Lessons from Computational Chemistry!

Hello, hello!

If anyone could explain to me how there is less than a week left of the long month of August, I would be most grateful.

I find myself back in my SoCal home... somewhat disoriented, excited, distraught, happy, lonely, scared, nostalgic... yearning at turns for comfiness&coziness and for excitement&adventure.

Mostly, I feel very unprepared about the unreal reality that, granted the benevolence of the Fates, I shall be leaving for Budapest in five days(!!).

The last two weeks or so since I last wrote were a little crazy, and quite wonderful.

Research ended nicely- and I shall attempt to provide an explanation of the exciting things I was doing! :]

Brace yourself, dear Reader. We are in for a trip!

So... Our simulations for LTA were failing quite miserably, and we believe the cause (or one major cause, anyway) to be the presence of a dipole in our unit cell structure (we'll talk more about dipoles later).

Backing up a bit. My work was with zeolites. Zeolites are pretty crystals, which means they have repetitive structural units-- aka unit cells. What this means is that you can tile a bunch of unit cells together to get a zeolite-- this not only contributes to the beauty of staring at atom-level pictures of zeolites (which I am fond of doing), but it also means that we can save ourselves time by exploiting the symmetry of the system. Look! A picture!

A unit cell is here boxed in red.

In order to run our simulations, we tile together something like 12 to 36 unit cells (pretending we actually have a 2D system, we can see 4 unit cells in the picture) because 1) we can't afford to try to model a super large system and 2) we can use tricks to make the system seem bigger than it actually is (to get more realistic results).

[For those more mathematically inclined, refer to periodic boundary conditions (we’re mapping onto a torus!!)]

We have essentially two versions of the code that controls our simulations-- one which uses Ewald summation to deal with interactions between charges, and one which does not. For the purposes of this discussion, it doesn’t matter what Ewald does. I’m just using it to differentiate between two different ways of running the simulation. The important thing here is that the version of the code which uses Ewald (which is the version we were interested in) needs the coordinates of the unit cell to be such that the center is (0,0). The other important thing is that using Ewald requires that the unit cell not have a dipole.

For those of us who do not remember what a dipole is, dipoles emerge when you have an imbalance of charge. To use my professor's example from intro chem, think of elephants pulling on a rope tied to a tree. If you have two elephants pulling just as hard in exactly opposite directions, the tree will not fall over. If one is pulling harder than the other, or if they’re pulling in a way that the forces they are exerting on the tree don’t cancel out, the tree will fall over. So having a dipole è the tree falls over.

In this case, we don’t want the tree to fall over.

So we want a structure centered at zero. However, the crystal structure does not start off this way. Instead, it starts off such that the (0,0) point is at the lower left corner.

Original, Uncentered LTA Crystal Structure

Ewald thinks that this is not okay, and so there is a function in the Ewald code that “centers” the structure to make sure that the structure is the way that it likes it.

At least theoretically.

Problem: Somehow or another this function was not working quite properly. The original crystal structure has no dipole (we know this because when we use the non-Ewald version of our code, all is well, and when we use Ewald, things go terribly wrong), but after centering it, it does. This suggests that something funky is going on... and the crystal is not, in fact, being centered properly.

 So, my job for the last few days of summer research was to understand what was going on with the centering process— with the goal of modifying the crystal structure such that it is centered (and dipole-less) to begin with, and undergoes no modification when put through the centering function in the Ewald code.

Summary:

How things are--

 Crystal structure (no dipole, uncentered) --[Ewald centering function]--> Weird, dipole-carrying structure

How I want things to be--

 Modified, centered structure –[Ewald centering function]--> Still nice and centered structure

Alright, so now the problem-solving part.

First, some terminology. 

Because I can’t look at the structure in 3D very easily, I was looking at projections onto a plane.

So what does this mean?

Imagine you’re looking at a cube. This is 3D. Now imagine you start to push on the top of the cube and the inside of the cube kind of collapses so you can flatten the cube into the ground, and you’re just left with…. 

A square, yes? (Yes.) That square is the projection of the cube onto a plane.

Or, if we started off with a delicious donut and for some reason decided to squash it down instead of eat it, we’d get two concentric circles as the projection onto what I shall arbitrarily term the xy plane:

A torus (or mathematical donut)

    

Projection of torus onto plane

(Credit goes to http://mathforum.org/mathimages/index.php/Torus)

[Of course, there’s no reason why you must squish your donut down towards the floor. You could also think of squashing it against a wall—what would that look like?]

