John C. Baez

I still saw this in my feed, so that's good.

👍

Yes, this is the easy way to see rotations as points in a ball of radius π. A vector v in ℝ³ tells you to rotate clockwise by an angle ||v|| around that vector - but when ||v|| reaches π you'd get the same rotation by rotating π around the opposite vector.

But if you say "a ball with each point on its surface glued to the opposite point", people may say WHAT THE HELL???

I feel journalists don't want that. As a blogger, that's exactly what I *do* want. You may be able to figure it out. But if you've got questions, I'm happy to answer them.

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I guess that's why I'm not a journalist. If you say "a complicated shape that lives in nine-dimensional space", most people will feel this is utterly beyond their powers to understand. And in a way, that's relaxing: it means math is only for geniuses, not us, so we can stop thinking.

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I'd rather say

"The group of all rotations of a ball in space, known to mathematicians as SO(3), is itself a ball with each point on its surface glued to the opposite point."

If you're gonna scare people, I feel you might as well scare them with a puzzle they can actually chew on.

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The article says:

"The group of all rotations of a ball in space, known to mathematicians as SO(3), is a complicated three-dimensional shape that lives in nine-dimensional space."

That makes SO(3) sound more complicated than it really is!

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What Are Lie Groups? | Quanta Magazine By combining the language of groups with that of geometry and linear algebra, Marius Sophus Lie created one of math’s most powerful tools.

But what is a Lie group? This Quanta article does a pretty good job of explaining the basic idea.

I have one quibble, though. (Where would mathematicians be without quibbles?)

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www.quantamagazine.org/what-are-lie...

Lie groups let us describe symmetries that can vary continuously, not just discretely. Noether's theorem shows how these continuously varying symmetries give conserved quantities like energy, momentum, angular momentum and others.

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Lie groups and Noether's theorem are the tools that let 20th-century physicists wield *symmetry* as a powerful tool to study crystals, molecules, atoms, and elementary particles.

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However, the main thing is to do whatever works for you (where "you" = anyone), and not to be drowning in half-written, unreleased drafts. There's something really liberating and energizing to getting a thought out into the world.

If you build it, they will come.

That's another option. I just don't have thoughts that fit well in 300 characters. (I guess they would if I were talking only to myself, and maybe I should do that.) I could chop thoughts into slices, but over on Mathstodon I get 1729 characters per post and I get more engagement.

In blogging, the perfect is the enemy of the good. I urge to start writing a cool idea as soon as you have it, keep polishing the writing as you clarify the idea in your own mind, and when it's half-way decent put it out there. Twice a week for a year and people will eagerly await your next post.

I didn't rhapsodize over how odd it is that a system in one state can, with some probability, be in some other state.

But I stated it both that way and also more "operationally" as "you put it in one state, check to see if it's in some other state, and with some probability you get "yes"."

Blog!

The Linear Pottery Culture ended around 5000 BC... with grim signs of something like a genocide: mass graves, with fractured skulls and beheaded skeletons. Nobody knows why, though there are theories.

Details here: archive.is/v4HYp

YouTube video by John Baez Standard Model - Part 4: Quantum Physics

The main rule of quantum mechanics answers: if a system is in one state, what's the probability that it's in some different state? Shockingly, it's not zero!

I explain this with minimum jargon, and fear not: I say what all the funky symbols here mean: ∈, ℂᵈ, etc.

www.youtube.com/watch?v=Y0a8...

YouTube video by Rick Beato Why Adults Can't Develop Perfect Pitch

At least one expert says no, it's impossible to learn absolute pitch. Also people who have it almost always lose it as they age.

www.youtube.com/watch?v=816V...

Wow, you're really getting into this stuff! Great notes!!!

Similarly, logicians go around using logic to argue that they're being logical.

The largest fundamental science agency in Europe will save €1.4 million annually by breaking free from Clavariate Analytics' huge databases of references and citations.

"We have worked for free to lock ourselves collectively into a paid system", one head of the CNRS explains - but no more! 🎉

The more you know about something, the more teaching it can serve as an excuse to ponder it, strengthen and question your knowledge, learn more, and pass along the coolest facts to a new generation - all of which are really satisfying.

Sounds worth trying: people may or may not like math teachers but at least they know they've seen one!

Has anyone here tried it?

I never specialized very much, though I tried to learn lots of math and fundamental physics.

I had a very relaxed and happy life - until I retired and became even *more* relaxed. But I was not trying to do another career (like writing SF, or whatever) on top of teaching. For me it's always been important to have many days where I get to do whatever I want that day - at least for a while.

I never felt teaching took too much time. I taught either 1 or 2 courses per semester. Sure, grading midterms and finals for large undergrad courses could be hell. But teaching itself was fun, and I had summers free to do whatever I wanted (as long as it was writing papers and publishing them).

You could say that and then "Just kidding, I'm a mathematician!" I bet that would be a good conversation starter.

No, but that reminds me of the old joke:

I was hitch-hiking. A few miles after I got picked up, the driver asked if I wasn't afraid that he might be a serial killer.

"No, it would be incredibly unlikely to have two in the same car."

Then he said "architect" - and his new ride turned out to be an architect.

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Newspaper headline: 'We hate math', say 4 in 10 - a majority of Americans

Saying you do math is a bad conversation starter. So when a mathematician friend of mine went on a hitchhiking trip, he told each ride that his profession was that of the *last* ride he'd gotten! He learned how to ask lots of good questions so he could simulate different professions.

But...

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