Anyway, so the whole calculus of variations thing revolved around having some kind of integrand of the form if you want an system of equations to solve for your coefficients of the polynomial that will approximate the real solution that will minimize the functional. Well, as luck would have it, things are much easier than that! I mean, you don’t even need higher order derivatives, or really derivatives at all. For some functional

you can just make a sequence of polynomials and then evaluate . Define , . Same deal as before– is a function of the coefficients of the polynomials as defined by the functional . So, for an th degree approximation of the function that will minimize , you can just find the kernel of the matrix

.

Voil! To me, this makes sense. However, in practice, it’s hard to check. Some of the integrands you encounter get REALLY out of hand REALLY fast.

Ahh, flight to Atlanta is boarding, time to go!  FINALLY!

Now, this normally wouldn’t be a problem. Overpriced everything aside, I actually really like airports a lot. I feel like you can tell a lot about a city by its airport. How much art there is inside of it, what kind of stores there are, how it’s designed architecturally, etc., etc. Well, as it turns out, Tampa’s airport is nice, it’s just…boring. I guess all of the terminals are disconnected or something, so I can’t exactly go hopping in between concourses and checking out what’s around. I’m confined to terminal E, gates 69 through 80…something. I don’t know. And ALL there is is your standard airport shit–you know, Starbucks, overpriced sandwich shop, those smoothie shops that try to make it look all Euro by putting in as many accents as possible on every word, bland magazine shops and book shops, and a Delta Crown Club on a key-code protected second floor that overlooks the peons with low frequent flier miles below. The terminal itself takes about a minute to walk from one end to the other, so it’s not like I can do some serious, moody pacing to pass the time. Nope. Shut down.

I can’t wait to get to MIT. I know there are things I could be doing for that right now–like studying for the ASE or something–but…I just don’t feel like it. I got a grand total of two hours of sleep last night, so just…no. I’ll just screw around on the Internet for the next five hours or so, like any REAL MIT student would do.

Have you ever gotten the urge to watch Total Recall? You know, Arnold Schwarzeneggar goes to Mars for a “vacation,” then winds up in a crazy adventure that ends in him saving the WHOLE PLANET and making the atmosphere accessible to humans? No, you haven’t had that urge? I assure you, it’s quite surreal. There are far better things that could be surreal and time-worthy than wanting to watch Total Recall.

What is real these days anyway? The line between reality and fantasy is blurring. No, the line has always been blurred. I just stopped squinting my eyes to make it something that it wasn’t and never will be. Focus, focus, focus.

I hope the bottle of shampoo in my luggage didn’t explode.

EDIT: Looks like the TPABOS flight is total fail, so I’m being rerouted to Atlanta, then to Boston, with only a 1hr30 delay. At least I won’t have to be bitching about airports anymore!

Today, I went to see Dr. Pappas in Birmingham, AL, four hours away by car. He’s the doctor that operated on my ears about a year ago, removing the big ol’ cholesteatoma and giving me my lovely prosthetic ear bones. Well, I had another cholesteatoma over the summer (a small one!), and in the process of removing it, he went ahead and adjusted my prosthesis. I saw him today for a 6 weeks post-op follow up, and he told me that my hearing in my right ear–the one that got itself all screwed up–is basically back to normal! I have minimal hearing loss in the speaking voice frequencies. The only thing I could be consider really “hearing impaired” for anymore is in the high frequencies (for which it takes about 50-60 dB for me to hear, as versus a normal 10-20 dB). Either way, it’s actually really amazing–this kind of full recovery is pretty rare. I walked into Pappas’s with significant hearing loss, and a year later, it’s back to normal! I’m really excited. You guys can’t make fun of me for being deaf anymore!

While in Birmingham, my mom and I also took the opportunity to do some shopping, since Podunk(Pensacola) doesn’t have shit for stores. (Read: mother buys me not purely functional clothing that I want instead of me paying for it.) My neighbor gave me a $100 gift card to Urban Outfitters, so that was pretty boss. I also became the douchiest person on earth, and I’ll tell that lovely story next week.

