Severian of Nessus, Amateur Bayesian

Severian sounds like a much more sophisticated Bayesian than Noah Smith, whoever he is (surely some kind of fictional character).

As Severian and Anderson imply, Noah is being a bad Bayesian here. A signal that has only one possible (observable) value has no information content.

This is another version of the anthropic fallacy

Proposition H: “Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me …. etc” Sorry, I’m not religious, but the King James Bible expresses it so much more eloquently! :)

The Bayes’ rule delusion is just the unjustified confidence of the Russian roulette survivor: if there are enough subjects, some will survive.

He could easily test the hypothesis by jumping off a tall building.

There is a belief, at least as old as Homer, that dolphins are benevolent and push distressed swimmers closer to shore . . . .

12: Just because God says a few nice things about moral hazard doesn’t mean he won’t vote for the bail-out when the time comes.

“How such primitive minds come to believe in their charms”

That is not very polite or respectful. Apparently the character was a horrible cold hearted torturer and mercenary. Best not to agree with such a character.

Anyway, this topic is reminiscent of the argument about how one can know about others knowing about the death of Captain Cook/Lono in Hawaii.

unhelpful @10: John Quiggin is correct above that Bayes’s theorem has nothing to say about survivorship fallacies. When playing Russian roulette, you may sum over five expected outcomes or over six, as you prefer. But in nonfatal games, the quantum mechanic is in slightly better shape than the classical believer in empiricism. When we define “likely” as a sum over past trials, and then blindly apply it to a sum over future counterfactuals, we are standing on a metaphysical foundation that cannot possibly be supported by past experience; the very notion that we can learn from experience is in the dock. In a deterministic world, “likely” as a sum over counterfactuals is not even coherent: what does “likely” mean, if only one outcome happens?

The Everett (QM) Bayesian has no such problem. He (metaphysically) lives in a superposition of wavefunctions, and has a unified theory of both historic and contingent probability: namely, that they are both given by the square of the wavefunction amplitude. He’s “likely” to see what’s mostly happened before, because most of his wavefunction ends up there, and he’s got a prospective calculation to prove it. Contrariwise, he cares where most of his wavefunction ends up, because that’s how he got here himself, and again he can do the retrospective calculation, using the same machinery, to prove it. His metaphysics are still prior to his empiricism, but at least they treat all empirical inputs (past and future) the same way.

Actually, ZM, “cold-hearted” would not be the right term for Severian if you want to judge him according to our times. “Badly damaged” would be much closer.

Re: Jake b, and Henry ‘are a transposed version of how his fellow soldiers…’

This article The Education of a Torturer investigates how soldiers etc are picked and turned into torturers by their masters

http://psychhome.weebly.com/uploads/1/3/7/7/1377191/education_of_torturer.pdf

ZM

Bear in mind that Severian believes in the efficacy of a charm which on at least once occasion not merely saved his life, but actually resurrected him from the dead. The character trait on exhibit here isn’t callousness: Severian is distinguishing between True Religion and superstion.

Smith says the probability you assign to proposition H should increase but will always remain extremely low. Severian describes people who think the probability of their being invincible is very high. BIG difference.

Dr. Quiggin –

Being the veteran of many physics cocktail-hour arguments about the anthropic principle, I anticipated your objection, and in my post I noted that you could modify H very slightly to allow someone to observe himself being mortally wounded.

If you like, you can apply my argument to “becoming a paraplegic” instead of “being violently killed”…

– N

Not constellation – contestation sorry. They were written by Margaret Cavendish, Duchess of Newcastle

@Noah I missed the mortally wounded bit. But I don’t think it does all the work you want it to. Certainly in the immediate aftermath of a death-cheating experience you can raise the posterior probability of invincibility (a little). But, you can’t update repeatedly in this fashion, because you can’t be mortally wounded twice.

Of course, this doesn’t invalidate your final point that lots of people (most notably teenagers) reason this way.

So surviving one round of Russian roulette tells you nothing about the probability the next one is loaded? That seems wrong.

If it’s a revolver with 6 shots, and you don’t spin the cylinder between shots, then surviving one round tells you nothing about the next round. Unless the round you survived was the sixth-oldest.

