R.I.P., Arthur C. Clarke

No doubt there is going to be quite an outpouring of posts like this on all the nerd blogs all over the world, but I don’t care. It still needs to be said.

Today, Arthur C. Clarke, one of the most well-known science fiction writers and futurists of the twentieth century, died.

I’m not going to launch into a long, sentimental retrospective of the man’s life. That’s what obituaries are for. I just wanted to say that he will be missed. A lot.

R.I.P., Arthur C. Clarke

December 16th, 1917 — March 19th, 2008

Freedom in Mathematics

When I was in primary school, I hated math. It bored me to no end. To me, all it was was some heavyset woman making us do endless addition or subtraction or multiplication drills, for no reason other than the fact that we were ordered to. What was worse, all I ever saw of mathematics was a single, linear path. You started with a problem, and then you proceeded by the same old steps through the same old terrain until you found the solution. Even if the numbers involved changed, the methods didn’t, and after a few years, I started to realize that it was really all just repeating the same few problems over and over again, in different guises.

It wasn’t until I entered college that I started to re-discover the beauty of numbers and patterns (which the public school system had blinded me to, but that’s another post entirely). And today, I came to an amazing realization.

You see, I’ve been taking Differential Equations for the past few months, and it’s always struck me as the way math is supposed to be. Differential Equations is a class where it must be acknowledged that there are some problems we don’t know how to solve in the traditional way, or that we can’t solve at all. It’s the logical opposite of algebra.

You see, algebra was the first subject that really made me despise math. There was no freedom in the solutions: all you did was shuffle some numbers around, and eventually figured out the value of the variable in question. There was no room for beauty or creativity; it was just a very roundabout way of doing regular arithmetic.

Not so with calculus. Not so with differential equations. You see, in calculus, there is more freedom. You’re usually not searching for a number, but for a function. And whether or not you can find the solution depends on how creatively you can construct and reconstruct the problem. For example, in order to find the area under the curve defined by y = exp(2x), when x varies between -1 and 1, you have to use an integral. But you can’t just integrate right away. First, since there’s only a fairly small types of integrals that can actually be evaluated, you have to rebuild the problem from the ground up. Usually, this particular problem would be solved by saying that u = 2x, which turns the problem into the one of integrating y = exp(u), which is solvable.

That’s why I’ve always loved calculus: there’s always room for creativity and exploration. And the more complex the mathematics, the more ways there are to solve any given problem.

Thinking about all of this led me to an epiphany while I was walking home from my philosophy class: once you get past arithmetic, mathematics is not about doing the same thing over and over to slightly different problems in order to get slightly different answers. In fact, most problems don’t have a single answer. For example, take Schrödinger’s Equation, which is the basis of most of quantum mechanics:

What the variables represent isn’t terribly important. What’s much more important is what the equation represents. If this were an algebraic expression, it would simply represent an answer that you haven’t found yet. But Schrödinger’s equation, and other equations like it (such as the Einstein Field Equations of general relativity), they simply represent constraints that select certain solutions and correct, and others as incorrect. They’re not number just waiting to be found, they’re more like intelligent little computers that decide what is real and what is not, mathematically.

 To understand what I mean, consider a much simpler differential equation (and please forgive the ugliness of the notation, but I’m working from some pretty severe graphical limitations):

y’ = k * y

This is not just a number in disguise. Instead, it’s a pattern that any function f(x) must fit in order to be called a solution of the equation. Contained in that tiny equation is the “truth filter” that passes through any exponentially growing or decaying solution. Likewise, Schrödinger’s equation is merely a filter that determines whether or not a given function can occur in real life or not. According to Schrödinger’s equation, electrons can change energy levels and emit photons, and particles can occasionally jump through barriers.

That is the true beauty of mathematics: every equation, every principle, every theorem is nothing more and nothing less than a little filter that produces reality from all the infinite possibilities inherent in the universe. Mathematics is incredibly intelligent in that regard, a perfect structure that selects real reality from the infinitude of possible realities.

And that is why I’m a math major.

Happy Pi Day

As a card-carrying nerd (all right, so there is no card, but there should be), I am obligated to wish my readers a happy pi day. Today is March th 14th, which means that the date is 3-14. To commemorate the occasion, I present to you: all the digits of pi that I have memorized:


Okay, so it’s not much, but I occasionally forget my own telephone number, so it’s quite a feat as far as I’m concerned.

