I used to think that way before I knew about Bayesianism. Once I learned about it I realized that the prior probability for psi was very VERY low, e.g. its complex and there’s no reason to expect it so one in a bajillion, while the probability for the observed evidence for psi, given what we know about psychology, was well in excess of 50% in the absence of psi, so the update couldn’t justify odds greater than two in a bajillion.
One in a bajilion? Guys, the numbers matter. 10^-9 is very different from 10^-12, which is very different from 10^-15. If we start talking about some arbitrarily low number like “one-in-a-bajillion” against which no amount of evidence could change our mind, then we’re really just saying “zero” but not admitting to ourselves that we’re doing so.
Other than that, I agree with Yvain and have found this to be perhaps the most belief-changing so far on LW!
It takes only 332 pieces of evidence with likelihood ratios of 2:1 to promote to 1:1 odds a hypothesis with prior odds of 1:googol, that is 10^-100, which would be the appropriate prior odds of something you could describe with around 70 symbols from a 26-letter equiprobable alphabet.
“A bajillion to one” are odds that Bayesian updating can overcome surprisingly quickly—it isn’t anything remotely like “no amount of evidence can change my mind”. Now odds of one to a googolplex—that might as well be zero, relative to the amount of evidence you could acquire over a human lifetime. But the prior probability of any possibility you can describe over a human lifetime should be much higher than that.
A nitpick: it takes 332 pieces of all mutually independent evidence to perform that level of update.
More confusing, for these purposes the independence level of the evidence depends on what hypotheses you’re trying to distinguish with it. E.g. if you’re trying to distinguish between “that subject has ESP powers” and “that experiment was random luck” then 332 repetitions of the same experiment will do. If you’re trying to distinguish between “that subject has ESP powers” and “that experimenter’s facial expressions differ based on what cards he was looking at”, then you can’t just repeat it; you’ve got to devise new and different experiments.
You’re right that I completely missed the Bayesian boat, and I’m going to have to start thinking more before I speak and revise my estimates down to <1%.
But I’m still reluctant to put them as low as you seem to. The anthropic principle combined with large universe says that whatever complexity is necessary for the existence of conscious observers, we can expect to find at least that level of complexity. Questions like consciousness, qualia, and personal identity still haven’t been resolved, and although past experience suggests there is probably a rational explanation to this question, it isn’t nearly dissolved yet. If consciousness really is impossible without some exotic consciousness-related physics (Penrosean or otherwise), then our universe will have exotic consciousness-related physics no matter how complex they need to be. And since evolved beings have been so proficient at making use of normal physics to gain sensory information, it’s a good bet they’d do the same with exotic consciousness-related physics too if they had them...
...is a somewhat hokey argument I just invented on the spot, and I’m sorry for it. But the ease with which I can put something like that together is itself evidence that there are enough possible sides of the issue that hadn’t been considered (at least I hadn’t considered that one; maybe you’ve been thinking about it for years) that it needs at least a little more room for error than two in a bajillion (sorry, Alex).
I also disagree with your assessment of the amount of evidence. Have you ever read any good books by intelligent believers in the subject? It’s not all John Edwards psychic chat shows. I also think you might be double-counting evidence against psi here—psi doesn’t exist so we know any apparent evidence must come from human psychology, therefore there never was any apparent evidence in the first place. Or have you read the studies and developed separate explanations for each positive result?
Anyway, let’s settle this the LW way. Give me your odds that psi exists, and we can make a bet at them. If it’s one in a million, then I’ll give a cent to your favorite charity on the condition that you give $10,000 to my favorite charity if psi’s shown to exist within our lifetimes (defined however you want; possibly as evidence sufficient to convince any two among Randi, Dawkins, and Eliezer that psi is >50% likely).
One problem with this argument is that if psi exists, we are very bad at using it, and we don’t see other organisms using it well either. The world we see appears to be almost completely described by normal physics at worst.
I don’t think that I’m double-counting evidence. I certainly know that there can be intelligent believers, after all, MANY intelligent people believe that one is compelled to accept the conclusions of the scientific method over those of the scientific community. Also, beliefs can be compelling for any variety of irrational reasons. The evidence I have seen though looks to me like exactly the evidence you would expect given known psychology and no psi. We can surely agree that there is a LOT of evidence that hyman psychology would create belief in psi in the absence of psi, can’t we.
