@Caution Sorry!

@JasonPerseus Good thing you haven’t attended my lecture on Gauss’s Law.

@yours_truly Did not know this!

You’ll never guess what’s behind all these high prices. (You absolutely will guess.)

https://www.theguardian.com/business/2024/jan/19/us-inflation-caused-by-corporate-profits

The 11yo had a Calvin and Hobbes book out, and I made the mistake of reading the one she dog-eared.

The pathological nature of the subsets of the ball used in the construction make it impossible to produce a truly faithful visualization of the decomposition and assembly process. But this video still manages to do a pretty nice job!

https://www.youtube.com/watch?v=s86-Z-CbaHA&t=675s&pp=2AGjBZACAQ%3D%3D

The trick is that the ball has to be broken up into pieces that have a well-defined mathematical meaning, but are pathological when you try to think about them in terms of concepts like volume.

The decomposition relies on the axiom of choice. There are other approaches to set theory without the axiom of choice that do not lead to the Banach-Tarski paradox.

Mathematician Alfred Tarski was born #OTD in 1901.

The Banach-Tarski paradox asserts that a ball in three dimensions can be decomposed into a finite number of pieces which, after translation and rotation, can be reassembled into *two* distinct copies of the original ball.

The paradox also works in more than three dimensions, but not in one or two without significant technical modifications.

“You should never be proud of doing what's right. You should just do what's right."

Watching the UNC-Syracuse game, happy to see ESPN talking about Charlie Scott’s legacy and Dean Smith’s involvement in the civil rights movement.

I think about this story all the time:

https://www.washingtonpost.com/sports/colleges/memories-of-dean-smith-linger-even-as-his-memory-sadly-fails-him/2014/03/01/fade81c0-a0ae-11e3-b8d8-94577ff66b28_story.html

BRB going to chase this whale. Should be back in no more than three days, tops.

https://www.bbc.com/news/av/world-asia-67959732

@glasspusher Thanks!

@jrdmb Thanks!!

Besides that Chandrasekhar story I just reposted, not much to talk about on January 11. No notable physicists associated with this date, afaik.

Oh, RIP Jennell Jaquays. One of the RPG greats.

He went on to explain that the answer to our question *might* be in a book or paper somewhere, but we'd learn a lot more if we figured it out ourselves.

He was right!

At that point, maybe my second year of grad school, I thought answers were found in papers and books. Bryce challenged me to come up with my own answer, which I did.

It was hard, but the calculation worked, and I published my first paper.

Thanks, Bryce.

So we went to Bryce and explained our problem. We had to argue with him for a while, to convince him that the question we were asking could possibly be relevant for anything. It took a very, very long time.

Finally, he growled "You know what your problem is? Too much book learning."

(Bryce sounded just like Charlton Heston. He could sound kind of intimidating.)

Bryce DeWitt also gave me the best piece of advice I ever got in graduate school.

I was working on a paper with another grad student, and we were stuck on a technical detail of a calculation. It was something we were sure Bryce had worked on at some point, but it wasn't written down in any books or papers we could find.

But there are a few things I want to mention. Though it's not what he is primarily known for, DeWitt was an advocate of Everett's "Many Worlds" interpretation of quantum mechanics. He did lots to popularize it among physicists.

Max Jammer was writing a book on the interpretations and history of QM, and told DeWitt he'd never heard of Everett. So DeWitt took it on himself to raise the profile of Everett's work.

In 1970 he wrote this popular article in Physics Today:
https://pubs.aip.org/physicstoday/article/23/9/30/427387/Quantum-mechanics-and-realityCould-the-solution-to

When DeWitt described a supernumber Z, he split it into two parts: Z = Z_b + Z_s.

The first term, Z_b, is a single complex number. It’s the simplest part of Z. But the second term, Z_s, has an infinite multitude of complex numbers hidden inside.

He refers to Z_b as "the body," and Z_s as "the soul." It's lovely.

(Complex numbers look like 𝛼 + i 𝛽, where i is the square-root of -1 and both 𝛼 and 𝛽 are just plain old real numbers. So it's sort of like that, but with a lot more numbers.)