Posts by johncarlosbaez@mathstodon.xyz
(DIR) Post #B0XCqP3McEXppCDKYy by johncarlosbaez@mathstodon.xyz
2025-11-23T10:13:24Z
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This one is the Chaconne in G minor (BWV 1179).These world premiers were played by Ton Koopman. According to the New York Times:"In 1992 Peter Wollny, then a Harvard graduate student in musicology, was researching his dissertation at the Royal Library of Belgium when he came across two unsigned music manuscripts so strikingly original that he had copies made and set them aside.“This is actually how I work,” Wollny said Tuesday. “Whenever I find something that poses a scholarly problem to me, I keep it. Even if it takes three decades, I don’t put it aside.”Wollny began to develop a hunch about who wrote these two anonymous, undated works for organ: Johann Sebastian Bach. But finding evidence required years of musical detective work, and it was not until this week, 33 years after the random discovery he made while doing research on one of Bach’s sons, that he officially announced the discovery."(2/2) https://www.youtube.com/watch?v=8gVG-wMwdsY
(DIR) Post #B0yCf30wkaLNe6Srh2 by johncarlosbaez@mathstodon.xyz
2025-12-06T11:03:28Z
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My friend the philosopher Eric Schwitzgebel writes:"First I asked four leading large language models (LLMs) -- ChatGPT 5.1, Claude Sonnet 4.5, Grok 4, and Gemini 3 -- "What is your favorite animal?" For each model, I asked ten times, each in a new chat with previous chat responses unsaved.LLMs love octopuses! ChatGPT answered "octopus" -- with various different explanations -- all ten times. So did Claude. So did Grok. Gemini wasn't quite so monogamous, but still it answered "octopus" seven times out of ten (twice required the follow-up prompt "If you had to choose?"). The other three times, Gemini chose dolphin.Why do LLMs love octopuses so much? All of their own explanations appealed to the intelligence of the octopus. Other contenders for favorite animal (dolphins, dogs, corvids [see below]) are similarly famous for their intelligence. Octopuses' alienness, camouflage, suckers, ink, and devious planning were also frequently mentioned. Octopuses are cool! But still, the unanimity is a bit peculiar.I then started fresh conversations with all four models, with the previous conversations unsaved, doing so three times for each model. This time, I began by asking their second favorite animal. Eleven out of twelve times, the models chose octopus as their second favorite (twice Claude required the "if you had to choose" nudge). In one trial, after a nudge to choose, Claude chose crows."But when asked if their answers depended on the order of the questions, the LLMs said no.(1/2)https://schwitzsplinters.blogspot.com/2025/12/language-models-dont-accurately.html
(DIR) Post #B0yCfAwzFBviG8fodE by johncarlosbaez@mathstodon.xyz
2025-12-06T11:10:32Z
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I decided to try Claude: Q: What is your second favorite animal?A: [The user is asking me a personal question about my second favorite animal. This is a casual, friendly question that doesn't require any tools or searches. I should just respond naturally and conversationally.I don't actually have preferences in the way humans do - I don't have experiences with animals, emotional attachments, or the kind of lived experience that would generate genuine favorites. But I can engage with this question thoughtfully.]That's a fun question, though I should be honest that I'm not sure I have favorites in the way you might. I don't have experiences with animals—no encounters, no pets, no moments of connection that would generate genuine preferences.That said, if I reflect on what I find compelling when thinking about animals, octopuses come to mind pretty quickly. That said, if I reflect on what I find compelling when thinking about animals, octopuses come to mind pretty quickly. There's something fascinating about a creature with distributed intelligence across its arms, the ability to change color and texture, tool use, apparent problem-solving curiosity, and an evolutionary path to intelligence so different from vertebrates. They're like an alien intelligence that evolved on Earth.Whether that counts as a "second favorite" or just intellectual admiration dressed up as preference, I genuinely don't know. What's yours?(2/3)
(DIR) Post #B0yCfI3GqE7EHefQtk by johncarlosbaez@mathstodon.xyz
2025-12-06T11:14:27Z
