John C. Baez's Blog, page 6

ACT 2025

The Eighth International Conference on Applied Category Theory (https://easychair.org/cfp/ACT2025) will take place at the University of Florida on June 2-6, 2025. The conference will be preceded by the Adjoint School on May 26-30, 2025.

This conference follows previous events at Oxford (2024, 2019), University of Maryland (2023), Strathclyde (2022), Cambridge (2021), MIT (2020), and Leiden (2019).

Applied category theory is important to a growing community of researchers who study computer scie...

Black Hole Puzzle

101 starship captains

101 starship captains, bored with life in the Federation, decide to arrange their starships in a line, equally spaced, and let them fall straight into an enormous spherically symmetrical black hole—one right after the other. What does the 51st captain see?

(Suppose there’s no accretion disk or other junk blocking the view.)

Background

A somewhat surprising fact is that the more massive a black hole is, the closer to flat is the spacetime geometry near the event horizo...

Compact Multi-Planet Systems

Happy Thanksgiving! I’m thankful to be living in the age when humanity got to know planets outside our Solar System. I remember being awed when we detected the first one in 1992. I never expected that we’d soon be seeing thousands of them and starting to learn what planets are typically like. That’s actually much more interesting.

We can only detect planets that are large enough and/or close enough to their star, so what we’re seeing is biased. But taking that into account, we still see s...

Threats to Climate-Related US Agencies

Trump’s cronies are already going after US government employees involved in the response to climate change. You can read about it here:

• Hadas Gold and Rene Marsh, Elon Musk publicized the names of government employees he wants to cut. It’s terrifying federal workers, CNN, 27 November 2024.

When President-elect Donald Trump said Elon Musk and Vivek Ramaswamy would recommend major cuts to the federal government in his administration, many public employees knew that their jobs could be on th...

The Great Conjunction

 

Near the end of December 2020, I saw Jupiter and Saturn very close in the sky just after sunset. I didn’t know this was called a great conjunction. The next one will happen in November 2040. And it will happen in a very different part of the sky: close to 120° away.

This is how it always works. People have known this for millennia. They just forgot to teach me about it in school. The time between great conjunctions is always roughly 20 years, and if you keep track of them, each one is...

ASKAP J1935+2148

MeerKAT is an amazing array of 64 radio telescopes in South Africa. Astronomers want to expand this to the Square Kilometer Array, which will actually consist of thousands of telescopes in South Africa and Australia. But it’s already seeing great stuff. For example, this June they found a weird thing that flashes like a pulsar, but extremely slowly: roughly once an hour, instead of many times a second like an ordinary pulsar!

That’s insane! What is this thing? We don’t know, and that’s...

Polarities (Part 5)

Today I’d like to dig a little deeper into some ideas from Part 2. I’ve been talking about causal loop diagrams. Very roughly speaking, a causal loop diagram is a graph with labeled edges. I showed how to ‘pull back’ and ‘push forward’ these labels along maps of graphs. But it turns out that to make pulling back and pushing forward functorial, we need to take two very different approaches to graphs with labeled edges:

We can ignore the meaning of the edge labels—treat them as elements of an...

Polarities (Part 4)

In Part 2, I explained some stuff you can do with graphs whose edges are labeled by elements of a rig. Remember, a rig is like a ring, but it might not have negatives. A great example is the boolean rig, whose elements are truth values:

The addition in this rig is ‘or’ and the multiplication is ‘and’.

So what’s the point? If we have a graph with edges labeled by booleans, we can use them to describe whether one vertex affects another. For example:

Here directly affects because the fir...

Summer Research at the Topos Institute

You can now apply for the 2025 Summer Research Associate program at the Topos Institute! This is a really good opportunity.

Details and instructions on how to apply are in the official announcement.

A few important points:

• The application deadline is January 17, 2025.
• The position is paid and in-person in Berkeley, California.
• The Topos Institute cannot sponsor visas at this time.

These positions will last for 8 – 10 weeks, starting in June 2025 and ending in August. Each position will ...

The Mean Speed Theorem

Did you know students at Oxford in 1335 were solving problems about objects moving with constant acceleration? This blew my mind.

Medieval scientists were deeply confused about the connection between force and velocity: it took Newton to realize force is proportional to acceleration. But in the early 1300s, a group of researchers called the Oxford Calculators made huge progress in understanding objects that move with changing velocity. That was an incredibly important step.

You see, Aristo...