Math-Frolic Interview #43
"[James Dilts] works as a mild-mannered mathematician by day and as… well… a mild-mannered mathematician by night. The Missus disputes the mild-mannered part. Despite the best efforts of his middle and high school teachers, he discovered that math is awesome, and has decided that everyone else needs to know this too. His academic research is some combination of general relativity, differential equations and differential geometry, which he promises is super cool. He has an Erdös number of three."
-- from James Dilts' blog
Dr. James Dilts is the proprietor (with his wife) of the "Infinity Plus 1" blog which I stumbled across a bit over a year ago, and have enjoyed since. His posts aren't particularly frequent, but always cover some interesting, and sometimes difficult or unpredictable topic, in a lively, entertaining, well-planned-out fashion (with "the Missus" adding the illustrations). He definitely has a knack for writing. While currently a west-coast post-doc, he has plans to leave the "panic mode" of academia for possible opportunities in computer programming. And here's more:
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1) Tell us a little about your background that led to a major in mathematics.
Honestly, I have no idea how I ended up as a math major. My family growing up
was more science-y than most. (My 3 older brothers are all programmers, for instance.) But, I didn't have any particular role models at all. I didn't know a single professor. I'm not even sure how I learned that "mathematician" was a valid job! But, sometime in high school, I decided I wanted to do research, and figured that I'd try math first, and if that didn't work, switch to physics or chemistry. I went to Brigham Young University for my undergraduate, and my first year there I took the intro to proofs class. I loved it! When we covered Cantor's diagonalization proof (available on our post "
A bigger infinity"), I knew that I wasn't going to switch to physics.
2) Is there any particular backstory to the name of your blog, “Infinity Plus 1”?
When I decided to start writing the blog, we of course wanted a name that was light-hearted and memorable. And every kid has, at some point, tried to pull out "infinity plus one" to win an argument, so it seemed like a good fit. It also was a great segue into our first posts, where I wanted to talk about Cantor's diagonalization proof, for obvious reasons.
3) Your posts always have a light-hearted feel to them, even when you’re dealing with difficult, abstract ideas. I get the feeling you have a lot of fun writing them. Do you have a couple of favorite posts that were especially fun or satisfying to write? And do you have any idea which posts have been most popular with readers?
The most popular question is easy. Every time we've written a biography post (for
Cantor,
Schwarzschild, and
Godel), they've always been more popular than the rest. The Godel post, in particular, got picked up by some service, and ended up with about as many views as the rest of the posts combined!
Oh, I'm bad at "favorite" questions. I've only written posts about topics I feel passionate about, and that I think are super interesting, so it's kind of hard to pick. Well, if I have to pick, let's pick the black hole posts, of which there are a few, starting with Black holes suck. Black holes are something that lots of people know about, but very few people actually understand. It doesn't help that the mathematics uses graduate level geometry... So, in those posts, I got to talk about the actual mathematics behind these super cool objects, and talk about all the interesting things we still don't know. (Really, there are a
ton of questions left about black holes, which I never got to cover. Ah well.)
4) Who are some of your own favorite math/science writers (or, feel free to mention writers of any sort who have been important to you)?
Honestly, I've gotten most of my information from class and textbooks and talking to professors, even the fun stories. But probably the most important science writer for me was Isaac Asimov. Most people who've heard of him know him for his science fiction, which I love. But he also had a PhD, and wrote a lot of science essays about all sorts of topics, from mathematics to physics to nuclear chemistry to why it's a tragedy we have a moon. Sure, none of the science is up to date anymore, but I'd still recommend his essays to anyone. His style was always light-hearted, and though I didn't think about it till now, I'm confident he heavily influenced my own writing.
[...interesting, I grew up when Asimov was the most prolific science-writer around, but I rarely hear his name brought up anymore, except maybe in science fiction circles; as some folks know, he was also quite a limerick-writer, but I won't go there ;)]
5) You write that “My research is focused on the Einstein constraint equations, a coupled system of non-linear elliptic equations, and related geometric problems, such as the (conformally) prescribed scalar curvature problem. The main goal is a complete parametrization of the set of solutions of the constraint equations.”
Is it possible to put that in more layman terms? ;)
And is this an area that involves more strictly abstract or pure mathematics, or applied math as well?
In normal, Newtonian gravity, initial data is arbitrary, which means that you can plop down planets wherever you want, and feel free to evolve them. Newtonian gravity won't break. But relativity is different. In general relativity, your initial state of the universe has to satisfy certain conditions, and those conditions are the Einstein constraint equations. Now, unlike some equations, there are a lot of solutions to the constraint equations.
One goal is to try to understand all the possible solutions to the constraint equations. One way to approach that is to try to parameterize all of the solutions, which means that if you give me some inputs x, y, and z, then I can turn around and give you a unique solution. That turns out to be a difficult problem. My research has focused on trying to find ways to show that the equations do or do not have solutions for certain inputs.
It's a pure mathematical question, but numerical techniques have been helpful. Relatively recently, we realized that no one really knew what the right thing to try to prove was, which makes it really hard to prove anything. It was a huge road block. So, we used some numerical techniques to figure out what was going on, which turns out to be much more complicated than anyone had thought.
6) I believe you’re currently job-hunting (coming off of a post-doc) and looking more into computer programming… say a little about what you’re most looking for in a new position or in the future?
I want to continue to work on interesting problems. A lot of programming jobs are just making another app, or working on the company's website and backend. Those are important jobs, but not what I want to do. Programming can be a powerful tool for investigating difficult questions, as I saw in my research, and my ideal job would let me contribute to that.
7) Besides your blog, are there any social media or other websites where readers can particularly look for you?
I'm actually anti-social media! I have a Facebook page and a Twitter for the blog, since many people want to receive them in that way, but I'm otherwise completely off of Facebook and Twitter and all the usual culprits. I'd much rather spend my time on more important things.
8) When you’re not doing mathy sorts of things, what are some of your favorite activities/hobbies/interests?
I'm an avid rock climber and unicyclist. I also love reading, especially classic science fiction, and playing games of all sorts. Of course, a lot of my time is spent making sure the Epsilons [my kids] don't destroy the Missus!
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Thanks for participating here James, and take care to keep your rock-climbing and unicycling separate, OK! ;)
Hope too you find what you desire in a computer career, and hope your clear talents for writing and explaining continue as well in some form!
If you've never read James' blog before, definitely check it out; you're in for a treat!
(His list of posts/topics is
HERE.)
