Settling for Starbucks?

Whether over lunch, the phone or just g-chat, catching up with old friends these days inevitably turns into a discussion of how the hell to carve out a meaningful and satisfying professional life. We're all just a few stints into the career game that we'll keep playing until we're 65 (or much older, considering how social security doesn't look likely to pan out for us these days). But even with so little time elapsed since college graduation, it seems like my friends and I have all flip-flopped at least once between idealistic visions of healing the world and feeding ourselves solely on our passion for our work, versus the simpler, perhaps more jaded aim of making a good buck to maintain the Starbucks habit and live in trendy lofts.

I think that there are only very few freaks with an intense driving passion that directs their career path and makes choices along the way easy. And yet all of my overachiever friends and I feel like we should be one of these (lucky!) freaks on a straight fast track to exactly where we want to go. But it takes work to even bring the ultimate destination into view, let alone focus. And it's hard to remember to value the process of trying out multiple experiences and learning, especially about oneself, from each.

The only way to keep it fun along the way is to continue making time for friends and such excellent events as Sausagefest.

I Finally Take Advantage of Where I Live

A few days ago, I went on a road trip with two good friends to defray some post-qualifying exam stress. (No, I haven't heard the results of the test yet.) We drove about 6 hours, hung-over after a celebratory kegger, from Tucson to Lake Powell, which is smack in the center of the border between Arizona and Utah. It's a cool drive; you get to watch desert turn into pine forest as you drive up a mountain through Flagstaff on the way and the temperature drops 30 degrees. Then it gets friggen hot again as you come back down and drive through the Painted Desert, which consists of blobby dunes that look like some little kid's crayon set melted into the sand.

Lake Powell used to be Glen Canyon, yet another magnificent geological feature of the area carved out by the Colorado River. In the early 1950's, the Bureau of Reclamation build the Glen Canyon Dam under Eisenhower, which flooded the canyon for the purpose of creating a reservoir for the southwestern states. Environmentalists of the time strongly opposed the whole dam construction, but Lake Powell is still a very beautiful spot to visit. The water is a caribbean turquoise blue against the canyon walls-- totally unnatural looking, but gorgeous nonetheless. I have to say it's nice too that there's a body of water for desert dwellers to go in the summer to motor boat around, go swimming, and escape the heat.

Megan, Lori and I rented kayaks for a day, and did some awesome canyon exploring by water and our own arm power! We found some cool canyon walls to jump off of into the water below for an adrenaline rush.

On our way back toward civilization, we stopped in Page, AZ to hook up with a tour of Antelope Canyon with Navajo guides (access to this canyon is restricted to the Navajo tribe). This narrow canyon, carved out of sandstone by rushing floods, is gorgeous for the vibrant color of its walls, and for the smooth, awesome shapes of the walls. Some of the "rooms" of the canyon are shaped like a corkscrew from a whirlpool effect. We took some pictures of the canyon, but here are a couple taken by professionals, since ours don't really do the experience justice.

How cool is it that all of this was just a car ride away?

I'm Waiting for the Locusts....

A dust storm rolling in on Phoenix (see Chase Field at right).
Just to give you a sense of what we're dealing with here.

I just experienced my first Southwestern dust storm.

I was driving back to the math department this evening after dinner, and noticed as I was pulling out of my parking spot that the sky was a really strange dark orange color. It's officially been monsoon season for a few weeks now, and the sky often looks pretty crazy before a monsoon, so I thought we were only about to get hit with a ton of rain.

But as I rounded a corner and pointed my car south down the street, I saw a wall of thick yellow fog a few blocks ahead moving toward me head-on. God, I thought, how bizarre to have such thick fog in the middle of the dry desert. I have only even seen fog this heavy roll in on the harbors of Cape Cod a few times.

Curious, I drove out of my way a few blocks south to investigate. The way it blotted out the ever-present mountains was absolutely ominous. Even apocalyptic, I thought, as the wind now picked up to scary speeds. The palm trees started bending like you see in footage of hurricanes in Florida. Metal construction signs on the side of the road rippled like pieces of paper. I had to drive around an industrial strength, rock-sided trash can that got toppled over into the street, and I heard the sound of glass smashing around me. I felt like I was driving through a scene from War of the Worlds.

