Right, so what is the prior probability that a baby dying is worse than an adult woman dying?
How would you even start to collect such a statistic?
The purpose of Bayesian Reasoning is, ultimately, to make decisions. Beyond even its issues coming from being derived from an existing framework, the problem is that, even if priors can be calculated, all reasoning begins and ends at human judgment and human values. Bayesian calculations are just something that can make the middle part easier. I strongly suspect Reverend Bayes would have been the first one to tell the modern Bayesian this. (Would have replaced the concept 'human values' with 'divinity,' though.)
Thursday, December 17, 2009
Saturday, December 12, 2009
Homelessness
Specifically, hardcore, chronic homelessness.
After having read that, I thought about homeless people for a while. Then, I decided that at the first opportunity I would talk to one. So I did.
People seem to have an instinct about me. I was sitting in the bus station waiting for an intercity bus, and he walked in. Tall man. Not stringy but not too meaty. Scruffy as you'd expect. The kind of hands that get called 'ham.' He made a beeline for me.
I tried to talk to him for a bit. According to plan, when he asked for money I obliged, in an attempt to gain goodwill. Fifty cents.
It was like speaking to a robot, a wind-up thing that reacted almost at random to my queries...unless the subject was money. His fuzzy incoherence was suddenly pierced by the subject; he talked almost like a normal. And my plan worked; he felt the need to continue the exchange while hugging me. I didn't object. He clearly didn't know any better.
But not with me. I was unable to get him to attend to me at all except when he decided to call me a 'good guy' or something. Instead he tried to panhandle the rest of the room. Now it was more like talking to a television.
I know he was sober. They only panhandle when sober, because the point is to get drunk, and they stop for a while when they reach their goal, if for no other reason than that they're busy passing out.
I've met people who had more mental cohesion when stoned out of their minds than this man was when stone cold sober. If it wasn't about money, he couldn't focus. In any real sense, he didn't have a human mind anymore.
The drink - or whatever it was that put him on the street - had drained his soul. He was already dead in every meaningful way.
I couldn't help wondering, where was this man's family? What tragedy befell him that he's now living on the street now? Why hasn't anyone just scooped him and up and kept him away from the booze? What happened to his parents? Does he have children? Siblings? What do they think of him?
I tried asking him.
These people are not really people anymore. The reason we generally don't interfere with the lives of other adults is that they're responsible for their actions, and since we don't want our responsibility taken from us, we don't take it from others. However, the chronically homeless are not responsible anymore. They're not on the street by choice, or because they're lazy.
"We also believe that the distribution of social benefits should not be arbitrary."
They're on the street because they're dead inside. That's why treating them for efficiency isn't arbitrary. The only ways to stop these people from acting like beasts, from harming themselves, from costing our social services millions of dollars, is to kill them or take away their 'freedom.' Institutionalize the chronically homeless.
Go on, try it yourself. Talk to a bum.
After having read that, I thought about homeless people for a while. Then, I decided that at the first opportunity I would talk to one. So I did.
People seem to have an instinct about me. I was sitting in the bus station waiting for an intercity bus, and he walked in. Tall man. Not stringy but not too meaty. Scruffy as you'd expect. The kind of hands that get called 'ham.' He made a beeline for me.
I tried to talk to him for a bit. According to plan, when he asked for money I obliged, in an attempt to gain goodwill. Fifty cents.
It was like speaking to a robot, a wind-up thing that reacted almost at random to my queries...unless the subject was money. His fuzzy incoherence was suddenly pierced by the subject; he talked almost like a normal. And my plan worked; he felt the need to continue the exchange while hugging me. I didn't object. He clearly didn't know any better.
But not with me. I was unable to get him to attend to me at all except when he decided to call me a 'good guy' or something. Instead he tried to panhandle the rest of the room. Now it was more like talking to a television.
I know he was sober. They only panhandle when sober, because the point is to get drunk, and they stop for a while when they reach their goal, if for no other reason than that they're busy passing out.
I've met people who had more mental cohesion when stoned out of their minds than this man was when stone cold sober. If it wasn't about money, he couldn't focus. In any real sense, he didn't have a human mind anymore.
The drink - or whatever it was that put him on the street - had drained his soul. He was already dead in every meaningful way.
I couldn't help wondering, where was this man's family? What tragedy befell him that he's now living on the street now? Why hasn't anyone just scooped him and up and kept him away from the booze? What happened to his parents? Does he have children? Siblings? What do they think of him?
I tried asking him.
These people are not really people anymore. The reason we generally don't interfere with the lives of other adults is that they're responsible for their actions, and since we don't want our responsibility taken from us, we don't take it from others. However, the chronically homeless are not responsible anymore. They're not on the street by choice, or because they're lazy.
"We also believe that the distribution of social benefits should not be arbitrary."
They're on the street because they're dead inside. That's why treating them for efficiency isn't arbitrary. The only ways to stop these people from acting like beasts, from harming themselves, from costing our social services millions of dollars, is to kill them or take away their 'freedom.' Institutionalize the chronically homeless.
Go on, try it yourself. Talk to a bum.
Tuesday, December 8, 2009
Code_of_Laws AND ~Code_of_Laws
Curiously, it appears my laws are circular. Here's theft:
So if you lie or don't have the right to take something, you don't have the right to take it. The code refrains from defining who actually has rights, and who does not, notwithstanding a few oddities like this one:
So geologist definitely aren't thieves. (And a mining company will probably let you take a pebble or two if you ask nicely.)
Err. Hmm. So about that lying stuff...
Committing fraud by fraudulent means. Nice. Was there an alternative about committing fraud without deceit or fraud?
But surely, the murder code will be more stringent?
That's...that's actually pretty reasonable.
I wonder where they screw it up. Emphasis mine:
"Yes I'd like to be tried under section 229(b)...yes, the one that's a contradiction."
The next is just amusing. Perhaps there's an obscure legal reason for this:
So if I, for a lawful object, go ahead and kill someone, it's A-okay, as long as my goal was compatible with keeping them alive? I somehow doubt that would fly in court, and yet...
Even more amusingly, the code explicitly exempts effecting an execution by false evidence. Canada has no death penalty, and indeed if we did the executioner does not appear to have their own exemption.
But, actually, I've been taking you for a bit of a ride. There's a problem I've overlooked:
All the listed punishments are for murder. All murders are special cases of culpable homicide. Culpable homicide is this special kind of homicide: unlawful homicide.
Progressive. Outlawing unlawful homicide. What will they come up with next? I guess the executioner doesn't really need their own exception.
My motivation for looking up this was the libertarian and anarchist bon mot "taxation is theft." I'd assumed there would be specific exemptions for taxation, but I found that the whole code is meaningless. Reality is more interesting than radical philosophies, it turns out.
I find this puzzling since many of the code's details go to great lengths to be logically rigorous. It would actually be beautiful, if the whole thing wasn't flying on dreams. I don't demand that the code justify itself entirely - it never actually states that it is outlawing crimes, never states that crimes are wrong, and never states who will hand down punishments, nor that these punishments are mandatory, and I don't expect it to do any of this. All logic must start at axioms, and while it's nice if they're explicit, I don't expect lawyers to follow philosophical best practise. I'm naturally too lazy to look up the precedents, and perhaps there's actual statements of 'doing X is fraud' there, but even if so, that just means the code itself is dead weight.
