John C. Baez's Blog, page 77

Good News (Part 1)

As we head toward the new year, I’d like to talk about some good news!

Most news is bad news. Why? Because the news media are like the immune system: their job is to warn us of threats. But an over-sensitive immune system can actually cause diseases, like allergies and auto-immune disorders. And the same thing can happen to the body politic when the news media exaggerates threats!

You’ve already heard more than enough bad news. But you may not have heard this good news:

• From 1990 and 2015...

The Paris Agreement

The world has come together and agreed to do something significant about climate change.

Not as much as I’d like: it’s estimated that if we do just what’s been agreed to so far, we can expect 2.7C of warming, and more pessimistic estimates range up to 3.5 C. But still, something significant. Furthermore, the Paris Agreement set up a system that encourages nations to ‘ratchet up’ their actions over time. Even better, it helped strengthen a kind of worldwide social network of organizations dev...

Operads and Phylogenetic Trees

A few years ago, after hearing Susan Holmes speak about the mathematics of phylogenetic trees, I became interested in their connection to algebraic topology. I wrote an article about this here:

• John Baez, Operads and the tree of life, 6 July 2011.

In trying to the make the ideas precise I recruited the help of Nina Otter, who was then a graduate student at ETH Zürich. She came to Riverside and we started to work together.

Now Nina is a grad student at Oxford working on mathematical biology...

Relative Entropy in Biological Systems

Here’s a draft of my paper for the proceedings of a workshop on Information and Entropy in Biological System this spring:

• John Baez, Relative Entropy in Biological Systems.

I’d love any comments or questions you might have. I’m not happy with the title. In the paper I advocate using the term ‘relative information’ instead of ‘relative entropy’—yet the latter is much more widely used, so I feel I need it in the title to let people know what the paper is about!

Here’s the basic idea.

Life rel...

Regime Shift?

There’s no reason that the climate needs to change gradually. Recently scientists have become interested in regime shifts, which are abrupt, substantial and lasting changes in the state of a complex system.

Rasha Kamel of the Azimuth Project pointed us to a report in Science Daily which says:

Planet Earth experienced a global climate shift in the late 1980s on an unprecedented scale, fueled by anthropogenic warming and a volcanic eruption, according to new research. Scientists say that a majo...

Tale of a Doomed Galaxy

Part 1

About 3 billion years ago, if there was intelligent life on the galaxy we call PG 1302-102, it should have known it was in serious trouble.

Our galaxy has a supermassive black hole in the middle. But that galaxy had two. One was about ten times as big as the other. Taken together, they weighed a billion times as much as our Sun.

They gradually spiraled in towards each other… and then, suddenly, one fine morning, they collided. The resulting explosion was 10 million times more pow...

Fires in Indonesia

I lived in Singapore for two years, and I go back to work there every summer. I love Southeast Asia, its beautiful landscapes, its friendly people, and its huge biological and cultural diversity. It’s a magical place.

But in 2013 there was a horrible haze from fires in nearby Sumatra. And this year it’s even worse. It makes me want to cry, thinking about how millions of people all over this region are being choked as the rain forest burns.

This part of the world has a dry season from May to...

Biology, Networks and Control Theory

The Institute for Mathematics and its Applications (or IMA, in Minneapolis, Minnesota), is teaming up with the Mathematical Biosciences Institute (or MBI, in Columbus, Ohio). They’re having a big program on control theory and networks:

• IMA-MBI coordinated program on network dynamics and control: Fall 2015 and Spring 2016.

• MBI emphasis semester on dynamics of biologically inspired networks: Spring 2016.

At the IMA

Here’s what’s happening at the Institute for Mathematics and its Applicati...

A Compositional Framework for Markov Processes

This summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a nice step towards understanding the math of living systems.

Admittedly, it’s just a small first step. But I’m excited by this step, since Blake and I have been trying to get this stuff to work for a couple years, and it finally fell into place. And we think we know what to do next.

Here’s our pap...

The Inverse Cube Force Law

Here you see three planets. The blue planet is orbiting the Sun in a realistic way: it’s going around an ellipse.

The other two are moving in and out just like the blue planet, so they all stay on the same circle. But they’re moving around this circle at different rates! The green planet is moving faster than the blue one: it completes 3 orbits each time the blue planet goes around once. The red planet isn’t going around at all: it only moves in and out.

What’s going on here?

In 1687, Isaac...