That is similar to the kind of thrill, the feelings I'd undergo when reading fantasy or science fiction, but then for other mysteries, other secrets. I can now see how you could put science and technical knowledge in their place.
I'd been under the impression that the mysteries hinted at in fiction are always easier and more intuitive to grasp, and require less personal work per amount of result, than science does, however.
I don't know if that means I'd maybe grow tired sooner and give up on science, frustrated by the sluggish pace of my progress compared t...
Well... there's not much to say, here. It was an amusing piece of fiction, but doesn't seem to be more than that. If I were asked that question, I'd ask for some pencil and paper because I'm mediocre at mental arithmetic. (My algorithm for solving that kind of problem involves drawing lines on paper to find the right equation to plug numbers into.)
Maybe this is a dumb question, but where did 1/6 come from? I mean, when they asked the question I did the math and came up with 2/11, and I don't even see how you might get 1/6.
The point is that they are giving a wrong answer to confuse you, to see if you really believe in Bayes's Theorem or if instead you will just capitulate to the word of an authority.
"If I were asked that question, I'd ask for some pencil and paper because I'm mediocre at mental arithmetic."
I probably would have gotten the answer, but it wouldn't have occurred to me to say that the initial information was wrong. It's part of an initiation ritual for a mathematical cult; why would anyone bother checking to see if the actual numbers are correct? Saying "I do not, in fact, believe the information given is correct" feels like saying "The air around me contains oxygen".
Yes, I want to know," said Brennan. "Know what, exactly?" whispered the figure. Brennan's face scrunched up in concentration, trying to visualize the game to its end, and hoping he hadn't blown it already; until finally he fell back on the first and last resort, which is the truth: "It doesn't matter," said Brennan, "the answer is still yes."
If you don't care what you know, as long as you know it, you'd be better off studying theology. I have some crystals and tarot cards you'll probably want to purchase, too.
Great creative effort, in thinking about useful solutions to a tough problem (getting people to better value our best developed forms of rational decision-making).
Dave Orr, the rite of passage is to give the correct answer, 2/11, in the face of pressure to conform.
Nice picture.
I don't know if a verbal examination like this is suitable of a scientific conspiracy, though. Keep the mysticism and ritual, but give the initiates the chance to return their answers in writing, to make it more fair and reduce the stress factor.
Stepping inside the Great Library, Brennan breathed in surprise as he let his gaze wander around the hall. All these books! Shelves after shelves of writing - and when he saw the names on them, he could feel his heart skip a beat. Darwin, Tooby & Cosmides, Kahneman & Tversky... this was the sacred hall of the true grand masters, the depository of all their wisdom!
Hearing a sound, Brennan lowered his gaze, noticing the robed figure that had appeared in front of him. Remembering his manners, he bowed deep. "Respected master, I am novice Brennan of the Bayesian Conspiracy, here to scour the depths of my mind for answers to the questions you pose. I am at your service."
"Oook."
Following the robed figure, Brennan was led to a table and a chair. He sat down, and patiently waited as he was brought the Implements of Testing: the Pencil of Masters, the Notebook of Understanding, and the Eraser of Mistakes Undone. Finally, he was brought The Envelope, marked with the seal of the Conspiracy, personally sealed by the Council of Twelve.
And so it begins... he thought as he drew one more breath, then broke the seal and pulled out the contents to see what challenges he would be met with this time.
I really like "The Eraser of Mistakes Undone" for some reason.
We should name all our mundane magic this way. "The Car of Traveling" "The Airplane of Flying Metal" "The Laptop of Encapsulated Thought"
(And I just realized that I misread half of the story. Yes, for this particular scenario a verbal examination makes more sense than a written one. Ah well. goes to hunt for a new brain)
I don't know if a verbal examination like this is suitable of a scientific conspiracy, though. Keep the mysticism and ritual, but give the initiates the chance to return their answers in writing, to make it more fair and reduce the stress factor.
You may have already realized this, but what you do when you're under stress, in life, does count.
Of course this is true, as far as it goes.
