### Fourier transforms and grad student life

Graduate student life can contain some hidden contradictions. From the outside, it might seem stable, even boring, as one spends pretty much every day doing much the same thing (staring at papers for me, mixing chemicals for some, writing computer code for others).

So one might, if one were so inclined, plot the external appearance of grad student life as a flat line. Now the thing about flat lines, if I may appeal to your mathematics and/or quantum mechanics classes, is that Fourier transformed into momentum space, they look like delta functions — that is, infinitely steep-sided spikes of unit area.

Irrelevant, you say? Nonsense, I say. And anyway, don’t interrrupt me halfway through my post.

Because lurking beneath the surface of any grad student’s apparent calm are dramatic spikes in things such as work satisfaction, fear of advisors (or specifically, running into them and so needing to explain the progress one has / has not made), and perception of progress toward the Valhalla of PhD-dom (Valhalla since progress sometimes seems like a battle to the death, in order to enter paradise. And not because of the plentiful women, the thought hadn’t even crossed my mind).

In somewhat related news, I changed research direction entirely on Tuesday. The old direction was really going nowhere, so it’s something entirely new that we’re looking at now. You might think I’d be disappointed after a good many months’ work on the old area, but I’m actually quite pleased, since I had run out of ideas for the old project. And thank goodness I have no candidacy exams coming up soon!

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You know, I was really hoping that you’d spend some more time on the Fourier transform side of things, seeing as how I’ve had to learn and relearn about Fourier and Fast Fourier transforms numerous times in the Applied Math side of my college career.

By the way, for clarity, you might consider talking about what this new diretion in research is, and how it differs from your old direction. And pursue your Fourier analogy further. I’d like to see where it goes.

Comment by Adam — 12 Apr 2005 @ 11:20 pm

*shrieks*

*pause*

Oh, there were no actual Fourier Transforms *shudder* I hate Fourier transforms, the only good thing about them is that they’re not LaPlacian Transforms. Horrid, horrid things.

Comment by xaosseed — 13 Apr 2005 @ 12:01 pm

Man, so much confusion about Fourier transforms! What seems to be causing the uncertainty?

As regards the new and old directions, it’s hard to explain without a lengthy excursion into some principles of string theory. Basically, the old area was an aspect of what is called AdS/CFT correspondence, which is a mapping from (typically) ten-dimensional supersymmetric gravity theories (ie. curved space), to (typically) four dimensional quantum field theories (ie. particles). The attraction of the correspondence is that it allows one to solve hard problems on one side by transforming them to easy problems on the other side. We were trying to extend some recent work which had classified a particular class of the supersymmetric gravity solutions (specifically, those with maximal supersymmetry), entirely in terms of a single function on a distinguished two-dimensional surface.

The new work is part of the growing ability of string theory to explain black hole entropy in terms of actual states of D-branes, a particular object in string theory. We are looking at some recent work that does some of these calculations by using a duality between two types of string theory, compactified (dimensionally reduced) on various particularly-weird six-dimensional spaces.

Anyway, that was probably unintelligible. I can try to expand on some of the things I mentioned, if anyone is interested.

Comment by paulcook — 13 Apr 2005 @ 7:04 pm

I’ll probably not visit this site again to see answers to this message, but I just want to share with everyone here my deepest hate for Fourier Transforms, Fast Fourier Transforms, Discrete Fourier Transforms, Fourier Transform of an aperiodic signal, periodic signal, and also I hate Fourier himself. We should start a support group for Fourier Haters. Association of Fourier Transform Haters.

We are the Transformers when we need ‘em.

Comment by Charles — 3 Apr 2006 @ 11:15 am

sorry, I meant “where are”

Comment by Charles — 3 Apr 2006 @ 11:16 am

I saw something recently that made me giggle - someone has named their code/program/technique (something) the FFTW - fastest fourier transform in the west!

Which made me laugh and then reflect that I should get out more. Oh well. Hope you’re having a good time in Jhb Paul. Don’t forget my jelly tots!

Comment by ccj — 27 Apr 2006 @ 11:26 am