Initiation Ceremony

Joy in the Merely Real

    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."

 

Elimonk2darker

Image:  The Bayesian Master, by Erin Devereux

 

Part of the Joy in the Merely Real subsequence of Reductionism

Next post: "Awww, a Zebra"

Previous post: "To Spread Science, Keep It Secret"

Comments

sorted by
magical algorithm
Highlighting new comments since Today at 7:09 AM
Select new highlight date
All comments loaded

No comments? Either you're all stunned speechless, or you've simply gotten used to me by now.

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 happen, after all.

(B) This test is confounding rationality with the ability to do mental arithmetic reliably. I was no less rational then than I am now.

If A is true, then you and the guide would be correct to exclude me from the club, and all is as it should be.

But if B is true, doing so would be an error. Not because it wasn't fair, or wasn't my fault, or anything like that, but because you'd be trying to build a group of rationalists while in fact excluding rationalists based on an irrelevant criterion.

Now, perhaps the error is negligible. Maybe the Bayesian Conspiracy will collect enough of the most rational minds of each generation that it's not worth giving up the benefits of in-group formation to attract the remainder.

OTOH, maybe not... in which case the Bayesian Conspiracy is on the wrong track.

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.

Beware the hidden prior: that all Virtuists are assumed to be either men or women.

That's true; we did not rule out transgender Virtuists.

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"

It's very Napoleon of Notting Hill, isn't it?

Dave Orr, the rite of passage is to give the correct answer, 2/11, in the face of pressure to conform.

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.)

If he counted them, then he could have given a better calculation than "2/11", since he had one additional prior that was unstated: the probability that he himself was (or was not) a male virtuist. In the same scenario, the best candidate would ask what the virtuist heresy was first, and then give an answer based on that additional information. (If the interrogator refused to answer, the answer might still be 2/11.)

I had guessed something like that was the reason why the answer was supposed to be 1/6.

"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".

I thought of the possibility that Brennan might be counted as one of the people in the room (and thus he has more information than was stated) as a possible reason the one-sixth answer could be correct. From that angle, whether the information given describes the current moment is a very relevant concern.

After doing the math, it works out that if there are exactly 80 people in the room, and Brennar himself belongs to the Heresy of Virtue (highly unlikely), then one-sixth is in fact the correct estimation (based on 45 female virtuists, and 9 male virtuists other than Brennar).

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."

It's an ethics question.

Brennan didn't take the guide at his word, he re-checked his own results to see if he made a mistake. Confirming his own results, he restated them in the face of Authority telling him he was wrong, which is precisely why he was permitted into the Beyesian Conspiracy. Had he said "one-sixth", he would undoubtedly have been denied admittance.

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.

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.)

I write them out as frequencies instead of probabilities; it makes it much easier to conceptualize, a fact which is well documented but poorly understood.

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 interactions with others.

So yes, in order to learn, you have to be "arrogant" enough to believe that you actually can. That is, you have to have the confidence that you personally can fully appreciate the insights of "authority figures" like Issac Newton. Unfortunately, social pressures seem to discourage such "presumption" in favor of deference to authority.

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.

That isn't "knowing" something. That's believing it.

Not necessarily. I know a large amount of halachah (Orthodox Jewish law). I don't believe any of it. I also know a smaller amount of Catholic theology. I don't believe any of that either. Prioritization still makes sense. These really aren't great things to know much about if one wants any sort of real understanding.

You know the fact "the content of the halachah is _" (I don't know what the halachah says). However, you do not know "the content of the halachah is true", because that is a falsehood. If it were costless, I would choose to know the former, but not the latter.

But you CAN'T know the latter, not on the standard theory of knowledge as "justified true belief". You'd have belief, but probably not justified and surely not true.

That hasn't been 'standard' since Gettier, I think.

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 at your work, smiles, and says: "Four times five does not equal twelve"... Oh. Yeah. Right. Good point.

We all make mistakes. Even very skilled people sometimes make elementary mistakes. Brennan in the story is doing a calculation that is very trivial for him, but it is still possible. Even if he can't see a flaw, can't even imagine a flaw, that doesn't mean the odds are zero.

Yes, they are certainly very small. Brennan is saying "The odds of me making a mistake are very small, so I am confident I am correct". But this is the Bayesian Conspiracy, not the Frequentist Conspiracy. Brennan should be asking: "Given that someone has clearly made a mistake, what are the odds of me having made it, instead of every other person in the Conspiracy. The answer is obvious.