But I'm inferring something from it in context that you perhaps don't mean, and I'd like to clarify. (Assuming you even read comments from this far back.)
Specific example: a couple of months after you posted this, I suffered a brain aneurysm that significantly impaired my working memory, to the point where even elementary logic problems -- the sort that currently would barely register as problems that needed solving in the first place - required me to laboriously work them out with paper and pen. (Well, marker... my fine motor control was shot, also.)
The question arises: could I have passed this initiation ceremony?
I certainly could not have given the right answer. It would have been a challenge to repeat the problem, let alone solve it, in a verbal examination. My reply would in fact have been "I'm not sure. May I have a pen and paper?"
If the guide replies more or less as you do here, then I fail.
I draw attention to two possibilities in that scenario:
(A) This is a legitimate test of rationality, and I failed it. I simply was less rational while brain-damaged, even though it didn't seem that way to me. That sort of thing does ha...
you'd be trying to build a group of rationalists while in fact excluding rationalists based on an irrelevant criterion.
They aren't trying to build a group of rationalists. They are trying to build a group of people who can achieve certain goals.
A lot of people need some specialized scientific knowledge to do their jobs. They may not be interested in the rest of it, but they are interested in that because it matters to what they're doing. If we hide science behind a general scientific conspiracy, people like that won't join, and they won't be able to do their jobs effectively, and society will be poorer as a result.
How does he know there are an odd number of people in the room?
He... um... er... counted them?
(Just like he counted the stairs, note.)
Kaj Sotala:
Your story is written decently, but it sounds like a parody of pretty much any traditional exam. If you remove the write-in answers requirement, you can have much more colorful examination scenarios.
Eliezer:
This seems like a cool motivation tactic. At the same time, I'm a little afraid that thinking my knowledge makes me special and unique will cause me to be arrogant.
Any commited autodidacts want to share how their autodidactism makes them feel compared to traditional schooled learners? I'm beginning to suspect that maybe it takes a certain ...
Actually, I have been running on pure curiosity, which is great for finding out about lots and lots of things, but now I'm having trouble focussing like I want. Thirty years of following my curiosity has developed some bad habits I need to break.
In my experience, the problem with running on curiousity is that, to be effective at something, one has to not take the time to investigate lots of unrelated things one is curious about.
billswift, that's a really good point. This explains why newspapers can be bad--they arouse your curiosity, but on many different subjects, many of which are completely unproductive (such as the status of the US presidential election. For some reason, extensive coverage of voter opinion trends is within the realm of prestigious reporting.)
Is this a maths question or a reasoning question?
What would the cult have said if the man had said something a long the lines of this to the first question.
"As probability is a subjective quality which must take all the information available to me to be valid, I'm not going to take the assumptions that were given to me. From the my estimate of your bodily proportions and the distribution of the height and weight of the general populace, and your low tone of voice compared to the average I would give you a 90% chance of being male."
"to be effective at something"
This was less of a problem for me. When I am actually doing something, my curiosity tends to focus on what I'm doing. My problem now is that I am trying to study in preparation for changing my direction, and it is very hard to stick to it.
All I can say is that when I scrolled down and saw the photo, my first thought was 'awesome'.
Nice illustration of your previous post, Eliezer.
Any commited autodidacts want to share how their autodidactism makes them feel compared to traditional schooled learners? I'm beginning to suspect that maybe it takes a certain element of belief in the superiority of one's methods to make autodidactism work
First, "traditional school learning" is itself inherently problematic. Consequently, "belief in the superiority of one's [own] methods" is not hard to acquire.
Second, all actual learning is necessarily autodidactic anyway, because where it takes place is in your own mind, not in your ...
"Re Will Pearson's question: something like "didn't you hear me say 'if'", I should think."
Well they should phrase their questions better, and say what would be the probability (and probably put some caveat about that being the only information available no other prior knowledge etc), rather than what is* the probability. Imagine someone says, "If it takes 4 secs for light to move 5 metres, what is the speed of light?". The answer should still be 3x10^8 or there abouts, the data given by someone should not always change your p...
