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Categorizing Has Consequences

25 Eliezer_Yudkowsky 19 February 2008 01:40AM

Followup toFallacies of Compression

Among the many genetic variations and mutations you carry in your genome, there are a very few alleles you probably know—including those determining your blood type: the presence or absence of the A, B, and + antigens.  If you receive a blood transfusion containing an antigen you don't have, it will trigger an allergic reaction.  It was Karl Landsteiner's discovery of this fact, and how to test for compatible blood types, that made it possible to transfuse blood without killing the patient.  (1930 Nobel Prize in Medicine.)  Also, if a mother with blood type A (for example) bears a child with blood type A+, the mother may acquire an allergic reaction to the + antigen; if she has another child with blood type A+, the child will be in danger, unless the mother takes an allergic suppressant during pregnancy.  Thus people learn their blood types before they marry.

Oh, and also: people with blood type A are earnest and creative, while people with blood type B are wild and cheerful.  People with type O are agreeable and sociable, while people with type AB are cool and controlled. (You would think that O would be the absence of A and B, while AB would just be A plus B, but no...)  All this, according to the Japanese blood type theory of personality.  It would seem that blood type plays the role in Japan that astrological signs play in the West, right down to blood type horoscopes in the daily newspaper.

This fad is especially odd because blood types have never been mysterious, not in Japan and not anywhere.  We only know blood types even exist thanks to Karl Landsteiner.  No mystic witch doctor, no venerable sorcerer, ever said a word about blood types; there are no ancient, dusty scrolls to shroud the error in the aura of antiquity.  If the medical profession claimed tomorrow that it had all been a colossal hoax, we layfolk would not have one scrap of evidence from our unaided senses to contradict them.

There's never been a war between blood types.  There's never even been a political conflict between blood types.  The stereotypes must have arisen strictly from the mere existence of the labels.

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How An Algorithm Feels From Inside

88 Eliezer_Yudkowsky 11 February 2008 02:35AM

Followup toNeural Categories

"If a tree falls in the forest, and no one hears it, does it make a sound?"  I remember seeing an actual argument get started on this subject—a fully naive argument that went nowhere near Berkeleyan subjectivism.  Just:

"It makes a sound, just like any other falling tree!"
"But how can there be a sound that no one hears?"

The standard rationalist view would be that the first person is speaking as if "sound" means acoustic vibrations in the air; the second person is speaking as if "sound" means an auditory experience in a brain.  If you ask "Are there acoustic vibrations?" or "Are there auditory experiences?", the answer is at once obvious.  And so the argument is really about the definition of the word "sound".

I think the standard analysis is essentially correct.  So let's accept that as a premise, and ask:  Why do people get into such an argument?  What's the underlying psychology?

A key idea of the heuristics and biases program is that mistakes are often more revealing of cognition than correct answers.  Getting into a heated dispute about whether, if a tree falls in a deserted forest, it makes a sound, is traditionally considered a mistake.

So what kind of mind design corresponds to that error?

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Disguised Queries

57 Eliezer_Yudkowsky 09 February 2008 12:05AM

Followup toThe Cluster Structure of Thingspace

Imagine that you have a peculiar job in a peculiar factory:  Your task is to take objects from a mysterious conveyor belt, and sort the objects into two bins.  When you first arrive, Susan the Senior Sorter explains to you that blue egg-shaped objects are called "bleggs" and go in the "blegg bin", while red cubes are called "rubes" and go in the "rube bin".

Once you start working, you notice that bleggs and rubes differ in ways besides color and shape.  Bleggs have fur on their surface, while rubes are smooth.  Bleggs flex slightly to the touch; rubes are hard.  Bleggs are opaque; the rube's surface slightly translucent.

Soon after you begin working, you encounter a blegg shaded an unusually dark blue—in fact, on closer examination, the color proves to be purple, halfway between red and blue.

Yet wait!  Why are you calling this object a "blegg"?  A "blegg" was originally defined as blue and egg-shaped—the qualification of blueness appears in the very name "blegg", in fact.  This object is not blue.  One of the necessary qualifications is missing; you should call this a "purple egg-shaped object", not a "blegg".