I have trouble imagining that the courts never use the code, though. (I could only find Supreme Court records, and they would never have a reason to cite basic code. They did, as expected, cite precedent often, and occasionally legislative act.) Since it is impossible that they use the actual logical content of the code, they must be reading something into it.
Ultimately, it's not the code but the attitude of the people who support and execute the system. I don't know who these people actually are, in practice, other than I know it isn't who we're told it is. The last thing I have difficulty with is how these people can be simultaneously responsible, and allow the code to remain like this. As it is, formal reality and actual reality cannot converge, which usually means that formal spirit and informal spirit will continue to diverge.
"Every one commits theft who fraudulently and without colour of right takes, or fraudulently and without colour of right converts to his use or to the use of another person, anything, whether animate or inanimate, with intent"
So if you lie or don't have the right to take something, you don't have the right to take it. The code refrains from defining who actually has rights, and who does not, notwithstanding a few oddities like this one:
"No person commits theft by reason only that he takes, for the purpose of exploration or scientific investigation, a specimen of ore or mineral from land that is not enclosed and is not occupied or worked as a mine, quarry or digging."
So geologist definitely aren't thieves. (And a mining company will probably let you take a pebble or two if you ask nicely.)
Err. Hmm. So about that lying stuff...
"Every one who, by deceit, falsehood or other fraudulent means, whether or not it is a false pretence within the meaning of this Act, defrauds the public or any person, whether ascertained or not, of any property, money or valuable security or any service"
Committing fraud by fraudulent means. Nice. Was there an alternative about committing fraud without deceit or fraud?
But surely, the murder code will be more stringent?
"Culpable homicide is murder(a) where the person who causes the death of a human being"
That's...that's actually pretty reasonable.
I wonder where they screw it up. Emphasis mine:
"(b) where a person, meaning to cause death to a human being or meaning to cause him bodily harm that he knows is likely to cause his death, and being reckless whether death ensues or not, by accident or mistake causes death to another human being, notwithstanding that he does not mean to cause death or bodily harm to that human being;"
"Yes I'd like to be tried under section 229(b)...yes, the one that's a contradiction."
The next is just amusing. Perhaps there's an obscure legal reason for this:
"(c) where a person, for an unlawful object, does anything that he knows or ought to know is likely to cause death, and thereby causes death to a human being, notwithstanding that he desires to effect his object without causing death or bodily harm to any human being."
So if I, for a lawful object, go ahead and kill someone, it's A-okay, as long as my goal was compatible with keeping them alive? I somehow doubt that would fly in court, and yet...
Even more amusingly, the code explicitly exempts effecting an execution by false evidence. Canada has no death penalty, and indeed if we did the executioner does not appear to have their own exemption.
But, actually, I've been taking you for a bit of a ride. There's a problem I've overlooked:
"(5) A person commits culpable homicide when he causes the death of a human being,(a) by means of an unlawful act;(b) by criminal negligence;(c) by causing that human being, by threats or fear of violence or by deception, to do anything that causes his death; or(d) by wilfully frightening that human being, in the case of a child or sick person."
All the listed punishments are for murder. All murders are special cases of culpable homicide. Culpable homicide is this special kind of homicide: unlawful homicide.
Progressive. Outlawing unlawful homicide. What will they come up with next? I guess the executioner doesn't really need their own exception.
My motivation for looking up this was the libertarian and anarchist bon mot "taxation is theft." I'd assumed there would be specific exemptions for taxation, but I found that the whole code is meaningless. Reality is more interesting than radical philosophies, it turns out.
I find this puzzling since many of the code's details go to great lengths to be logically rigorous. It would actually be beautiful, if the whole thing wasn't flying on dreams. I don't demand that the code justify itself entirely - it never actually states that it is outlawing crimes, never states that crimes are wrong, and never states who will hand down punishments, nor that these punishments are mandatory, and I don't expect it to do any of this. All logic must start at axioms, and while it's nice if they're explicit, I don't expect lawyers to follow philosophical best practise. I'm naturally too lazy to look up the precedents, and perhaps there's actual statements of 'doing X is fraud' there, but even if so, that just means the code itself is dead weight.
I have trouble imagining that the courts never use the code, though. (I could only find Supreme Court records, and they would never have a reason to cite basic code. They did, as expected, cite precedent often, and occasionally legislative act.) Since it is impossible that they use the actual logical content of the code, they must be reading something into it.
Ultimately, it's not the code but the attitude of the people who support and execute the system. I don't know who these people actually are, in practice, other than I know it isn't who we're told it is. The last thing I have difficulty with is how these people can be simultaneously responsible, and allow the code to remain like this. As it is, formal reality and actual reality cannot converge, which usually means that formal spirit and informal spirit will continue to diverge.
Monday, December 7, 2009
References to Hume's Ought
My youngest memory of the phenomenon:
I often see similar constructions, all error. My apologies, but Hume never proved his is-ought distinction, he simply pointed out many instances of people failing to derive is from ought.
Additionally, it turns out I have a counter-proof.
Assume something has value. Intrinsically, avoiding or preventing this thing results in a less valuable world.
Actually that's a false start, which I'm leaving in to help steer you into the right frame of mind.
Imagine the world has no intrinsic value - that the world 'value' is actually meaningless. (Nihilism is true.)
Imagine the world does in fact have some contingent quantity of value in it - positive or negative.
We must prefer the latter world. The former world renders even our preferences meaningless; it cannot be preferred (or preferred against). In other words, this is another species of Cogito: by our having values, the world is imbued has value...even if our values somehow turn out to be inconsistent.
'Ought' is defined thusly; it is better to do what we ought to do, than not. The world we ought to work toward is more valuable than the world we ought not to.
The problem is not that 'oughts' may not be refined from 'is,' but only in defining 'value' and working out what it picks out.
Now I'm going to perform a check. Famous, prestigious philosopher, John Searle also tackles the is-ought problem. Can he (by proxy) refute my analysis?
Searle says that institutions, which require rules to exist at all, bind the participants by the rules. (Elaborated here, as Searle is not part of the internet generation and hasn't spoken for himself online.)
"For example, when it is my turn to bat I am obligated to step up to the plate." Or, you could fail to continue to play baseball by violating this rule. This is the twofold problem with Searle's analysis. Yes, to perpetuate the baseball game, one is required to adhere to the rules of baseball, but at no point is one obligated, by this analysis, to perpetuate baseball.
In one situation, baseball continues - the bat is swung, the ball is hit or not. In the other, baseball ceases, at least momentarily, perhaps people are angry, or confused. So what? Can we really say, objectively, that one is better than the other? (Hint: maybe.) Let's say you choose not to step up to the plate, for no reason other than that you just realized there's no ought here, and people are angry. Even on pure intuition, is that really so bad? Again: so what?
There will be consequences to each action, and again, so what? Say they find your behaviour so contrary you're off the team, despite it being a casual league. It's not important; baseball is not something anyone can prove you ought to do, nor is it necessary to define pissing people off as 'wrong' to persuade an agent to avoid doing it.
I will ignore the second problem - that from this account, there is no direct link between institutional rules and the definition of 'ought.' Even without this, the oughtness of baseball must be inherited from the more fundamental level, which Searle attempted to circumvent.
