16 07:07:45

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@npub1knz…c73p
“You can have various mixed-halogen things, all of which are reactive and toxic and are distinguished by their various degrees of vileness.”

2024-05-07 04:38:26

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@npub1c9m…9xjd I was kind of hoping it would turn out to be a version of “The Purple Rose of Cairo”.

2024-05-01 03:27:13

If you’re in Australia or New Zealand, you can help epidemiologists keep track of influenza and Covid by answering a very short weekly questionnaire. I’ve been doing this for a few years, and it takes about 15 seconds to click through the multiple choice responses.
https://info.flutracking.net

2024-04-24 00:45:32

Heard on the radio this morning: “M*sk is a free speech absolutionist.” [sic] I guess that entails an absolute right to be absolutely forgiven for saying absolutely anything.

2024-04-22 23:17:52

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@npub1knz…c73p
–3/2 is the dot product between two nearest neighbours among the set of points on the hyperboloid whose 2X2 matrices have Eisenstein integer entries.

2024-04-22 14:44:47

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@npub1knz…c73p
Right, sorry, I was confused about that. I’ll see if I can figure out the correct distance between the hexagon centres.

2024-04-21 07:26:26

No smooth curve that lies on a sphere can contain an inflection point (a point where the curvature is zero).
But on a surface of constant negative curvature, like this tractroid, no such obstacle exists, and every non-meridian geodesic on the tractroid has 2 inflection pts (black).
https://media.mathstodon.xyz/media_attachments/files/112/308/018/651/774/660/original/8556afd6712d6131.png

2024-04-15 13:10:45

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@npub1psd…9sr7 I like the line that article quotes from a Nicholas Ray movie, Wind Across the Everglades:
"the only tree that carves its initials into you."

2024-04-09 07:02:48

My new novel MORPHOTROPHIC is available now!
You can read the first two chapters here:
https://www.gregegan.net/MORPHOTROPHIC/00/MorphotrophicExcerpt.html
https://media.mathstodon.xyz/media_attachments/files/112/239/978/574/551/730/original/b383977da3c0b966.png

2024-04-04 13:48:24

It’s 30 years this month since PERMUTATION CITY was first published. But of course, all the same letters had been present in other books for centuries before, they just hadn’t been read in that order.
Excerpt at:
https://www.gregegan.net/PERMUTATION/Excerpt/PermutationExcerpt.html
https://media.mathstodon.xyz/media_attachments/files/112/213/257/528/650/020/original/14ce7cc2e2086142.jpg

2024-03-27 01:26:14

You can read the first two chapters of my new novel MORPHOTROPHIC here:
https://www.gregegan.net/MORPHOTROPHIC/00/MorphotrophicExcerpt.html
https://media.mathstodon.xyz/media_attachments/files/112/167/411/609/335/313/original/f008e88df993056e.png

2024-03-26 17:32:10

My new novel MORPHOTROPHIC will be published on 9 April.
Amazon is now accepting preorders for the ebook; other venues will follow soon.
There will also be print-on-demand editions from Amazon available on 9 April, but they can't be pre-ordered.
https://www.amazon.com/dp/B0CZ46L396

2024-03-15 07:26:59

Of course you can estimate π by dropping needles on the floor, but it’s much more fun to do it by integrating the Gaussian curvature across the surface of any 3-holed doughnut, then dividing the result by –8.
https://media.mathstodon.xyz/media_attachments/files/112/098/515/987/368/510/original/2a8547ca26eafdc6.mp4

2024-03-07 12:51:08

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@npub1psd…9sr7 Is that a cover of Fad Gadget’s 1980 song? (AKA Francis John Tovey, sadly no longer with us.)

2024-03-02 02:52:51

“A supernova has been observed in great detail just 3.5 light years from Earth... and that's close!”
WTF, Science Show? The story itself is a perfectly reasonable account of the new evidence for a neutron star remnant for 1987A, 168,000 ly away, so ... ?
https://www.abc.net.au/listen/programs/scienceshow
https://media.mathstodon.xyz/media_attachments/files/112/023/827/450/045/919/original/cdeaa9984742fd54.png

2024-03-01 13:15:19

For French readers, Le Bélial' have just published translations of the three stories in my “Bit Players” series in a single volume:
Figurants virtuels
Triadique
Instanciation
https://www.belial.fr/legacy/a/greg-egan/instanciations
[The English versions are in my collection “Instantiation”, alongside 8 other stories:
https://www.gregegan.net/BIBLIOGRAPHY/Ebooks.html#Instantiation]

2024-02-29 08:55:40

If you think leap years are a nuisance, spare a thought for the poor people of Apophis as they struggle to prepare for the 2029 bug:
“Earth will perturb Apophis from an Aten-class orbit with a semi-major axis of 0.92 AU to an Apollo-class orbit with a semi-major axis of 1.1 AU.”