If you do spin the cylinder, then surviving one round shows you there is at least one that’s unloaded, and you can work out the math for the odds on successive survivals. The chance that there’s only one unloaded one and you get it each time goes down fast. The chance that there is one loaded one and you miss it each time goes down slower.

Anyway, consider the plot of Catch-22. If you started the war with a bunch of others and now there are few of them left and no end in sight to the war, and a lot of guys who haven’t been in it as long as you have died, the natural Bayesian approach is to figure that everybody who’s reasonably competent has about the same chance of survival, and you have been lucky so far just by the luck of the draw. If the average soldier lasts less than a year, then your chance of lasting another year is not good. People find this unpleasant to think about.

Far easier to believe that there’s something special about you so the statistics about the others doesn’t apply to you.

So if at some point you have a choice — everybody agrees that you have done your part, you don’t owe it to them to keep fighting, so you can go home to a million-dollar job with good food and four beautiful girlfriends and everybody thinks you’re a hero, or you can keep fighting, at that point it makes sense to do reasonable Bayesian thinking.

But if instead you have a choice — keep fighting, or abandon your surviving buddies and try to sneak home through enemy territory and occupied territory with heavy security and if they ever catch you, you will be hanged, take up a new identity from scratch and never call attention to yourself in any way and feel ashamed for life — then it might feel a lot better to pretend you’re special.

“So surviving one round of Russian roulette tells you nothing about the probability the next one is loaded? That seems wrong.”

My understanding is that there’s a fixed chance that one chamber is loaded. If you spin the barrel between shots, you can think of it as being like throwing a die. Say the probability that a chamber is loaded is 1/6: then surviving any one round tells you nothing about your chances of surviving the next*: surviving n rounds has a probability of (5/6)^n, which will always be a finite possibility. Although you have just been lucky, the experience may convince you that you’re special. Bad drivers and smokers often think this way.

*though I am reminded of the old joke: “if your parents didn’t have any children, it’s highly unlikely that you will either …”

H0 is that you are not special and you die. H1 is that you are special and that your survival is due to divine intervention and not to chance. In the above example, the random chance of surviving 20 shots is (5/6)^20 = 0.026 (3dp), about 1 in 40. So the alternative hypothesis of supernatural protection* is supported with a probability of 97.4%.

If 39 others spun it until they died and the bullet was replaced, chances are the bullet is not a dud.

But now it’s an open question whether you are special. If nobody was special we’d get about 1 in 40 surviving, and we have that. If we had 2 in 40 survive, then maybe one of them is special but we don’t know which one.

But with Bayesian analysis we can consider other data. Maybe before you started playing russian roulette, God had already spoken to you and told you that you were special, that he had important plans for you and you would not die until the right time. That certainly makes you special. You might give it an 80% chance it was really God talking to you, and a 20% chance you are having auditory hallucinations, based on how convincing God was when he talked to you. Then the fact that you were the one who survived when 40 mundanes died, tends to confirm that it was God instead of a hallucination.

I think this method of trialling people about their faith has been done before, back around Francis Bacon’s day, often on ‘superstitious’ women :(

Kind of related, in one of Bank’s Culture books there is a political pundit who is right on every controversy that comes up over the course of several centuries.

The Minds, aware of the possibility that they might be completely wrong about how everything fundamentally works, pay serious attention to her opinion.

But she doesn’t show up in later books in the series. So presumably she was just the kind of statistical anomaly you would expect given a population size of mega trillions.

Of course, someone who was wrong on every controversy would be equally useful.

Soru @43. But see Tom Friedman, always uselessly wrong.

Combine with @8, perhaps, and you get a rather good argument for polytheism.

Byron the Bulb lives on.

Given that most religions seem to revere martyrs more than the living I’m not sure survival is evidence of God’s will.

Henry mentioned Robert Charles Wilson’s short story “Divided by Infinity” about someone who discovers that quantum immortality is real after improbably avoiding or surviving death many times.

What’s driving me crazy is that I know I’ve read another short story about quantum immortality, where someone tests the hypothesis with a suicide attempt but the attempt succeeds. The person who commits suicide isn’t the narrator, so really we can’t be sure about the quantum immortality hypothesis… There was nothing science fictional actually evidenced in the story, only people acting on a belief about quantum immortality. You wouldn’t even call it SF if it hadn’t been published by a SF author alongside other SF stories. Does anyone recall the story I’m talking about? My Googling fails me.