"Our form of government and efforts at "emancipation" cannot change the fundamental fact of their existence (there is no way to get to "ought".)"
I often see similar constructions, all error. My apologies, but Hume never proved his is-ought distinction, he simply pointed out many instances of people failing to derive is from ought.
Additionally, it turns out I have a counter-proof.
Assume something has value. Intrinsically, avoiding or preventing this thing results in a less valuable world.
Actually that's a false start, which I'm leaving in to help steer you into the right frame of mind.
Imagine the world has no intrinsic value - that the world 'value' is actually meaningless. (Nihilism is true.)
Imagine the world does in fact have some contingent quantity of value in it - positive or negative.
We must prefer the latter world. The former world renders even our preferences meaningless; it cannot be preferred (or preferred against). In other words, this is another species of Cogito: by our having values, the world is imbued has value...even if our values somehow turn out to be inconsistent.
'Ought' is defined thusly; it is better to do what we ought to do, than not. The world we ought to work toward is more valuable than the world we ought not to.
The problem is not that 'oughts' may not be refined from 'is,' but only in defining 'value' and working out what it picks out.
Now I'm going to perform a check. Famous, prestigious philosopher, John Searle also tackles the is-ought problem. Can he (by proxy) refute my analysis?
Searle says that institutions, which require rules to exist at all, bind the participants by the rules. (Elaborated here, as Searle is not part of the internet generation and hasn't spoken for himself online.)
"For example, when it is my turn to bat I am obligated to step up to the plate." Or, you could fail to continue to play baseball by violating this rule. This is the twofold problem with Searle's analysis. Yes, to perpetuate the baseball game, one is required to adhere to the rules of baseball, but at no point is one obligated, by this analysis, to perpetuate baseball.
In one situation, baseball continues - the bat is swung, the ball is hit or not. In the other, baseball ceases, at least momentarily, perhaps people are angry, or confused. So what? Can we really say, objectively, that one is better than the other? (Hint: maybe.) Let's say you choose not to step up to the plate, for no reason other than that you just realized there's no ought here, and people are angry. Even on pure intuition, is that really so bad? Again: so what?
There will be consequences to each action, and again, so what? Say they find your behaviour so contrary you're off the team, despite it being a casual league. It's not important; baseball is not something anyone can prove you ought to do, nor is it necessary to define pissing people off as 'wrong' to persuade an agent to avoid doing it.
I will ignore the second problem - that from this account, there is no direct link between institutional rules and the definition of 'ought.' Even without this, the oughtness of baseball must be inherited from the more fundamental level, which Searle attempted to circumvent.
"Don't be Evil"
A promise made in ignorance.
I wistfully imagine a day when it's just known that our present companies are evil due to institutional evils, due to emergent evils, and not because some cackling bastard plans to take over the world.
Google can no more avoid these institutional situations than any other corporation. It was never possible that they'd follow their motto. We should let the journalists alone with their fauxtrage when we or they see Google's latest fall from grace.
Still, this site is called Accepting Ignorance, which includes me accepting that of course Google's "Don't Be Evil" will be taken seriously.
I wistfully imagine a day when it's just known that our present companies are evil due to institutional evils, due to emergent evils, and not because some cackling bastard plans to take over the world.
Google can no more avoid these institutional situations than any other corporation. It was never possible that they'd follow their motto. We should let the journalists alone with their fauxtrage when we or they see Google's latest fall from grace.
Still, this site is called Accepting Ignorance, which includes me accepting that of course Google's "Don't Be Evil" will be taken seriously.
Atheists on Consciousness
"But defenders of religion like [Kathryn] Lofton and Karen Armstrong and the not-quite-pro-religion-but-getting-there types like Terry Eagleton invariably attack atheists for their lack of charm, style, empathy and another nebulous quality (I think of it as *mysterianism*) which keeps them from fully appreciating the true nature of religion."
Mysterianism, eh?
Only problem is that this 'nebulous quality,' does, in fact, exist. I think that confirms it; these atheists have the mental equivalent to colourblindness. Indeed, why would their from-scratch philosophy have to account for all facets of my experience?
Thursday, December 3, 2009
Kids and Kuriosity
"A child's never-ending "whys" aren't meant to exasperate parents, scientists say. Rather, the kiddy queries are genuine attempts at getting at the truth, and tots respond better to some answers than others."I'm so glad scientists have been able to join us on planet Earth.
Still, I do wonder why parents are exasperated by tot's questions. It seems counter-productive to bar your own child from your knowledge.
The reason questions exasperate people is because it is a form of challenge, like a staring contest. Being challenged for the sake of challenge, especially when you're busy, is exasperating. Small children cannot credibly challenge you, which should, in theory, short-circuit the exasperation mechanism, just like how some people find threats from children, no matter how strident, adorable instead of scary. ("I'm gunna punch you till you fall down!" *Scowl*)
The other reason for exasperation is to avoid acknowledging that the askee doesn't have the answer. I think this is in play, as children are excellent epistemologists and can find logical holes without trying. Humans are born to use the Socratic method on their parents. Parents don't usually respond well.
But even this I find puzzling, as I can't find a reason to not just tell the kid you don't know.
There's no apparent reason question-asking should be annoying, and yet....
"Past research from the early to mid 1900s on child development had suggested that young children were only aware of temporal relationships between two events and couldn't differentiate cause from effect until about 7 or 8 years of age. More recent work has suggested otherwise, that as early as age 3 children get causality."
Never forget that scientists often use their skills to act as stupid as possible. Anyone with kids will immediately think, "They must have not had children!" and be able to cite chapter and verse on their kids getting causality. This is a mistake; they likely did have children. I'd guess the story goes as thus: at home, their personal observations aren't science and thus poor evidence, but their personal observations during a study at work are scientific, and thus good evidence.
(This gets ironic if you read the comments on the other study just linked. I can easily understand the source of the above misperception.)
If I were a journalist I would say it's "frightening" that people like this are in charge of the education system. Calling the status quo frightening seems off. It's certainly depressing, though.
You may note that the science is getting better. Indeed it is, but nobody ever thinks to wait 20-50 years to properly verify a scientific finding before acting on it, despite the massive number of errors, like this one, freely admitted. (Or, you know, find a faster verification method, like logic.)
Incidentally, children as young as zero understand causality, you just don't yet know how to produce a statistically significant study showing this. Causality is innate the human brain - and to many nonhuman brains, for that matter.
"Lacking from such studies are kids' reactions to the information they get to their causal questions. "A scientist failed at study design? Shocking. You'd almost think that universities don't demand courses on epistemology of their Ph.Ds.
I have no reason to believe the above quote is accurate. It certainly isn't precise. However, if it is right: told you so. You might wonder if the scientists have kids, I wonder if they have brains. They must be using them for something else.
Are the current crop of scientists less determined to be stupid, or are they just playing to my preconceptions better, being closer to my age? Ahh, questions....
"Results showed kids were more than twice as likely to re-ask their question after a non-explanation compared with a real answer. And when they did get an explanation, which was about 37 percent of the time, they were more than four times as likely to reply with a follow-up inquiry as if they had received a non-explanatory response."