But it so happens that, in addition to being purple and egg-shaped, the object is also furred, flexible, and opaque.  So when you saw the object, you thought, "Oh, a strangely colored blegg."  It certainly isn't a rube... right?

Still, you aren't quite sure what to do next.  So you call over Susan the Senior Sorter.

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The Cluster Structure of Thingspace

40 Eliezer_Yudkowsky 08 February 2008 12:07AM

Followup toTypicality and Asymmetrical Similarity

The notion of a "configuration space" is a way of translating object descriptions into object positions.  It may seem like blue is "closer" to blue-green than to red, but how much closer?  It's hard to answer that question by just staring at the colors.  But it helps to know that the (proportional) color coordinates in RGB are 0:0:5, 0:3:2 and 5:0:0.  It would be even clearer if plotted on a 3D graph.

In the same way, you can see a robin as a robin—brown tail, red breast, standard robin shape, maximum flying speed when unladen, its species-typical DNA and individual alleles.  Or you could see a robin as a single point in a configuration space whose dimensions described everything we knew, or could know, about the robin.

A robin is bigger than a virus, and smaller than an aircraft carrier—that might be the "volume" dimension.  Likewise a robin weighs more than a hydrogen atom, and less than a galaxy; that might be the "mass" dimension.  Different robins will have strong correlations between "volume" and "mass", so the robin-points will be lined up in a fairly linear string, in those two dimensions—but the correlation won't be exact, so we do need two separate dimensions.

This is the benefit of viewing robins as points in space:  You couldn't see the linear lineup as easily if you were just imagining the robins as cute little wing-flapping creatures.

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Typicality and Asymmetrical Similarity

25 Eliezer_Yudkowsky 06 February 2008 09:20PM

Followup toSimilarity Clusters

Birds fly.  Well, except ostriches don't.  But which is a more typical bird—a robin, or an ostrich?
Which is a more typical chair:  A desk chair, a rocking chair, or a beanbag chair?

Most people would say that a robin is a more typical bird, and a desk chair is a more typical chair.  The cognitive psychologists who study this sort of thing experimentally, do so under the heading of "typicality effects" or "prototype effects" (Rosch and Lloyd 1978).  For example, if you ask subjects to press a button to indicate "true" or "false" in response to statements like "A robin is a bird" or "A penguin is a bird", reaction times are faster for more central examples.  (I'm still unpacking my books, but I'm reasonably sure my source on this is Lakoff 1986.)  Typicality measures correlate well using different investigative methods—reaction times are one example; you can also ask people to directly rate, on a scale of 1 to 10, how well an example (like a specific robin) fits a category (like "bird").

So we have a mental measure of typicality—which might, perhaps, function as a heuristic—but is there a corresponding bias we can use to pin it down?

Well, which of these statements strikes you as more natural:  "98 is approximately 100", or "100 is approximately 98"?  If you're like most people, the first statement seems to make more sense.  (Sadock 1977.)  For similar reasons, people asked to rate how similar Mexico is to the United States, gave consistently higher ratings than people asked to rate how similar the United States is to Mexico.  (Tversky and Gati 1978.)

And if that still seems harmless, a study by Rips (1975) showed that people were more likely to expect a disease would spread from robins to ducks on an island, than from ducks to robins.  Now this is not a logical impossibility, but in a pragmatic sense, whatever difference separates a duck from a robin and would make a disease less likely to spread from a duck to a robin, must also be a difference between a robin and a duck, and would make a disease less likely to spread from a robin to a duck.

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Similarity Clusters

26 Eliezer_Yudkowsky 06 February 2008 03:34AM

Followup toExtensions and Intensions

Once upon a time, the philosophers of Plato's Academy claimed that the best definition of human was a "featherless biped".  Diogenes of Sinope, also called Diogenes the Cynic, is said to have promptly exhibited a plucked chicken and declared "Here is Plato's man."  The Platonists promptly changed their definition to "a featherless biped with broad nails".

