John C. Baez's Blog, page 41

Banning Lead in Wetlands

An European Union commission has voted to ban the use of lead ammunition near wetlands and waterways! The proposal now needs to be approved by the European Parliament and Council. They are expected to approve the ban. If so, it will go into effect in 2022. The same commission, called REACH, may debate a complete ban on lead ammunition and fishing weights later this year.

Why does this matter? The European Chemicals Agency has estimated that as many as 1.5 million aquatic birds die annually...

Electric Cars

Some good news! According to this article, we’re rapidly approaching the tipping point when, even without subsidies, it will be as cheaper to own an electric car than one that burns fossil fuels.

• Jack Ewing, The age of electric cars is dawning ahead of schedule, New York Times, September 20, 2020.

FRANKFURT — An electric Volkswagen ID.3 for the same price as a Golf. A Tesla Model 3 that costs as much as a BMW 3 Series. A Renault Zoe electric subcompact whose monthly lease payment might equal...

Ascendancy vs. Reserve

Why is biodiversity ‘good’? To what extent is this sort of goodness even relevant to ecosystems—as opposed to us humans? I’d like to study this mathematically.

To do this, we’d need to extract some answerable questions out of the morass of subtlety and complexity. For example: what role does biodiversity play in the ability of ecosystems to be robust under sudden changes of external conditions? This is already plenty hard to study mathematically, since it requires understanding ‘biodive...

Enayat on Nonstandard Numbers

Michael Weiss and I have been carrying on a dialog on nonstandard models of arithmetic, and after a long break we’re continuing, here:

• Michael Weiss and John Baez, Non-standard models of arithmetic (Part 18).

In this part we reach a goal we’ve been heading toward for a long time! We’ve been reading this paper:

• Ali Enayat, Standard models of arithmetic.

and we’ve finally gone through the main theorems and explained what they say. We’ll talk about the proofs later.

The simplest one is this:

• ...

The Brownian Map

Nina Holden won the 2021 Maryam Mirzakhani New Frontiers Prize for her work on random surfaces and the mathematics of quantum gravity. I’d like to tell you what she did… but I’m so far behind I’ll just explain a bit of the background.

Suppose you randomly choose a triangulation of the sphere with n triangles. This is a purely combinatorial thing, but you can think of it as a metric space if each of the triangles is equilateral with all sides of length 1.

This is a distorted picture of what...

Open Systems: A Double Categorical Perspective (Part 2)

Back to Kenny Courser’s thesis:

• Kenny Courser, Open Systems: A Double Categorical Perspective, Ph.D. thesis, U. C. Riverside, 2020.

One thing Kenny does here is explain the flaws in a well-known framework for studying open systems: decorated cospans. Decorated cospans were developed by my student Brendan Fong. Since I was Brendan’s advisor at the time, a hefty helping of blame for not noticing the problems belongs to me! But luckily, Kenny doesn’t just point out the problems: he shows how ...

Open Systems: A Double Categorical Perspective (Part 1)

My student Kenny Courser‘s thesis has hit the arXiv:

• Kenny Courser, Open Systems: A Double Categorical Perspective, Ph.D. thesis, U. C. Riverside, 2020.

He’s been the driving force behind a lot of work on open systems and networks at U. C. Riverside. By the way, he’s looking for a job, so if you think you know a position that’s good for someone who can teach all kinds of math and also strong on applied category theory, give him or me a shout.

But let me describe his thesis.

His thesis is big!...

Diary, 2003-2020

I keep putting off organizing my written material, but with coronavirus I’m feeling more mortal than usual, so I’d like get this out into the world now:

• John Baez, Diary, 2003–2020.

Go ahead and grab a copy!

It’s got all my best tweets and Google+ posts, mainly explaining math and physics, but also my travel notes and other things… starting in 2003 with my ruminations on economics and ecology. It’s too big to read all at once, but I think you can dip into it more or less anywhere and pull ou...

Open Systems in Classical Mechanics

I think we need a ‘compositional’ approach to classical mechanics. A classical system is typically built from parts, and we describe the whole system by describing its parts and then saying how they are put together. But this aspect of classical mechanics is typically left informal. You learn how it works in a physics class by doing lots of homework problems, but the rules are never completely spelled out, which is one reason physics is hard.

I want an approach that makes the compositionality...

Linear Logic and Petri Nets

Wow! Elena Di Lavore and Xiaoyan Li explained how to make a category of Petri nets that’s a model of linear logic! I consider myself a sort of expert on Petri nets, but I didn’t know this stuff:

• Elena Di Lavore and Xiaoyan Li, Linear logic flavoured composition of Petri nets, The n-Category Café, 27 July 2020.

It has great pictures, too. Let me summarize a tiny bit.

A Petri net is a very simple thing. Here’s a Petri net that shows how healthy white blood cells (H), individual viruses ...