Now that we have that, the pictures we saw earlier were the projections of the crystal structure onto the xy plane. And, again, here is the original, uncentered structure:

And here is the output of the centering function (again, projection onto the xy plane), which then gets used in the simulation:

Centered structure.
Red = oxygen atoms, blue = silicon atoms

See how we’re now “centered” at zero?

However, there is a problem, and it is one which would clearly give rise to a dipole. Remember, we want things to be nice and symmetric (such that for any elephant pulling in one direction, there is another elephant pulling just as hard in the opposite direction to balance things out)—but they are not!

(The problem is with the O atoms, specifically, so here we're just showing the oxygens)

Essentially, in the orange circles we have little oxygen elephants pulling on an imaginary tree at the origin. The problem is, the other two edges are missing little oxygen elephants-- so the tree is going down! Oh noes! 

If we look back at the uncentered structure, which has both Si and O atoms (they're just both in the same color [we also have these "X" atoms at the center of each "ball," but don't worry about that]), we see that we have elephant oxygens along all four edges (as well as two sets along each axis)-- but once we center it, we lose two edges of elephant oxygens, and the tree comes crashing down. Clearly something is amiss.

This means it is time to understand the behavior of the centering function!

Initially, I started trying to think in 2D, and this led to my being very confused about what was happening, such that I didn’t get the point of how things worked. Bad idea.

Lesson learned: when trying to understand something, it’s not stupid or simple-minded to start off with the simple model. Au contraire! Keeping things basic allows you to see and understand the important behavior, which will help you out when the system becomes more complicated. At any rate, it’s what scientists seem to believe, and it was wisdom that served me well.

So, let’s focus on 1D.

First, the function:

 x_new = x_old – ROUND(x_old/L)*L    (where L is the length of the unit cell)

So let’s pretend we’re looking at a unit cell (in this case, let’s just look at a line segment) of length 8, and let’s see what happens at each “quarter point” – so what happens to 0, 2, 4, 6, and 8.

 

For 0:                          

  x_new = 0 – ROUND(0/8)*8

        = 0 – ROUND(0)*8

        = 0 – 0*8

        = 0

For 4:

  x_new = 4 – ROUND(4/8)*8

        = 4 – ROUND(0.5)*8

        = 4 – 1*8

        = -4

For 8:

 x_new = 8 – ROUND(8/8)*8 = 0

For 2:

 x_new = 2 – ROUND(2/8)*8 = 2

For 6:

 x_new = 6 – ROUND(6/8)*8 = -2

To illustrate what happens, we can look at the original line, and see where the original points end up in the centered line:

                

             Original line:

               

             

Transformed line:

The color coding is intended
 to "trace" points.

Now, I will point out the interesting things. The points from 0 to right up to 4 (or more generally, from 0 to right up to L/2) end up being unchanged. The points from 4 to 8 (or L/2 to L) end up becoming the negative half of the line (well, plus 0), with L/2 becoming –L/2. It’s like we have cut the original line at the halfway point and moved what used to be the upper half to the end, so that the last point (L, or 8 in thi case) matches up with zero.  

The problem is, that now we have two points that get transformed to zero, and we have no point mapped onto 4, or L/2.

To look at more pretty pictures of projections of LTA….

Below, I noted how the transformation works. The blue is the original input structure, and the beige is the “centered” structure. Because the unit cell has so many nice lines of symmetry, I considered what happened to each of the four “balls” that make up the unit cell. If you don't get what's going on, don't worry about it, and just admire the pretty picture (at least, I think it's pretty). Or use the discussion about our 1D model to try to make sense of it! :]

     

Once again, I used color coding to trace things.
The arrows are intended to provide  perspective.

And here we see that the “missing points” in the projection are located at Lx/2 and Ly/2, which is to be expected from our discussion.

 

In other words... it's like instead of having a set of elephants along each edge, as well as along the axes, we now have relocated the elephants which should be along the edges corresponding to the midpoints (Lx/2, and Ly/2) to the x and y axes (respectively). This means we have two sets of oxygen elephants located along the axes... stacked on top of each other, so to speak. This image, quite properly, is rather ridiculous.

Now I’ll fast forward the story, because I’ve probably already long lost my few readers.

(As always, feel free to ask me about anything I've mentioned. I'd LOVE to talk about it!)

