What is true of one apple may not be true of another apple; thus more can be said about a single apple than about all the apples in the world.
—“The Twelve Virtues of Rationality”
Within their own professions, people grasp the importance of narrowness; a car mechanic knows the difference between a carburetor and a radiator, and would not think of them both as “car parts.” A hunter-gatherer knows the difference between a lion and a panther. A janitor does not wipe the floor with window cleaner, even if the bottles look similar to one who has not mastered the art.
Outside their own professions, people often commit the misstep of trying to broaden a word as widely as possible, to cover as much territory as possible. Is it not more glorious, more wise, more impressive, to talk about all the apples in the world? How much loftier it must be to explain human thought in general, without being distracted by smaller questions, such as how humans invent techniques for solving a Rubik’s Cube. Indeed, it scarcely seems necessary to consider specific questions at all; isn’t a general theory a worthy enough accomplishment on its own?
It is the way of the curious to lift up one pebble from among a million pebbles on the shore, and see something new about it, something interesting, something different. You call these pebbles “diamonds,” and ask what might be special about them—what inner qualities they might have in common, beyond the glitter you first noticed. And then someone else comes along and says: “Why not call this pebble a diamond too? And this one, and this one?” They are enthusiastic, and they mean well. For it seems undemocratic and exclusionary and elitist and unholistic to call some pebbles “diamonds,” and others not. It seems . . . narrow-minded . . . if you’ll pardon the phrase. Hardly open, hardly embracing, hardly communal.
You might think it poetic, to give one word many meanings, and thereby spread shades of connotation all around. But even poets, if they are good poets, must learn to see the world precisely. It is not enough to compare love to a flower. Hot jealous unconsummated love is not the same as the love of a couple married for decades. If you need a flower to symbolize jealous love, you must go into the garden, and look, and make subtle distinctions—find a flower with a heady scent, and a bright color, and thorns. Even if your intent is to shade meanings and cast connotations, you must keep precise track of exactly which meanings you shade and connote.
It is a necessary part of the rationalist’s art—or even the poet’s art!—to focus narrowly on unusual pebbles which possess some special quality. And look at the details which those pebbles—and those pebbles alone!—share among each other. This is not a sin.
It is perfectly all right for modern evolutionary biologists to explain just the patterns of living creatures, and not the “evolution” of stars or the “evolution” of technology. Alas, some unfortunate souls use the same word “evolution” to cover the naturally selected patterns of replicating life, and the strictly accidental structure of stars, and the intelligently configured structure of technology. And as we all know, if people use the same word, it must all be the same thing. These biologists must just be too dumb to see the connections.
And what could be more virtuous than seeing connections? Surely the wisest of all human beings are the New Age gurus who say, “Everything is connected to everything else.” If you ever say this aloud, you should pause, so that everyone can absorb the sheer shock of this Deep Wisdom.
There is a trivial mapping between a graph and its complement. A fully connected graph, with an edge between every two vertices, conveys the same amount of information as a graph with no edges at all. The important graphs are the ones where some things are not connected to some other things.
When the unenlightened ones try to be profound, they draw endless verbal comparisons between this topic, and that topic, which is like this, which is like that; until their graph is fully connected and also totally useless. The remedy is specific knowledge and in-depth study. When you understand things in detail, you can see how they are not alike, and start enthusiastically subtracting edges off your graph.
Likewise, the important categories are the ones that do not contain everything in the universe. Good hypotheses can only explain some possible outcomes, and not others.
It was perfectly all right for Isaac Newton to explain just gravity, just the way things fall down—and how planets orbit the Sun, and how the Moon generates the tides—but not the role of money in human society or how the heart pumps blood. Sneering at narrowness is rather reminiscent of ancient Greeks who thought that going out and actually looking at things was manual labor, and manual labor was for slaves.
As Plato put it in The Republic, Book VII:
If anyone should throw back his head and learn something by staring at the varied patterns on a ceiling, apparently you would think that he was contemplating with his reason, when he was only staring with his eyes . . . I cannot but believe that no study makes the soul look on high except that which is concerned with real being and the unseen. Whether he gape and stare upwards, or shut his mouth and stare downwards, if it be things of the senses that he tries to learn something about, I declare he never could learn, for none of these things admit of knowledge: I say his soul is looking down, not up, even if he is floating on his back on land or on sea!
Many today make a similar mistake, and think that narrow concepts are as lowly and unlofty and unphilosophical as, say, going out and looking at things—an endeavor only suited to the underclass. But rationalists—and also poets—need narrow words to express precise thoughts; they need categories that include only some things, and exclude others. There’s nothing wrong with focusing your mind, narrowing your categories, excluding possibilities, and sharpening your propositions. Really, there isn’t! If you make your words too broad, you end up with something that isn’t true and doesn’t even make good poetry.