First let me re-write that last part. "Kids ask [presumably meaningful] follow up questions to meaningful answers four times as often as to non-answers." I think that's what they're trying to say, but I'm not exactly sure how you ask a follow-up question to a non-answer unless you already know the answer. Given the ignorance on display, I also have to mention kids aren't sophisticated enough to ask questions they already know the answer to, and regardless have far too many questions to which they don't know the answer to bother with the former.
Incidentally, I wonder why parents hate their kids so much. Answer about a third of their questions? Do you want them to be educated, or not?
So, when they were highly curious and receptive, you answered about a third of their questions, and then you wonder why they don't listen to you as a teenager? Sorry bub, it's too late by then, you've already told them they can't rely on you for information.
How do you react if someone who won't answer your queries suddenly turns around and starts trying to dictate how you act?
At least there's no institution that supposedly gets paid based on its ability to teach parents to parent well, so lapses aren't anybody's fault, per se.
"Preliminary results from a separate new study of Frazier's suggest there is such a thing as too much information in a response. "It seems like kids might have an optimal level of detail they're interested in," Frazier said."Again, I welcome you to planet Earth, journalists'-representation-of-Frazier. On Earth, you see, we pitch answers to children at their level of understanding. What do you do on your own planet?
For an example of the education system (shockingly) getting it right, when teaching addition, we don't start with the Peano axioms. We start with apples, and how if you have two apples in one basket and three in another, you have five total. Similarly, when teaching exponents, we don't do the full definition that allows x0 to be obviously one, but instead say, "exponents are repeated multiplication (which is repeated addition)." These statements are not fully correct, but kids understand when we later tell them that the simple things they learned earlier were not complete.
Plus, if they get into the habit of asking their parents and guardians when they're curious, if one notices a hole in their understanding, they'll ask you about it. Which makes me wonder whether odd behaviours like watering plants with coke could be largely prevented by answering questions consistently.
From a comment;
"Maybe when their whys get you riled up it becomes a game, but it's initially to learn."If you allow your children to get one over on you, they enjoy it, and it starts Pavlovian conditioning. (Small children do not consciously plan these things.) That's why it's important to figure out why the questions are exasperating, and use the knowledge to short-circuit the exasperation.
As a bonus, letting your kids exasperate you can help you do this, because if you watch yourself carefully during the exasperation, you can figure out why it exasperates you. Often, this knowledge alone will alleviate the condition, without actually needing to act on it in any intentional way, albeit I've yet to try it on this particular example, and regardless my experience may or not mirror yours in particulars. At the very least, it will help you to understand when to stop the question flow - and to do it consciously and openly, before you actually become exasperated. If you want to do this, remember to stop a few questions short, because when you say, "That's enough questions for now," they will ask "Why?" and it would be nice if you could give them an answer.
Saturday, November 14, 2009
Bayesian 'Reasoning' and Fallacies
That the process of rational reasoning works cannot be justified by reason. The simplest way of looking at why I have to use scare quotes on Bayesian 'reasoning' is that it attempts to justify itself. Why would anyone hold up Bayesian thinking as better than regular thinking? Because they think it's a good idea - they come to the conclusion that Bayesian conclusions are better than their regular conclusions.
Oops.
Bayesian reasoning pre-supposes regular reasoning, and further supposes that it can be reasonably justified, which puts Bayesian reasoning entirely inside regular reasoning. Indeed, Bayes worked out and proved his theorem as a special case with existing tools in an existing framework, just like all mathematical theorems.
While boring to do so, I must disclaim that I do use simple Bayesian kinds of inference, though it seems I've just found the natural Bayesian network in the brain and I use it - I don't ever actually do the Bayes theorem calculation.
If you haven't considered it deeply before, there's an introduction I can recommend, both for showcasing the advantages of Bayes' theorem, and diving with both feet into many of the associated fallacies.
Tribes, Grass, and Rain
As lethal as my single point is, were I Bayesian Bicurious, I would find it unsatisfying.[1] The rest of this section is illustration. The goal is that each point will also be fatal, but be a special case of the overall error.
To start with, Bayes' theorem requires three pieces of information, (as you can see in La Wik) the prior probability of A, the same of B, and the probability of B given A. That scans as utter gibberish to me, so here's an example.
I'm going to use wet grass as evidence of rain. To calculate the probability it has rained if the grass is wet, p(A|B), (as opposed to the probability it's because someone has been washing their car) you need the probability the grass is wet in general, p(B), the probability it has rained in general, p(A), and the probability that the grass gets wet if it has rained, p(B|A). The probability p(B) can also be expressed like this: p(B|A)*p(A) + p(B|~A)*p(~A), which has applications when you don't know p(B) per se but you do know of a lot of possibilities that aren't rain - like car washing - that second part essentially reads, "the probability the grass gets wet from not-rain, times the probability it hasn't rained."
The first problem is that is an awful lot of probabilities to need. The second, more serious problem is that in a controversy, it is easy to the point of inevitability that these probabilities are going to be fudged.
Notice how this computation spirals out of control as more priors are added; p(A|BCDE), isn't too bad, as it's essentially just four of these calculations, but what if, say, C and D are also in dispute, and you need to calculate p(C|XY) as well, and so on? It rapidly becomes a hierarchy of tears, except maybe for a few specialists in the field of A-ology. You, poor schmuck layman, are forced to simply accept the probability calculations of expert A-ologists. (Oh wait, don't we already do this? Err...revolution where now?) To be fully 'rational,' apparently you need a multimillion research budget.
However, the second problem is the pernicious one. Take a moment and realize how ridiculous it is that water falls from the sky. What, do little leprechauns take it up there with buckets? And it just hangs around, ignoring gravity for a while, before it gets into the mood to hang around on the ground again? If it weren't so pervasive, and thus familiar and normalized, rain would be far more mysterious and mystical to stone-age humans than silly little volcanoes. I strongly recommend it - open a door or window next time it rains, and consider how bizarre it is this liquid is just falling willy nilly out of nowhere.
Right, in that frame of mind, let's insert a rain controversy - democracy in the stone age. One clan thinks that when the rain fairies alight on the ground, they leave behind drops on the grass. Another clan thinks that the grass fairies excrete water when it rains, basically to say 'hi,' like they do to greet the morning. These lead to different calculations of p(A|B) - how likely it is that it has rained if the grass is wet. (Through convoluted logic, most of the clans believing one or the other determines who gets to go yak hunting.)
The first clan is certainly less wrong, and they see that the chance of wet grass if it rains is 100%: p(B|A) = 1. The second clan is not about to go down without fighting; observing grass on a hot, dry day, (only slightly missing the actual end of the storm) they notice the grass is dry. They declare that the grass fairies were just unhappy that day, conclusively showing that p(B|A) is actually somewhat less than one. The first clan is outraged, "You were obviously wrong about the rain! There's no way it can rain without the grass getting wet!"
(Technically you're not supposed to ever use probabilities 1 or 0, because they break Bayes' theorem, something I'll detail further down.)
This conflict cannot be resolved by Bayesian reasoning. To work out p(B|A) requires p(A|B) - the very thing that was in dispute to begin with. It's one equation with two unknowns. This is an example of the general problem of assigning probabilities to various pieces of data; the assigned probability unavoidably depends on that non-Bayesian reasoning stuff Bayesians are trying to improve upon.
