John C. Baez's Blog, page 20

Runaway Supermassive Black Hole

Many galaxies have a ‘supermassive black hole’ at their center. These range from hundreds of thousands to billions times the mass of our Sun.

I was surprised to read that astronomers have found evidence for a supermassive black hole shooting out of its host galaxy. They’ve seen a long thin feature—apparently a ‘wake’ of shocked gas and young stars—stretching 200,000 light years from the galaxy’s center and ending in a bright object that’s putting out 100 million times more power than our Su...

Azimuth Project News

It’s time to update you on the Azimuth Project. This project started out in 2010 when I moved to Singapore, had more time to think thanks to a great job at the Centre for Quantum Technologies, and decided to do something about climate change—or more broadly, the Anthropocene.

But do what? You can read my very first thoughts here. I rounded up some interested people, many of them programmers from outside academia, and we started a wiki to compile relevant scientific information. We thought a ...

Dividing a Square into 7 Similar Rectangles

This is a continuation of my post Dividing a square into similar rectangles, in which I discussed this puzzle: if you partition a square into n similar rectangles, what proportions can these rectangles have?

Some people on Mathstodon put a lot of work into this and made some nice progress. But there’s been a surprising new twist, and I’m not even talking about the fact that the New York Times ran an article about this puzzle:

• Siobhan Roberts, The quest to find rectangles in a square, New York...

Category Theory Outreach Panel

They just don’t quit! Besides their Joy of Abstraction book club, the Topos Institute also has another way for you to start learning category theory. It’s called the CT Outreach Panel, and it’s happening on March 16 at 17:00 UTC.

Some of the best explainers of category theory in the world—Emily Riehl, Eugenia Cheng, Tai-Danae Bradley, Paul Dancstep and Oliver Lugg—will explain their approaches to the subject and answer questions.

You can submit questions here:

https://topos.site/ct-outreach-...

Upper Structures

 

Here Aimee Nolte shows us some ways we can stack a triad on top of the dominant 7th chord

1 3 5 ♭7

She plays this chord in C so it’s called C7. The 5th is so obvious and bland she often leaves it out, giving what’s called a ‘shell voicing’

1 3 ♭7

Then she puts a triad on top of this, giving ‘upper structures’ like a 9th, 11th or 13th.

This is right at my level now, so I like it. Let me say a bit about it.

The first one she plays is called a ‘C dominant 13 flat 9’. This amounts to

1 3 ♭7...

Talk on the Tenfold Way

There are ten ways that a substance can have symmetry under time reversal, switching particles and holes, both or neither. But this fact turns out to extend far beyond condensed matter physics! It’s really built into the fabric of mathematics in a deep way.

I gave a talk on this at Nicohl Furey’s seminar Algebra, Particles and Quantum Theory, and you can see a video of my talk here:

You can also watch another version, where I explain this stuff to my friend James Dolan:

I like the idea of ...

The Joy of Abstraction

The Topos Institute is excited to announce a book club for The Joy of Abstraction by Eugenia Cheng. This book is an introduction to category theory for anyone who wants to get into the formality of the subject but does not necessarily have the mathematical background to read a standard textbook. Part 1 starts gently, so that readers can build up to the formality of rigorous mathematics even if they haven’t encountered it before. Part 2 gets into formal rigorous category theory, including limits ...

Let Me Think

My friend Joshua Meyers, formerly a math grad student at U. C. Riverside, is now trying to develop new scholarly institutions: alternatives to universities.

So, he’s started a project called Let Me Think. He’s gotten money from Jaan Tallinn and the Survival and Flourishing Fund to run a meeting where 20 people will stay in rural New York for two months and plan how to build these new institutions. The venue is a 93-acre site on top of a mountain, with its own lake.

It’ll happen this summer....

Applied Category Theory 2023

You can now submit a paper if you want to give a talk here:

• 6th Annual International Conference on Applied Category Theory (ACT2023), University of Maryland, July 31 — August 4, 2023

The Sixth International Conference on Applied Category Theory will take place at the University of Maryland from 31 July to 4 August 2023, preceded by the Adjoint School 2023 from 24 to 28 July. This conference follows previous events at Strathclyde (UK), Cambridge (UK), Cambridge (MA), Oxford (UK) and Leiden (NL)...

The Italian Sixth

I showed my wife Lisa a nice video of Tommaso Zillio explaining a chord called the ‘Italian 6th’:

But she had a complaint: where the chords finally resolve to a C major triad, he writes the final chord as CCE—but those first two notes don’t sound like they’re an octave apart!

What do you think? Here’s the video:

Just for my own sake, let me explain how an Italian 6th works.

Zillio explains it in the key of C but I prefer numbers. One of the big motors that drives classical music is the prog...