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This is: Disguised Queries, published by Eliezer Yudkowsky on the LessWrong.
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.
"Oh, yes, it's a blegg," Susan says, "you can put it in the blegg bin."
You start to toss the purple blegg into the blegg bin, but pause for a moment. "Susan," you say, "how do you know this is a blegg?"
Susan looks at you oddly. "Isn't it obvious? This object may be purple, but it's still egg-shaped, furred, flexible, and opaque, like all the other bleggs. You've got to expect a few color defects. Or is this one of those philosophical conundrums, like 'How do you know the world wasn't created five minutes ago complete with false memories?' In a philosophical sense I'm not absolutely certain that this is a blegg, but it seems like a good guess."
"No, I mean..." You pause, searching for words. "Why is there a blegg bin and a rube bin? What's the difference between bleggs and rubes?"
"Bleggs are blue and egg-shaped, rubes are red and cube-shaped," Susan says patiently. "You got the standard orientation lecture, right?"
"Why do bleggs and rubes need to be sorted?"
"Er... because otherwise they'd be all mixed up?" says Susan. "Because nobody will pay us to sit around all day and not sort bleggs and rubes?"
"Who originally determined that the first blue egg-shaped object was a 'blegg', and how did they determine that?"
Susan shrugs. "I suppose you could just as easily call the red cube-shaped objects 'bleggs' and the blue egg-shaped objects 'rubes', but it seems easier to remember this way."
You think for a moment. "Suppose a completely mixed-up object came off the conveyor. Like, an orange sphere-shaped furred translucent object with writhing green tentacles. How could I tell whether it was a blegg or a rube?"
"Wow, no one's ever found an object that mixed up," says Susan, "but I guess we'd take it to the sorting scanner."
"How does the sorting scanner work?" you inquire. "X-rays? Magnetic resonance imaging? Fast neutron transmission spectroscopy?"
"I'm told it works by Bayes's Rule, but I don't quite understand how," says Susan. "I like to say it, though. Bayes Bayes Bayes Bayes Bayes."
"What does the sorting scanner tell you?"
"It tells you whether to put the object into the blegg bin or the rube bin. That's why it's called a sorting scanner."
At this point you fall silent.
"Incidentally," Susan says casually, "it may interest you to know that bleggs contain small nuggets of vanadium ore, and ru...
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