Pi has always been one of my favorite mathematical constants. It’s probably the most abstract. What pi is to me is the perfect expression of the structure of mathematics, a sort of symbol for the deeper order that lurks beneath the foamy surface of our universe. Pi is built into the structure of everything, from the geometry of spacetime to the fluctuations of quantum mechanics, and I have a hunch that it will appear in some form at the intersection of the two. I like to think of it, if you’ll forgive the theological reference, as God’s Rivet, the little pin that holds everything else together.

So, happy pi day.

And also, happy birthday Albert.

And I hope you’ll all join me in my Ultimate Pi Day celebration on March 14th, 2015, at 9:26 and 53 seconds (AM or PM, your choice)!

Review: “10,000 B.C.”

I went into this movie not expecting much. I’ve seen a lot of the older movies about the stone age, and none of them have impressed me either in storyline or in scientific or historical accuracy. The “prehistoric” genre has a tendency towards cliché and unoriginality.

On the whole, however, I was pleasantly surprised. 10,000 BC thrusts you into the world of Dalay (or Delay…I don’t know), a hunter of woolly mammoth for his tribe. As a result of a prophecy of some sort, he finds himself wandering through the wilderness, beyond the borders of the tribe’s tiny known universe. There’s a lot of action and adventure along the way and good things happen and tragedies happen and then it all gets wrapped up by the ending.

All in all, it’s a very atmospheric movie, seemingly filmed partly in that same beautiful stretch of New Zealand that served as Middle Earth in the Lord of the Rings films. The tribe’s social organization feels genuine, as does the technology and the characters’ daily lives. I also like the fact that, when they encounter other tribes, none of them speak the same strangely-accented English that Dalay’s tribe speaks. It’s a refreshing change from films where everybody speaks English, although, in this film, apparently everybody else in the world speaks a common language, which seems rather odd.

The film starts to lose me when the characters walk over a snow-covered mountain range to find themselves in a rainforest, and then only a few minutes later, in a desert. I’m not certain, but it seems unlikely to have those three climes so close together. Even so, the environment is used to good advantage throughout the film, and they manage to make even the desert look pretty, in a desolate sort of way.

The film loses me even more, though, as it plunges into a series of strange semi-spiritual “spirit-guide” sort of side sequences, which seem to me not to add anything to the film but to allow them to hack together a happy ending. It all seems rather unnecessary, and did a great job of keeping me distracted from the main plot.

That aside, though, the film rapidly degenerates into a slag heap of sentimentality, clichés, and overwrought action sequences. About halfway through, it seems that the creative members of the writing staff went home, and from then on, 10,000 BC follows the standard cookie-cutter action movie plot almost to the letter. Also, there were some sequences that looked to be copied right out of 300. Now, it’s possible to copy from or pay homage to a film without looking pathetic, but that’s not the case here. Here, it feels more like sycophantic desperation to soak up some of 300‘s impressive success.

In the end, though, it’s not a bad movie. The various tribes feel authentic enough, and the casting and writing were done competently enough that they really feel like different cultures with different traditions. The landscapes are pretty and, in general, it certainly feels like prehistory, which is fairly impressive, considering the difficulty of making a movie about a period with no historical record on which to base the plot. Perhaps, in light of this, some of the historical inaccuracies can be forgiven (unless, that is, you’re a hardened and obsessive science nerd, like me). The plot’s not much to speak of; it’s basically standard adventure movie canon, with some interesting extra bits tacked on. But still, you have to admire the filmmakers for being bold enough to build a film around such an innovative historical setting, even if the story does fall flat in the telling.

Final Judgment:

* * * * * * ~ ~ ~ ~ (6/10 asterisks)

Films to Watch Out For: “Interstellar”

Most of the time, I hate the Internet, because most of the time, it’s merely a conduit for people telling me I need to buy a new cell phone or enlarge various parts of my anatomy. Sometimes, though, I love the Internet. Sites like Wikipedia seem to be bringing about a cultural revolution. So much information, right at our fingertips (how’s that for a well-worn cliché?). A shining example of that kind of encyclopedic accessibility is imdb.com, the Internet Movie Database. Nowhere else can you find such accessible and detailed information on any movie or actor or director or writer you’re interested in.

Case in point: one of the greatest mathematicians of modern times was Paul Erdös. He was the second most prolific mathematician in history. And he is credited on imdb.com, for an almost-unknown forty-five minute film about himself. Unbelievable.

By now, dear reader, you’re probably wondering just what the hell I’m driving at. Well, the previous two paragraphs were a long-winded, roundabout way of telling you that, sometimes, the Internet allows neat little serendipitous accidents.