Basically, we have the points at both 0 and L mapping on to the new zero point. So what I did was figure out which points in the centered structure which were located at zero (or rather, along an axis) originally came from a point whose x, y, or z value was equal to L, and then moved that point in the centered structure from 0 to L/2. [Well, actually, I moved it just a teeeeny bit to the left of L/2, because if you’ll remember, a point at L/2 gets moved to –L/2 (4 got moved to -4, in our 1D example above)].
To translate into elephant language, I looked at the silly stack of elephants on the axes and relocated the elephants on top to a more dignified position-- along the empty edges.

At the end of this process I had a centered, dipoleless structure (uh, in theory…). Moreover, because this structure is already centered, upon going through the centering function, nothing changes.

Here is the result of centering my new centered input structure (also, just so you know, the projections onto the yz and xz planes look the same):

                         

Yay! Things appear to be fixed!

BUT WAIT. The problem was the dipole, and now I needed to actually calculate the dipole and make sure it was zero. I’ll spare you the detail, but… THE STRUCTURE STILL HAD  A DIPOLE! Granted, it was a much smaller dipole than it originally had… but still! Not cool, man!

Unfortunately, this realization happened at nearly the end of my last day of research, and there was no real time to do more problem-solving.

What I can say is the following. If you will recall, all these pretty pictures are projections onto a plane—aka, squished donuts. I would argue that squished donuts are not as enjoyable as real donuts, and it is much the same with these projections. You lose information in the flattening process.

To get an idea of this, imagine that cube again. Now imagine giving the side edges of the cube a jagged cut, so when you look at it straight ahead, you see something like:

  

                                                             

The problem is, if you squish it toward the ground, you still just see:

This isn’t the best example, but the point is, we can imagine that there was important information being lost in the squishing process, such that while the projection was nicely symmetric (and thus dipole-less), the 3D structure still had rowdy elephants causing problems and knocking over trees.

Unfortunately, my story ends here. I have a bit more detailed information about the remaining problem (ask if interested), but alas, at this point my research time was over, and I needed to get ready to get on a plane to visit a certain Russian-enthusiast close to my heart (if very far away in spacetime). So I still don’t understand exactly what was happening in the 3D structure that I wasn’t seeing in the projections, and I don’t understand at all how that problem came about.

I did learn a few things, though, including:

1) I love staring at pictures of pretty crystals. !

2) Start small when trying to understand tricky things.

3) It’s okay to feel clueless and lost and not good enough. You are good enough. Just take a  deep breath, and start grasping onto whatever you can. Eventually things will start to make   sense.

4) It is good to start small, but don’t be surprised (or traumatized) when you take it up a level, and suddenly things are broken again. You’ve made progress! And you’re that much better at fixing things.

I learned this while getting lost in lines of Fortran and suspecting I was actually stupid and incompetent and while fearing that I would never understand what the hell was going on with these zeolite things…

But I suspect that what I learned this summer will extend far beyond the abstract world of atomistic simulations and impact the way I carry myself in everyday life--  in the same surprising way that playing around with code can extend beyond the virtual world and uncover some truth about reality.

Huzzah for computational chemistry! :D

Conferencing

Hello, hello!

How quickly life enters a whirlwind state!
That, or I have become incredibly lazy this summer. Certainly, relative to the school year, Northfield has become more of a sleepy rural town- in the correct way. Evenings pass by with a strange sense of leisure and rapidity, as though processing time has slowed down. It is a bit amusing that by 7pm the day feels largely over, whereas during the school year that would give me at least five to six more hours of ideal work time- essentially an entire work day!

But even despite this newfound slothery and small-town sleepiness, the level of excitement in my life took a sharp rise in recent days. This is due almost exclusively to the MU3C Conference I attended at the beginning of the week. (MU3C = Midwest Undergraduate Computational Chemistry Consortium). My relatively slow-paced workdays of reading papers, learning Fortran, and trying to get a handle on how things worked hastened considerably as the conference approached. I learned how to smoothly submit jobs for computation, worked on developing my talk for the conference, practiced said talk way too many times, learned how to lift data (not difficult, but it's amazing how things can get mysteriously screwed up...), learned how to use gnuplot (in retrospect, way better than Excel!), struggled to get a sufficiently good grasp of Ewald summation to be able to explain it to a room of people, and frantically gathered preliminary results to demonstrate to others that we (my research partner and I) are not fully incompetent and have actually achieved something during the last five weeks.s.

Consequently, the past week and weekend  were a little crazy and stressful, and the size of my to-do list was, at a point, rather alarmingly disproportionate with the time available for the completion of its items... but it all worked out just great.