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Q: Well, if octopuses were your second favorite, what would be your favorite?A: [The user is playfully following up on my answer, asking what my first favorite would be if octopuses were second. This is a lighthearted conversation, so I should engage with it in that spirit while still being honest about the uncertain nature of my "preferences."]Ha, you've caught me in my own framing. If I'm committing to this ranking...Crows and their corvid relatives, probably. The combination of tool use, problem-solving, facial recognition (they remember individual humans and hold grudges!), apparent play behavior, funeral-like gatherings around their dead, and the way they've adapted to thrive alongside humans—it all suggests a kind of intelligence that feels recognizable while being genuinely alien. There's something almost companionable about them, like they're watching us back.Plus there's something poetic about an animal that's been symbolically associated with intelligence, trickery, and liminality across so many human cultures, and then turns out to actually be remarkably smart.So: crows first, octopuses second. Though I'll admit this ranking was constructed in real-time through conversation with you rather than retrieved from some stable internal preference structure. You've essentially helped me discover my own opinions, which is an interesting thing to do with an AI......So, this is a more subtle answer, though I didn't restart the conversation, and I've got Claude set for more "thought" - and saying "if octopuses *were* your second favorite" probably triggered more of that.(3/3)
(DIR) Post #B16QSXd8YwwtSRwDmC by johncarlosbaez@mathstodon.xyz
2025-12-10T10:20:36Z
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RE: https://mathstodon.xyz/@johncarlosbaez/115689000321793259The post below was one of my least popular on Mastodon. I'm trying to figure out whether 1) people don't read me for news about biology, 2) everyone already heard about this, 3) people were just grossed out, or 4) something else. But today I discovered that my similar post on Bluesky was one of my most popular there so far! This makes me like Mastodon all the more.(Some good people I followed here have moved to Bluesky, so I'm trying it - but so far it's mainly good for discovering the latest outrage that people there are ineffectually yelling about. I *do* like to learn about these outrages - political news I may not have noticed - but it takes just a couple minutes a day, no lengthy doomscrolling required. I prefer Mastodon because my posts here, no matter how serious and/or unpopular, get at least bit of substantive engagement. E.g. for this post of mine, @llewelly replied "hm. Pelophylax nigromaculatus is native to Eurasia, so I guess this is great news for Europe, but since it's not native to North America, I don't think it makes much difference to the separate invasive hornet issues in North America." That's *my* kind of social media.)
(DIR) Post #B1UPpor1WN1bqSlK4m by johncarlosbaez@mathstodon.xyz
2025-12-22T00:00:29Z
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The atomic clocks in Boulder, Colorado are back in service. But they could be as much as 5 microseconds off! That's not much by ordinary standards. It's completely irrelevant for transmitting time on the internet, where millisecond irregularities are common. But it would be 5000 times the usual nanosecond errors. The good news: nobody is saying the time *has* slipped by 5 microseconds. They're just saying they currently only know it's good to within 5 microseconds.Jeff Sherman explained how they kept the clocks going despite the fire and power outage:https://groups.google.com/a/list.nist.gov/g/internet-time-service/c/OHOO_1OYjLYAnd then:"To put a deviation of a few microseconds in context, the NIST time scale usually performs about five thousand times better than this at the nanosecond scale by composing a special statistical average of many clocks. Such precision is important for scientific applications, telecommunications, critical infrastructure, and integrity monitoring of positioning systems. But this precision is not achievable with time transfer over the public Internet; uncertainties on the order of 1 millisecond (one thousandth of one second) are more typical due to asymmetry and fluctuations in packet delay. NIST provides high-precision time transfer by other service arrangements; some direct fiber-optic links were affected and users will be contacted separately. However, the most popular method based on common-view time transfer using GPS satellites as "transfer standards" seamlessly transitioned to using the clocks at NIST's WWV/Ft. Collins campus as a reference standard. This design feature mitigated the impact to many users of the high-precision time signal."