Well, I guess I'm not talking about the learning process itself so much as what keeps you going. In a traditional school environment, grades are the de facto student motivator.
My old Creative Minds professor has plenty of anti-school arguments. But when he tried attending a school without grades, he learned that it sucked: many students didn't show up for class, and of the ones that did, the only ones who participated in classroom discussions were those who had strong opinions.
So my question is when you're learning on your own, how do you find ways to mo...
No, Mr. Pearson. The answer includes the if-statements attached to the question - saying that c is 3x10^8 would be incorrect.
Incorrect, an interesting phrase... In what manner would the phrase, "c is approximately 3x10^8," be incorrect. You say it is wrong, I say it is right. Who is to decide? Could I not go and measure it, and find c in the vacuum to be approximately 3x10^8?
Why is the questioner always assumed to be correct about every bit of data given? Sure I may not pass many exams taking this attitude, but the only examiner that really matters is reality, surely? We are here to learn how to reason about the world surely, not to learn to pass exams, or other random human tests.
In a traditional school environment, grades are the de facto student motivator
Motivator of what? The point is that whatever behavior it is that grades in school serve to motivate, it is not learning per se. Indeed, grades are more often than not a motivator against learning. To quote Eliezer (emphasis added):
"[S]tudents aren't allowed to be confused; if they started saying, 'Wait, do I really understand this? Maybe I'd better spend a few days looking up related papers, or consult another textbook,' they'd fail all the courses they took that quarter.&q...
Grades in school motivate people to gain the ability to successfully take exams, which is actually pretty well correlated to understanding the material, especially compared to, e.g., drinking until you pass out. You may be able to achieve some gains by being motivated by learning rather than by grades, but you're way better off being motivated by grades than by nothing.
We have to accept the reality of the situation; the system is not set up to haelp people learn who desperately want to. That is actually just and good, because the fraction of the population who actually desperately want to learn is the size of a rounding error.
So, any ideas on how to become one of that incredibly tiny number of people who desparately want to learn?
Re: Will Pearson's comment: "Well they should phrase their questions better".
In the context of an initiation ceremony perhaps a bit of stress-inducing ambiguity may be appropriate. Anway, the hypothesis that the "if" is true appears to be refuted by the fact that there are actually an odd number of people in the room.
"One-tenth" could not have been the correct answer - not even if Brennan already belonged to the Heresy of Virtue, and this was his initiation into some other cult ;-)
Any commited autodidacts want to share how their autodidactism makes them feel compared to traditional schooled learners? I'm beginning to suspect that maybe it takes a certain element of belief in the superiority of one's methods to make autodidactism work.
As Komponisto points out, traditional schooling is so bad at educating that belief in the superiority of one's [own] methods is easily acquired. I first noticed traditional schooling's ineptitude in kindergarten, and this perception was reinforced almost continuously thru the rest of my schooling.
PS: I liked the initiation ceremony fiction, Eliezer.
Tim, one-tenth would be the correct answer if Brennan were in the Heresy of Virtue, AND there were 16 people in the room. There would be 9 women in the HoV in the room, and 1 man who wasn't Brennan; hence, one in ten.
Thanks to Mike Vassar for pointing out that, if Brennan is in the HoV, you need to count how many men are in the room.
Since there are an odd number of people in the room, the guide must be posing a hypothetical question. If Brennan is in the HoV, the correct answer would be for him to say that he needs to know how many people are in the room in the hypothetical situation.
This is a great blog post. Reading it was actually fun as I anticipated what would happen next as I do for regular fiction. I liked how the story reiterated messages you've talked about before but in a way that seems more clear(combined with the previous formal essays) - this is probably because storytelling has an appeal that is more accessible to most people.
At first I thought he paused after saying "one" because nothing has a probability of one or zero but that was cause I didn't read carefully. I think something like this really would be a go...
Re: Phil Goetz: There are not 16 people /currently/ in the room - since Brennan counted them. Brennan is not told in the scenario that he is in the room.
He is not told other things that might impact on the answer, such as whether there were any non-human AIs in the room who were members of the Heresy of Virtue.