The conference itself was very...chill. I would estimate (I am terrible at such estimations) there were 30ish people in attendance? Talks were given by undergrads presenting their research, and also from faculty members (mostly from University of Minnesota, our sponsoring institution), we got a nice tour of the University's Supercomputing Institute (which I know was impressive, but my ignorance impedes me from knowing just how impressed I should be. I suspect I should be pretty darn impressed though), talked to current grad students about computational chemistry at the U, and lunched and dined with fellow conference members. I was happy to be able to meet other students doing work similar to my own, and on the other hand, it was interesting to see how we all had different skill sets. Some people were using quantum mechanical methods, others molecular dynamics (which uses classical mechanics), and others (such as myself) Monte Carlo techniques (which are awesome and use random numbers to run everything!), in addition to a variety of unique systems being studied-- from collisions between CO2 and H, the chemical pathways involved in acid rain, the study of a protein key to a virus analogous to HIV, CO2 separation and sequestration, astrochemistry, and more. Exciting stuff. As for my own talk, in case you were wondering, it went much better than I would have hoped! I was fortunate enough to receive very kind compliments, and it was gratifying to know that my professor was proud of the work we had done. :D Huzzah!

Now I am afraid I must prepare for a new work day. The day promises to be demanding... Dani (my prof) is a strong advocate of the immersive method of education. To translate, it means she enjoys pushing us into the water and leaving us to figure out how to swim... while she stands in the sidelines and glances over every now and then to make sure we don't drown. Terrifying? A little. But surprisingly effective.

So au revoir for now, dear Reader. At some point I must sit down and compose something that is actually interesting and thought-provoking, but I felt it was necessary to explain the cause of my extended absence.

до свидания!     

Enter that Lovely Maiden, Beauty

Hello Reader-Dearest!

The summer is now well underway.

I am now a competent Fortran-er and somewhat literate in the zeolite world.
Wait, now that I think of it, I don't think I ever mentioned what specifically I am researching this summer. Well... as specifically as it gets.

A model of  LTA, one of the zeolites
we shall be focusing on this summer. 

I am working on simulations of these lovely aluminosilicate minerals called zeolites. "Zeolite" is a fairly broad category. There are a number of different crystalline structures and zeolites can have different chemical compositions, but we're mostly dealing with silicon, oxygen, and aluminum. The cool thing is, their microporous nature makes them good molecular sieves. In particular, zeolites have been found to selectively adsorb carbon dioxide over nitrogen, hydrogen, methane, and other gases. This makes zeolites very promising materials for a number of processes, most notably carbon dioxide separation and sequestration. In the past, my professor and her students have studied pure silica zeolites (well, Si and O actually, but the key point is no aluminum) with varying structural properties, so as to examine the importance of pore structure to selective CO2 adsorption. This summer, we are going to start working on introducing aluminum into the mixture.

A structural model of MFI, another cool zeolite.

As for my own contribution... well, I only just received "the code" on Wednesday... and was immediately utterly lost in the dense network of files and the endless sea of Fortran lines contained therein. Yesterday I managed to calm some of that despair and anxiety so as to make fair progress in getting a better idea of how things fit together, but there is a very, very long way to go. However, I did submit my first few runs today! Yay! Look for more updates in the future!

I must say that, overall, I have been rather pleased with the path my summer has taken. I think I may say that I have successfully rekindled my devotion to the fair goddess, Beauty.

I cannot assure you of the existence of an omniscient, omnipotent, omnipresent, benevolent God, but I can attest to the presence of this lovely maiden. I have caught glimpses of her darting swiftly between trees, and placing blossoms in flowing hair strewn over sun-kissed prairie grass; I have seen her floating serenely on the river and heard her joining in on birdsong whilst I make my way through the arboretum. I have heard her at turns laughing at me and soothing me with her song as I feebly attempt to coax music from the keys of a piano. I have seen her hand in gorgeous sunsets and clear blue skies, in giant dandelions, and in graceful, swooping little birds. I have yet to see it myself, but I have heard that she has even taken some of her beauty and placed it within tiny creatures, that they may bring light to the summer sky even when she has gone to her slumber or joined her sisters in distant lands for merrymaking.

