Mathematical Instruments: John Baez

January 18, 2013 § 1 Comment

Mathematical Instruments.

Mathematical Instruments

via Wikimedia Commons

This post is part of the series Mathematical Instruments in which we introduce you to some of the math bloggers listed on our site. Today:

John Baez — Azimuth

Apart from Azimuth, any other places (other blogs, Twitter, Google+, Facebook, etc.) we can find you on?

I post lots of short articles about math and other things on Google+.

Especially check out the series called #4d, about Platonic solids and their 4-dimensional relatives…and the series I’m currently writing, called #bigness, which is about large numbers and large countable ordinals.

Would you tell us a little bit about yourself?  E.g., Where are you coming from (both geographically and philosophically)? What is your (scientific) background?

I was born in California but grew up on the east coast of the US. I started out being interested in physics, and only drifted toward math when I found it was easier for me to discover things with pencil and paper than with experiments. My uncle, Albert Baez, is mainly known as the father of the folk singer Joan Baez. But he was a physics professor, and was the one who got me interested in physics in the first place. Since his specialty was physics education, he would always come to town with lasers, holographs, diffraction gratings and the like. I especially liked the green corrugated plastic tubes you could whirl over your head to make sounds — different harmonics illustrating the physics of standing waves.

When I was eight he gave me his college physics textbook, The New College Physics: A Spiral Approach. I remember staring fascinated at the hand-drawn pictures. Later that’s where my interest in particle physics started.

He had the first electronic calculator I ever saw. He gave me Silvanus P. Thompson’s classic Calculus Made Easy, and that’s how I learned calculus. He gave me Feynman’s Lectures on Physics, and that’s how I learned quantum mechanics, the summer of my junior year of high school, when I was working at a job building trails at a state park, living in a trailer with 9 other guys.

I went to college at Princeton and arranged my schedule so all I took was math and physics courses. For social sciences — mathematical economics. For philosophy — mathematical logic. I decided not to go into physics when I burned a hole in my coat with battery acid while doing an experiment. I was still passionately interested in physics, but I decided lab work was not for me. Plus, on math tests I always knew exactly what was being asked.

I was really interested in logic, and took courses with Benacerraf and Kripke. I was also interested in the anthropic principle. I hoped that ideas from logic might help us determine the amount of complexity a universe would need to have for life to arise in this universe and learn the laws of physics. But I had to water down this grand dream considerably to write a senior thesis. I wound up showing that time evolution for Schrodinger’s equation with inverse-square force laws are computable, in the sense of recursive analysis. In the process, I decided that anything worth computing in physics was computable. I gradually lost interest in logic. It was only a lot later, when I learned about topos theory, that it became interesting to me. Everyone who likes logic should learn that stuff.

I took a course on general relativity with Malcolm Perry and read Misner, Thorne and Wheeler’s wonderful book Gravitation. The poetic last chapter made me decide that nothing was more interesting than quantum gravity. However, I went to grad school at MIT and found that nobody in the math department was interested in quantum gravity, except for string theory, which was just becoming popular at the time. I wound up working with Irving Segal on constructive quantum field theory: the task of rigorously proving that quantum field theories exist. It seemed like a good idea to understand quantum field theory and its difficulties if I wanted to work on quantum gravity someday.

Constructive quantum field was too hard for me. After grad school, I wound up working with Segal and Zhengfang Zhou on classical field theory — that is, hyperbolic nonlinear partial differential equations, like the Yang-Mills equations. We studied scattering for equations like this.

After a two-year postdoc at Yale I was hired by U. C. Riverside in 1989. I was hired for my work on differential equations and thus considered an ‘analyst’. But after I got tenure I started working on quantum gravity, right when loop quantum gravity was catching on. I got to know a bunch of physicists and had a lot of fun doing what I’d been wanting to. We figured out a lot of stuff about spin networks and spin foams. My hope was to connect these ideas with some abstract math called higher category theory and come up with a purely algebraic (rather than differential-geometric) way of thinking about the laws of physics.

We reached the point where we could write down lots of theories of this sort, called ‘spin foam models’. But we didn’t find one for which we can show that General Relativity emerges as a good approximation at macroscopic distance scales. Around 2002, I helped my colleagues Dan Christensen and Greg Egan do some simulations to study this problem. Most of our results went completely against what everyone had expected. But worse, the more work we did, the more I realized I didn’t know what questions we should be asking!

