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I got an email from someone asking for my "Essential Trigonometry for Calculus" cheat sheet, which I give to my calculus students. So, I thought I'd put it on GitHub for anyone to download (compiled PDF and source code). github.com/divisbyzero/Essenti

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@bibliolater @ai I cannot for the life of me imagine why lawyers still do this. There was that Mata v. Avianca case back in 2023 where a lawyer got flamed by the court for doing it, and ok, I have a little sympathy for him because he probably sincerely thought that ChatGPT was a fancy natural-language search interface. Under those circumstances it was an understandable error, though it's NEVER ok to cite things without checking that the citation supports the proposition you're citing it for even if you're copying out of a treatise or another case, so the guy deserved what he got. However, one of the things he got was a vast amount of mainstream media exposure, and at this point this has come up so often that there's really no excuse for not knowing how bad an idea it is. There's a guy in France who's trying to keep track of all the times it's happened; his database is up to 139 entries, and I'm sure there are a lot of cases he doesn't know about.

damiencharlotin.com/hallucinat

🇺🇸 :youtube: **When Does US Debt Become Genuinely Bad?**

“_The U.S. national debt is on its way to $30 trillion dollars and is projected to be more than 100% of GDP at the end of this year. So is that… bad?_”

length: seven minutes and thirty-five seconds.

🔗 youtube.com/watch?v=Xi7RvweuIU.

@economics

🇬🇧 💻 **Lawyers face sanctions for citing fake cases with AI, warns UK judge**

“_A senior judge lambasted lawyers in two cases who apparently used AI tools when preparing written arguments, which referred to fake case law, and called on regulators and industry leaders to ensure lawyers know their ethical obligations._”

🔗 reuters.com/world/uk/lawyers-f.

@ai

Towering tornadoes of plasma the size of planets dance over the Sun's surface in this timelapse from the Solar Dynamics Observatory spacecraft.

Credit: NASA GSFC/SDO

"AI companies claim their tools couldn't exist without training on copyrighted material. It turns out, they could — it's just really hard. To prove it, AI researchers trained a new model that's less powerful but much more ethical. That's because the LLM's dataset uses only public domain and openly licensed material."

tl;dr: If you use public domain data (i.e. you don't steal from authors and creators) you can train a LLM just as good as what was cutting edge a couple of years ago. What makes it difficult is curating the data, but once the data has been curated once, in principle everyone can use it without having to go through the painful part.
So the whole "we have to violate copyright and steal intellectual property" is (as everybody already knew) total BS.

engadget.com/ai/it-turns-out-y

Race, ethnicity don’t match genetic ancestry, according to a large U.S. study
science.org/content/article/ra
Data from the All of Us program confirm what many geneticists have long promoted

Full paper here sciencedirect.com/science/arti (paywalled)

🇺🇸 **Is It Really The End Of The Bromance?**

Just arrived home after spending the day away from the news. It seems that the bromance that was the Trump-Musk relationship has ruptured. Who could have envisaged this outcome at the start when all those hundreds of millions of dollars were first donated by Musk to Trump's MAGA presidential campaign?

🇺🇸 "Rejected" or ejected?

Gift Articles  
Revealed: Elon Musk wanted to stay in White House but was rejected https://www.telegraph.co.uk/gift/93ea18ab2ba8f028

🇬🇧 **Five outstanding manuscripts acquired for the nation**

“_Together, these manuscripts shed exceptional light on the study of Hebrew by Christian monks in medieval England, on the administration of a medieval English town, and on spiritual devotion in medieval England and Ireland._”

🔗 blogs.bl.uk/digitisedmanuscrip.

@medievodons @histodons

**Nearly 40% of the world’s glaciers are already doomed, scientists say**

"_Researchers estimate glaciers will eventually lose 39% of their mass relative to 2020, a trend that is already irreversible no matter what comes next and will likely contribute a 113-millimeter increase to global sea level rise._"

🔗 edition.cnn.com/2025/06/02/cli.

@climatechange @science

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