I finally realized it was dust, and not fog, when a big gust of it picked up off the road in front of my car, temporarily blinding me as my headlights reflected off of it. Lightning slashed through the pea-soup sky as I parked and hurried into the math department for safety.

I've been waiting excitedly for the dramatic storms of monsoon season ever since I moved to Tucson. I have not been dissapointed. Arizona delivers a caliber of storm I never could have imagined!

Season of Love (and Civil Rights) in Massachusetts

Last Thursday, June 14th, the legislators in Massachusetts voted not to put an amendment that would ban gay marriage on the ballot for public vote. (Translation of confusing double negatives: gay couples in MA continue to have the right to marry and have the same legal rights as every other married couple in the state. Conservative hicks in the state will not be given the opportunity to vote to change those rights.)

Last Friday, June 15th, my best friend Megan (left in the pictures) and her fiancee Lori (right) were married in a beautiful ceremony at scenic Harrington Farms in Princeton, MA. The day was a wonderful celebration of their lifelong commitment to one another among close friends and family from all over the country. It is hard for me to imagine two people not having the opportunity to say their vows before all their other loved ones, especially when they have loved and supported each other through as much as Megan and Lori have. I feel simultaneously grateful that Massachusetts allows them this opportunity, and indignant that this right is something anyone should have to feel grateful for.

At any rate, politics played absolutely no role in Megan and Lori's wedding day. It was a lovely and memorable experience for guests and brides alike. Congratulations, Megan and Lori, and best wishes for your future together!

Revealing Climate Change with MATH!

About a year and a half ago, I had a little spat with one of my very best friends.

"It's SO getting warmer in Massachusetts," I declared off-the-cuff, and without any qualifiers. "We only got snow once this year. This is totally global warming. Our kids will never get to play in the snow like we did when we were young." (As in this picture from the Good Ol' Days... when the walk to school was uphill both ways.)

"Nah," said my friend, "some years are just warmer than others. The climate goes through natural cycles, and everyone's way too hyper and quick to cry the global warming wolf these days. You are completely full of shit, Suz." (This friend is extremely articulate, and my paraphrasing here doesn't do justice to the way her razor-sharp rhetoric sliced me to shreds.) So, I put my tail between my legs, and didn't think about climate change in Massachusetts for a whole year.

BUT..... the saga continues. This past semester, I did a term project on some recently developed tools in signal processing. A signal is any time-varying quantity, and signal processing is a set of methods that allows us to glean information from a signal. In fact, one example of a signal is the temperature over a number of years in any given place.

The method I researched is called Empirical Mode Decomposition, or EMD if you want to sound cool and in-the-know. This is a way to decompose the signal into a number of modes which add back up to give the original signal, but each helps us understand different aspects of the signal. Let me explain in English. If you ever took high school physics, you might remember vectors. These were little arrows pointing in perpendicular directions (x and y directions, eg.) that you could pin together tip-to-tail to describe more general motion in two-dimensions. Here, let me refresh your memory with a picture:
So in this case, the vectors along the "Up" and "Right" directions decompose the "Up and Right" vector, which describes the actual motion of, say, a baseball flying through the air. This is a useful way to break up the motion of the baseball, as you might remember from your homework sets, because it's much easier to understand the motion in the horizontal and vertical directions separately. Then at the end of the problem, you can just add 'em back together to describe the entire motion.

A standard generalization of this idea can be applied to functions or signal, where the different components that add up to give the function are sine waves of different frequencies. (A sine wave is just a nice, regular wave, as shown below. The red sine pictured below has a frequency three times greater than the blue sine wave.)
An amazing, beautiful mathematical fact is that any function can be represented as the sum of a bunch of these nice, simple sine waves (modulo a few technical details). This is exactly analogous to the way that any 2-D motion vector can be written as a sum of vectors along vertical and horizontal directions. The different sine wave modes are "perpendicular" in a general sense, just as vectors along x- and y- axes are. This lovely decomposition is called a Fourier Series for this signal, and is the bread and butter of any undergraduate education in physics or mathematics.