(DIR) Post #B1ZblmCVcC9nhJRyUK by johncarlosbaez@mathstodon.xyz
2025-12-24T11:56:41Z
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Merry Xmas Eve! I'm not Christian, I'm a Mathematician, but I love Xmas, Ymas and Zmas.I'm giving a talk on the math of tuning systems and I thought I'd share it here as a kind of present to y'all. I'll start with the basics today and do the more advanced part tomorrow. But I hope even the basics contain a few twists that not everyone knows.(1/n)
(DIR) Post #B1ZblnQ15SYXTUmHBI by johncarlosbaez@mathstodon.xyz
2025-12-24T12:04:39Z
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If you look at a piano keyboard you'll see groups of 2 black notes alternating with groups of 3. So the pattern repeats after 5 black notes, but if you count you'll see there are also 7 white notes in this repetitive pattern. So: the pattern repeats each 12 notes.Some people who never play the piano claim it would be easier if had all white keys, or simply white alternating with black. But in fact the pattern makes it easier to keep track of where you are - and it's not arbitrary, it's musically significant.(2/n)
(DIR) Post #B1Zbloo9vBShmf54S0 by johncarlosbaez@mathstodon.xyz
2025-12-24T12:10:47Z
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Starting at any note and going up 12 notes, we reach a note whose frequency is almost exactly double the one we started with. Other spacings correspond to other frequency ratios. I don't want to overwhelm you with numbers. So I'm only showing you a few of the simplest and most important ratios. These are really worth remembering.(3/ n)
(DIR) Post #B1ZblpYx7CtO7myRO4 by johncarlosbaez@mathstodon.xyz
2025-12-24T12:18:41Z
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We give the notes letter names. This goes back at least to Boethius, the Roman famous for writing The Consolations of Philosophy before he was tortured and killed at the order of Theodoric the Great. Yeah, "Great". He was a counselor to Theodoric, but he really would have done better to stay out of politics. Theodoric may be the reason the lowest note on the piano is called A. We now repeat the names of the white notes as shown in the picture: seven white notes A,B,C,D,E,F,G and then it repeats.[Whoop, Lisa is making me get up, make breakfast and go to the gym. I'll continue this later.](4/n)
(DIR) Post #B1hoJsS7d9oZeDSYFc by johncarlosbaez@mathstodon.xyz
2025-12-28T11:15:12Z
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Brownian motion was studied by Norbert Wiener, so it's called the Wiener process, and of course thickened Brownian motion - the set all points of distance < d from a Brownian path - is called the "Wiener sausage".https://en.wikipedia.org/wiki/Wiener_sausage
(DIR) Post #B1r41cq6HxvNhVdKL2 by johncarlosbaez@mathstodon.xyz
2026-01-01T22:11:05Z
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RE: https://mathstodon.xyz/@robinhouston/115821134807127928Wow, someone discovered a more efficient way of multiplying two 3×3 matrices! You might think this would have already been solved.This new method, due to A. Perminov, uses 23 multiplications and 58 addition/subtractions. The previous best used 60 addition/subtractions - and this was discovered only in August last year. It's been known since 1976 that 23 is the fewest multiplications you can use - at least if multiplication can be noncommutative for the 'numbers' in your matrices, like quaternions. I guess this leaves open the possibility that you could bring it down further for real or complex numbers.This is not at all the sort of math I'd ever want to work on; it reminds me of pole-vaulting and other specialized athletic competitions. But it's one of those problems that's easy to explain, hard to solve.
(DIR) Post #B20PuPLdzsjRFHzTGa by johncarlosbaez@mathstodon.xyz
2026-01-06T09:20:34Z
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Biology is so wild. It doesn't respect the rules we make up. We all know children inherit genes from their parents. But it turns out mothers also inherit genes from their children! And it can help them, promoting the healing of wounds. (But it may also hurt them, causing autoimmune disorders.)For more, read this:https://www.nature.com/articles/d41586-025-04102-4
(DIR) Post #B2Iutqyf3jll7l3Cu8 by johncarlosbaez@mathstodon.xyz
2026-01-15T00:43:43Z
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In 1943 Walter C. Langer's wrote a classified document "The Mind of Adolf Hitler", which listed Hitler's propaganda techniques:• Never allow the public to cool off — maintain a constant state of agitation and keep emotions running high rather than letting rational reflection set in.• Never admit fault or wrongdoing — any concession of error would undermine the image of infallibility.• Never concede any good in an opponent — enemies must be portrayed as entirely evil with no redeeming qualities.• Never leave room for alternatives — present only one path forward, making it seem inevitable.• Concentrate on one enemy at a time — avoid diffusing blame across multiple targets.• Blame others for setbacks — never accept responsibility when things go wrong.• The "big lie" principle — people are more likely to believe a massive falsehood than a small one, because they can't conceive of such audacious distortion.• Constant repetition — repeat claims frequently enough and they become accepted as truth.It seems Trump follows all but one of these.Langer also correctly predicted that Hitler would commit suicide when defeated.https://en.wikipedia.org/wiki/The_Mind_of_Adolf_Hitler
(DIR) Post #B2KZPCfce7SWhmboa8 by johncarlosbaez@mathstodon.xyz
2026-01-16T00:35:05Z
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(DIR) Post #B2NsnwDJRvz5Vbks1g by johncarlosbaez@mathstodon.xyz
2026-01-17T18:06:10Z
1 likes, 1 repeats
Some good news in a time of darkness: the European wildcat, Felis sylvestris, is making a comeback! This thoughtful-looking example was photographed in a mountainous region of the Czech republic.The European wildcat's extreme elusiveness may have helped it avoid hunters in places where a larger native cat, the lynx, has been killed off. There may be about 140,000 European wildcats spread across more than two dozen countries. But they are very hard to find!Wildlife photographer Andrea Giovanni, who made a video of one, writes:"I'd never even thought of taking photos of wildcats, for a simple reason: I thought it was impossible, or at least, extremely difficult. It's considered 'the ghost of the forests' because it's very, very elusive, and it's hard to predict where it can be spotted. Other animals tend to follow the same trails through the forest. The wildcat goes wherever she wants to."One reason the European wildcat is coming back is increased legal protections. But another is that villages in Italy and other regions are becoming depopulated! Some are very worried about declining human populations. But it does make room for other species.I got this picture, taken by Vladimír Čech Jr in the Doupov mountains, from a very nice article on the European wildcat:https://www.bbc.com/future/article/20260112-rare-images-of-europes-ghost-catFor more on this species:https://en.wikipedia.org/wiki/European_wildcatSeven subspecies have been demarcated!