I would set my odds at “top twenty most astoundingly surprising things ever discovered but maybe not top ten”. That seems to me like odds of many billions to one against, but not trillions. Unfortunately, the odds for almost any plausible winning conditions occurring without psi being real are much higher, making the bet difficult to judge. I have a standing 10,000 to one bet against Blacklight Power’s “Hydrino Theory” with Brian Wang based on a personal estimate of odds MUCH less than 1-in-10K for “Hydrino Theory” and I’m happy to extend those odds when the odds are still more favorable, but psychotic breaks by two people in a group of three? If the odds per person are 1%, that gives odds of about 1:3300. I’m happy to give those odds on the Dawkins, Randi Yudkowsky bet and count “psi is actually real” as a rounding error.
Have donated $10 to SIAI (seemed less likely to lose you guys money in transaction fees than $1) with public comment about the bet . Will decide where you can donate your $33000 in the unlikely event it proves necessary.
I’d feel ridiculously overconfident stating a probability of less that 1e-6, yet I don’t have the slightest hesitation to take that bet. (Brain sucks at small probabilities.) Condition is any two among {Randi, Dawkins, Eliezer, Vassar, me}, but if one is reported to have developed a new mental illness at least two months before they say psi is real, they don’t count.
Also, let’s make it purchasing power as of 2011, not dollar amount. Assuming scarcity lasts long enough.
One in a bajillion? You are saying you actually know how complex psi is without even saying what aspect of psi you are talking about.
We know biology is very complex. So when testing a supplement like creatine, the pseudoskeptic could say “biology is extremely complex. We do not know the mechanism that makes creatine work so I assign a very low bayesian probability. Today I feel like a hundred trillion to one”.
Keep in mind this is after several studies have shown an effect in the predicted direction whose odds are not easily explained by chance. Indeed, there is nothing wrong with you assertion about complexity just the subjective part where you assign a number to a phenomena you are not very familiar with.
I used to think that way before I knew about Bayesianism. Once I learned about it I realized that the prior probability for psi was very VERY low, e.g. its complex and there’s no reason to expect it so one in a bajillion, while the probability for the observed evidence for psi, given what we know about psychology, was well in excess of 50% in the absence of psi, so the update couldn’t justify odds greater than two in a bajillion.
One in a bajilion? Guys, the numbers matter. 10^-9 is very different from 10^-12, which is very different from 10^-15. If we start talking about some arbitrarily low number like “one-in-a-bajillion” against which no amount of evidence could change our mind, then we’re really just saying “zero” but not admitting to ourselves that we’re doing so.
Other than that, I agree with Yvain and have found this to be perhaps the most belief-changing so far on LW!
It takes only 332 pieces of evidence with likelihood ratios of 2:1 to promote to 1:1 odds a hypothesis with prior odds of 1:googol, that is 10^-100, which would be the appropriate prior odds of something you could describe with around 70 symbols from a 26-letter equiprobable alphabet.
“A bajillion to one” are odds that Bayesian updating can overcome surprisingly quickly—it isn’t anything remotely like “no amount of evidence can change my mind”. Now odds of one to a googolplex—that might as well be zero, relative to the amount of evidence you could acquire over a human lifetime. But the prior probability of any possibility you can describe over a human lifetime should be much higher than that.
A nitpick: it takes 332 pieces of all mutually independent evidence to perform that level of update.
More confusing, for these purposes the independence level of the evidence depends on what hypotheses you’re trying to distinguish with it. E.g. if you’re trying to distinguish between “that subject has ESP powers” and “that experiment was random luck” then 332 repetitions of the same experiment will do. If you’re trying to distinguish between “that subject has ESP powers” and “that experimenter’s facial expressions differ based on what cards he was looking at”, then you can’t just repeat it; you’ve got to devise new and different experiments.
You’re right that I completely missed the Bayesian boat, and I’m going to have to start thinking more before I speak and revise my estimates down to <1%.
But I’m still reluctant to put them as low as you seem to. The anthropic principle combined with large universe says that whatever complexity is necessary for the existence of conscious observers, we can expect to find at least that level of complexity. Questions like consciousness, qualia, and personal identity still haven’t been resolved, and although past experience suggests there is probably a rational explanation to this question, it isn’t nearly dissolved yet. If consciousness really is impossible without some exotic consciousness-related physics (Penrosean or otherwise), then our universe will have exotic consciousness-related physics no matter how complex they need to be. And since evolved beings have been so proficient at making use of normal physics to gain sensory information, it’s a good bet they’d do the same with exotic consciousness-related physics too if they had them...
