Freshman year of college my friend Rebecca tried to explain to me the literary school of deconstruction. After some time I tried to sum up what I had heard in a phrase that (be it my own or not, and whether it be accurate or not) I have kept with me six years later.
Words have meanings, but meanings don’t have words.
Now I’m still not sure what that means, but I do know it has to be true. My friend’s grandmother, sage that she is, disagrees entirely. Meanings are the words they mean—sometimes people misuse words—but that doesn’t detract from their instrinsic definitions. But if that were true, we wouldn’t have any need for dictionaries. If words were their meanings, then words couldn’t be defined in terms of other words. That’d be silly. The other words have their own (other) meanings, after all. Imagine what a dictionary entry might look like in this alternate semantic universe:
apple, n., apple. What don’t you understand? Apple means apple.
Of course, maybe I’m taking too naive an approach. DJ’s grandmother might be onto something. How can you sufficiently define terms like ‘this’, or ‘I’, or ‘you’? This is what it is. It’s nothing else. It’s this. I am who I am. Or am I? Words, like people, take on a meaning that emerges from their use. How words are used, though, follows from larger, guiding principles. Culture helps define who we are. So, too, culture—which is really no more than a vast set of complex and subtle rules—defines what are words mean. So, words do have meaning. But only in relationship to other things (that have meaning). It’s sort of like music.
In music syncopated rhythms accent the beats which normally go unaccented. But without some concept of normal, syncopation doesn’t exist. But it does because in our music there is a structured sense of normal. And if we let loose the structure, we loose some of the meaning. Syncopation just disappears. Ironically, the tighter a straight-jacket we put on rhythm the freer we can be within its constraints: we get things like syncopation back.
In mathematics, too, Kahler manifolds are surfaces that exhibit a rich geometry. It’s thought that the physics of our universe is actually encoded on one of a special class of these surfaces known as Calabi-Yau manifolds. The thing about Kalher manifolds, though, is that their geometry is so highly structured that the surfaces are almost flat. Flat surfaces are the simplest to investigate. It turns out that these guys, by comparison, are notoriously difficult to analyze. There may be something to that—that the most useful, interesting cases often lie just on the cusp between simple and intractable—but I’m not sure what it is.