Note also that neither p(A) nor p(B) can even be properly collected by the clansmen. Their sample size is too small and the demands of hunting and gathering don't help. When our society attempts to probe questions at the limit of our understanding, we run into the same problem - plus, just like the clansmen, it is difficult to even know that our sample is somehow flawed.
In the end, the first clan was mostly from a warm, wet sub region, while the second clan's region had days that were significantly hotter and drier. Their error was not in their logical progression - the first thought that they could tell from the grass if it rained while they slept, the second realized that they couldn't tell for sure - but in how they tried to state their observations. Ultimately, both were right, and both were wrong. And, obviously, I should be the one who gets to go yak hunting.
This is just not compatible with how human reasoning naturally works. Setting aside true random events - for which Bayes' theorem undoubtedly works better than human reasoning - the actual probability of any hypothesis being true is either 0 or 1. (Within certain tolerances - otherwise all hypotheses are false, probability 0, because they're not exactly true.) Bayesians aside, all human reasoning reflects this by backing one horse above all others. Personally I find this handy, as for some reason once I've strongly stated the hypothesis that wins given my available information, I find it much easier to gather and remember related information, often poking holes in my own ideas within days.
Fallacies
Hot Hand Fallacy
So rather than focusing on how it might be true, (ironically, the best way to activate one's confirmation bias) let's turn this fallacy around and see what it might be useful for. (As inspired by a comment.)
How many fair rolls were there in the ancestral environment? Look at how much effort has to go into making fair dice and roulette wheels, and how much effort goes into certifying and inspecting them. Fair gambling is high tech; the stone age would never have seen a truly fair gamble.
However, look at the exact detail of people's beliefs about dice. A die that is giving up wins easily is likely to give up more wins, but each win deplete the die, making further wins less likely. I can't think of a place that kind of belief would have not been useful for a hunter-gatherer. Plants grow in patches. Animals need to find each other to breed. But, every time you actually bag a particularly juicy plant or animal, that's one less left to find.
Even setting that aside, I can bring up the issue of how random distributions actually look:
(from here)
Notice that even if a plant is actually randomly distributed, it will still end up in clumps and veins. There will be hot spots and cold spots. Similarly, if animal activity is linked to weather, the good days and bad days will often occur in clumps. In general, if your hunting or gathering is going well, it is highly rational to expend some extra effort that day, because it will likely be rewarded more efficiently than usual.
The Base Rate Fallacy actually has a point, as these kinds of calculations come up almost exclusively in professional contexts. However...I can get them right, and it's not by trying Bayes' theorem. I instead use the physicist approach. "Probability is defined as the prevalence divided by the total population," I say to myself. Then, using this definition, I simply have to find the relevant numbers, which is straightforward as long as I understand their definitions. In the case linked, it's the number of homosexuals with the disease divided by everyone with the disease, and indeed they also dodge Bayes' theorem by doing the calculation explicitly.
Moreover, when I get the wrong, the reason is because I'm using shortcuts learned during probability classes in public school. I strongly suspect that a physician mis-estimating, say, the odds of a positive mammography to mean cancer, is being mislead by exactly the same training. The cure is not Bayesianism. The cure is to teach math properly.
Conjunction Fallacy
This is a fun one. First, I will forward a hypothesis as to why framing is important. It's because survey subjects will always read things into the question that aren't there, and survey designers not only have no idea what those things are, but are often ignorant that they need to design surveys to account for this. My source for this hypothesis is something I think every philosopher will empathize with; how long it took me to train myself to only read what was there, and not hallucinate all sorts of interesting random things, and subsequently ascribe them to the author.
With this in mind, between the possibilities,
Here's another: in amateur introspectors, the positive feeling of reading a narrative and the positive feeling of high probability are not distinguishable, as they're quite similar.
Oh great Bayesian survey-writer, Accept your Ignorance. You have no idea what your surveys are actually testing, which kind of means more surveys will not help very much.
As below, I like testing things. Let's take these ideas for a spin.
Why will they read it this way? Because that's how the average person talks. For me, it took quite a bit of mathematical education before I read 'x > 3' as what it means; x can be four, or ten, or a million, or 29 436 502 974, or infinity. Before that point, I read 'x is more than three' as meaning something like eight or so, but probably not beyond ten. As indeed, if you want to talk about things that are in the millions, you need to say, 'x is somewhere over a million.' If it's absolutely necessary to talk about things with a wide range, people say so explicitly, "The variable 'x' can vary widely, sometimes as low as four, but can reach heights vastly exceeding a billion." Further, what non-mathematical object has properties like that? Certainly, that quoted sentence is not one a journalist will ever have cause to use.
Note that you probably just made the exact error I'm detailing. 'have cause to use' does not mean it's the best option, only that it could be accurately used. I'm saying that a journalist will never cover a subject where this sentence will even be useful. (Point of prose: I could say that, but it doesn't seem any less likely to produce the same error, and is drier.)
These ideas spin well. Let's do it again.
Um...no it doesn't? Again, I have no idea what the subjects are actually perceiving when they read those options, but it's almost certainly not strictly what's there.
Perhaps they're taking the examples as characteristic of a longer sequence.
Or...it's quite difficult to set aside one's general problem solving habits - which must work, or they'd be rapidly changed - just because some researcher is offering you $25. They may solve the problem this way: "What does the most probable sequence look like?" (In me, this part is involuntary.) They then compare the presented sequences to their ideal sequence. This is much, much faster and more efficient than actually solving the problem at hand. (Employers constantly complain that their employees can't follow directions, incidentally.) The gains from efficiency, in real life, outweigh the costs in efficacy. As a bonus, this interpretation post-dicts their responses.
Or...as amateur introspectors, they're solving it by comparing the greenness feeling of the dice to the greenness feeling of the sequences. For some bizarre reason, this process works better with ratios than with precise numbers. This error is solvable with better math education; mine makes me accept that, oddly, my feelings don't perform math well, and that I have to do the calculation explicitly if I want a precise answer. Err, kind of like all logic.
Moreover, it's not even guaranteed they have an accurate definition of 'probability.' So...are we assuming people are born knowing what 'probability' actually means, and we just later learn the word for it? Are we assuming that, since everyone assumes their own reason is reliable, (as indeed you must) that the default assumption is that each person will assume they can accurately calculate probabilities? Before speculating at the assumptions of the subjects, it's kind of necessary to know the assumptions of the researchers.
While this section is largely made up of just-so stories, these plausible scenarios are not even acknowledged, let alone addressed, by Bayesian proponents.
Ironically, all these fallacies are the result of a Bayesian process. Evolution picks priors by chance, and then the priors are decremented by killing people holding the wrong ones. Literally, your possible ancestors who thought more 'rationally' all got killed. At the very least they got killed in the contest of baby counts - our actual ancestors were just better baby factories. While it may throw up some interesting bugs in a modern environment, are you really comfortable saying that all those people who died were right, and the ones who lived were wrong? So what...does that mean their rightness or wrongness was irrelevant at the time, or have humans, as a species, just been monumentally unlucky?