Around this time, string theorists took note of loop quantum gravity and other critics — in part thanks to Peter Woit’s blog, his book Not Even Wrong, and Lee Smolin’s book The Trouble with Physics. String theorists weren’t used to criticism like this. A kind of “string-loop war” began. There was a lot of pressure for physicists to take sides for one theory or the other. Tempers ran high.

I eventually decided to quit work on quantum gravity and focus on math. When I’d first gotten involved with higher categories, around 1993, almost nobody cared about them. It was really my friend James Dolan who convinced me they were the key to the mathematical universe. I put a lot of time into popularizing them in my column This Week’s Finds. After a while, they became quite fashionable. I had a lot of fun with them until around 2010. By that point, so many smart mathematicians had become involved that my own contributions started seeming pointless. It was as if a few people had been pushing a snowball, and it had grown so big and started rolling so fast that I couldn’t keep up with it anymore.

So, I started looking around for something else to do. I followed my wife to Singapore and got a position at the Centre for Quantum Technologies for two years. At first I thought I’d switch to working on quantum technologies — that would make sense, right? But I’d become so concerned with environmental problems, especially global warming, that I decided to work on those. I want to find a way for mathematicians to help do something about what looks like an oncoming disaster. I’ve been spending a lot of time learning new stuff: climate physics, biology, chemistry, information theory and so on. It’s actually very exciting and rejuvenating.

When and how did you first discover mathematical blogs?

Some people say I was the first blogger, or ‘proto-blogger’. When I first went to U. C. Riverside I was very lonely but there was this new thing called the internet. The web didn’t exist then, so people chatted in ‘usenet newsgroups’ like sci.math and sci.physics. Eventually a flood of crackpots moved in, so I wound up moderating a group called sci.physics.research, meaning that I served as a bouncer who kicked out the crazy people. In 1993, I started an online column called This Week’s Finds in Mathematical Physics, where I’d summarize the cool papers I’d recently read, and explain math and physics. I’d post it on the newsgroups and people would post comments. It was like a blog, but before the modern technology of blogs existed. This was the most consistently fun aspect of my life for a long time.

When did you start blogging?

In 2006, when blogs were becoming popular, I joined some other folks and started The n-Category Café, a group blog with a focus on higher categories. I started posting links to This Week’s Finds in Mathematical Physics there. Later, in 2010, I started a blog called Azimuth focused on applications of math to environmental issues. That’s my main focus now. I try to keep this blog pretty serious. For fun random tidbits, I use Google+.

What is the story behind the name of your blog?

My wife helped me pick the name Azimuth. I considered things like Green Mathematics but decided they were all too limiting and didn’t quite fit what I had in mind. Azimuth sounds cool and most people don’t know exactly what it means, so it leaves open lots of possibilities. However, it comes from an Arabic word meaning “the ways,” which seems suitable for a blog that’s trying to explore solutions to the planet’s big problems.

What wouldn’t have happened to you without the internet?

Without the internet, I might not have found my favorite activity, which is explaining technical subjects in informal settings. I love teaching in classrooms, but it’s even more fun to blog, because I have no obligation to cover any particular material — I just write about whatever seems like the coolest thing in the universe at that particular moment.

What does the internet need more of?

We need to overthrow the dominance of journals that get scholars to write and referee papers for free and then charge people lots of money to read those papers. We need ways to publish our ideas in open-access forums that still give us the ‘reputation points’ needed for hiring, tenure and promotion.

Mathematicians on the web have…

more fun than mathematicians off the web.

Your daily web reading (mathematical or otherwise)

These days I have a bunch of interesting people in my Google+ circles and get a lot of good stuff through them. I’m also constantly scouring the web for whatever topic happens to interest me at the moment. Wikipedia is a great starting-point for mathematical investigations. And don’t forget books! I don’t have an electronic book reader, so I always keep a stack by the bed to learn more about whatever I’m interested in. Right now the stack consists of:

Judith Curry and Peter Webster’s Thermodynamics of Atmospheres and Oceans.

Stanislaw Ulam’s  Analogies Between Analogies.

Frank Drake’s Set Theory.

Akihiro Kanamori’s The Higher Infinite.

John Harte’s Maximum Entropy and Ecology.

Nichomachus the Pythagorean’s The Manual of Harmonics, translated by Flora Levin.

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