John C. Baez's Blog, page 4

Meteor Burst Communications

Back before satellites, to transmit radio waves over really long distances folks bounced them off the ionosphere—a layer of charged particles in the upper atmosphere. Unfortunately this layer only reflects radio waves with frequencies up to 30 megahertz. This limits the rate at which information can be transmitted.

How to work around this?

METEOR BURST COMMUNICATIONS!

On average, 100 million meteorites weighing about a milligram hit the Earth each day. They vaporize about 120 kilometers up. ...

Visions for the Future of Physics

On Wednesday May 14, 2025 I’ll be giving a talk at 2 pm Pacific Time, or 10 pm UK time. The talk is for physics students at the Universidade de São Paulo in Brazil, organized by Artur Renato Baptista Boyago.

Visions for the Future of Physics

Abstract. The 20th century was the century of fundamental physics. What about the 21st? Progress on fundamental physics has been slow since about 1980, but there is exciting progress in other fields, such as condensed matter. This requires an adjustment in...

Civilizational Collapse (Part 5)

A tale of civilizational decline and rebirth.

Around 250 BC Archimedes found a general algorithm for computing pi to arbitrary accuracy, and used it to prove that 223/71

By the Middle Ages, math had backslid so much in Western Europe that scholars believed pi was actually equal to 22/7.

Around 1020, a mathematician named Franco of Liège got interested in the ancient Greek problem of squaring the circle. But since he believed that pi is 22/7, he started studying the square root of 22/7.

Ther...

Quantum Ellipsoids

With the stock market crash and the big protests across the US, I’m finally feeling a trace of optimism that Trump’s stranglehold on the nation will weaken. Just a trace.

I still need to self-medicate to keep from sinking into depression — where ‘self-medicate’, in my case, means studying fun math and physics I don’t need to know. I’ve been learning about the interactions between number theory and group theory. But I haven’t been doing enough physics! I’m better at that, and it’s more visce...

The McGee Group

This is a bit of a shaggy dog story, but I think it’s fun, and there’s a moral about the nature of mathematical research.

Act 1

Once I was interested in the McGee graph, nicely animated here by Mamouka Jibladze:

This is the unique (3,7)-cage, meaning a graph such that each vertex has 3 neighbors and the shortest cycle has length 7. Since it has a very symmetrical appearance, I hoped it would be connected to some interesting algebraic structures. But which?

I read on Wikipedia that the sym...

Visual Insights (Part 2)

For several years I ran a blog called Visual Insight, which was a place to share striking images that help explain topics in mathematics.  Last week I gave this talk about it at the Illustrating Math Seminar:

It was fun showing people the great images created by Refurio Anachro, Greg Egan, Roice Nelson, Gerard Westendorp and other folks. For more info on the images I talked about, go here:

• 2015 – 01 – 15 — Hammersley Sofa
• 2015 – 12 – 01 — Golay Code
• 2014 – 07 – 15 — {7,3} Tiling
•...

Critique of Yarvin’s System

guest post by Fred Mott

John, thank you for your thought‐provoking post. I’d like to offer a detailed, rigorous critique of Yarvin’s system by juxtaposing it with the deep insights of political philosophy, social choice theory, and fair division mathematics—domains that, contrary to what might be immediately apparent, all converge on the fundamental principles of justice, fairness, and the good. (Indeed, as Aristotle wisely noted, “man is by nature a political animal,” meaning that understanding...

The Dark Enlightenment

For some years now I’ve been going around telling friends that we need a ‘New Enlightenment’. It would aim at a reboot of civilization, based on sounder principles, which picks up where the so-called Age of Enlightenment left off. It would have a theoretical wing: completely rethinking politics and the economy in a way that takes the biosphere and the patterns of human behavior into account. It would also have a practical wing: fighting for freedom and justice against the authoritarians and...

Visual Insights (Part 1)

I’m giving a talk next Friday, March 14th, at 9 am Pacific Daylight time here in California. You’re all invited!

(Note that Daylight Savings Time starts March 9th, so do your calculations carefully if you do them before then.)

Title: Visual Insights

Abstract: For several years I ran a blog called Visual Insight, which was a place to share striking images that help explain topics in mathematics.  In this talk I’d like to show you some of those images and explain some of the mathematics they il...

Visual Insights

I’m giving a talk next Friday, March 14th, at 9 am Pacific Daylight time here in California. You’re all invited!

(Note that Daylight Savings Time starts March 9th, so do your calculations carefully if you do them before then.)

Title: Visual Insights

Abstract: For several years I ran a blog called Visual Insight, which was a place to share striking images that help explain topics in mathematics.  In this talk I’d like to show you some of those images and explain some of the mathematics they il...