John C. Baez's Blog, page 19

Euler

 

It’s Leonhard Euler’s birthday today! He was born in Basel on April 15, 1707.

Euler was a relentlessly energetic mathematician, physicist, astronomer, geographer, logician and engineer who founded the subjects of graph theory and topology and made pioneering discoveries in analysis, number theory, mechanics, fluid dynamics, optics, and even music theory. When he lost sight in his right eye, he remarked

“Now I will have fewer distractions.”

and even when he became almost blind in his ot...

Kignits

Here you can listen to some cool Ethiopian scales called ‘kignits’:

• Listen to Ethiopian kignits.

Twenty of them, all pentatonic! One of the most popular is Ambassel 1, shown above. If you listen to just one, please try that!

Ambassel 1 sounds good because of its charming mix of symmetry and asymmetry. If you count the octave, this scale consists of two identical blocks. But each of these blocks is very lopsided: first a half step and then four half steps!

You can think of Ambassel 1 a...

ACT 2023 — Submissions

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.

Detailed instructions are below!

The Sixth International Conference on Applied Category Theory is happening at the University of Maryland from 31 July to 4 August 2023, preceded by the Adjoint School 2023 from 24 to 28 July. This event will be hybrid.

This conference follows previous events at Strathclyde (UK), ...

Chemistry and Invariant Theory

In an alternative history of the world, perhaps quantum mechanics could have been discovered by chemists following up on the theories of two mathematicians from the late 1800s: Sylvester, and Gordan.

Both are famous for their work on invariant theory, which we would now call part of group representation theory. For example, we now use the Clebsch–Gordan coefficients to understand the funny way angular momentum ‘adds’ when we combine two quantum systems. This plays a significant role in physica...

Four ‘Universes’

This chart made by Toby Ord shows four things:

• Everything we can observe now is the ‘observable universe’.

• Everything we can ever observe if we stay here is the ‘eventually observable universe’.

• Everything we can ever observe if we send spacecraft out in every direction at all speeds slower than light is the ‘ultimately observable universe’.

• Everything those spacecraft can ever affect is the ‘affectable universe’.

His chart is drawn in funny coordinates where a galaxy at rest moves st...

The Galactic Center

You’ve probably heard there’s a supermassive black hole at the center of the Milky Way—and also that near the center of our galaxy there are a lot more stars. But did you ever think hard about what the Galactic Center is like?

I didn’t, until recently. As a kid I read about it in science fiction—like Asimov’s Foundation trilogy, where the capital of the Empire is near the Galactic Center on the world of Trantor, with a population of 40 billion. That shaped my impressions.

But now we know...

The Vela Pulsar

If you could see in X-rays, one of the brightest things you’d see in the night sky is the Vela pulsar. It was formed when a huge star’s core collapsed about 12,000 years ago.

The outer parts of the star shot off into space. Its core collapsed into a neutron star about twice the mass of our Sun—but just 20 kilometers in diameter! Today it’s spinning around 11.195 times every second. As it whips around, it spews out jets of charged particles moving at about 70% of the speed of light. Thes...

Scorpius X-1

If you could see X-rays, maybe you’d see this.

Near the Galactic Center, the Fermi bubbles would glow bright… but the supernova remnant Vela, the neutron star Scorpius X-1 and a lot of activity in the constellation of Cygnus would stand out.

Scorpius X-1 was the first X-ray source in space to be found after the Sun. It was discovered by accident when a rocket launched to detect X-rays from the Moon went off course!

But why is it making so many X-rays?

Scorpius X-1 is a double star about 9,000...

X-Ray Chimneys

First astronomers discovered enormous gamma-ray-emitting bubbles above and below the galactic plane—the ‘Fermi bubbles’ I wrote about last time.

Then they found ‘X-ray chimneys’ connecting these bubbles to the center of the Milky Way!

These X-ray chimneys are about 500 light-years tall. That’s huge, but tiny compared to the Fermi bubbles, which are 25,000 light years across. They may have been produced by the black hole at the center of the Galaxy. We’re not completely sure yet.

Here’s an X-...

The Fermi Bubbles

 

How come nobody told me about the ‘Fermi bubbles’? If you could see gamma rays, you’d see enormous faint glowing bubbles extending above and below the plane of the Milky Way.

Even better, nobody is sure what produced them! I love a mystery like this.

The obvious suspect is the black hole at the center of our galaxy. Right now it’s too quiet to make these things. But maybe it shot out powerful jets earlier, as it swallowed some stars.

Another theory is that the Fermi bubbles were made by s...