John C. Baez's Blog, page 31

Court Orders Deep Carbon Cuts for Shell

Whoa! Today a Dutch court ordered Shell to reduce its carbon emissions by 45% by 2030 from 2019 levels!

“The court orders Royal Dutch Shell, by means of its corporate policy, to reduce its CO2 emissions by 45% by 2030 with respect to the level of 2019 for the Shell group and the suppliers and customers of the group,” the judge said.

Including customers—people who buy gasoline and other products from Shell and burn the stuff—means that Shell has to sell less of that stuff.

This is the first tim...

Electrostatics and the Gauss–Lucas Theorem

Say you know the roots of a polynomial P and you want to know the roots of its derivative. You can do it using physics! Namely, electrostatics in 2d space, viewed as the complex plane.

To keep things simple, let us assume P does not have repeated roots. Then the procedure works as follows.

Put equal point charges at each root of P, then see where the resulting electric field vanishes. Those are the roots of P’.

I’ll explain why this is true a bit later. But first, we use this trick to see s...

Parallel Line Masses and Marden’s Theorem

Here’s an idea I got from Albert Chern on Twitter. He did all the hard work, and I think he also drew the picture I’m going to use. I’ll just express the idea in a different way.

Here’s a strange fact about Newtonian gravity.

Consider three parallel ‘line masses’ that have a constant mass per length—the same constant for each one. Choose a plane orthogonal to these lines. There will typically be two points on this plane, say a and b, where a mass can sit in equilibrium, with the gravita...

Non-Equilibrium Thermodynamics in Biology (Part 1)

Together with and Larry Li, I’m helping run a minisymposium as part of SMB2021, the annual meeting of the Society for Mathematical Biology:

• Non-equilibrium Thermodynamics in Biology: from Chemical Reaction Networks to Natural Selection, Monday June 14, 2021, beginning 9:30 am Pacific Time.

You can register for free here before May 31st, 11:59 pm Pacific Time. You need to register to watch the talks live on Zoom. I think the talks will be recorded.

Here’s the idea:

Abstract...

Non-Equilibrium Thermodynamics in Biology

Together with and Larry Li, I’m helping run a minisymposium as part of SMB2021, the annual meeting of the Society for Mathematical Biology:

• Non-equilibrium Thermodynamics in Biology: from Chemical Reaction Networks to Natural Selection, Monday June 14, 2021, beginning 9:30 am Pacific Time.

You can register for free here before May 31st, 11:59 pm Pacific Time. You need to register to watch the talks live on Zoom. I think the talks will be recorded.

Here’s the idea:

Abstract...

Crimson Solar

A bit of good news near my home.

On Monday May 3rd, the U.S Department of the Interior approved a new solar project in southern California. It’ll occupy about 2000 acres in the desert near Blythe—a town near the border with Arizona, and the Colorado River.

It’s called the Crimson Solar Project. It’s a 350-megawatt solar photovoltaic facility that will cost about $550 million. They say it will be able to power about 87,500 homes.

The choice of site for this solar project is part of California’s ...

Renaissance Polyphony: the Franco-Flemish School

Near the beginning of the pandemic I heard a conversation where Brian Eno said that he’d been listening to a radio station on the internet, based somewhere deep in rural Russia, that plays nothing but Eastern Orthodox chants 24 hours a day, with no announcements. He said that this sort of music appealed to him while locked down at home.

Somehow this led to me listening to a lot of early music on YouTube. I started with some Baroque composers I’d never paid attention to before, like Corelli and...

Net Zero Carbon Emissions—A Trap?

You’ve got to read this article:

• James Dyke, Robert Watson and Wolfgang Knorr, Climate scientists: concept of net zero is a dangerous trap, The Conversation, 22 April 2021.

By “net zero” they mean the idea that by cutting carbon emissions and introducing technologies that suck carbon dioxide from the air, we can reach net zero carbon emissions by around 2050 and stay below 1.5° warming.

This idea is built into the Paris Agreement. They’re saying this idea, especially the 2050 deadline, is ma...

Dufay’s Isorhythmic Motets

I’ve been reading about Renaissance music. People sometimes say that it began in the early 1400s when musicians rebelled against the dry, complicated mathematical structures of late medieval music and switched to a more emotionally expressive style. For example, the New Oxford History of Music writes:

The isorhythmic motet, the highest achievement of medieval rationalism, reached its climax during Dufay’s prentice years (c. 1410-20), with works in which the quasi-mathematical construction ...

Compositional Robotics

A bunch of us are organizing a workshop on applications of category theory to robotics, as part of the IEEE International Conference on Robotics and Automation:

• 2021 Workshop on Compositional Robotics: Mathematics and Tools, online, 31 May 2021. Organized by Andrea Censi, Gioele Zardini, Jonathan Lorand, David Spivak, Brendan Fong, Nina Otter, Paolo Perrone, John Baez, Dylan Shell, Jason Kane, Alexandra Nilles, Andew Spielberg, and Emilio Frazzoli.

Submit your papers here by 21 May 2021!

He...