Thus, Brennan fails as a Bayesian, and should not be accepted into the Conspiracy.

And I am not merely making a pedantic point here. This is a very important point for the real world as well. Yes, standing up to peer pressure is important, but only when it is rational. Global warning deniers also think they are standing up to peer pressure. Creationists also think they are standing up to peer pressure. And often for the exact same reason that Brennan is doing so, in this story. They thought about the issue themselves, they may even know a thing or two about it, and they really can not see any flaw in their logic, so they stick with it, convinced the odds of them having made a mistake are very small, forgetting about the huge prior.

This is actually my first post on this site. I have read quite a bit, but not everything, so I hope I am not inadvertently saying something that has been discussed before. I couldn't find anything, and I think it's an important point.

This is actually my first post on this site.

Welcome!

Given that someone has clearly made a mistake, what are the odds of me having made it, instead of every other person in the Conspiracy. The answer is obvious.

But this assumes that the Conspirator is telling him the truth, instead of testing him. I think Brennan is right in considering alternative hypotheses about the Conspirator's motives.

And I am not merely making a pedantic point here. This is a very important point for the real world as well.

There are questions of 'epistemic hygiene' here. If I hold a belief because someone else I trust holds that belief, I need to be careful that I don't give other people the impression that I'm providing independent verification of that belief instead of just importing their belief. If Brennan calculated a different answer, him telling the group that will allow them to converge more quickly to the correct belief (even if he acts on the group consensus belief, because that's the one that he trusts more than his private belief!).

Thanks!

You are right that there is also the scenario that the test givers are lying (which in this case turns out to be the truth). But this is not something Brennan in the story considers, so it can not have affected his decision. So he arrived at the correct answer, but did so by faulty logic. His two errors (not considering one possible scenario, and assigning wrong odds to the two scenarios he does consider) just happen to cancel out. It would certainly be a way to fix this story: Let Brennan first realize that he should trust everybody else over himself, and then realize that the examiner may be lying.

Though there remains a problem. If the conspirators are lying, it is not clear what answer they want. It may be a test to see if he can withstand peer pressure, but it might also be a test to see if he is willing to entertain the notion of being wrong!

Finally, yes, you are absolutely right that holding a believe because others hold it does not constitute proof. So perhaps the most rational answer would be: "My own independent calculation tells me that the answer is 2 in 9, and for the purpose of establishing a consensus opinion on this question, that is my answer. However I do not think that my evidence is enough to shift the consensus opinion away from the answer of 1 in 6, and thus this is what I shall consider the correct answer, despite my own intuition".

But this is not something Brennan in the story considers,

But it is! He recalculates - aloud, which makes him less likely to repeat a mistake, and more likely to catch it if he does - and then, reaching the same conclusion as before, gives it again. He thinks he might have made a mistake, which is a reasonable thought, so he works it out again.

In other words,

It may be a test to see if he can withstand peer pressure, but it might also be a test to see if he is willing to entertain the notion of being wrong!

but he does the correct thing for both of those scenarios. He entertains the notion of being wrong, and calculates his odds publicly, where anyone could point out to him if he has found that 4 times 5 is 12, but, finding the same conclusion as before, he stands up to peer pressure.

Brennan should be asking: "Given that someone has clearly made a mistake, what are the odds of me having made it, instead of every other person in the Conspiracy.

But in fact, in the story neither of those hypotheses hold. No-one is making a mistake.

(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)

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.

Because, as my daughter learned the other day, that still hurts. Also, the person could have been a non- or pre-op transsexual woman (leaving out other variants merely for brevity).

Maybe a different experimental method...

Edit: See also: Tim_Tayler's comment above re: hidden prior.

If you guys are going to rig elections, I want in.

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 to the efforts I put into my learning, or if the difficulty of learning the innumerable details of science would make it all the more worthwile, and would make the fun last much longer than it would for, say, fantasy magic learning.

Probably both.

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!

It only goes to show how we are all susceptible to power of stories, rather than able to examine them dispassionately, like a rationalist presumably should.

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."

I like the test. It seems to have multiple levels, each of which Brennan passes:

  • Can you do a simple bayes theorem calculation?
  • Can you resist conformity bias when necessary?
  • Can you spot when you're fed bad data?