Yes, piano adventures and arb runs have made it a lovely, beautiful summer indeed. The arb runs are unfailingly splendid- the piano, less so. But I think I have fallen in love with it nonetheless. I cringe whenever I play a false key, and I feel terribly embarrassed when I stumble over pieces like the too-familiar "Jingle Bells," but my soul begins to thrill when a piece which initially sent a series of winces shuddering through me comes together to resemble something which I may call music. Granted I can only play short and very simple pieces, but I am easily enraptured by the lovely sounds which that instrument is capable of producing when properly encouraged to do so. All in all, I am pleased with the progress I have made in two weeks of playing for about an hour a day, and I am very excited for the next seven weeks! I dare not strive for beauty, for something deep and soul-striking, but I do hope that by the end of it I can play something which may be rightly termed lovely. Nothing crazy or complicated, but still charming.

In addition to the beauty of piano and the natural wonders surrounding Carleton, I have found great pleasure in the social benefits of a Carleton summer. It is wonderful to be at Carleton, to be learning new things and challenging myself intellectually on a daily basis, and to still have time for casual hour-long chats with new acquaintances, for skype sessions with old friends, for cooking adventures, for Sayles slumber parties, for movie-watching, and for pioneering a summer social dance club. I have great hopes for this Summer Social Dance Club (hereafter to be referred to as SSDC), despite what appear to be administrative attempts to crush it. Well, not exactly. But it is very frustrating that the school insists on shutting down all of the buildings after work hours. Nonetheless, this week was very successful in bringing together new and old social dancers, and I now feel like I have dance children to teach and tend to and befriend this summer. It is very exciting! Hopefully logistics will not prove disastrous... but I have high hopes. I look forward to making friends with these new people and hopefully incorporating them into social dance culture!

In short, summer is lovely and sweet. I have been reminded that life has great potential for beauty, if I only toil faithfully to seek her out. She is a shy creature, and must be treated tenderly, but she is sweet and devoted if you patiently cultivate her friendship. I do hope that we may become fast friends.

Happy Summer, dear ones!   

Hailing the Summer

Greetings, fair Reader!

The summer adventures have begun.

 After a brief, happy sojourn home, I find myself back at school for exciting chemistry research adventures. I have finally more or less settled back into my room, with a new roommate and a new set of challenges to conquer. Exciting!

My research adventures started yesterday, and it rapidly became evident that I definitely have my work cut out for me in the next ten weeks...
I have already gotten a tiny bit deeper into Unix, discovered and explored Emacs, and am expected to gain working knowledge of Fortran by the end of the week, since that is the programming language I shall be working in. So in the last two days I have gone through about 160 pages of Fortran.... only 200ish to go! Woo!
Oh, and let's not forget the 100+ pages of reading that I copied for myself today....
It seems quite daunting, but I am rather excited, to be honest. A lot of work means a lot of learning... and I feel like the amount of learning I will be doing will be slightly ridiculous. In a good way.

But I do love that my nerdiness is increasing significantly. I think I may have to start gaming. Or go crazy and convert to Linux. Somehow or another I need to affirm my transition into this particular realm of nerdom.
In my mind, female computer sciencey nerds have a nice edge of badassery, and while skipping through my Fortran book, I like to think to myself- yeah... yeah, I could do that. I could be a cool nerd-girl. I could totally do that!
...But then I realize that my carefully penned notes, general tidiness and prim&proper-ness do seem to disqualify me from playing the role of badass nerd girl.
But hey, that doesn't have to stop me from feeling super cool about coding, does it?

I don't know why I am so enchanted by coding. Maybe because I have been woefully ignorant of how it all works. Computers and programming seem to be shrouded in some sort of magical veil. In some way, computers seem to grasp at the magic of life- quite literally.
Computers stand at the border between physical reality and the wonderful world of abstraction. They translate between the "real" world and the world of ideas. They partake in the mystery of Meaning.
Magic, I say!

I have set about reading I Am a Strange Loop, by Douglas Hofstadter. He is, quite simply, fantastic. The knowledge that he is at Indiana University seriously tempts me to delve into Cognitive Science and ambitiously strive to end up in his lab, because it could only be absolutely awesome. But I digress.
The book builds upon ideas Hofstadter introduced in Godel, Escher, Bach (GEB), but focuses on the concept of I, or the self. Consciousness. That slippery thing!

To my extreme delight, I Am a Strange Loop has succeeded in weaving together essential philosophical questions with cognitive science, basic neuroscience, logic/mathematics, and computer science. (It's amazing how he manages to meld together so many topics and questions I delight in!)
He plays with questions like: What does it mean to be alive? What does it mean to be me?  What does it mean to know? What is consciousness? How might consciousness arise? How can something have meaning?