Norbert Huang recently developed Empirical Mode Decomposition, which is a different way to decompose a signal. Instead of a pre-prescribed set of modes, as in a Fourier Series, EMD creates a decomposition which is specific to the signal being analyzed. The power of this method is that this special decomposition separates phenomena occuring on different time scales from the original data series. What's more, EMD leaves behind a "residue, after subtracting off the fluctuating, cyclic modes, which reveals the trend in the signal, if one exists.

The National Oceanic and Atmospheric Agency has free weather data on its website dating back to the 1920's. For my project, I took a look at some temperature data from 1988 to 2005 (roughly the length of my memory) taken in Amherst, MA (the closest data site I could find to where I grew up). Unfortunately, the image files of data and decompositions look like crud when I try to upload them to this blog. But, running EMD on this data subtracts off seasonal and other cyclic fluctuations, to give this punchline: The mean temperature in Amherst, MA has increased unambiguously by a little over a half a degree Fahrenheit over this 17-year period. Kind of scary... but the mathematics is absolutely beautiful.

Don't Mean A Thing if it Ain't Got That Swing

Sometimes, I think I was born in the wrong era. Because I absolutely love swing dancing. I just can't get enough. Maybe I should have lived during a time where everyone was as obsessed with swing as I am.

I went Lindy-Hoppin' last night at a great monthly dance in Tucson put on by the University of Arizona Swing Cats. I tried to take some photos, but let's just say that for now, I'm a better dancer than photographer. (Hopefully I'll get some good dancing action shots for this blog in the future after I master my manual settings).

When two people swing dance together, one is the leader, and the other follows (usually a man and a woman, respectively). It took me a long time to get used to this format. At first I felt that as a follower, this left me little room for my own expression and creativity. But as I've matured as a swing dancer, I've realized that the dance is a conversation, and the leader-follower structure merely allows that conversation to happen. When you're talking to your friend, you could both just talk at once. But this modus operandi pretty much guarantees that your conversation won't be very interesting. You need to be able to hear one another so that you can play off of each others' ideas and achieve a unity in the topic and mood of the discussion. It's the interplay between friends' ideas that can make a conversation fascinating and engrossing and fun, and the same goes for a swing dance. The leader-follower scheme is the channel for this interplay.

Learning to follow well, so that you can feel and react to your partner's signals, is a technical skill that takes a lot of practice. The leader must be able to read, react, and adjust to the follower too. Getting to this point in partnered dancing can take on the order of a year of consistent practice after you've got the basic steps down. But after reaching this point, swing goes from "pretty fun" to something you're addicted to and want to do all the time. You dream about it at night, and get pumped up every time you hear about a swing band playing in your city. Because finally, you've got the tools to create and explore your own chemistry on the dance floor.

There's just nothing more satisfying than catching your lead's unexpected funky break, or feeling the synchrony lock in when you figure out his unique rhythmic gait and reproduce it in or your own steps. Or maybe it's most satisfying to surprise your partner by throwing in a double turn where he'd only planned for a single, or making him laugh as you add in some outlandish embellishment inspired by the saxaphone. Actually, with so many great moments in every swing dance, I don't really feel the need to choose.

Math Gives me Fever

The good and the bad kind, it turns out.

I sacrificed my whole weekend to study for a midterm I had today. Really, the whole weekend-- Friday day and night, Saturday day and night, and Sunday day and night. The exam was long and tough, but I do feel extremely pleased with having all these new techniques and methods solidified in my mind. That's the good kind of fever.

The bad kind is the actual fever and wet cough I came down with today. BLECH. So since I'm just lying here burning up in bed, pouring Vitamin Water down my throat like it's my job, and since Shel Silverstein is my preferred bathroom reading lately, here's a little poem I wrote to commemorate the day of my Math 583b midterm.

Professor, O Doctor of this stuff, come quick-
Advanced mathematics is makin' me sick.

Contours for integrals tangle my hair,
singular points fly like knives through the air.

Limits that threaten like time-bombs to blow-up
wreak havoc on guts. They just might make me throw up.

My codes iterate- IF WHILE FOR- so inane!
The looping forever short-circuits my brain.

Interior complimentations of sets
in this space may be dense, but they sure make me sweat.

Staying up late every night for analysis
Surely will usher in spinal paralysis.

Doctor, Professor, please tell me the cure.
I guess you know best. Better study some more.