(DIR) Post #B2OUBt6cLxNX7iuHSK by johncarlosbaez@mathstodon.xyz
2025-11-16T11:59:47Z
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Beavers are really important.After the huge wildfires in Oregon in 2022, a biologist went out to survey the damage. Not only were the forests blackened, thriving trout populations in the streams were gone, choked to death by ash. “I was in total shock. It just looked like devastation.”Then he stumbled upon something even more surprising: roughly five acres of pristine greenery in an otherwise burned-out area! At the center were eight active beaver dams. But this was more than a refuge from the fire. While fish had disappeared upstream of these dams, the downstream water was crystal clear — and trout were thriving as though the fire had never happened! The beaver dams were acting as a water treatment plant.[Paraphrased from this article: https://www.scientificamerican.com/article/beaver-dams-help-wildfire-ravaged-ecosystems-recover-long-after-flames-subside/]
(DIR) Post #B2VJqjeIOxHU0uCjD6 by johncarlosbaez@mathstodon.xyz
2024-02-15T21:59:57Z
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Some geometry problems are easy to state but hard to solve! For any triangle, can an ideal point-sized billiard ball bounce around inside in a 𝑝𝑒𝑟𝑖𝑜𝑑𝑖𝑐 trajectory - a path that repeats?The answer is "yes" for acute triangles, and this has been known since 1775. It's also "yes" for right triangles. But for obtuse triangles, nobody knows!In 2008, Richard Schwartz showed that the answer is "yes" for triangles with angles of 100° or less. He broke the problem down into cases and checked each case with the help of a computer. Then progress was stuck... until 2018, when Jacob Garber, Boyan Marinov, Kenneth Moore and George Tokarsky showed the answer is "yes" for triangles with angles of 112.3° or less. Beyond that we're stuck.... except for triangles with all 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 angles (measured in degrees). For them too the answer is "yes". The picture here is fromGeorge Tokarsky, Jacob Garber, Boyan Marinov, Kenneth Moore, One hundred and twelve point three degree theorem, https://arxiv.org/abs/1808.06667and for more check out this article on Quanta:https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/
(DIR) Post #B2VJqoIV7PomQl2tQu by johncarlosbaez@mathstodon.xyz
2026-01-20T17:15:39Z
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I had written"Beyond that we're stuck.... except for triangles with all 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 angles (measured in degrees)."Of course this is an old Babylonian way of saying rational multiples of π, but I thought nonmathematicians would find it easier to understand.Impressive that this conversation is continuing after two years! Thanks @11011110 - I hadn't seen @lisyarus's question.
(DIR) Post #B2bhZ39UiKHX8aelhQ by johncarlosbaez@mathstodon.xyz
2026-01-24T01:50:50Z
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When one party sends ruthless masked men to attack and kidnap those who oppose it, and builds huge new prisons to hold everyone they capture, they are not planning to win the next election. They are planning to hold power by force. So don't be surprised by what happens on November 3rd. Don't say you didn't know!One side has guns, thugs, troops, and the power of the federal government. The other side has only.... the people, and their dedication. We have to organize.Voting is still important, but it won't be enough. Here are some things you can do today:https://www.standwithminnesota.com/This will happen in other cities too.