2024-02-22 12:42:05

The 19th century was a golden age for the differential geometry of surfaces. Gauss blazed the trail, and then many successors continued in the same vein in later decades.
One vast chapter of this work involved surfaces of constant negative curvature, like those shown below.
https://media.mathstodon.xyz/media_attachments/files/111/975/183/082/654/727/original/11b1af2c28409f25.mp4

2024-02-15 14:29:42

Yeow. Corporation suffers weird fantasy that it somehow doesn’t matter if it uses a hallucinating chatbot to supply information to customers because it can somehow wash its hands of whatever nonsense it says ... only to find out that the law doesn’t work like that.
“Air Canada, for its part, argued that it could not be held liable for information provided by the bot.
"In effect, Air Canada suggests the chatbot is a separate legal entity that is responsible for its own actions. This is a remarkable submission. While a chatbot has an interactive component, it is still just a part of Air Canada’s website," Rivers wrote.
"It should be obvious to Air Canada that it is responsible for all the information on its website. It makes no difference whether the information comes from a static page or a chatbot."”
https://bc.ctvnews.ca/air-canada-s-chatbot-gave-a-b-c-man-the-wrong-information-now-the-airline-has-to-pay-for-the-mistake-1.6769454
H/T @npub1lau…uqs9

2024-02-09 10:47:37

The fallacies about bad software:
• If software would do harm, it won’t be deployed.
• If it *does* get deployed, the harm won’t be significant.
• If the harm *is* significant, it will quickly be identified, acknowledged and rectified.
Australia has gone through its own horrendous episode of persecution and suicides with the Robodebt scandal:
https://en.wikipedia.org/wiki/Robodebt_scheme
so I’m looking forward to watching the acclaimed dramatisation of the UK’s Horizon scandal:
https://en.wikipedia.org/wiki/British_Post_Office_scandal
“Mr Bates vs The Post Office”, which screens on Channel 7 / 7plus in Australia starting next Wednesday.
Needless to say, everyone rushing to insert LLMs into every conceivable nook and cranny of the commercial, scientific, administrative and judicial systems should be strapped to their chairs with their eyelids pinned open and made to watch this fifteen times.

2024-02-03 07:11:22

Me: Please simplify this horrible expression.
Mathematica: No, I have no idea how to make that any simpler.
Me: What if all those πs were just ... anything? Say, z?
Mathematica: Oh, sure, that can be simplified enormously!
Me: What if it was e instead of π?
Mathematica: Nope.
https://media.mathstodon.xyz/media_attachments/files/111/866/299/836/649/265/original/8a5fc7bcb5094dc0.png

2024-02-01 22:55:04

My novel “Scale” — a political thriller set in a world where people belong to seven groups that differ vastly in size — is included in the 2023 Locus recommended reading list.
https://locusmag.com/2024/02/2023-recommended-reading-list/
https://www.gregegan.net/SCALE/SCALE.html
https://media.mathstodon.xyz/media_attachments/files/111/858/685/563/690/212/original/98ca34319032e6ad.png

2024-01-30 03:41:19

"As is common practice, the image was resized to fit our specs. During that process, the automation by Photoshop created an image that was not consistent with the original.”
(A) Adobe, WTF?
(B) Users: either dump the app or learn to switch the “AI” off.
https://www.abc.net.au/news/2024-01-30/victorian-mp-georgie-purcell-altered-image/103403664

2024-01-25 14:25:50

“Today, ESA’s Science Programme Committee approved the Laser Interferometer Space Antenna (LISA) mission, the first scientific endeavour to detect and study gravitational waves from space.”
https://www.esa.int/Science_Exploration/Space_Science/Capturing_the_ripples_of_spacetime_LISA_gets_go-ahead

2024-01-19 11:15:37

Just bought a Cambridge University Press book from Amazon Aus. No ebk was available, so I thought I was buying a pbk printed by CUP.
But when it arrived: “manufactured by Amazon Aus.” So it was print-on-demand! The quality is fine, but I didn’t realise POD was so mainstream now.
I have POD editions of my own self-published titles, and I've seen them for some small press books, but this is the first time I’ve come across it for a book from a major publisher.

2024-01-11 03:59:46

Wireless keyboards shouldn’t need to be charged, they should just power themselves by trapping and metabolising spilt crumbs.

