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.)

I Don’t Know Anything About Economics

Sorry for the long gap between posts. A lot’s been going on recently. Anywho, I’ve started up my linear algebra class, so hopefully I’ll have some interesting things to post about that soon. I’ve already learned techniques that would have made problems in both E&M and multivariable calculus a lot easier to solve. Oh, well.

But on to the meat of this post. Re: economics, it’s not strictly speaking true that I know nothing about it. Like most sciences, I’ve paid enough attention to get a general idea of what it’s about. I even took a semester of economics in high school, but it was taught by a brand new teacher who used to be a banker and for some reason felt the need to confide in us that he didn’t actually have a teaching certificate and we really shouldn’t tell anyone that. Oops.

On the whole, however, my knowledge of the dismal science is quite limited. But economics is a science, however sad and soft it may be. And I think this is an important fact that a lot of people seem to forget, which is where this post is coming from.

You see, I used to have very strong opinions about economics. (Those that know me in real life may wonder about the “used to” there, but I think it’s largely true.) I was raised in a leftish household and with that came mostly leftish politics and economics. My politics, however, took a turn toward the weird after a bit of philosophical revelation ten years ago. But my economics remained mostly leftish for a long time.

Recently, however, that’s begun to change. Now, this isn’t the story of me transforming into a commie-hating libertarian, or even someone who’s moderately right, or even someone who is staunchly in the middle. Rather, this is the story of me deciding that if I don’t actually know anything about economics, I shouldn’t have (strong) opinions about it.

As I said, economics is a science. And in science, there are two kinds of debates you can have: debates where the answer is already known but one side refuses to acknowledge it, and debates where an answer won’t be forthcoming until more data is collected.

For example, there is a “debate” about whether evolution is true. As far as science is concerned, this debate is quite settled and has been for a long time (up to a hundred and fifty years). Some believe the issue is not settled, but their belief is incorrect. That’s not to say their beliefs in general are wrong—just their beliefs about evolution.

And then there’s the second kind of debate, where we just don’t know enough yet. Take cosmology’s dark energy as an example. Dark energy is a proposed mechanism to explain the observed accelerating expansion of the universe, but cosmologists don’t yet know what dark energy really is. There are theories, but no solid evidence. A good cosmologist may prefer one theory over another, and argue its case, but a good cosmologist will also ultimately admit ignorance on the topic. More data is needed before the issue can be settled.

In both of these scenarios, the right answer is not decided upon by the voting public. In the case of evolution, a vote is inappropriate because one answer is obviously correct and the public may vote incorrectly. In the case of dark energy, it’s too early to hold a vote because the answer isn’t known yet. But in both cases, there’s not ever a situation in which the public should be voting on the issue because the public is not informed enough about the topic to make the correct choice (except by accident).

You see where I’m going with this. If economics is a real science that requires years of study to master, then economic questions are either settled (and should simply be policy) or not settled (and should be left to experts to study). Thus, when I vote, I don’t really do it based on economic policy. Philosophically speaking, there are issues that are more important to me, and about which I am more knowledgeable.

Some may see this as cowardice. I’m too wishy-washy to take a stance, too scared of being wrong. But I (surprise!) see it differently. I think one of the most important lessons of science is that it’s okay to say you don’t know, okay to profess ignorance. In the words of Newton, “Hypotheses non fingo.” You don’t have to invent explanations when you can’t see one. You don’t have to come to a conclusion before you have all the data.

In fact, I think admitting ignorance can be seen as a brave act. Belief is hard-wired in humans; it’s what we do naturally. We observe a phenomenon and we attribute a cause to it, no matter how tenuous the connection, because we’re scared of not knowing. Withholding judgment, however, is much harder, and takes care and concentration.

Some may see my lack of an opinion as irresponsible. While many sciences tend toward the academic and lack real-world consequences, economics is, by definition, something we cannot ignore. Resources are scarce and we have to do something about it. By refraining from taking a stance on economic issues, I refrain from solving the problem of allocating scarce resources.

But I think that perspective misses the point, which is that resources are scarce and that’s not going to change any time soon. There’s no solution within economics to the fact of scarcity, only solutions to dealing with it. As far as I’m concerned, the best solution is to eliminate the need for economics completely. With sufficiently advanced technology, we can have practically unlimited resources. We’re nowhere close to that, and in the long run it’s distinctly untrue, but it can be true within the lifetime of our species.

Again, we’ve stumbled on another reason why I’ve decided to study science. It may seem as if I’m a delusional believer in a techno-utopia… and I’m not going to deny that. Getting into why that’s the case would require another post, however, and I think this one is long enough as it is.

So in the meantime I think it’s best to leave economics to the economists and be okay with admitting ignorance.

The Community College Syllabus

This is a pet peeve of mine and nothing more, but I've seen it a lot in similar contexts. Logging in "at least three to five times a week" makes no sense. We can log in at least 3 times a week. If we happen to log in 5 times a week, then that would still be at least 3 times a week.

You could argue that "at least" only applies to the three, but then he's telling us to log in a minimum of 3 times and a maximum of 5 times per week. Who knows, maybe's that the case. Given how often the website goes down, maybe they're trying to limit bandwidth usage.

Or he could be telling us that we must log in a minimum of 3 times per week, but he'd like to see us logging in between 3 and 5 times per week. Clearly, this is what is actually meant, but it is not what is written. Now, I know that no one is going to be confused by this. So it is what's conveyed, even if it is not what's written. So why am I complaining?

My reasons are three. First, he's an English teacher. He's going to be correcting our grammar for the next five weeks with varying degrees of exactitude, so it'd be nice if he showed the same amount of care in his own writing.