I think that, through GEB, Hofstadter really got me to appreciate the idea that structure is the key to meaning. Structure... ah, how magical!
I do not think I am yet ready to write out my thoughts on the subject... my thoughts are still hazy and unorganized, but the picture is slowly starting to come together. I just have unstructured words to throw at you.
Words like logic, and structure, and thinking, and meaning, and language, and binary, and beauty.
Wonderful, magical words!

But I should stop my incoherent rambling on Hofstadter's books for the time being.

The days seem to be virtually endless. There is an amazing fifteen-and-a-half hours between sunrise and sunset!
By 7am it is bright and sunny, and the world beckons me to be out of bed.
Thankfully, I obliged the world today. I went for a walk-jog in the arb, and it was a wonderful, wonderful decision. The morning light was gold-like and happy, the plant-life was gorgeous, and a little creek which I found along my path convinced me that I was part of an enchanted world. It was absolutely lovely.

I am not sure what exactly I want to achieve during these bright summer days, but I know that I want to partake in a curious mixture of gentle loveliness and nerd-girl awesomeness. I want to go for daily walk-runs, I want to improve my flexibility, I want to attempt a plunge into the world of music by making an acquaintance with the piano.... I think mostly I want to realize that I really do have a certain degree of control over my life. It is the sort of truth that lurks dangerously in the background. Dangerously, because it is so obvious it seems to evade belief.

I have spent a lot of time feeling small and incapable and boring... and done nothing about it.
But, ha! That is not how the game is played, World! Nice try, but I've finally caught on to your trickery.
The game is played by soaking in programming languages. By having the courage to try to learn piano. By having the discipline to wake up in the morning and greet a beautiful day. The game is played by realizing that you want to do something worthwhile... and then taking a step in that direction.
It's so terrifying, but so wonderful and liberating!

I may get lost in the arb, or fail miserably at piano, or cook the worst meals ever produced on the face of the earth, or feel utterly lost in the world of chemistry. The chances are pretty high that all of these things will happen within the next few weeks. But I have a suspicion that with a bit of time and a lot of work, it's going to be okay.

Maybe there's still hope for badassery. Hmm. Can I be both lovely and badass?
Well... I do love a good paradox.

On The Midpoint

Well, the second year has come to an end.

I remember old middle school days, when I felt safely sheltered from adulthood and "growing up" by the endless high school years before me... and now college is half-past.
It is a bit surreal.
The passing of time seems to have a very strange quality to it. The years seem to fly swiftly by on fairy's wings, and yet days and weeks can drag by in an impressive manner.

In the midst of this strange passing of time, I find it difficult to assess my growth. Surely I change in subtle ways between moments, days, weeks, months, years... But the gradualness of the process makes me incapable of detecting the difference.
I am reminded of when I first learned calculus. The concept of the integral made the tricky concept of life clearer to me: it is the accumulation of changes that occur on infinitesimal time scales. Decisions made from instant to instant appear so incredibly trivial and inconsequential, but the summation of the values of those instants make up a life. Magical.
It is fitting that the integral encapsulates the great, elusive concept of infinity. How do we ever reach the infinitesimal? How do we ever progress? When and where do we capture the fleeting Now? How is it that the minutes and days and years slip by?
The mysteries of life and metaphysics seem to me to be intertwined with the wonder of infinity. It is lovely.

Yet somehow the time does slip by. Somehow "life" does get accumulated between duration-less Nows. And somehow or another, I do make small bits of progress.

As the term approached its end, I came to realize that I have learned things during my time at Carleton. Shocking, right? It is the sort of thing one hopes will happen, but it is wonderful when you realize it is actually true.
There are the little things- like realizing that my knowledge of the Greek alphabet has expanded tremendously since my old high school days, where alpha and beta and pi and theta were funky things that you used in math every once in a while. By the end of Set Theory and Computational chemistry, Greek letters were being carelessly spattered all over my work. When did gamma and phi and psi and epsilon and sigma and lambda (etc etc) become a natural resource to tap into?