2024-01-05 03:36:27

A great series of articles by Chad Orzel (@npub12q2…2gs2) on the history of laser cooling:
https://physicsworld.com/a/cold-how-physicists-learned-to-manipulate-and-move-particles-with-laser-cooling/
https://physicsworld.com/a/colder-how-physicists-beat-the-theoretical-limit-for-laser-cooling-and-laid-the-foundations-for-a-quantum-revolution/
https://physicsworld.com/a/coldest-how-a-letter-to-einstein-and-advances-in-laser-cooling-technology-led-physicists-to-new-quantum-states-of-matter/
H/T @npub1qlr…p0gc

2024-01-04 12:50:41

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@npub1zdp…vqv8
If I wanted students to appreciate this property more, I’d give them a puzzle to solve where it has been taken away!
Let x be a number on a 12-hour clock, where we have changed the “12” to read zero.
For which choices of x will moving
(x-2)(x-3)
hours clockwise from zero take you back to zero?

2023-12-17 12:42:34

AppleScript is a very weird language.
https://media.mathstodon.xyz/media_attachments/files/111/595/810/973/669/378/original/f82e328b0b255f72.png

2023-11-29 23:30:54

"You could always have just written, 'Isla Gorge that way', but then if it didn't say, 'Trust me not Google', they would have said, 'How do they know?', because Google knows everything."
This farmer paid $1000 out of his own pocket for a sign to stop travellers getting lost, when Google Maps directed them across his property towards a tourist spot which could not actually be accessed by that route.
(Google finally fixed the problem after a journalist contacted them.)
https://www.abc.net.au/news/2023-11-30/grazier-makes-sign-trust-me-not-google-after-maps-confusion/103142386
https://media.mathstodon.xyz/media_attachments/files/111/496/397/639/893/340/original/515c480ff05f1725.png

2023-11-28 12:48:09

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@npub1zdp…vqv8
FWIW, if I had to memorise this I’d focus on:
2662
where the 2s tell me the 6 is repeated, and
4977
because 49 = 7 times 7
Then I’d think of the 5s as starting two parts of the sequence. That last bit, 57247, has a certain rhyming of the 7s, and also maybe thinking of the 727 and 747 planes would help me remember it.

2023-11-22 05:09:54

The volume of a ball of radius r in n dimensions is
B(n,r) = π^{n/2}/Γ(n/2+1) r^n
If you look at the volumes of the balls (blue circles) inscribed inside hypercubes with edge length 1 and volume 1, they go to zero as n gets larger:
lim n→∞ B(n,½) = 0
If you look at the volumes of the balls (red circles) that circumscribe each hypercube (of diagonal √n), they go to infinity:
lim n→∞ B(n,½√n) = ∞
But what if you always choose the radius of an n-ball so that its volume is exactly 1 (green circles)?
r₁(n) = Γ(n/2+1)^{1/n} / √π
This gives us B(n,r₁(n)) = 1
It turns out that:
lim n→∞ (r₁(n) - √[n/(2eπ)]) = 0
In other words, r₁(n) is asymptotic to a multiple of √n, so it approaches a fixed ratio with the length of the diagonal of the hypercube with the same volume.
https://media.mathstodon.xyz/media_attachments/files/111/452/398/135/656/733/original/00bbe26ae60909af.mp4

2023-11-22 05:02:49

2023-11-19 14:22:10

- reply

@npub1zdp…vqv8 Right! An “n-cube” means the equivalent of a cube in n dimensions; a “unit n-cube” means it has edges of length 1.

2023-11-19 14:02:25

The probabilities that if you pick two points at random in a unit n-cube they’re less than a distance 1 apart.
Equivalently, the average volume of the intersection between a unit n-ball with centre chosen at random within the n-cube, and the n-cube.
https://media.mathstodon.xyz/media_attachments/files/111/437/577/921/195/916/original/70ed4d40368244db.png

2023-11-05 11:53:38

Looks like my web site will be down for the rest of November, because, err, someone decided to burn through my monthly quota in the last 6 hours.
(The entire web site is about 1.2Gb, so this is either a weird malicious bot attack, or some kind of web crawler stuck in a loop.)
*Edit: Thanks to @npub1hkd…rpzu I just learned that a GIF-heavy page of animations on my site got featured on Hacker News, so ... not malice, just ten times more traffic in a few hours than I usually get in a month.
https://media.mathstodon.xyz/media_attachments/files/111/357/800/137/136/174/original/69281771e968b41b.png

2023-10-17 12:51:16

Enjoying “An Immense World” by Ed Yong, on animal senses. I think I heard once before that scallops have up to 200 eyes with mirrors made from guanine crystals, but failed to be sufficiently amazed at the time, so I’m glad to have been reminded.

2023-10-10 12:38:17

Me: Now I just have to spend ~$300 to get light fittings in my new ceiling so I don’t have to keep illuminating 3 rooms with one desk lamp.
Electrician: Your fuse box predates Tutankhamun and no one can touch your wiring until everything is upgraded, that will be $3000 thanks.

