# D_Malik comments on The Virtue of Narrowness - Less Wrong

56 07 August 2007 05:57PM

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Comment author: 28 May 2012 04:53:45PM *  11 points [-]

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.

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:

• Reversed stupidity is not intelligence.

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.)

• No power hath noise.

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.

• The fallacy of grey.

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.)

Comment author: [deleted] 29 May 2012 11:17:42AM 1 point [-]

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.

Wouldn't it make more sense to use a grey scale? :-)