John C. Baez's Blog, page 78

The Physics of Butterfly Wings

Some butterflies have shiny, vividly colored wings. From different angles you see different colors. This effect is called iridescence. How does it work?

It turns out these butterfly wings are made of very fancy materials! Light bounces around inside these materials in a tricky way. Sunlight of different colors winds up reflecting off these materials in different directions.

We’re starting to understand the materials and make similar substances in the lab. They’re called photonic crystals....

The Game of Googol

Here’s a puzzle from a recent issue of Quanta, an online science magazine:

Puzzle 1: I write down two different numbers that are completely unknown to you, and hold one in my left hand and one in my right. You have absolutely no idea how I generated these two numbers. Which is larger?

You can point to one of my hands, and I will show you the number in it. Then you can decide to either select the number you have seen or switch to the number you have not seen, held in the other hand. Is there...

Carbon Budget

On Quora someone asked:

What is the most agreed-on figure for our future carbon budget?

My answer:

Asking “what is our future carbon budget?” is a bit like asking how many calories a day you can eat. There’s really no limit on how much you can eat if you don’t care how overweight and unhealthy you become. So, to set a carbon budget, you need to say how much global warming you will accept.

That said, here’s a picture of how we’re burning through our carbon budget:

It says that our civiliz...

Trends in Reaction Network Theory (Part 2)

Here in Copenhagen we’ll soon be having a bunch of interesting talks on chemical reaction networks:

• Workshop on Mathematical Trends in Reaction Network Theory, 1-3 July 2015, Department of Mathematical Sciences, University of Copenhagen. Organized by Elisenda Feliu and Carsten Wiuf.

Looking through the abstracts, here are a couple that strike me.

First of all, Gheorghe Craciun claims to have proved the biggest open conjecture in this field: the Global Attractor Conjecture!

• Gheorge Craciun...

Higher-Dimensional Rewriting in Warsaw (Part 2)

Today I’m going to this workshop:

• Higher-Dimensional Rewriting and Applications, 28-29 June 2015, Warsaw, Poland.

Many of the talks will be interesting to people who are trying to use category theory as a tool for modelling networks!

For example, though they can’t actually attend, Lucius Meredith and my student Mike Stay hope to use Google Hangouts to present their work on Higher category models of the π-calculus. The π-calculus is a way of modelling networks where messages get sent here...

On Care For Our Common Home

There’s been a sea change on attitudes toward global warming in the last couple of years, which makes me feel much less need to determine the basic facts of the matter, or convince people of these facts. The challenge is now to do something.

Even the biggest European oil and gas companies are calling for a carbon tax! Their motives, of course, should be suspect. But they have realized it’s hopeless to argue about the basics. They wrote a letter to the United Nations beginning:

Dear Excellenci...

World Energy Outlook 2015

It’s an exciting and nerve-racking time as global carbon emissions from energy production have begun to drop, at least for a little while, yet keeping warming below 2C seems ever more difficult.

The big international climate negotiations to be concluded in Paris in December 2015 bring these issues to the forefront in a dramatic way. Countries are already saying what they plan to do: you can read their Intended Nationally Determined Contributions online!

But it’s hard to get an overall picture...

Information and Entropy in Biological Systems (Part 7)

In 1961, Rolf Landauer argued that that the least possible amount of energy required to erase one bit of information stored in memory at temperature is where is Boltzmann’s constant.

This is called the Landauer limit, and it came after many decades of arguments concerning Maxwell’s demon and the relation between information and entropy.

In fact, these arguments are still not finished. For example, here’s an argument that the Landauer limit is not as solid as widely believed:

• John D. Nort...

Information and Entropy in Biological Systems (Part 6)

The resounding lack of comment to this series of posts confirms my theory that a blog post that says “go somewhere else and read something” will never be popular. Even if it’s “go somewhere else and watch a video”, it’s too much like saying “Hi! Want to talk? Okay, go into that other room and watch TV, then come back when you’re done and we’ll talk about it.”

But no matter: our workshop on Information and Entropy in Biological Systems was really exciting! I want to make it available to the wo...

Information and Entropy in Biological Systems (Part 5)

John Harte of U. C. Berkeley spoke about the maximum entropy method as a method of predicting patterns in ecology. Annette Ostling of the University of Michigan spoke about some competing theories, such as the ‘neutral model’ of biodiversity—a theory that sounds much too simple to be right, yet fits the data surprisingly well!

We managed to get a video of Ostling’s talk, but not Harte’s. Luckily, you can see the slides of both. You can also see a summary of Harte’s book Maximum Entropy and Ec...