No dictionary, no encyclopedia, has ever listed all the things that humans have in common.  We have red blood, five fingers on each of two hands, bony skulls, 23 pairs of chromosomes—but the same might be said of other animal species.  We make complex tools to make complex tools, we use syntactical combinatorial language, we harness critical fission reactions as a source of energy: these things may serve out to single out only humans, but not all humans—many of us have never built a fission reactor.  With the right set of necessary-and-sufficient gene sequences you could single out all humans, and only humans—at least for now—but it would still be far from all that humans have in common.

But so long as you don't happen to be near a plucked chicken, saying "Look for featherless bipeds" may serve to pick out a few dozen of the particular things that are humans, as opposed to houses, vases, sandwiches, cats, colors, or mathematical theorems.

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Extensions and Intensions

32 Eliezer_Yudkowsky 04 February 2008 09:34PM

Followup toWords as Hidden Inferences

"What is red?"
"Red is a color."
"What's a color?"
"A color is a property of a thing."

But what is a thing?  And what's a property?  Soon the two are lost in a maze of words defined in other words, the problem that Steven Harnad once described as trying to learn Chinese from a Chinese/Chinese dictionary.

Alternatively, if you asked me "What is red?" I could point to a stop sign, then to someone wearing a red shirt, and a traffic light that happens to be red, and blood from where I accidentally cut myself, and a red business card, and then I could call up a color wheel on my computer and move the cursor to the red area.  This would probably be sufficient, though if you know what the word "No" means, the truly strict would insist that I point to the sky and say "No."

I think I stole this example from S. I. Hayakawa—though I'm really not sure, because I heard this way back in the indistinct blur of my childhood.  (When I was 12, my father accidentally deleted all my computer files.  I have no memory of anything before that.)

But that's how I remember first learning about the difference between intensional and extensional definition.  To give an "intensional definition" is to define a word or phrase in terms of other words, as a dictionary does.  To give an "extensional definition" is to point to examples, as adults do when teaching children.  The preceding sentence gives an intensional definition of "extensional definition", which makes it an extensional example of "intensional definition".

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Words as Hidden Inferences

40 Eliezer_Yudkowsky 03 February 2008 11:36PM

Followup toThe Parable of Hemlock

Suppose I find a barrel, sealed at the top, but with a hole large enough for a hand.  I reach in, and feel a small, curved object.  I pull the object out, and it's blue—a bluish egg.  Next I reach in and feel something hard and flat, with edges—which, when I extract it, proves to be a red cube.  I pull out 11 eggs and 8 cubes, and every egg is blue, and every cube is red.

Now I reach in and I feel another egg-shaped object.  Before I pull it out and look, I have to guess:  What will it look like?

The evidence doesn't prove that every egg in the barrel is blue, and every cube is red.  The evidence doesn't even argue this all that strongly: 19 is not a large sample size.  Nonetheless, I'll guess that this egg-shaped object is blue—or as a runner-up guess, red.  If I guess anything else, there's as many possibilities as distinguishable colors—and for that matter, who says the egg has to be a single shade?  Maybe it has a picture of a horse painted on.

So I say "blue", with a dutiful patina of humility.  For I am a sophisticated rationalist-type person, and I keep track of my assumptions and dependencies—I guess, but I'm aware that I'm guessing... right?

But when a large yellow striped feline-shaped object leaps out at me from the shadows, I think, "Yikes!  A tiger!"  Not, "Hm... objects with the properties of largeness, yellowness, stripedness, and feline shape, have previously often possessed the properties 'hungry' and 'dangerous', and thus, although it is not logically necessary, it may be an empirically good guess that aaauuughhhh CRUNCH CRUNCH GULP."

The human brain, for some odd reason, seems to have been adapted to make this inference quickly, automatically, and without keeping explicit track of its assumptions.

And if I name the egg-shaped objects "bleggs" (for blue eggs) and the red cubes "rubes", then, when I reach in and feel another egg-shaped object, I may think:  Oh, it's a blegg, rather than considering all that problem-of-induction stuff.

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