...is a somewhat hokey argument I just invented on the spot, and I’m sorry for it. But the ease with which I can put something like that together is itself evidence that there are enough possible sides of the issue that hadn’t been considered (at least I hadn’t considered that one; maybe you’ve been thinking about it for years) that it needs at least a little more room for error than two in a bajillion (sorry, Alex).
I also disagree with your assessment of the amount of evidence. Have you ever read any good books by intelligent believers in the subject? It’s not all John Edwards psychic chat shows. I also think you might be double-counting evidence against psi here—psi doesn’t exist so we know any apparent evidence must come from human psychology, therefore there never was any apparent evidence in the first place. Or have you read the studies and developed separate explanations for each positive result?
Anyway, let’s settle this the LW way. Give me your odds that psi exists, and we can make a bet at them. If it’s one in a million, then I’ll give a cent to your favorite charity on the condition that you give $10,000 to my favorite charity if psi’s shown to exist within our lifetimes (defined however you want; possibly as evidence sufficient to convince any two among Randi, Dawkins, and Eliezer that psi is >50% likely).
One problem with this argument is that if psi exists, we are very bad at using it, and we don’t see other organisms using it well either. The world we see appears to be almost completely described by normal physics at worst.
I don’t think that I’m double-counting evidence. I certainly know that there can be intelligent believers, after all, MANY intelligent people believe that one is compelled to accept the conclusions of the scientific method over those of the scientific community. Also, beliefs can be compelling for any variety of irrational reasons. The evidence I have seen though looks to me like exactly the evidence you would expect given known psychology and no psi. We can surely agree that there is a LOT of evidence that hyman psychology would create belief in psi in the absence of psi, can’t we.
I would set my odds at “top twenty most astoundingly surprising things ever discovered but maybe not top ten”. That seems to me like odds of many billions to one against, but not trillions. Unfortunately, the odds for almost any plausible winning conditions occurring without psi being real are much higher, making the bet difficult to judge. I have a standing 10,000 to one bet against Blacklight Power’s “Hydrino Theory” with Brian Wang based on a personal estimate of odds MUCH less than 1-in-10K for “Hydrino Theory” and I’m happy to extend those odds when the odds are still more favorable, but psychotic breaks by two people in a group of three? If the odds per person are 1%, that gives odds of about 1:3300. I’m happy to give those odds on the Dawkins, Randi Yudkowsky bet and count “psi is actually real” as a rounding error.
Have donated $10 to SIAI (seemed less likely to lose you guys money in transaction fees than $1) with public comment about the bet . Will decide where you can donate your $33000 in the unlikely event it proves necessary.
I’d feel ridiculously overconfident stating a probability of less that 1e-6, yet I don’t have the slightest hesitation to take that bet. (Brain sucks at small probabilities.) Condition is any two among {Randi, Dawkins, Eliezer, Vassar, me}, but if one is reported to have developed a new mental illness at least two months before they say psi is real, they don’t count.
Also, let’s make it purchasing power as of 2011, not dollar amount. Assuming scarcity lasts long enough.
What if they’re dead?
Well, then I lose the bet...unless someone contacts their ghosts...in which case I win the bet!
Psi doesn’t even explain consciousness or qualia.
[edit] Oops, necro. Disregard me.
[edit edit] okay! nevermind that then :D
I don’t think there’s a prejudice against replying to old posts around here...
One in a bajillion? You are saying you actually know how complex psi is without even saying what aspect of psi you are talking about.
We know biology is very complex. So when testing a supplement like creatine, the pseudoskeptic could say “biology is extremely complex. We do not know the mechanism that makes creatine work so I assign a very low bayesian probability. Today I feel like a hundred trillion to one”.
Keep in mind this is after several studies have shown an effect in the predicted direction whose odds are not easily explained by chance. Indeed, there is nothing wrong with you assertion about complexity just the subjective part where you assign a number to a phenomena you are not very familiar with.
Bajillion isn’t exactly a precise measure. In this context it means ‘lots’. That isn’t hard to assign to the all aspects of psi.