In other news, I’ve discovered I REALLY like Serge Gainsbourg.

Less than a week until I go up to MIT! Now, if only I can manage to avoid having my cat puke on my new clothing before I leave…

Musing #2: I bit into my tongue like I was biting into a tough steak. In other words, ow. That’s not really a musing as much as it is a complaint.

Musing #3: I’m reading The Wind-Up Bird by Haruki Murakami on a half-suggestion that SOMEONE wants to take credit for It’s really good so far. I love the Japanese style of writing–it’s more succinct, yet the words pack more meaning than usual. The clipped, to-the-point phrases provide a perfect balance between the emotional impression of the events and the characters and the factual surface of the plot. Speaking of Japanese authors, we had to read Snow Country by Kawabata in my junior English class, and I’m really, really glad we did. It’s one of my favorites now. I highly recommend it.

Musing #4: Next time you’re driving while it’s raining, look out one of your side windows (also, don’t get in a wreck.) If you’re driving fast enough, you should see streaks of rain traveling across your window until they hit the boundary of the window, whether it be the top, bottom, or at the other side of the window. The interesting thing is, though, that these paths seem like they change very little. A raindrop will hit the windshield, be pushed over to the side window by the windshield wipers, and then depending on where the raindrop ends up on the edge of the side window, it’ll join one of many nearly pre-determined paths, until it reaches the end of the window. Okay, so, what’s the big deal? It’s not that hard to see that the water will follow the path of least resistance, which will be determined by the shape and curvature of the windshield, the friction between the window and the water at each point on the window, the speed of the car (not as important), and how much water is collected along the edge of the window (i.e., how hard it’s raining, or how efficient your windshield wipers are). But the really cool thing is that when you look at the window, you can see each of these variables playing into effect over the entire window, since there are many drops of water going to the window at once. The end effect is that you basically see the simultaneous graphs of the solutions of a (stochastic) differential equation describing the flow of the water droplets for initial starting positions on the edge of the windshield. All at once! Your window becomes a giant graphing calculator. Isn’t that badass?! (Also, I definitely didn’t almost get into a wreck looking at this in the car today.)

Musing #5: Let . When is there a function such that

i.e., when can I find a function transform between them? I feel like this could be an easy question–especially because is so well-behaved–and I really just don’t know enough to answer it properly. Well, it’s first worth nothing that the kernel is very acceptable. Actually, any reproducing kernel multiplied by the function I just gave would also work (given, of course, that you’re in an appropriate subspace of ), even though that’s still trivial and very constraining. Otherwise, though, what else could you do? My best guess would be to first look at the dual space of , treat the function transform as a functional, and then use the Riesz representation theorem to start finding appropriate kernels that would work. By the Riesz representation theorem, we know that for every point there exists a unique function in such that . That specific function takes care of that one specific point . Here’s where it starts getting shady to me. Well, if we can string all of these functions together somehow for all of your points in the image of , you could maybe coerce them into making a our desired function . One idea would be to expand into its Fourier series representation, and then use the individual functions you get for each point to solve for the coefficients of the Fourier expansion of , and hope a pattern emerges or something converges. At the least, you could do a MASSIVE piecewise function, but that’d be extremely impractical and not at all elegant. In conclusion: lolwut

Musing #6: I DON’T KNOW WHAT I’M DOING

It makes perfect sense, though. Everyone wants their ideas to be seen and heard. Everyone wants to be an expert, no matter how obscure the field. And that brings me precisely to the title of my post. People are pretty into fish, right? But most people are just at the level of “Let’s go down to the river and fish for snapper.” Well, that’s just for amateurs. The experts can’t waste their time with that. They’re busy reading books like Quantitative Fish Dynamics and making fish such SERIOUS BUSINESS that they probably forget that fish are nothing more than tasty snacks (unless they’re Betta fish, at which point they become fearsome warriors ready for insta-battle.)