One such accident is my finding out about the movie Interstellar. Scheduled to debut in 2009, interstellar is, and this is a direct quote from imdb, “An exploration of physicist Kip Thorne’s theories of gravity fields, wormholes and several hypotheses that Albert Einstein was never able to prove.” What’s more, Kip Thorne himself is credited as the creator of the film’s story. I still fondly remember reading Thorne’s incredibly accessible book Black Holes and Time Warps. It was funny and richly informative, and if Interstellar is anything like Thorne’s little explanatory vignettes in that book, then it’s going to be an impressive film.

What’s more, Steven Spielberg is listed as the film’s director. I’ve always been a great fan of Speilberg’s films. Most of them are at least competent, and many of them are classic. And even if Spielberg’s sentimentality kicks in on this film, he’ll be counterbalanced by writer Lynda Obst, executive producer of Contact, which is arguably one of the most realistically compelling science fiction films of our time.

And that’s all I know. Since it isn’t, as far as I know, even in production yet, there’s not much to know. Still, for a geeky fan of hard science fiction (such as myself), Interstellar smells of a great film. It may in fact be one of the first films to competently handle the subject of wormholes.

I wait with breathless anticipation. (How’s that for a melodramatic conclusion?)

Review: “Michael Clayton”

I don’t like films about corporate intrigue, generally speaking. Most of them are either so slow that I don’t bother to follow the plot, or have been so artificially inflated with action sequences that I can’t tolerate what plot there is. This was the same sort of problem that I had with Syriana (and yes, I know that’s not really a corporate espionage film, but I’m making a point here!): the plot was too fast, too disjointed, and too confusing.

Tony Gilroy’s Michael Clayton is one of the few exceptions I’ve seen. Starring George Clooney, Michael Clayton is a story of the life of…well…Michael Clayton, a professional sweeper of corporate problems under the corporate rug (or “fixer”, as they call them). After being sent to control the ravings of another mentally-unstable fixer who decides to go on a personal crusade against the company he’s currently “fixing” for, Clayton comes to some realizations about his job and just what he’s gotten himself involved in.

The film is executed incredibly. At times, it’s so well-written and well-acted that even the incredibly boring office scenes become exciting. Director Gilroy certainly has a gift for pacing as well, ensuring that no scene is uninteresting. Even if it would be under normal circumstances, Gilroy somehow manages to add a detail, or a character, or a voice-over, or sometimes just the right piece of music to prevent the action from stalling.

This may be because Michael Clayton is a character-driven film, a precious rarity in modern cinema. The characters are all fairly well-defined, even those that make only a single brief appearance. None of them feel like cardboard cutouts. One gets the impression that they all have problems of their own, even if those problems aren’t explicitly handled in the actual movie.

The plot, too, is masterfully composed. Most movies of Michael Clayton‘s sort — and here again I refer to Syriana as a reference point — have a tendency towards plots with incredible complexity. It’s hard to squeeze a broad-ranging, international, lifelike series of events into a few-hour movie, and the result is often that the scene transitions are so choppy and hard-to-follow that the plot baby is thrown out with the runtime-reduction bathwater (and yes, I know that’s not exactly an intuitive analogy, but give me a break, I’m tired). Michael Clayton, however, manages to make the plot make sense. Being a child of crappy action movies, I’ve always had a bit of difficulty following complex plots, but Michael Clayton conveys plot with enough clarity and simplicity that it made sense on the first viewing.

Regular readers of my movie reviews know what comes next: the complaints. That’s one thing I’m good at: finding fault with movies.

First of all, as tight and well-constructed as the plot is, it still manages to meander at times. There are some scenes which don’t make sense, or seem utterly random. It’s almost as though there was a bit of backstory written into the original script that ended up on a cutting-room floor somewhere. This lends parts of the movie an uncomfortable senselessness, which may actually have been intentional, considering the kind of senseless malevolence many corporate entities engage in, but when it comes to films, I give nobody the benefit of the doubt.

Also, the film is depressing. Of course, this kind of film is bound to be, but there’s just a certain darkness to it so that even in its brighter moments, it only ever manages to break even, emotionally. This is good, of course. This is what a good film is supposed to do, create an emotional atmosphere, but it means that Michael Clayton can be hard to watch if you’re in a bad mood. Then again, the air of doom that the film constructs fits so well with the overall storyline that I think I can forgive it for being depressing.

All in all, an excellent film. Probably one of the best of 2007. I’d say the best of 2007, but it has to compete with films like Sunshine, and I’m a huge science fiction nerd.

Final Judgment:

* * * * * * * * ~ ~ (8/10 asterisks)