"I need more information" might have been an acceptable answer - at least on the latter grounds.
"One-tenth" requires the assumption that Brennan is in the Heresy of Virtue (which is something he ought to know), the assumption tha...
Fun Fact:
Electrical Engineers have been trying to budge "Old Yellow," the low-pressure sodium vapor lamp, from the top of the efficiency heap since the mid-1960s. They found some materials possibilities in the 1990s, but all have turned out to be too expensive.
I started reading the first chapter of Structure and Interpretation of Computer Programs and was reminded of this post.
...A computational process is indeed much like a sorcerer's idea of a spirit. It cannot be seen or touched. It is not composed of matter at all. However, it is very real. It can perform intellectual work. It can answer questions. It can affect the world by disbursing money at a bank or by controlling a robot arm in a factory. The programs we use to conjure processes are like a sorcerer's spells. They are carefully composed from symbolic exp
You may have already realized this, but what you do when you're under stress, in life, does count.
indeed. And one of the things we are prone to do under stress is delude ourselves: I think that the following:
"It doesn't matter," said Brennan, "the answer is still yes."
is perhaps the most important message. (Although I also like the message of not caving in to peer pressure. )
An excellent little parable, I shall keep it in mind ;-)
Come now, why doesn't Brennan take an experimental approach: kick him or her where the balls would be, and appraise the reaction? I mean, this is a conspiracy of scientists, not Aristotelian scholastics.
Caledonian: I assume he means that, for all X, if X is true, he wishes to know X. This opposed to "if the universe is made of puppies and unicorns, tell me about it, otherwise I don't want to know."
That was a brilliant story!
I liked the ring with n=1, nice touch. Beats wearing barbed wire round your underpants any day.
Oh my gosh but I actually am stunned speechless.
I can't even begin to express the way I feel right now, Eliezer Yudkowsky, my friend, you are in possesion of a rare and powerful gift!
I called my math teacher over to help. We couldn't find the answer. This isn't promising, as I had hoped to summon him for help whenever I needed help to understand something above my highschool math education. I will make a quick request for what steps of math i should follow to have a better chance of wrapping my mind around this probability stuff, since part of my exam test seriously has 'there are four playing cards, one is red, what is the probability of randomly picking red' or something like that.
Regardless of such concerns; I'm pretty sure the 'I d...
I know this is a very old story, but I have some thoughts on it I wanted to share.
Let me first share an experience that I think everybody who has ever seriously studied math (or any complicated subject) has had. You're working on a difficult math problem, say a complicated differential equation. You are certain your method is correct, but still your answer is wrong. You've checked your work, you've double checked it, you've checked it again. Your calculation seems flawless.. Finally, in desperation, you ask a friend for help. Your friend takes one glance a...
I like the test. It seems to have multiple levels, each of which Brennan passes:
Presumably Brennan knows their own gender (they are "one of the humans in this room"). The self-include skews all the maths in a nasty way. (three quarters in the room are women, which means that 12 of the 15 other people are women which means that ...)
The torches that lit the narrow stairwell burned intensely and in the wrong color, flame like melting gold or shattered suns.
192... 193...
Brennan's sandals clicked softly on the stone steps, snicking in sequence, like dominos very slowly falling.
227... 228...
Half a circle ahead of him, a trailing fringe of dark cloth whispered down the stairs, the robed figure itself staying just out of sight.
239... 240...
Not much longer, Brennan predicted to himself, and his guess was accurate:
Sixteen times sixteen steps was the number, and they stood before the portal of glass.
The great curved gate had been wrought with cunning, humor, and close attention to indices of refraction: it warped light, bent it, folded it, and generally abused it, so that there were hints of what was on the other side (stronger light sources, dark walls) but no possible way of seeing through—unless, of course, you had the key: the counter-door, thick for thin and thin for thick, in which case the two would cancel out.
From the robed figure beside Brennan, two hands emerged, gloved in reflective cloth to conceal skin's color. Fingers like slim mirrors grasped the handles of the warped gate—handles that Brennan had not guessed; in all that distortion, shapes could only be anticipated, not seen.
