On the Particular Qualities of Good SF

Science fiction is in the subtitle of this blog, but I haven’t really talked about it beyond flaunting my nerd cred. It’s been on my mind lately, however. So here’s a post in which I pontificate on what I think makes good SF. Feel free to tune out if you came here for more than just my opinions dressed up as theory.

I’m a little late on the review bandwagon, but this post is more or less inspired by my thoughts on star: trek Into darkness. If you haven’t seen the movie yet, you should cover your eyes while you read this part because here’s the spoiler to the earth-shattering final twist of the movie: Kirk doesn’t die. I know, I know—shocking. How the writers managed to keep a lid on that one is anyone’s guess.

Anyway, why doesn’t Kirk die? It turns out the reason he doesn’t die is because the brilliant physician Bones McCoy has made a monumental discovery in medicine that will change every life in the Federation forever and surely be the focal point of the next Star Trek movie. Yes, Bones has managed to discover the secret to immortality in the blood of a man created with 200 year old technology.

At least one thing I said in the preceding paragraph is true. (There will be another Star Trek movie.) But let’s put aside the snark for a moment. Why does this grate me so? Because it’s a missed opportunity. If Bones really had discovered immortality, and it really did change the Federation in some way, then that would make for some pretty interesting science fiction. Instead it will likely never be mentioned again, because it was only a gimmick to create suspense at the end of the movie.

But who cares about discussing immortality, right? It’s never going to happen, or life is only meaningful because of death, or it’s just some nerd boy’s fantasy, right? Well, yes, immortality isn’t real, but that would seem to make it excellent fodder for fiction. Good fiction is traditionally supposed to explore the human condition, and that’s a nearly endless fount from which to plumb. There’s love, hatred, war, jealousy, and all that other good human condition stuff. But those elements of the human condition are the low-hanging fruit; they’ve been picked. What else is being human about?

If there are examples we can point to that are solidly within the domain of the human condition, then the next place we can look is outward at the edge cases. Edge is a good word here. After all, how do you identify objects you can see? You look to the edge of the thing, see where it stops, trace its shape. If you want to know what something is, find out where it stops and draw a line.

I’m reminded of a topic from linear algebra that might make for a useful analogy or might just confuse people even more. Stick with me. Take a matrix with, say, 10 columns. If this matrix is full of unknowns, then there’s a method for figuring out every single way to add those unknowns together and come out with 0.

This is called the nullspace of a matrix. In essence, it tells you everything a matrix is not. The nullspace of a matrix is described by a number of dimensions. Let’s say we have a matrix with a nullspace of 6 dimensions. One of the neat things about linear algebra is that the number of columns (10) minus the dimensions of the nullspace (6) is always equal to the dimensions of the row space (4). What’s the row space? Well, in short, it’s everything a matrix could be. What does that all mean? It means that you can find out what something is by figuring out what it’s not.

Which takes us back to science fiction. Good science fiction tells us about the human condition specifically by telling us about something other than the human condition. It tells us about things near the human condition, at the edge, making up the border. And by doing so, it lets us create a rough outline of what the human condition really looks like.

So, then, magic is science fiction, right? I mean, it’s definitely not human, which means stories about it tell us about what is human, right? Ah, uh, no. The key here is that you have to look at the edges of a thing where you think it might be. The reason is that there’s generally a lot more that a thing isn’t than a thing is.

If you’ll allow me, let’s return to the linear algebra example. If the nullspace of a matrix is infinite and the row space is finite, then I can start calling out random numbers and have a pretty good chance of giving you a number in the nullspace rather than the row space. But what does this tell me about the matrix? Basically nothing. However, when you’re done finding the nullspace of a matrix, you’re left with a formula that tells you how to figure out what’s in it. The formula lets you extract useful information from the problem.

A formula is basically just a set of rules to follow. And it’s these rules that get to the heart of good science fiction. They let you find the line between what’s human and what’s not. Technology in fiction might follow rules, but it also might not. That’s the difference between your hard SF and something like Star Wars. Star Wars has lasers and spaceships, but they don’t follow any rules, which means they’re not telling you anything about the boundaries of the human condition.

And it’s also the difference between good science fiction and the most recent Star Trek movie. Because we’re never going to see Khan’s immortal blood again, it’s not following any rules; it’s essentially magic. If it had been explored as a topic, we could have learned something from it.

Now, magic systems in high fantasy might have intricate rules, but if those rules are describing something completely alien, they’re not telling you about what it means to be or not be human. In linear algebra, it’s akin to knowing the formula for a different matrix. It tells you something, but it doesn’t tell you what you want to know.

By the way, I’m not bashing Star Wars or fantasy. Both of them can be good fiction, and both of them can tell you things about the human condition. But they’re really only doing so the old-fashioned way—by looking at what we know for certain is human. They’re not doing it by exploring the edge cases.

