About

This is a blog about using topology to compute, hopefully educating a few people on the subject of topology, and tossing a career aside to pursue a PhD. If you’ve come here expecting a topo map geek, you’re looking for a much different kind of geek (and one that’s probably in much better shape). I do like maps quite a bit, though. And I’ll probably talk about them in an abstract sense.

Topology is a branch of math that deals with geometry in regards to general and local structure. It’s also a big topic and difficult to pin down. The subtopics that I’m most interested in are differential geometry and algebraic topology. These will probably take whole posts just to gloss over and if you’re not in mathematics or at least a grad student in a related field (like physics or computer science), you probably won’t care. I’m not trying to be condescending. Topology can be insanely difficult to comprehend; it’s the single hardest topic that I have ever studied, hands down.

My interest in topology comes from two directions: first, it was the reason that I got started in math (and subsequently the topic that broke me), and second, I found out over the last year that topology plays a prominent role in several research areas of computer science. These applications to CS are what really got me interested in the topic again. Algebraic (or combinatorial) topology is useful in studying the structure of data like meshes and graphs. Differential geometry is applicable when your data lives in another space, or on something called a manifold, and you want to do the same kinds of things that you’re used to doing in regular, old-fashioned space. Ultimately, both have to do with geometry, albeit in a very general way. That’s why these topics interest me; I want to know how to better get at the essence of data, and much of the time you can do that geometrically.

So what’s this about tossing away my career? My undergrad degree is in math, but that’s not where I ended up. I landed in software, and I’ve been working as a programmer long enough to qualify for “senior software engineer” positions. Despite the fact that I’ve been laid off a few times due to various economic fluctuations, it was a good career. About a year ago, I decided that I was tired of working on other people’s ideas. I wanted to command a better salary, have more choice in what I could do, and above all, get some freedom in choosing projects. I decided to see about a Master’s. I took a few classes to get a feel for it, and at the end of a semester, one of my profs convinced me to try for a PhD instead. It’s almost a year later, and I’ve been accepted to the program at the University of Utah and officially start in Fall (though I’m doing research now).

People who know what’s involved in my choices probably think that I’m crazy. That’s certainly true. However, I’d have to say that it would be more insane for me to keep a career that seems (to my experience) to reward mediocrity. It’s not that you can’t do good work in software. I have known many excellent engineers over the years, and they are extremely bright people. I get the idea that the tech industry as a whole isn’t interested in pushing the boundary, especially during recessions. There are, of course, companies that do push the boundary, but they hire researchers to do it. Microsoft, nVidia, Google, AT&T, Cisco; all of them have the juice to hire docs. The rest are more than happy to reward a good idea that sells, but investing in the effort is a concept that seems to be lost on them. After a while, it becomes a matter of investment for the engineer as well. If for the same amount, I can do less work, why do more? This is the sad state of affairs for many industries, not just software.

So my decision was basically made for me when my company laid me off and 4 other engineers (it wasn’t for my whining either; I still have a good relationship with my old bosses and coworkers). I decided that it was an opportunity to make school a priority. Research is what I really want to do, despite my advisor’s warnings. So here I am. And you get to read me babble about topology.