It's time to have that talk with your kids. About quantum mechanics:
Notices by John Carlos Baez (johncarlosbaez@mathstodon.xyz)
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Wednesday, 01-May-2024 06:18:24 UTC John Carlos Baez -
John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Tuesday, 16-Apr-2024 13:11:08 UTC John Carlos Baez Mathematicians describe points on the plane with coordinates (x,y). The first coordinate says how far 𝑎𝑐𝑟𝑜𝑠𝑠 you go and the second says how far 𝑢𝑝 you go. Then they describe entries of a matrix Mᵢⱼ with indices where the first says how far 𝑑𝑜𝑤𝑛 you go and the second says how far 𝑎𝑐𝑟𝑜𝑠𝑠 you go.
In each case I've had teachers who insinuate that this is the only reasonable thing to do and you'd have to be nuts to dream of doing anything else.
I think some teachers don't distinguish between facts and conventions. Actual facts of mathematics are worth thinking about - understanding them more and more deeply is a never-ending quest. But for arbitrary conventions, you should just memorize them and move on.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Friday, 01-Mar-2024 17:12:55 UTC John Carlos Baez @mcnees - I think you might enjoy this book by Penrose and Hawking. It's much more advanced, but still an attempt to explain mainly in words what's going on with general relativity and quantum gravity. Warning: Penrose's sections are often very speculative. But Hawking does things like explain his famous black hole radiation calculation, the Penrose-Hawking singularity theorems, and more.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Tuesday, 30-Jan-2024 03:10:35 UTC John Carlos Baez @dom - we don't laugh at Neolithic stone circles like Stonehenge. At least I don't. I find them impressive.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Wednesday, 24-Jan-2024 17:27:38 UTC John Carlos Baez The music director of Leipzig died in 1722, so the city council held an audition for his replacement. The winner was Georg Philipp Telemann. He went back to Hamburg, where he worked, and demanded a raise. They gave him the raise, so he stayed in Hamburg.
Next they tried to hire Christoph Graupner, one of the foremost composers of the day. He worked in Darmstadt, but the city wouldn't let him go. Back then you often needed permission from your employer to get a new job.
One of the Leipzig city councilors said: "Since the best men cannot be obtained, we must make do with the mediocre."
So they hired Johann Sebastian Bach.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Monday, 01-Jan-2024 03:44:25 UTC John Carlos Baez @mcnees - it's 2¹⁰+10³.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Monday, 25-Dec-2023 16:25:05 UTC John Carlos Baez For my Christmas present this year I hope someone fixes this website - or shuts it down. This symbol does not mean "approximately equal to" - that's
≈
This symbol means "isomorphic to", or "congruent to". I cannot stand another year with this misinformation ruining my Google searches for the Unicode and HTML for "approximately equal" to.
https://www.fileformat.info/info/unicode/char/266f/index.htm
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:35:13 UTC John Carlos Baez @Garrett - P and T commute in many situations, e.g. in a scalar field theory. I don't know why they'd anticommute...
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:34:42 UTC John Carlos Baez @Garrett - that's really interesting! I'll have to think abot whether these 8 double covers are related to the 8 in the 10-fold = 8+2-fold way. That is, whether these 8 covers are at all related to the 8 Morita equivalence classes of real Clifford algebras. It's sure not obvious, but it's tempting!
It's VERY weird that (some?) quantum field theorists are using a cover that's neither Pin(1,3) nor Pin(3,1), since pinors work for those pin groups.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 21-Dec-2023 14:34:38 UTC John Carlos Baez @Garrett - you may be interested in Cecile DeWitt-Morette's article on CPT and the physical difference between Pin(1,3) and Pin(3,1):
https://arxiv.org/abs/math-ph/0012006
Teaser:
"In a neutrinoless double beta decay, the neutrino emitted and reabsorbed in the course
of the interaction can only be described in terms of Pin(3,1)"not Pin(1,3).
You can skip Section 0 until it matters.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 14-Dec-2023 16:46:36 UTC John Carlos Baez @mcnees - and I believe "Boltzmann's constant" k was introduced in the same paper by Planck where he introduced what we now call "Planck's constant" - a nice confirmation of the deep unity between statistical mechanics and quantum mechanics.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Sunday, 10-Sep-2023 16:13:53 UTC John Carlos Baez @waldi @gregeganSF - it sounds like it's not photovoltaic, i.e. does not use solar cells that convert light directly into electricity:
"Unlike a traditional solar array, the Carwarp project uses an array of mirrors which are arranged to face a tower.
Sunlight is concentrated at the top of the tower, heating up the solar modules that turns around a third of the captured sunlight into electricity."
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Wednesday, 12-Jul-2023 13:37:05 UTC John Carlos Baez @mcnees - I remember enjoying that on Twitter. Glad you're here now.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Sunday, 18-Jun-2023 17:04:26 UTC John Carlos Baez @internic @mcnees - yes, Woit, Smolin and Hossenfelder aren't antivaxxers; they actually know quite a lot of physics and they like to complain about string theorists and fans of supersymmetry hogging all the funding and making exaggerated claims. There are also lots of people who don't know much physics (at least not general relativity and quantum field theory) and believe there's a grand conspiracy to suppress or ignore new ideas - almost always *their own* new ideas. I can easily imagine many of the latter are antivaxxers, but I haven't been keeping track.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Sunday, 11-Jun-2023 18:08:15 UTC John Carlos Baez One reason we need to preserve biodiversity: over billions of years, life has accumulated amazing knowledge, which we are scarcely beginning to tap.
For example, 'glass sponges' are sponges living in the mud at the ocean floor which have beautifully optimized skeletons made of glass: that is, silica. This one is called Venus’ Flower Basket. As we zoom in, we see more and more structure. Its lattice of silica has diagonal bracings for extra strength.
But the true beauty of it only becomes clear under a microscope!
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Tuesday, 16-May-2023 01:52:38 UTC John Carlos Baez The surprising part is not that math grad students named Cox and Zucker would come up with the idea of writing a paper together just as a joke.
It's that they followed through after they were professors, and wrote a paper that was actually rather significant.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Sunday, 14-May-2023 02:11:30 UTC John Carlos Baez @gmusser - 4.6 billion years of floating in space, only to land in New Jersey.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Friday, 03-Mar-2023 04:38:55 UTC John Carlos Baez Wayne Shorter, August 25, 1933 – March 2, 2023, was an absolutely amazing jazz sax player. Endlessly inventive, he had a rich tone and catchy compostions that makes his music easy to love even when he's exploring advanced harmonic concepts.
Let me try linking to a few of my favorite pieces of his.
Here he is with Miles in 1967.
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John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Friday, 10-Feb-2023 00:16:08 UTC John Carlos Baez @mcnees - wow, I didn't know that! I have that book, and love it. Just seeing the cover provokes a Pavlovian response.