And DON’T EVEN GET ME STARTED on people who think Wikipedia is an “Artificial Intelligence,” the invention of LSD was a “Singularity,” or that corporations are “superintelligent”!
Here's a way to visualize this. Write down a horizontal list of all the things. Write down a vertical list of all the things. Now draw columns and rows so you have a table of all the things with all the things. Now colour a square white if two things are connected, and colour a square black if two things aren't connected. So if all the things are connected, then you have a white canvas. And if all the things are unconnected, you have a black canvas.
Now these are opposites, but they're not opposites like apples and democracy, they're opposites like heads and tails. They're two sides of the same coin is what I'm saying. On the axis of total colour they're as far apart as possible, but in the space of information, where distance is proportional to the complexity of transformations you have to do to transform one set of information to another, they're right next to each other. You just invert that thing. So saying everything's connected is a lot like saying nothing's connected.
This metaphor can be extended to apply to some other Yudkowskian wisdom:
Suppose we draw a person's set of beliefs as a pattern on this canvas. And suppose the set of correct beliefs looks like a black-and-white picture of a cat. (Please quote that line out of context.) Now if you take an idiot, his beliefs don't look like a cat. But they also don't look like a picture of an anticat, the inversion of a cat, because to draw an anticat, he'd have to go to all the trouble of knowing exactly what the cat looks like and then getting everything precisely wrong. He'd have to be exactly right about what to be wrong about. He'd have to know exactly what a cat looks like, to draw something that looks exactly not like a cat. So what do the idiot's beliefs look like? They're like a badly-drawn cat. It might have a really big nose, or only three legs. But it's still a lot more like a cat than an anticat.
So if you just decide to believe the opposite of what the idiot believes, you just invert his badly-drawn cat. What you get won't be a well-drawn cat. It'll be a badly-drawn anticat, with three badly-drawn antilegs and an antinose that's too big. The only way to get a better drawing is to actually look at the Canonical Cat and draw Her well. (Obviously, the Canonical Cat symbolizes reality.)
Now I have a picture of a badly-drawn cat, and I want to maximize the number of pixels that are the same as they are in Omega's picture of the Canonical Cat. So I pick a few random pixels and flip them. Does this get me closer to a picture of Her furry-pawed splendour?
Well, maybe. If I started out with more pixels opposite to the Canonical Cat than pixels that truly reflect Her feline glory, then randomness will boost me closer to having half my pixels right. But if I started out with a picture that looks more like the Canonical Cat than like Her nemesis, the Anticanonical Anticat, then randomizing is bad, for it moves my picture further from an accurate representation of Her whispy whiskers and closer towards the hairball-choked darkness of the dread Anticat.
But since most people are closer to the Cat's light than to the darkness of Her nemesis, randomizing doesn't work. It only works to boost you back if were originally dwelling in the valley of the shadow of the Anticat.
Her pixels are so radiant and Her light so blinding that no mortal can truly gaze upon the Canonical Cat. So we don't know which pixels would be black and which would be white in a faithful portrayal of Her furry visage. (The Anticanonical Anticat is likewise shrouded in darkness.) In fact, we mortals are so weak before the Divine Pixels, their light so bright beyond our vision and their mysterious ways so far, so very far beyond our comprehension, that we know not the colour of a single pixel with absolute certainty.
The best that mortals such as we can do is to guess at how likely each pixel is to be white or black, and then colour the pixel grey with a value indicative of how confident our best felinosophers are that a white pixel there would be an accurate indication of Her eternal beauty, rather than one of the Marks of the Anticat. And in so doing, we may form a picture of Her, even if, being the work of mere mortals, it is a bit blurry and unclear. And we must be careful to not paint the Canonical Cat too darkly, for else She will smite us for our insolence. And neither may we colour the darkness of the Anticat too brightly, lest we see the hideous horrors that hide in His depths.
But some, seeing that not a single pixel has been coloured absolutely, now shout, as if they were the bearers of some new and deep wisdom, that all our pixels are the same, for they are all shades of grey! And, so steeped are they in wickedness, they do proclaim that, since no perfect image has ever been graven, all images are equally representative of the Canonical Cat (Her paws be praised). And they hold aloft their unholy tome, The Dog Delusion, and speak out against "The Doctrinal Dog, the Canonical Cat, and all other Orthodox Organisms". And so these heathens equate the Lady of the Light, Her holiness the Canonical Cat, with the Duke of Darkness, the Earl of Evil, the Anticat Himself! What blasphemy!, and O! what sacrilege!
(Sorry, I got a bit carried away.)
Wouldn't it make more sense to use a grey scale? :-)