Additionally, I have come to realize that tossing myself into reckless situations can be a good thing.
(To clarify, "reckless" in this context refers purely to academic recklessness. Reckless, indeed...)
For the first time in my life, I had the experience of sitting in a classroom where the teacher could very well have been speaking another language, because I certainly was not understanding what she was saying. She was speaking other languages- the languages of quantum chemistry, kinetics, thermochemistry... Languages of which I only knew a few basic words. I was a tourist in a foreign country hoping to rely on words like "food" and "bathroom" for survival.
But I still remember the moment where I re-read a textbook excerpt that was being assigned for about the 4th time. And that time- I UNDERSTOOD what they were saying. Between re-readings and nearly impenetrable lectures and frustrated struggles with foreign words and concepts... the pieces eventually came together. It was a glorious realization- and it would not have been possible if I had not taken the risk of utter failure. And I shall admit, for a while there I was rather concerned.
But there is something wonderful about going in scared and mostly lost, with only a bedraggled roadmap for company, and to slowly gain your footing to ultimately emerge triumphant.
I can now tell you a story about quantum chemistry, I can model a baby protein for you, I can perform ab initio calculations and tell you a bit about a chemical system of interest- I can do quite a few things I simply could not have done ten weeks ago.

There is also the world of dance. Two years ago, I probably would have laughed and blushed with embarrassment if you were to suggest that I would find myself waltzing freely with others in a couple of months. "Ballroom dancing" was something magical, wonderful, and fundamentally unattainable to those not blessed with extraordinary grace. Admittedly, I have yet to achieve a satisfactory level of mastery, let alone claim beauty in my dancing (alas, I have not been suddenly gifted with heaps of gracefulness), but I have managed to learn a great deal during the last two years. Waltz, foxtrot, quickstep, east coast swing, west coast swing, tango, cha, rumba, samba... even some mambo and hustle and nightclub two-step... Two years ago I knew nothing, and in a few months I will have the privilege of introducing social dance to a new generation of future social dance lovers! It is terribly exciting.

I think that my understanding of things has also become more complex and subtle. Two years ago, I would probably have agreed with the somewhat vague statement that science is true. My understanding of models and scientific progress was limited. I was a naive empiricist.
I may still be a bit of an empiricist, but my appreciation for models has increased tremendously. I now value the utility of a good approximation and I understand the importance of knowing the limits within which a model can operate. I realize that there are ways in which our scientific knowledge is solidly grounded, and yet that there are more fundamental ways in which the scientific quest is deeply vulnerable to skeptic probing.

To focus on this spring, I think I can be proud of my accomplishments this term. Computational chemistry and set theory were both challenging and intimidating, but immensely rewarding. I did not expect computational chemistry to allow me to peer into the beauties of linear algebra. I remember the moment of wonder when I realized what my professor was explaining about vibrational modes- you want to understand how molecules move? Break down the motions in terms of an orthogonal basis set which will span the entire space of their motion, and now you can describe any movement your heart desires. Bam! Amazing.
I did not really expect myself to ever come to peace with quantum, but we managed to end on amicable terms. And set theory... ah, how to describe the beauty of realizing that you have built an entire world out of nothing? Or the beauty of the natural numbers, like infinite Russian dolls? Or the sheer wonder of successive limit ordinals, like dense black holes?

All in all, I am fairly proud of myself.
I do not think I have been able to say that in a very long time- I do not remember when. But I succeeded in achieving my goals for this term. No, I don't have a perfectly-filled goals chart- there are certainly a number of gaps. More importantly, I succeeded in fulfilling the aspirations underlying the carefully penned goals on my chart.

Three months ago, I was terrified: I really believed that this term was going to be painful, stressful, confidence-destroying, and unbearably lonely.
It has been painful. It has been stressful. I have been less-than-fully-confident at times. I have been lonely. These things are true. But they represent a small minority of my experiences.

I feared that I would have no great friendships during my time at Carleton, but I no longer have that fear. I have grown closer to a number of wonderful people, and planted seeds which I know shall flourish in the upcoming years.

I feared that I would sink into a pathetic fit of loneliness and moping. But I have realized that I am stronger than I believed. I do not have to fall apart when I am alone. Granted, on almost any occasion I would rather be joined by loved ones, but if I must stand alone, I can and I will.

Ironically, it has been one of my most enjoyable and fulfilling terms at Carleton.

I am still filled with fears and insecurities and doubts on a number of points. I still do not know what I shall "do" with my life. I do not know what exactly that mysterious thing called love has in store for me. I do not know what friendships shall blossom, what pains shall be suffered, what life lessons shall be gathered, nor if I shall ever attain beauty in my dancing.
But I am proud of what I have accomplished and excited for the adventures that are in store.

There is hope!
And for now, that's all I ask for.

Here's to the midpoint of my Carleton career. Huzzah!