Second, this is a course designed for writing in the workplace. Like, if you wanted to be a tech writer, you might start with a course such as this one. Well, I've been a technical writer before. And you know what? Imprecise language like the phrase used above is not cool. It leads to mistakes, complaints, and lawsuits.

(Source)

Third, as a professor of English, he should really care about doing right by the language. Yes, language changes. Yes, the point of a language is communication, and if that's achieved, who cares about anything else.

But here's what gets to me. The English language is a gigantic hodgepodge of words and there are an absolute crap-ton of ways to arrange them meaningfully. So we can communicate precisely if we have sufficient mastery over syntax and vocabulary, but we don't because it's hard. Instead we think whatever we're thinking, vomit out the words we most closely associate with said thoughts, and hope the listener has roughly the same associations for those words, thereby getting the gist of the message across. Blech.

State of the Student

Somehow now that I’m not leaving the house at 7:30 every morning and getting home at 10 every night I feel less inclined to blog. Odd, that. I don’t really have much to write about at the moment, but it’s been two weeks since I’ve posted and I don’t want to chance losing my legions of fans.

So, the semester is over and I’ve successfully completed a full year of schooling for the first time in 10 years. I should probably be more embarrassed about admitting that. Maybe now is a good time to take stock of things.

This time last year I had a cumulative GPA at my community college of 0.5, which was mostly a result of making some very poor choices in the early part of my college “career.” I wasn’t taking and failing classes; I was taking and not showing up to classes. But the end result was the same. Now, after having retaken all but one of my failed courses and taking a whole slew of new ones, my GPA is a 3.38.

Here’s a chart, so that I stay in character:

I’ve calculated that by the time I have my degree, I should have a GPA of 5.51. We’ll see how that works out.

What do I have left to do in community college? There are four more classes I need to take, and then I’ll be off to the big, scary 4-year university. This summer I start off by retaking another English course on writing for business and technology. That might be marginally useful for my future career, but I’m not betting on it being interesting. I consider having to retake classes like these my penance.

Later in the summer there will be a 5-week, whirlwind tour of linear algebra--the study of matrices. I understand that linear algebra is very important in computer graphics and a version of quantum mechanics. I’m not looking forward to learning it all in 5 weeks, but it’s what my schedule demands.

In the fall I’ll be taking differential equations and physics 3. DiffEq, as the cool kids call it, is at the heart of all physics. While calculus by itself is useful in that it allows you to make quantitative statements about change, differential equations are vital when those changes are recursive.

Way back in my second post, I mentioned that modeling air resistance is hard because it involves differential equations. The reason it’s hard is because of this recursive idea. How hard the air pushes on you depends on how fast you’re moving, and how fast you’re moving depends on how hard the air pushes against you. This would seem to be an infinite loop, but differential equations let you quantify that recursive relationship.

Then there’s physics 3, which is called Waves, Optics, and Modern Physics. The third semester of the introductory physics sequence typically gets a bad rap. And I don’t mean at my college, but all across physics departments. The usual complaint is that it tries to jam a whole bunch of not terribly related phenomena into one semester before the students really have the mathematical tools necessary to do these topics justice. Modern physics usually encompasses physics that is a mere century old--relativity, quantum mechanics, nuclear physics, and solid-state physics. There’s a lot to be said about all of these topics, and a good case can be made for there not being anything you can say about them in 2-week chunks.

I suspect I won’t mind much. What I’ve discovered so far is that most of my classmates come into the semester having virtually no background knowledge of the relevant material. Because I’ve been reading about science and math for so long, there was almost nothing I encountered this year that was entirely new to me. That’s not to say that I knew how to do the science--just that the concepts weren’t unfamiliar. I suspect the same will be true of modern physics, and I look forward to gaining more than just a surface-level understanding of these topics, even if it’s just below the surface.

And what comes after that? Well, the goal is that by spring 2014, I’ll be transferring to my state university where I will be approximately a junior. So 2 or 3 years from now I should have a bachelor’s degree in physics. I suspect I may get a double major in physics and astronomy because there’s a great deal of overlap between the two majors and astronomy is what I ultimately want to end up doing.

After that, the usual destination is grad school. At this point, that’s so far in the future that I haven’t given it much thought. I’ve heard repeatedly from academic bloggers that you should only go into grad school if you’re absolutely sure you want to go into academia. I can’t say that I’m absolutely sure right now, but we’ll see where I stand in a couple years.

Headlines Funniest Part of Onion Articles, Says Guy on Street

WASHINGTON, D.C.—In a suburb just 20 miles outside Washington, D.C., local man Charles “Chuck” Braxton has recently begun telling coworkers and friends that, “Really, the whole joke is in the headline, if you think about it.”

Chuck, who does banal office work for incompetent middle managers but has always styled himself a comedian, went on to say, “I mean, I could write these articles. The headline is an amusing observation, but the rest of the article just drags out the joke by having imaginary interviews with pedestrians.”

According to Wikipedia, The Onion is a satirical newspaper founded in 1988 by Tim Keck and Christopher Johnson. While originally just a joint project between the two college students with limited circulation on several campuses, The Onion has since flourished into a fully developed satirical news organization featuring a television network, website, and twitter account. But it’s the Facebook posts that really get to Chuck.

“I see the same headline 5 times a day on my timeline,” explained an exasperated Chuck. “And yeah, the jokes are funny, but it’s always the same pattern. I just wish they would spice things up a bit sometimes.”

Sources close to Chuck have indicated that, “If he doesn’t shut up about this ‘Only the headlines are funny’ thing, I’m seriously going to kick his ass.” At press time, The Onion had not responded to requests for comment.

The Community College Website

Human rights, brought to you by your local community college. Did we turn down the first offer?

As far as modern poetry online, I can only assume they're referring to this.

(And don't get me started on the missing apostrophe.)