Bayesian Reasoning Tells Us About Ignorance
The standard thing to do when you have multiple possibilities and no further information is to assign equal possibilities to each one. Say I find my car is flattened, and the possibilities are bigfoot and alien landing site, but as apparently alien ships are foot-shaped, there's no way to tell the difference, and thus they get 50% each. I can sue bigfoot, but the alien landing means we're being invaded, so it matters to get it right.
From this, I can narrow my search - if I find no bigfoot scat, it's probably aliens, and if I find no green glowing alien exhaust, it's probably bigfoot. However, as additional possibilities accumulate - 33% each, 20%, 16%, and so on, the first effect it that it starts telling me more about my own mind than about the singular event that actually happened. The possibilities I come up with start being less about my smushed car and more about what sheet metal reminds me of, or even ideas I just happen to find evocative. (Heh heh.)
What is the probability of dark matter, given our gravitational lensing pictures of colliding galaxies? The converse, the probabily of not-dark-matter, given same, is basically a function of how many other theories you can come up with - as a Bayesian, you have to share out equal probabilities in the case of ignorance, and as you add more possibilities, dark matter starts out as a smaller and smaller piece of the pie, but the relative growth from the pictures is the same...
More importantly, as possibilities multiply, the odds that even one of them are like-correct drops. So it's not really 33-33-33, it's more like there's three possibilities, plus the possibility I have no idea what I'm talking about, so 20-20-20-40. As ignorance grows, the chance you don't even know enough to properly quantify your ignorance grows as well.
Our ignorance of dark matter is probably on par with the ancient Greeks' ignorance of regular matter. It turns out Democritus was less wrong about this, but even he was wrong all over the place. Similarly, the odds that dark matter is neither MACHOs nor WIMPs is pretty high.
So whenever I learn something new, I want to try it out. I'm going to try this one out on extra-terrestrial civilization.
A lot of people want to know if there's other intelligence out there.
Actually, SETI is kind of ironic, as they're so sure ETI is out there, it's hardly worth their time to actually find it - a bit like the first clan was so sure the grass has to be wet after rain.
But, looking around the universe, we don't see evidence of any engineered structures. Now, p(ETI|solar-scale engineering) equals pretty much one, but what about p(ETI|~solar-scale engineering)? Well, it's not like we produce any solar scale structures, but who knows what we'll be capable of the in the future?
So, err, precisely - who knows what we will be capable of a million years in the future? Who knows what we'll find worthwhile a million years in the future?
Going back to the original equation - so what's p(solar engineering) - the general odds of looking at a solar system and finding engineering there? What's p(aliens) - the general odds of looking at a planet and seeing complex life there? We can't even gather these numbers. Drawing in the many-possibilities thread, we don't even know if life has to look all carbony like we do or not. You can run spectrographic analysis on exoplanets that transit the star, and you might find both water vapour and methane in the atmosphere, but it doesn't tell you very much.
If you limit yourself to Bayesian reasoning, these undefineable numbers will remain so forever. Sure, you can define any hypothesis[2] of p(aliens) and p(~aliens) you want, such as 50% each, and revise p(aliens) downward every time you see a planet with no life on it, but you'll run into something of a barrier in knowing how much to revise it downward; calculating p(aliens|lifeless planet) uses p(lifeless planet|aliens) which is zero, and this zero reduces Bayes' theorem to the trivial 0=0. (This is why you're not supposed to use 1 or 0 as probabilities, but it's not like 0.0001 is much better, and indeed even how many zeros to put after the decimal is a judgement call in this case.) Without knowing beforehand the actual p(aliens) and p(~aliens) for a random planet, Bayes' theorem is powerless. In other words, you have to already know the answer to get the right answer.
The summation of this debacle is thus: are you a philosopher? No? Then, if you have a philosophical thing to say, you should Google 'philosophy forums' and pick one, then sign up and post, "Hey there good Mr. and Ms. philosophy dudes, does this make any bloody sense at all?" They'll generally reply, "No! And get off my lawn!" In addition, they'll be happy to tell you what you should be doing instead, as vetted by thousands of years of the smartest people on the planet. (On many issues, philosophy hasn't advanced beyond Aristotle because he got it right.) If that doesn't work, I understand professors are more than happy to answer the curiosity of the public - find one's email and email them. (At least, it works for me. If it doesn't for you, try a second philosopher.) I don't run around saying I know statistics better than you, so how about you do me the honour of not pretending you know philosophy better than I do?
Tangents:
[1] Actual Bayesians, I would guess, have roughly zero percent chance of being persuaded, p(open-mind-on-this-issue|Bayesian) -> 0.
[2] Hypotheses come, surprisingly enough, from outside Bayesian reasoning, even according to Bayesians. How one comes up with a good hypothesis is not addressed.
As an epistemologist, I almost always should avoid probability. That particular problem is a problem for ontologists.
Oops.
Bayesian reasoning pre-supposes regular reasoning, and further supposes that it can be reasonably justified, which puts Bayesian reasoning entirely inside regular reasoning. Indeed, Bayes worked out and proved his theorem as a special case with existing tools in an existing framework, just like all mathematical theorems.
While boring to do so, I must disclaim that I do use simple Bayesian kinds of inference, though it seems I've just found the natural Bayesian network in the brain and I use it - I don't ever actually do the Bayes theorem calculation.
If you haven't considered it deeply before, there's an introduction I can recommend, both for showcasing the advantages of Bayes' theorem, and diving with both feet into many of the associated fallacies.
Tribes, Grass, and Rain
As lethal as my single point is, were I Bayesian Bicurious, I would find it unsatisfying.[1] The rest of this section is illustration. The goal is that each point will also be fatal, but be a special case of the overall error.
To start with, Bayes' theorem requires three pieces of information, (as you can see in La Wik) the prior probability of A, the same of B, and the probability of B given A. That scans as utter gibberish to me, so here's an example.
I'm going to use wet grass as evidence of rain. To calculate the probability it has rained if the grass is wet, p(A|B), (as opposed to the probability it's because someone has been washing their car) you need the probability the grass is wet in general, p(B), the probability it has rained in general, p(A), and the probability that the grass gets wet if it has rained, p(B|A). The probability p(B) can also be expressed like this: p(B|A)*p(A) + p(B|~A)*p(~A), which has applications when you don't know p(B) per se but you do know of a lot of possibilities that aren't rain - like car washing - that second part essentially reads, "the probability the grass gets wet from not-rain, times the probability it hasn't rained."
The first problem is that is an awful lot of probabilities to need. The second, more serious problem is that in a controversy, it is easy to the point of inevitability that these probabilities are going to be fudged.
Notice how this computation spirals out of control as more priors are added; p(A|BCDE), isn't too bad, as it's essentially just four of these calculations, but what if, say, C and D are also in dispute, and you need to calculate p(C|XY) as well, and so on? It rapidly becomes a hierarchy of tears, except maybe for a few specialists in the field of A-ology. You, poor schmuck layman, are forced to simply accept the probability calculations of expert A-ologists. (Oh wait, don't we already do this? Err...revolution where now?) To be fully 'rational,' apparently you need a multimillion research budget.