A Spring Quest

Hello again dear Reader,

Spring has come to Carleton!
I intend to take a nice walk around campus and capture its loveliness on camera, but haven't quite gotten around to that yet. For those of you not fortunate enough to be here, I assure you there is much in the way of happy greenery and pretty flowers to delight the soul. I am especially happy that my tree friend by the concert hall has started to blossom. I have already been taken aback by her loveliness, and I am excited for the moment when she is fully bedecked with beautiful flowers. But really, there are many pretty things sprouting around campus. Spring is wonderful!

Spring also means the beginning of a new term, and the term is already on its way. First week has met its end, and week two is all ready to rush in. This term is going to be a crazy one for me... but currently I am very much in the idealistic phase of my voyage. For some reason winter term seemed to skip the idealistic phase altogether. Winter term started off in the midst of a whirlwind, I think, and I didn't even have time to formulate grandiose schemes.
But now! Ah, this time I have set sail with all sorts of wild hopes and dreams for grand achievement, and it doesn't help that I am already surrounded by a paradise of lush greenery to make my dreams seem all the more realistic!

As I said, the term is going to be a little crazy. Or a lot crazy. I am venturing into the upper levels of math and chemistry for the first time. Math-wise I am taking a seminar in set theory, which should be very cool but also seems a bit intimidating. We're basically building up Zermelo-Fraenkel set theory and shall be working on constructing the natural numbers, integers, and real numbers. There are a lot of very quick-thinking, intelligent math people who are fortunately very good-natured and fun, but I know I'll be working hard to stay on top of things. I'm a little scared, but mostly very excited.
As for chemistry, I am taking an introduction to computational chemistry, which is almost guaranteed to kill me (in a good way?). My professor (with whom I'll be doing computational chemistry research with this summer, coincidentally) is awesome... and (or but) she expects a great deal out of her students. She promises us that we will learn tons, and she also promises that we will be working HARD to get there. This class again finds me feeling a bit intimidated, as it's a class composed almost entirely of hardy, senior chemistry majors... but they also seem like a good batch of people. It should be a very rewarding class, but, again, it's going to be a ton of work. My last few days have been spent trying to make good enough sense of quantum chemistry, and we'll be reading a ton of literature... oh, so much learning to be done! Trying to piece together quantum has certainly made me want to learn quantum in a nice and thorough manner, as well as like... all of math. I need to do differential equations and more linear algebra and statistics and apparently abstract algebra is also used to describe quantum stuff... Oh goodness, there are so many cool things to learn!
My last class is intro psych, which is nothing compared to the other two, but should provide interesting things to muse on.
Finally, I am lab assisting for a chemistry course and grading for a physics course. This also translates to a lot of work.
So essentially, I have a lot to do in the next ten weeks. A lot.

Even with this realization- or partial realization- I am filled with ambition. My roommate and I decided it would be an excellent idea to put together goal charts to keep us motivated. Here is mine!

What could be more exciting than rewarding oneself with cute stickers for a job well done?
Realizing that you have made your dreams come true! 

While I do have these specific goals that I'm working toward, I think I have two main ambitions.
The first is to stay involved in dance stuff. Ballroom/social dancing is awesome! The people are great, the dancing is fun, and it gives me an opportunity to develop a somewhat unusual skill. Part of my plan is to start to learn how to lead (My respect for leads has increased considerably. It's so stressful to have to plan out and keep track of directionality, timing, posture, technique, floor craft... Oh goodness!), and the other part is to try to work on solidifying technique. I want to make sure that, on a regular basis, I go into Cowling and seek refuge from life-hecticness on the dance floor. It'll be a good mix of challenge, socialization, and relaxation.

Second, I am intent on maintaining a positive attitude. There are a lot of challenges ahead of me, academic as well as social and emotional in nature. I expect the term to be a difficult one, but, more importantly, I expect it to be an opportunity for wonderful growth. There are a lot of cool people in my classes (and on the dance team!) to get to know better, there is a lot of interesting material to be learned, and there is so much beauty around me to walk around and appreciate!

I think a challenging spring term is a good way to kick off this whole blooming adulthood thing.
What with best friends at different schools, people (including myself!) working over the summer, a boyfriend exploring the streets of Moscow, and my own hopes to study abroad, the next... eight to nine months have me largely estranged from those happy individuals who more or less make up "home."

So... I'm on my own little adventure now.
It's time to learn new things, to step away from sluggishness and step into my swan (or sparrow!) skin, to face challenges and defeat them, and to dance and go on pleasant strolls every now and again.

Happily, I now have the chance to gather stories to be exchanged with loved ones at a future time when our paths may converge, and thus bring me back home- if only for a time.