But we need to explore the edge cases; we need to find the rules. Why? Because eventually we’re going to pick all the low-hanging fruit and we’re not going to have anything new to say about the human condition. The only way we’ll be able to keep learning about ourselves is by finding our boundaries and pressing up against them. And the best way to do that is by writing good science fiction.

This Is What You’re Really Doing

Again, it’s been awhile since my last post. Stuffing linear algebra into a 5-week course (with a not terribly awesome professor) turned out to be hard. But I said I would have a post about the class, and last night presented the nth example of what it is I wanted to write about.

You see, linear algebra is no ordinary math class, despite the deceptively benign name. Our professor told us we’d actually have to think in his class because linear algebra is the first math course where you have to prove things. That’s true enough, but it’s not the reason why linear algebra is different from other math.

The reason is that linear algebra is the first math course seemingly dedicated to the task of teaching you what you’re really doing in math. We kind of take it for granted that our teachers lie to us. They don’t (usually) do so maliciously; they do so because the “true” answer is significantly more complex than the “false” answer. But it happens pretty frequently that the lies teachers tell us are good enough.

Regardless, there comes a point at which you’re deemed capable of handling the truth. Now, there are plenty of times earlier in math when this happens. I think the most basic example is subtraction. You learn it shortly after you learn about addition, and you’re told that unlike addition, subtraction is not commutative. 10-5 is not the same as 5-10. But it turns out that whenever you’re subtracting, what you’re “really” doing is adding a negative. 10-5 becomes 10 + -5. And then subtraction is again commutative, because 10 + -5 is exactly the same as -5 + 10.

But linear algebra extends this drawing back of the curtain to many more ideas. In linear algebra, you learn that the vector dot product is really just a special case of a general operation called the inner product. You learn that vectors themselves are really just objects that follow a particular set of rules and don’t necessarily have anything to do with directed line segments. You learn that functions are really just a method of mapping one set to another.

At this point you might be wondering what “really” really means. Is there some true math underlying the universe that we simple humans are merely discovering, or are we just peeling back the layers of logic upon which our peculiar brand of mathematics is built? Since the 1600s, when calculus was discovered/invented, mathematics has proven enormously successful at describing the real world.

Many have seen this as distinct evidence that math is something real and not just a human construct. Math that was once thought to be purely theoretical in nature has turned out to have physical basis. So when a mathematician writes down a law no one has written down before, has that mathematician discovered the law or invented it?

Others do not hold math in such reverence, choosing to believe instead that we have simply made up math to serve our purposes. They point to the fact that mathematicians often make choices and that those choices don’t necessarily reflect anything deeper. We choose for 0! to equal 1. We choose for division by zero to give you a calculator error. At one point we chose for there to be no imaginary numbers or even negative ones. Did someone discover the complex numbers, or did we merely decide to define the square root of -1?

I try not to make definitive statements about the nature of the universe. I err on the side of caution as far as that’s concerned. So I’m not willing to say that math is a fundamental part of the universe. But I also don’t believe new branches of math are merely choices or inventions. Instead I believe that new math resembles the emergent phenomena you see in something like the Game of Life. Simple rules can lead to complex behavior. DNA is truly the perfect example. There is far more data contained in even an infant human brain than in the human genome, yet somehow the brain comes from DNA, from following relatively simple rules over and over again.

Math, then, is many complex rules that emerge from a few simple ones. Historically, mathematics began by matching sets. We used numbers to keep track of livestock in a pen or bushels of grain in a granary. We matched the number we observed with the number of notches in clay or wood. And it turns out that today—although this wasn’t always true—we still base mathematics on the idea of matching and counting sets.

So when a mathematician writes down a new law, that mathematician is discovering a novel application of the rules we invented. This doesn’t explain why math is so effective, but it does bridge a gap between discovery and invention.

The next question, I suppose, is why we invented the rules we did. I think that arises from the fact that, on large-ish scales, the universe is discrete. I see 1 tasty lamb; I’m being chased by 3 hungry wolves; I am saved by 5 human friends.

(On small-ish scales, the universe looks continuous. We don’t have 3 water; we have enough water to fill that bucket. We now know that water is made up of molecules, so you can count your water.)

Maybe that’s why it took us so long to get to calculus. Maybe our brains are designed to see things in a discrete, delineated fashion. We know it’s true that our brains are excellent at border detection, at filling in missing lines, at assigning meaning to individual objects. So perhaps our universe exists discretely, and we evolved discretely, and we came up with discrete math, too. No wonder the math we invented, and then discovered, is so effective.

(No, I don't believe I've solved the philosophy of mathematics in a 1000-word post.)