Archive for May, 2006

Cloaking devices!

Via Boing Boing I see that two different papers published in Science yesterday describe how to build cloaking devices. Obviously, it’s all still at a very preliminary stage, but it’s still undeniably cool. Note, though, that there are certain caveats; for example, in the second abstract linked above the author says that “Ideal invisibility devices are impossible due to the wave nature of light”.

That’s true, but actually a bit misleading; even were it not for the wave nature of light, an ideal invisibility device would be impossible for geometric reasons elucidated by Gromov in 1983. Chris Croke (who was on my orals committee, incidentally) mentions this result (as Theorem 2.1) along with many related theorems in this chapter from Geometric Methods in Inverse Problems and PDE Control, which is slightly more readable but still probably over the head of the non-specialist. Basically it says that if you can make it appear to an outsider that light (or anything that follows a “shortest path”) is traveling in a “straight line” through a particular region of space, then it really must be traveling in a “straight line”, Of course, this presupposes that space(time) is actually Euclidean, which it isn’t, but locally it’s probably close enough for the result to still hold. Also, the scare quotes are due to the fact that I don’t really mean a straight line (since space isn’t Euclidean) but rather a geodesic, for those that know what that means. i.e. not being intercepted and re-broadcast or bent around a spaceship or any other object in the region. That doesn’t mean that you couldn’t focus all the irregularities on a very small patch of the boundary (which would only be visible by an incredible stroke of luck on the part of the observer) or make the difference from expectation smaller than the observational error threshold, this latter being the (presumable, based on what I can glean from the abstracts) methodology of the Science papers.

Anyway, the point of the above paragraph is that a perfect cloaking device (i.e. one that is completely undetectable) is impossible for purely mathematical reasons, but it’s still pretty damn cool that close approximations seem to be in the works.

If ever a post needed to go in the “Bitching and Moaning” category, this is that post

If this site still had any regular readers in April, I’m sure that our not having posted in over a month has chased the last of them away. That having been said, if there are any of you still out there and reading this, I suppose some sort of explanation is owed.

As I’m sure most of you are aware, I’m in a Ph.D. mathematics program, so I don’t exactly have a lot of spare time to begin with. Add to that the fact that I’m a fundamentally lazy person and it’s a miracle that I ever wrote as much as I did the last few years (well, to be honest, the only reason I did was because blogging was a more guilt-free form of procrastination than laying on my bed or watching television). As if graduate school weren’t difficult enough, I had the added stress this semester of having to study for my qualifying exams, which happened in late April (and which I passed, incidentally). So I think that more or less explains why I haven’t been blogging much recently…except for the fact that I passed my orals nearly a month ago and haven’t written a blog post since then. My only explanation for that is that I needed nearly a week to celebrate passing, at least two weeks to reassemble my life from the neglect and abuse of months of studying and a week of celebrating, and the last week to drive most of the way across the country and go to my brother’s graduation (not quite in that order).

Which last little tidbit speaks to why Curt hasn’t been blogging either. Between writing/defending his senior thesis, taking various proficiency exams, finals, graduation and the requisite celebration that accompanies completing all of these tasks successfully, he’s been quite busy of late as well. Oh, and add in dealing with academic and governmental bureaucracies on two different continents in his spare time.

Anyway, the point is that we’ve both been just about as busy as we’ve ever been recently. We’ve both got some more unstructured time at present, so the blogging may get more frequent again, but I’ve got this niggling little issue of a dissertation to write and Curt’s starting a job in a couple of months that may or may not be particularly time-consuming but which will certainly make blogging more difficult (I’ll let him share the details if he feels like it).

I guess what I’d like to say is that I hope (and I think Curt does as well) to post here more frequently in the future, but that I don’t want to make any promises, given that there are higher priorities in my life that demand rather a lot of time and mental energy.

And yes, I know the archives link below the banner is broken. There seem to be extremely complicated .htaccess issues associated with this, along with some weird behavior of WordPress 2.0.2, which I had to upgrade to in order finally to do something about the thousands of spam comments we get here anymore. I’ll work on it someday.