However, the second problem is the pernicious one. Take a moment and realize how ridiculous it is that water falls from the sky. What, do little leprechauns take it up there with buckets? And it just hangs around, ignoring gravity for a while, before it gets into the mood to hang around on the ground again? If it weren't so pervasive, and thus familiar and normalized, rain would be far more mysterious and mystical to stone-age humans than silly little volcanoes. I strongly recommend it - open a door or window next time it rains, and consider how bizarre it is this liquid is just falling willy nilly out of nowhere.
Right, in that frame of mind, let's insert a rain controversy - democracy in the stone age. One clan thinks that when the rain fairies alight on the ground, they leave behind drops on the grass. Another clan thinks that the grass fairies excrete water when it rains, basically to say 'hi,' like they do to greet the morning. These lead to different calculations of p(A|B) - how likely it is that it has rained if the grass is wet. (Through convoluted logic, most of the clans believing one or the other determines who gets to go yak hunting.)
The first clan is certainly less wrong, and they see that the chance of wet grass if it rains is 100%: p(B|A) = 1. The second clan is not about to go down without fighting; observing grass on a hot, dry day, (only slightly missing the actual end of the storm) they notice the grass is dry. They declare that the grass fairies were just unhappy that day, conclusively showing that p(B|A) is actually somewhat less than one. The first clan is outraged, "You were obviously wrong about the rain! There's no way it can rain without the grass getting wet!"
(Technically you're not supposed to ever use probabilities 1 or 0, because they break Bayes' theorem, something I'll detail further down.)
This conflict cannot be resolved by Bayesian reasoning. To work out p(B|A) requires p(A|B) - the very thing that was in dispute to begin with. It's one equation with two unknowns. This is an example of the general problem of assigning probabilities to various pieces of data; the assigned probability unavoidably depends on that non-Bayesian reasoning stuff Bayesians are trying to improve upon.
Note also that neither p(A) nor p(B) can even be properly collected by the clansmen. Their sample size is too small and the demands of hunting and gathering don't help. When our society attempts to probe questions at the limit of our understanding, we run into the same problem - plus, just like the clansmen, it is difficult to even know that our sample is somehow flawed.
In the end, the first clan was mostly from a warm, wet sub region, while the second clan's region had days that were significantly hotter and drier. Their error was not in their logical progression - the first thought that they could tell from the grass if it rained while they slept, the second realized that they couldn't tell for sure - but in how they tried to state their observations. Ultimately, both were right, and both were wrong. And, obviously, I should be the one who gets to go yak hunting.
This is just not compatible with how human reasoning naturally works. Setting aside true random events - for which Bayes' theorem undoubtedly works better than human reasoning - the actual probability of any hypothesis being true is either 0 or 1. (Within certain tolerances - otherwise all hypotheses are false, probability 0, because they're not exactly true.) Bayesians aside, all human reasoning reflects this by backing one horse above all others. Personally I find this handy, as for some reason once I've strongly stated the hypothesis that wins given my available information, I find it much easier to gather and remember related information, often poking holes in my own ideas within days.
Fallacies
Hot Hand Fallacy
So rather than focusing on how it might be true, (ironically, the best way to activate one's confirmation bias) let's turn this fallacy around and see what it might be useful for. (As inspired by a comment.)
How many fair rolls were there in the ancestral environment? Look at how much effort has to go into making fair dice and roulette wheels, and how much effort goes into certifying and inspecting them. Fair gambling is high tech; the stone age would never have seen a truly fair gamble.
However, look at the exact detail of people's beliefs about dice. A die that is giving up wins easily is likely to give up more wins, but each win deplete the die, making further wins less likely. I can't think of a place that kind of belief would have not been useful for a hunter-gatherer. Plants grow in patches. Animals need to find each other to breed. But, every time you actually bag a particularly juicy plant or animal, that's one less left to find.
Even setting that aside, I can bring up the issue of how random distributions actually look:
(from here)
Notice that even if a plant is actually randomly distributed, it will still end up in clumps and veins. There will be hot spots and cold spots. Similarly, if animal activity is linked to weather, the good days and bad days will often occur in clumps. In general, if your hunting or gathering is going well, it is highly rational to expend some extra effort that day, because it will likely be rewarded more efficiently than usual.
The Base Rate Fallacy actually has a point, as these kinds of calculations come up almost exclusively in professional contexts. However...I can get them right, and it's not by trying Bayes' theorem. I instead use the physicist approach. "Probability is defined as the prevalence divided by the total population," I say to myself. Then, using this definition, I simply have to find the relevant numbers, which is straightforward as long as I understand their definitions. In the case linked, it's the number of homosexuals with the disease divided by everyone with the disease, and indeed they also dodge Bayes' theorem by doing the calculation explicitly.
Moreover, when I get the wrong, the reason is because I'm using shortcuts learned during probability classes in public school. I strongly suspect that a physician mis-estimating, say, the odds of a positive mammography to mean cancer, is being mislead by exactly the same training. The cure is not Bayesianism. The cure is to teach math properly.
Conjunction Fallacy
This is a fun one. First, I will forward a hypothesis as to why framing is important. It's because survey subjects will always read things into the question that aren't there, and survey designers not only have no idea what those things are, but are often ignorant that they need to design surveys to account for this. My source for this hypothesis is something I think every philosopher will empathize with; how long it took me to train myself to only read what was there, and not hallucinate all sorts of interesting random things, and subsequently ascribe them to the author.
With this in mind, between the possibilities,
- The United States will withdraw all troops from Iraq.
- The United States will withdraw all troops from Iraq and bomb Iranian nuclear facilities.
Here's another: in amateur introspectors, the positive feeling of reading a narrative and the positive feeling of high probability are not distinguishable, as they're quite similar.
Oh great Bayesian survey-writer, Accept your Ignorance. You have no idea what your surveys are actually testing, which kind of means more surveys will not help very much.
As below, I like testing things. Let's take these ideas for a spin.
"Is it more likely that Linda is a bank teller, or a bank teller and feminist?"The average person will read that as,
- Linda is a bank teller and not a feminist.
- Linda is a bank teller and a feminist.
Why will they read it this way? Because that's how the average person talks. For me, it took quite a bit of mathematical education before I read 'x > 3' as what it means; x can be four, or ten, or a million, or 29 436 502 974, or infinity. Before that point, I read 'x is more than three' as meaning something like eight or so, but probably not beyond ten. As indeed, if you want to talk about things that are in the millions, you need to say, 'x is somewhere over a million.' If it's absolutely necessary to talk about things with a wide range, people say so explicitly, "The variable 'x' can vary widely, sometimes as low as four, but can reach heights vastly exceeding a billion." Further, what non-mathematical object has properties like that? Certainly, that quoted sentence is not one a journalist will ever have cause to use.
Note that you probably just made the exact error I'm detailing. 'have cause to use' does not mean it's the best option, only that it could be accurately used. I'm saying that a journalist will never cover a subject where this sentence will even be useful. (Point of prose: I could say that, but it doesn't seem any less likely to produce the same error, and is drier.)
These ideas spin well. Let's do it again.
"Consider a regular six-sided die with four green faces and two red faces. The die will be rolled 20 times and the sequences of greens (G) and reds (R) will be recorded. You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you chose appears on successive rolls of the die. Please check the sequence of greens and reds on which you prefer to bet.1. RGRRR
2. GRGRRR
3. GRRRRR65% of the subjects chose sequence 2, which is most representative of the die, since the die is mostly green and sequence 2 contains the greatest proportion of green rolls. However, sequence 1 dominates sequence 2, because sequence 1 is strictly included in 2. 2 is 1 preceded by a G; that is, 2 is the conjunction of an initial G with 1. This clears up possible misunderstandings of "probability", since the goal was simply to get the $25."