Really, though, what’s so funny about Quantitative Fish Dynamics? If you look through the book at all, you’ll find that it actually is serious business, and that it gives good, hard, mathematical models of fish populations fisheries. But it’s funny, because who does that? Who gets a degree in (assuming applied) mathematics and then studies fish until s/he can write 566 pages worth of serious business on fish? I guess it all really depends on where your passions lie. If your passion happens to be probability/stats and fish (not necessarily fishing!), then Quantitative Fish Dynamics sounds like a book you might write. I mean, I wish I was passionate and knowledgeable enough about fish to write a book on fish dynamics!

All in all, it’s not so worthless as I protray it out to be. Someone equally as obscure uses for an equally obscure purpose. It’s just interesting how much information on things that you wouldn’t think about exists everywhere. (Actually, books about fishery population dynamics isn’t a far stretch, especially considering that it’s about making money.) Moral of the story: if it exists, it’s somewhere on the Internet, and its Google hits are over 1,000. \end{rambling}

Tonight, I head off to Boulder, Colorado for a visit with my uncle, aunt, and cousins, as well as a short climb on Flagstaff Mountain. It should be pretty interesting, especially considering it’s my brother, my dad, my uncle, and I all in the same place. It should also be interesting because I got told they’re going to celebrate my brother being 21, which means they’re going out and I’m tagging along exclusively to be DD. Yay. Expect pictures!

But it was business as usual. People broke off into their individual groups; we acted as the nuclei of our former social groups, protecting ourselves in a large membrane filled with copious amounts of “sticks and stones will break my bones but words will never hurt me.” And we chatted, and a member would break off and join another group, and we shifted around the entire night, mixing and matching, trying on new people, seeing who was different, sizing up  so-and-so, sifting and sorting the confusion that arises from a group of people you once knew very well. And we still knew each other very well. But some things were different. Yes, some things were different, that’s for sure.

And there will be people I will miss. Absolutely. Whether they be our class characters or simply just good friends of mine, there will absolutely be people that I’ll think about when I’m up in Boston, wondering to myself, “How is he doing these days?” There will be people that I’ll think of whenever I’m walking through the freezing winds in the winter, especially those with whom I walked from class to class and faced the terrible Pensacolian Arctic Winds. There will just be people, people I wonder about, but may not even ever take the time or chance to tell them I’ve been wondering about them. After all, isn’t that a weakness? Isn’t it embarassing? To tell someone you’ve thought about them, when maybe they haven’t thought about you?

And it was business as usual. I got my normal greetings, and I aggregated with my normal crowd. I bounced back and forth, and I swapped stories, swapped innumerous “What have you been up to?” ‘s, swapped little pieces of myself and other people back and forth. And I knew who I was going to keep in touch with and who I wasn’t, and I knew who I would maybe not talk to frequently but would always keep coming back to. Pay full price of postage. Return to sender.

There’s one person who I know I’ll definitely miss, simply because he’s one of those people that you meet once in your life, and you don’t forget easily. The reason why is difficult to say; he’s got a sort of draw and appeal with people, and I, too, was–and am–magnetized by his quirky and insatiable drive to make the world one great story. He’s got a way with words–speaks like he’s been alive for years and seen it all, and writes like he was bedfellows with Truman Capote. He brings back to life the lost art of story telling, and he pokes, prods, and otherwise provokes the imagination in ways that I thought were impossible to do. He brings art to life, and life to art. And he’s so unapologetically himself, so caught up in the world he lives in, so good at what he does, that he’s become the central character, that it’s around him the stories revolve–whether he’s the subject or not. And it’s easy to see why. He’s stumbled upon the secret to becoming exactly who you want to be without regards to others. He’s stumbled upon the secret of perfect illusionism. He’s stumbled upon the secret of living large–not because his life is necessarily large, but because he’s figured out a way to use the fact that life has no size. It’s deformable. It’s yours to make what you will. I’m going to miss him a lot, and I don’t say that about many people. While I don’t have regrets, I know for sure that I would have been better off if I was better friends with him sooner. Hopefully, I’ll run into him in the future, so he, in the likeness of Anansi’s creations, can continue to spin his stories for me, cobwebs upon a sleeping Truman Capote’s head.