Sasha @ 52
I was only taking what you said literally. Did you not mean it? (On a third or fourth reading, maybe I misunderstood what you meant by “of.”)

I really do see no reason why someone couldn’t interpret “chosen by God” in a way that doesn’t require breaking the laws of statistics (though I don’t think it’s the most natural way). As a general rule, Russian roulette is fatal, yet two or three out of a hundred lived. Why them? Once you’re permitting causes that can’t be observed and that have (by definition) no observable effect, you can do whatever you want. Maybe they must have cheated, maybe their God saved them, maybe they possess some as-yet unknown immunity to six-shooters.

Ok, the Russian roulette example is unnecessarily complicated for my purpose. Suppose there are two guns, A and B. You know one of the two is loaded (and 100% fatal) but have no information as to which. You shoot yourself with A and nothing happens. Does this tell you anything about the probability B is loaded?

I finally found the story I was thinking of: it was “Everlasting” by Alastair Reynolds.

Never play Russian roulette with a semi-automatic.

53 – I was going to mention “Divided by Infinity” – at least I can add value (assuming the spam filter lets this post) by pointing out that it’s available for free online.

Patriotic Bayesianism: https://www.youtube.com/watch?v=4l27MUEgyMQ

John Donne takes the frequentist side:

Let no man, no woman, no devil offer a Ne forte, (perchance we may die) much less a Nequaquam, (Surely we shall not die) except he be provided of an answer to this question, except he can give an instance against this general, except he can produce that man’s name, and history, that hath lived, and shall not see death. We are all conceived in close prison; in our mothers’ wombs, we are close prisoners all; when we are born, we are born but to the liberty of the house; prisoners still, though within larger walls: and then all our life is but a going out to the place of execution, to death. Now was there ever any man seen to sleep in the cart, between Newgate, and Tyburn? between the prison, and the place of execution, does any man sleep? And we sleep all the way; from the womb to the grave we are never thoroughly awake; but pass on with such dreams, and imaginations as these, I may live as well, as another, and why should I die, rather than another?

I should add that I see nothing wrong generically with the reasoning described in Noah’s post. Each of us is unusual in certain ways. We have to study our own experiences to learn how.

What’s driving me crazy is that I know I’ve read another short story about quantum immortality, where someone tests the hypothesis with a suicide attempt but the attempt succeeds.

Larry Niven’s All the Myriad Ways?

The reason why Noah seems a sophist: he isolates this one hypothesis. For Ideal Bayesians, a billion equations are tracked, not just magical prophecies.

Likewise, Pascal fails on the major premise sustaining his Wager. If Old Nick rewards his fiendish hordes, the Satanist starts to look sager.

But stats will not do in reality: physicality mandates frugality. The Best Explanation of our information thus beats doomed attempts at totality.

(Delete the first – it’s not intended. I’d be grateful, not offended. If it goes thenthis can too – sorry to make work for you.)

I don’t know of anybody believing in Proposition H. Many people believe they will be rewarded in an afterlife; some deliberately commit suicidal acts that they believe promote a good cause, and many more are willing to risk their lives for what they believe are good causes. Most of these people don’t imagine themselves invulnerable (there is still superstition of the sort that people carry medallions or charms but they also know that others who carried the same charms have died).

Another superstition is, I believe, far more relevant:

Proposition HH: “Humanity has nothing to fear from resource limits or environmental crises such as Global Warming because human ingenuity will overcome any obstacle and always find a solution.” Of course, belief in proposition HH is justified by past experience – we will continue surviving because we survived in the past.

It’s not difficult to come up with a long list of well-educated, seemingly rational thinkers who subscribe to this particular superstition. In fact its power can hardly be overestimated.

Someone once tried to convince Diogoras of Melos of the existence of the gods by pointing out all the offerings (votive pictures) left by grateful sailors who had survived storms after praying to the gods. Diagoras replied that “there are nowhere any pictures of those who have been shipwrecked and drowned at sea.”

Poorly Chosen Prior.