Um...no it doesn't? Again, I have no idea what the subjects are actually perceiving when they read those options, but it's almost certainly not strictly what's there.
Perhaps they're taking the examples as characteristic of a longer sequence.
Or...it's quite difficult to set aside one's general problem solving habits - which must work, or they'd be rapidly changed - just because some researcher is offering you $25. They may solve the problem this way: "What does the most probable sequence look like?" (In me, this part is involuntary.) They then compare the presented sequences to their ideal sequence. This is much, much faster and more efficient than actually solving the problem at hand. (Employers constantly complain that their employees can't follow directions, incidentally.) The gains from efficiency, in real life, outweigh the costs in efficacy. As a bonus, this interpretation post-dicts their responses.
Or...as amateur introspectors, they're solving it by comparing the greenness feeling of the dice to the greenness feeling of the sequences. For some bizarre reason, this process works better with ratios than with precise numbers. This error is solvable with better math education; mine makes me accept that, oddly, my feelings don't perform math well, and that I have to do the calculation explicitly if I want a precise answer. Err, kind of like all logic.
Moreover, it's not even guaranteed they have an accurate definition of 'probability.' So...are we assuming people are born knowing what 'probability' actually means, and we just later learn the word for it? Are we assuming that, since everyone assumes their own reason is reliable, (as indeed you must) that the default assumption is that each person will assume they can accurately calculate probabilities? Before speculating at the assumptions of the subjects, it's kind of necessary to know the assumptions of the researchers.
While this section is largely made up of just-so stories, these plausible scenarios are not even acknowledged, let alone addressed, by Bayesian proponents.
Ironically, all these fallacies are the result of a Bayesian process. Evolution picks priors by chance, and then the priors are decremented by killing people holding the wrong ones. Literally, your possible ancestors who thought more 'rationally' all got killed. At the very least they got killed in the contest of baby counts - our actual ancestors were just better baby factories. While it may throw up some interesting bugs in a modern environment, are you really comfortable saying that all those people who died were right, and the ones who lived were wrong? So what...does that mean their rightness or wrongness was irrelevant at the time, or have humans, as a species, just been monumentally unlucky?
Bayesian Reasoning Tells Us About Ignorance
The standard thing to do when you have multiple possibilities and no further information is to assign equal possibilities to each one. Say I find my car is flattened, and the possibilities are bigfoot and alien landing site, but as apparently alien ships are foot-shaped, there's no way to tell the difference, and thus they get 50% each. I can sue bigfoot, but the alien landing means we're being invaded, so it matters to get it right.
From this, I can narrow my search - if I find no bigfoot scat, it's probably aliens, and if I find no green glowing alien exhaust, it's probably bigfoot. However, as additional possibilities accumulate - 33% each, 20%, 16%, and so on, the first effect it that it starts telling me more about my own mind than about the singular event that actually happened. The possibilities I come up with start being less about my smushed car and more about what sheet metal reminds me of, or even ideas I just happen to find evocative. (Heh heh.)
What is the probability of dark matter, given our gravitational lensing pictures of colliding galaxies? The converse, the probabily of not-dark-matter, given same, is basically a function of how many other theories you can come up with - as a Bayesian, you have to share out equal probabilities in the case of ignorance, and as you add more possibilities, dark matter starts out as a smaller and smaller piece of the pie, but the relative growth from the pictures is the same...
More importantly, as possibilities multiply, the odds that even one of them are like-correct drops. So it's not really 33-33-33, it's more like there's three possibilities, plus the possibility I have no idea what I'm talking about, so 20-20-20-40. As ignorance grows, the chance you don't even know enough to properly quantify your ignorance grows as well.
Our ignorance of dark matter is probably on par with the ancient Greeks' ignorance of regular matter. It turns out Democritus was less wrong about this, but even he was wrong all over the place. Similarly, the odds that dark matter is neither MACHOs nor WIMPs is pretty high.
So whenever I learn something new, I want to try it out. I'm going to try this one out on extra-terrestrial civilization.
A lot of people want to know if there's other intelligence out there.
Actually, SETI is kind of ironic, as they're so sure ETI is out there, it's hardly worth their time to actually find it - a bit like the first clan was so sure the grass has to be wet after rain.
But, looking around the universe, we don't see evidence of any engineered structures. Now, p(ETI|solar-scale engineering) equals pretty much one, but what about p(ETI|~solar-scale engineering)? Well, it's not like we produce any solar scale structures, but who knows what we'll be capable of the in the future?
So, err, precisely - who knows what we will be capable of a million years in the future? Who knows what we'll find worthwhile a million years in the future?
Going back to the original equation - so what's p(solar engineering) - the general odds of looking at a solar system and finding engineering there? What's p(aliens) - the general odds of looking at a planet and seeing complex life there? We can't even gather these numbers. Drawing in the many-possibilities thread, we don't even know if life has to look all carbony like we do or not. You can run spectrographic analysis on exoplanets that transit the star, and you might find both water vapour and methane in the atmosphere, but it doesn't tell you very much.
If you limit yourself to Bayesian reasoning, these undefineable numbers will remain so forever. Sure, you can define any hypothesis[2] of p(aliens) and p(~aliens) you want, such as 50% each, and revise p(aliens) downward every time you see a planet with no life on it, but you'll run into something of a barrier in knowing how much to revise it downward; calculating p(aliens|lifeless planet) uses p(lifeless planet|aliens) which is zero, and this zero reduces Bayes' theorem to the trivial 0=0. (This is why you're not supposed to use 1 or 0 as probabilities, but it's not like 0.0001 is much better, and indeed even how many zeros to put after the decimal is a judgement call in this case.) Without knowing beforehand the actual p(aliens) and p(~aliens) for a random planet, Bayes' theorem is powerless. In other words, you have to already know the answer to get the right answer.
The summation of this debacle is thus: are you a philosopher? No? Then, if you have a philosophical thing to say, you should Google 'philosophy forums' and pick one, then sign up and post, "Hey there good Mr. and Ms. philosophy dudes, does this make any bloody sense at all?" They'll generally reply, "No! And get off my lawn!" In addition, they'll be happy to tell you what you should be doing instead, as vetted by thousands of years of the smartest people on the planet. (On many issues, philosophy hasn't advanced beyond Aristotle because he got it right.) If that doesn't work, I understand professors are more than happy to answer the curiosity of the public - find one's email and email them. (At least, it works for me. If it doesn't for you, try a second philosopher.) I don't run around saying I know statistics better than you, so how about you do me the honour of not pretending you know philosophy better than I do?
Tangents:
[1] Actual Bayesians, I would guess, have roughly zero percent chance of being persuaded, p(open-mind-on-this-issue|Bayesian) -> 0.
[2] Hypotheses come, surprisingly enough, from outside Bayesian reasoning, even according to Bayesians. How one comes up with a good hypothesis is not addressed.
As an epistemologist, I almost always should avoid probability. That particular problem is a problem for ontologists.
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