Business as usual. And I’m back. I’ll see these people probably at least one more time–after all, we’ve got a few more events on the calendar together–but I feel like I’m done. Pensacola’s always been a place where I never really feel like I fit in, and it’s in in its terminal stages. It’s kind of like those little toys you play with when you’re young where you have a tiny wooden bench with a square hole, a circle hole, a triangle hole, and then you fit the corresponding shape into the hole. Except for the fact that I’m a dodecahedron, and Pensacola is missing its dodecahedron hole. So, of course, I’m kind of jammed through whatever will take me for that moment until it starts to be uncomfortable, and then I switch. The child never cries, though, when he realizes that it doesn’t work; he just gets genuinely confused. Either way, Pensacola has always felt kind of odd to me. And now that I’m beginning to say goodbye, I feel like all those questions that I had—did I do everything I could? was I the problem, and not Pensacola? did I try hard enough?–are melting away into the copper colored shallows of Escambia Bay,  fallen into barnacle-ridden riff-raff aside the train tracks

Now, here’s the problem. THE SHIT LIST is almost empty. That’s to say, I’ve got only a few items on there. Why is it empty? Is it: (A) because I’m so productive that I did everything early; (B) beacuse I don’t know what I’m doing; or (C) because I wrote the rest of it in UV activated ink?

The correct answer is actually (C). [And now I hear Manu Chao in my head, "Deeeeeniiiiia, deni-deeeniiia..."]

Either way, today has been a let’s-get-things-done day, like most of them should be. I got done things on my daily SHIT LIST. I ran errands. I almost avoided the $50 fill-up for my ghetto Chrysler Sebring convertible, which thankfully only needs to last me two more weeks in P-town. (Did I mention how I actually modified the convertible to let water inside the car while it’s raining? It was pretty difficult, but since, you know, I’m such hot-shot MIT material, I figured it out.) I got forms notarized to give power of attorney to my parents for my Schwab account, and I sat and tried to fix  a T-shirt that I screwed up. (I just ended up screwing it up more, like a certain expert fashionista said I would. Oops.)

The biggest thing I’m attempting to work on, however, is cramming multivariable calculus into my head two weeks before the Advanced Standing Examination, to see if maybe I can skip out of it. Multivariable calc has always been one of those things that I kind of halfway knew, but I just never took the time out to really study it, do problems, and get it nailed down well. I know enough that I understand everything fine whenever I read about things/proofs in math books that happen to involve multivariable calculus, but I don’t know enough to actually sit down and give you pointers on how to evaluate that nasty contour integral, or to tell you why that specific surface in space isn’t smooth. So, given the lack of time I have left, I’m simply going to cram as much as I can in my brain, do some problems, and hope for the best. The worst that happens is I fail, I go to 18.022, learn everything right and proper, and MAYBE I feel slightly wasteful with my pass-fail semester. The best that can happen is I pass, I get credit, and I take 18.03 first semester, which I know less about. Either way, I’m going to learn something and meet new people, so I’m not too worried. If anything, it gives me an excuse to devote mucho tiempo to learning math, and avoid doing things on THE SHIT LIST.

All right, time to go to Spencer’s and buy a black light so I can figure out what I’m doing.

So, after musing and some white-board scribbling late in the evening/morning over Frosted Mini-Wheats, I came up with a scheme with too many conditions to be of practical use in many places. It is a start, however, so here it goes. Let’s assume we have a functional that we wish to minimize/maximize, where is the space of analytic functions with convergent power series representation on some open set . For , let be defined as

where is closed. Because is analytic, we know that it has some power series representation

.

Now, let’s truncate the power series representation up to the th degree–in other words, let’s assume that is well-approximated by . So, we have then

but, becauase is a polynomial, its derivatives are easy and known, and we end up with

which is the functional now in terms of the real variables . Now, define a function by

where (sorry, too lazy to write out a whole array ). So, from here you can simply find the extrema of to figure out the coefficients that will give the extrema for . The idea is then that the actual solution that will yield an extremum for the functional can be approximated by the coefficients that give an extremum for –i..e, .

