All that has not been said

As a consequence of the major drilling booboo near the Magallanes flyover, traffic slowed to a horrendous crawl and I was nearly late for the final episode ofMagkaribal. It was predictably lame, but of course I watched it anyway. These are the days when we can endure something so poorly contrived with such attention and satisfaction. After the show, my mom asked me if I had read one of the letters to the editor in the Philippine Daily Inquirer. I found it on the Internet (here's a link and here's the article he was objecting to) and was left feeling dazed, confused and saddened.

I once had a friendly debate with my friend regarding Jose Rizal and his novels. His point was that those novels' popularity were not so much a product of Rizal's writing prowess but more the result of a series of fortunate circumstances. Noli Me Tangere and El Filibusterismo, while probably an accurate depiction of 19th century Philippines, are nothing more than that and the critics and analysts lauding it for its depth of meaning are doing nothing but splitting hairs. It all feels so contrived, in a sense. Then again, one has to ask: if we "split hairs" reading meaning into something that one argues has none, and yet we still find something remarkably relevant and resonant with the times, how incorrect can we still possibly be? One man's trash is another man's treasure, so they say. Moreover, if we take that which has been said at face value, disregarding deeper readings as contrivances, what does it say about our comprehension of the supposed literary text? We are indeed, a nation that does not read. We either do not read at all, or we read but do not understand (which amounts to the same thing.)

Now let us go back to the topic at hand. Lavina's letter, nicely written and well-researched, reminded me almost instantaneously of my friend and our debate. The argument is sound; Damaso is obviously, clearly the greater villain here. Destroying a person publicly from the pulpit and exhuming his corpse to be defiled one last time? Salvi was just a Peeping Tom; Damaso was a rapist! The words are opaque! Ah, but therein lies the problem.

My objection to this line of thinking stems from a deadly assumption that people seem to make about texts; that is, to take them at face value. Literature revels in the fact that words are more than what they mean at first; the way words are used, the way they come together, all these make the underlying arguments explode exponentially so as to serve as a microcosm of the infinite vastness of meaning in the universe. I will not reiterate the salient points of Ocampo's article because the explanation there was precisely the counterargument to Lavina's reply. I will not recall my arguments against my friend in that debate, because the problem is not so much the issue at hand as it is the different points of view we are launching from. Maybe, if there is a better appreciation of what has not been said, more can be extracted from the text than what a cursory reading will yield.

Big on the edges

I finally got my grades today. Strangely enough, I got an A- for complex analysis. To the best of my knowledge, I suck in this subject (to the point that I think I never passed an exam.) Mirabile dictu, or something. The best that I can recall from my time spent on that subject (aside from an endless influx of drawings of contours) would be this tiny tidbit.

There is a theorem in complex analysis called the maximum modulus principle. Simply put, it says that a complex valued function analytic in a domain will have no maximum value within that domain. A consequence of this is that all maximum values of the function (if they exist) will occur on the contour enclosing the domain itself.

What does all that babble mean? Well, it just says that if I have a closed space and my function has values there, there is no area there that has a bigger value than everyone else. It's perfect competition at its finest; at most, the areas would have to be equal to each other (going back to our function, it would have to be constant-valued.) The consequence above follows from the theory almost intuitively (quite dangerous in mathematics, but a little proving exercise should validate this assumption.) That implication, on the other hand, has an application in a field significantly removed from such abstractions as complex analysis; that is, the field of operations research.

Consider a maximization problem. For example: you are assembling three different products using a set of raw materials, and you want to produce a certain number of each product such that you use up all your available material and (assuming you sell all the products you have made) yield the maximum possible profit. A method in operations research called linear programming will lay down the conditions that restrict your problem and offer a solution. One way would be to place all the conditions together in a graph, forming a polygon. Now, applying the maximum modulus principle, the maximum value for our function (in this case, the profit) would have to lie not inside the region but on the edges of the polygon itself.

Amazing stuff, eh? A simple solution to a practical problem, backed by an abstruse amount of abstraction. I guess therein lies the beauty of mathematics; to break things down to the finest, most incomprehensible core and reconstruct it into an elegant framework that makes things, if not easier, bearable.