2023-10-08 12:37:46

Calling the spacecraft that visits the asteroid Psyche, umm, Psyche, seems both confusing and unimaginative. Surely they could have come up with a better name? Then again, the most obvious mythic choice, Cupid, is also the name of a moon of Uranus.

2023-10-08 05:46:55

Take a 600-cell in 4D with 120 vertices ±v_i, i=1…60
Define F(x)=𝚷_i v_i·x
Stereographically project F from a 4-sphere to 3D, then Fourier-transform from momentum space to position space.
Result: this hydrogen wave function, with energy level n=61.
More at:
https://www.gregegan.net/SCIENCE/SymmetricWaves/SymmetricWaves.html
https://media.mathstodon.xyz/media_attachments/files/111/197/803/320/661/908/original/544ecb5078253e2d.mp4

2023-10-02 12:07:11

Have they fixed the bugs in Spotlight so that it will actually find all the files that contain a word you’re searching for?
Probably not, but at least the search bar has been made more rounded, so not finding the file you were looking for will be more aesthetically pleasing.
https://media.mathstodon.xyz/media_attachments/files/111/165/334/619/650/012/original/05f1d9a59912163e.png

2023-10-01 04:06:04

An engrossing account of both outright fraud and incredibly poor science in behavioural psychology over the last few decades. (Remember “power poses”? People on literally higher ground are more “prosocial”? Clairvoyant detection of erotic images ... ?)
https://www.newyorker.com/magazine/2023/10/09/they-studied-dishonesty-was-their-work-a-lie

2023-09-27 08:28:26

- reply

@npub1knz…c73p
The element has order n in PSL(2,F), and order 2n in SL(2,F); I don’t know if that makes things make more sense!

2023-09-27 08:05:12

It’s cool that
x = 1/(ϕ-(1/(ϕ-(1/(ϕ-(1/(ϕ-(1/(ϕ-x)))))))))
where ϕ is the golden ratio,
x = 1/(√2-(1/(√2-(1/(√2-(1/(√2-x)))))))
and
x = 1/(1-(1/(1-1/(1-x)))).
But why?
Consider the matrix:
cos θ -sin θ
sin θ cos θ
which rotates by θ, so call this R.
Every matrix is a zero of its own characteristic polynomial, so:
(I cos θ - R)^2 + (I sin θ)^2 = 0
R^2 = (2 cos θ) R - I
Now, pick any vector v, and define:
w = -R v
Then:
R v = -w
R w = -R^2 v
= v - (2 cos θ) R v
= v + (2 cos θ) w
This tells us that if we change to the basis {v,w}, the matrix for R becomes:
0 1
-1 2 cos θ
which we will call S.
R and S are conjugate matrices; they do the same thing, but they just describe it in different bases.
Suppose we set θ to π/n. Then:
R^n = -I
so:
S^n = -I
Now, any invertible 2×2 matrix:
a b
c d
can be used to define a rational function:
f(x) = (a x + b)/(c x + d)
If we *compose* the functions we get from two matrices, the result is the same as *multiplying* the matrices.
The function for -I is just:
f(x) = (-x+0)/(0x-1) = x
So the equation satisfied by S:
S^n = -I
means that if we take the function corresponding to S:
0 1
-1 2 cos θ
f(x) = 1/(2 cos θ - x)
and compose it with itself n times … we just end up with x.
The formulas at the top of this post are saying this for n=5, n=4 and n=3.

2023-09-21 03:36:10

“When I’m not thinking about the mysteries of the universe, I’m thinking about how to make our instruments survive and how to prevent musk ox from toppling our antennas.”
Great interview in @npub1cwu…wkw2 with an adventurous experimental cosmologist.
https://www.quantamagazine.org/the-experimental-cosmologist-hunting-for-the-first-sunrise-20230920/

2023-09-19 12:13:40

Death: Come with me now!
Me: But there are cakes on this list of cakes I haven’t eaten. Can’t I finish eating all the cakes?
Death: OK, sounds fair. Wait … what’s a “dynamic list”?
Me: Oh, just some silly Wikipedia jargon, don’t worry about that.
https://en.wikipedia.org/wiki/List_of_cakes

2023-09-14 04:25:14

The stuntmeisters at Virgin who took a few hominin bones into almost-space really missed their chance; they should have collaborated with the Mexican fraudster and touted them on their return as “ancient extraterrestrial remains”.
https://www.nature.com/articles/d41586-023-02882-1

2023-09-11 08:36:33

Postal voting applications are now open for Australia’s Indigenous Voice referendum:
https://aec.gov.au/referendums/vote/postal-voting.html