So, what’s good and bad about this technique? Well, let’s talk about the good. The good is that if is sufficiently nice, then you’ll end up with a hopefully pretty easy system to deal with, and you can get a nice polynomial in degrees that will approximate your answer. If you can add as many higher order derivatives as you want, you can even create a sequence of functions that will hopefully converge to an actual answer. Under the correct conditions, this could actually solve the problem at hand. Now, the downside to this technique is that there are already quite a few conditions to assume, and even worse, I can’t think of a single functional of any practical interest that uses, say, more than the second derivative of a function in its space of admissible functions. In other words, the best you could get would be a quadratic approximation to the answer, which probably won’t turn out to be all that helpful if you need a fairly good idea of what the solution looks like. Assuming, however, that you can use an arbitrary number of derivatives to get as many coefficients you need, the likelihood that the function will actually converge to an analytic function seems kind of slim, since the analytic functions are such a small class of functions. All in all, I think its biggest limitation is that most functionals (that I’ve seen) don’t always take lots of additional information in the form of higher order derivatives.

Either way, I’ll keep on tinkering with it, and we’ll see where it goes!

The major thing that’s changed since I last wrote is that I now go to MIT, and that I’m starting there in the fall. Moving date is August 18th. Temp room is 462C, Senior Haus (baller!). I’m going to be doing the DEECS FPOP, and then classes will start on September 3rd, where I’ll slowly begin to chip away at the GIR’s. Somewhere in between is orientation, getting used to MIT, figuring out what I’m doing with my life (course 6 and course 18 double major? neuroengineering group at the Media Lab? mathematical linguistics?), bending my mind to become like the angular curves on the Stata Center, and realizing that the Infinite Corridor really isn’t that infinite. (All right, it’s long, whatever, but seriously? Expectations were set WAY too high for all that it turned out to be.) Either way, I’m really EXTREMELY excited

Other things that have had just as big of an effect on me have changed, too, but I won’t get into them right now, mainly because they’re simply just personal things. Things that I keep close to me–things that I don’t let out of my sight. Things that stay, leash, chain and all, tied to the tree. Things that I slip under my pillow and mattress while I sleep at night. A pea-sized kernel of reality for the tidal wave of dreams that swept over me one week in the midst of the Florida heat and solitude. And you can dig if you want, I’ll tell you things, sure. I’ll tell you everything that natural language can say, I’ll permute my words and my phrases until they’re nonsense, until they’re zeroes and ones strung out in our binary universe, giving you nothing but those precious bifurcations needed to sort through a false hay stack in search of a true needle. But when you find the tired, dull needle in the haystack, you’ll find that when you prick yourself, you’ll draw no blood. You’ll find that that when you try to sew something new, something posh, fresh, fashionable–you’ll find your hands quite capable, but the needle unwilling. And it never will be willing, because it’s inherently something no one else can understand. And that’s exactly what I will do: I will prick my finger in silence, and watch the blood bead up around the cut. I’ll let my hands become not my own–better, more beautiful, and I’ll sew a cloak to protect me (ususus). I’ll sleep in my bed, and toss and turn endlessly throughout the night over a pea-sized reality that was born from the monster of a lucid dream.

There’s also a poem that I think of whenever I encounter one of these days. It’s a poem by Wallace Stevens, called, of course, Sunday Morning. It’s a poem more religion/Christianity, but the texture of the words flowing in the poem is much like the sundaymornings I’m describing. The only way it would be complete would be if it were Easter. (But last weekend had its chance to be poetic already. It had its chance to make a mark, but it didn’t. And perhaps that’s the most fitting outcome.)

sundaymorning. It’s a bit of a rarity. You don’t enjoy a sundaymorning, you become part of it. You join the tableau. You blend in with the wall of dying flowers.