"Do you want to know?" whispered the guide; a whisper nearly as loud as an ordinary voice, but not revealing the slightest hint of gender.
Brennan paused. The answer to the question seemed suspiciously, indeed extraordinarily obvious, even for ritual.
"Yes," Brennan said finally.
The guide only regarded him silently.
"Yes, I want to know," said Brennan.
"Know what, exactly?" whispered the figure.
Brennan's face scrunched up in concentration, trying to visualize the game to its end, and hoping he hadn't blown it already; until finally he fell back on the first and last resort, which is the truth:
"It doesn't matter," said Brennan, "the answer is still yes."
The glass gate parted down the middle, and slid, with only the tiniest scraping sound, into the surrounding stone.
The revealed room was lined, wall-to-wall, with figures robed and hooded in light-absorbing cloth. The straight walls were not themselves black stone, but mirrored, tiling a square grid of dark robes out to infinity in all directions; so that it seemed as if the people of some much vaster city, or perhaps the whole human kind, watched in assembly. There was a hint of moist warmth in the air of the room, the breath of the gathered: a scent of crowds.
Brennan's guide moved to the center of the square, where burned four torches of that relentless yellow flame. Brennan followed, and when he stopped, he realized with a slight shock that all the cowled hoods were now looking directly at him. Brennan had never before in his life been the focus of such absolute attention; it was frightening, but not entirely unpleasant.
"He is here," said the guide in that strange loud whisper.
The endless grid of robed figures replied in one voice: perfectly blended, exactly synchronized, so that not a single individual could be singled out from the rest, and betrayed:
"Who is absent?"
"Jakob Bernoulli," intoned the guide, and the walls replied:
"Is dead but not forgotten."
Abraham de Moivre,"
"Is dead but not forgotten."
"Pierre-Simon Laplace,"
"Is dead but not forgotten."
"Edwin Thompson Jaynes,"
"Is dead but not forgotten."
"They died," said the guide, "and they are lost to us; but we still have each other, and the project continues."
In the silence, the guide turned to Brennan, and stretched forth a hand, on which rested a small ring of nearly transparent material.
Brennan stepped forward to take the ring—
But the hand clenched tightly shut.
"If three-fourths of the humans in this room are women," said the guide, "and three-fourths of the women and half of the men belong to the Heresy of Virtue, and I am a Virtuist, what is the probability that I am a man?"
"Two-elevenths," Brennan said confidently.
There was a moment of absolute silence.
Then a titter of shocked laughter.
The guide's whisper came again, truly quiet this time, almost nonexistent: "It's one-sixth, actually."
Brennan's cheeks were flaming so hard that he thought his face might melt off. The instinct was very strong to run out of the room and up the stairs and flee the city and change his name and start his life over again and get it right this time.
"An honest mistake is at least honest," said the guide, louder now, "and we may know the honesty by its relinquishment. If I am a Virtuist, what is the probability that I am a man?"
"One—" Brennan started to say.
Then he stopped. Again, the horrible silence.
"Just say 'one-sixth' already," stage-whispered the figure, this time loud enough for the walls to hear; then there was more laughter, not all of it kind.
Brennan was breathing rapidly and there was sweat on his forehead. If he was wrong about this, he really was going to flee the city. "Three fourths women times three fourths Virtuists is nine sixteenths female Virtuists in this room. One fourth men times one half Virtuists is two sixteenths male Virtuists. If I have only that information and the fact that you are a Virtuist, I would then estimate odds of two to nine, or a probability of two-elevenths, that you are male. Though I do not, in fact, believe the information given is correct. For one thing, it seems too neat. For another, there are an odd number of people in this room."
The hand stretched out again, and opened.
Brennan took the ring. It looked almost invisible, in the torchlight; not glass, but some material with a refractive index very close to air. The ring was warm from the guide's hand, and felt like a tiny living thing as it embraced his finger.
The relief was so great that he nearly didn't hear the cowled figures applauding.
From the robed guide came one last whisper:
"You are now a novice of the Bayesian Conspiracy."
Image: The Bayesian Master, by Erin Devereux