new meetup policy: promote posts only with first-time meetups
I propose for comment the following alteration of the LW meetup promotion policy:
* The weekly meetup roundup will contain, in its title, only the names of cities which have not previously had an LW meetup, or which have not had an LW meetup in the last year.
* On occasions where no such name appears in the title, the meetup roundup post will still appear in Main but will not be Promoted.
* Cities having a first-time meetup, or where a new meetup is being started by a new organizer after a hiatus, should have additional info about that meetup and its organizer appearing in a prominent, top-of-post position in the roundup post.
This is intended to make it easier for new meetups to gain attention, by requiring hopeful LWers awaiting a new meetup in their area to pay attention to a smaller number of promoted posts and a smaller number of cities appearing in the titles of Main posts.
Justifiable Erroneous Scientific Pessimism
In an erratum to my previous post on Pascalian wagers, it has been plausibly argued to me that all the roads to nuclear weapons, including plutonium production from U-238, may have bottlenecked through the presence of significant amounts of Earthly U235 (apparently even the giant heap of unrefined uranium bricks in Chicago Pile 1 was, functionally, empty space with a scattering of U235 dust). If this is the case then Fermi's estimate of a "ten percent" probability of nuclear weapons may have actually been justifiable because nuclear weapons were almost impossible (at least without particle accelerators) - though it's not totally clear to me why "10%" instead of "2%" or "50%" but then I'm not Fermi.
We're all familiar with examples of correct scientific skepticism, such as about Uri Geller and hydrino theory. We also know many famous examples of scientists just completely making up their pessimism, for example about the impossibility of human heavier-than-air flight. Before this occasion I could only think offhand of one other famous example of erroneous scientific pessimism that was not in defiance of the default extrapolation of existing models, namely Lord Kelvin's careful estimate from multiple sources that the Sun was around sixty million years of age. This was wrong, but because of new physics - though you could make a case that new physics might well be expected in this case - and there was some degree of contrary evidence from geology, as I understand it - and that's not exactly the same as technological skepticism - but still. Where there are sort of two, there may be more. Can anyone name a third example of erroneous scientific pessimism whose error was, to the same degree, not something a smarter scientist could've seen coming?
I ask this with some degree of trepidation, since by most standards of reasoning essentially anything is "justifiable" if you try hard enough to find excuses and then not question them further, so I'll phrase it more carefully this way: I am looking for a case of erroneous scientific pessimism, preferably about technological impossibility or extreme difficulty, where it seems clear that the inverse case for possibility would've been weaker if carried out strictly with contemporary knowledge, after exploring points and counterpoints. (So that relaxed standards for "justifiability" will just produce even more justifiable cases for the technological possibility.) We probably should also not accept as "erroneous" any prediction of technological impossibility where it required more than, say, seventy years to get the technology.
Pascal's Muggle: Infinitesimal Priors and Strong Evidence
Followup to: Pascal's Mugging: Tiny Probabilities of Vast Utilities, The Pascal's Wager Fallacy Fallacy, Being Half-Rational About Pascal's Wager Is Even Worse
Short form: Pascal's Muggle
tl;dr: If you assign superexponentially infinitesimal probability to claims of large impacts, then apparently you should ignore the possibility of a large impact even after seeing huge amounts of evidence. If a poorly-dressed street person offers to save 10(10^100) lives (googolplex lives) for $5 using their Matrix Lord powers, and you claim to assign this scenario less than 10-(10^100) probability, then apparently you should continue to believe absolutely that their offer is bogus even after they snap their fingers and cause a giant silhouette of themselves to appear in the sky. For the same reason, any evidence you encounter showing that the human species could create a sufficiently large number of descendants - no matter how normal the corresponding laws of physics appear to be, or how well-designed the experiments which told you about them - must be rejected out of hand. There is a possible reply to this objection using Robin Hanson's anthropic adjustment against the probability of large impacts, and in this case you will treat a Pascal's Mugger as having decision-theoretic importance exactly proportional to the Bayesian strength of evidence they present you, without quantitative dependence on the number of lives they claim to save. This however corresponds to an odd mental state which some, such as myself, would find unsatisfactory. In the end, however, I cannot see any better candidate for a prior than having a leverage penalty plus a complexity penalty on the prior probability of scenarios.
In late 2007 I coined the term "Pascal's Mugging" to describe a problem which seemed to me to arise when combining conventional decision theory and conventional epistemology in the obvious way. On conventional epistemology, the prior probability of hypotheses diminishes exponentially with their complexity; if it would take 20 bits to specify a hypothesis, then its prior probability receives a 2-20 penalty factor and it will require evidence with a likelihood ratio of 1,048,576:1 - evidence which we are 1048576 times more likely to see if the theory is true, than if it is false - to make us assign it around 50-50 credibility. (This isn't as hard as it sounds. Flip a coin 20 times and note down the exact sequence of heads and tails. You now believe in a state of affairs you would have assigned a million-to-one probability beforehand - namely, that the coin would produce the exact sequence HTHHHHTHTTH... or whatever - after experiencing sensory data which are more than a million times more probable if that fact is true than if it is false.) The problem is that although this kind of prior probability penalty may seem very strict at first, it's easy to construct physical scenarios that grow in size vastly faster than they grow in complexity.
I originally illustrated this using Pascal's Mugger: A poorly dressed street person says "I'm actually a Matrix Lord running this world as a computer simulation, along with many others - the universe above this one has laws of physics which allow me easy access to vast amounts of computing power. Just for fun, I'll make you an offer - you give me five dollars, and I'll use my Matrix Lord powers to save 3↑↑↑↑3 people inside my simulations from dying and let them live long and happy lives" where ↑ is Knuth's up-arrow notation. This was originally posted in 2007, when I was a bit more naive about what kind of mathematical notation you can throw into a random blog post without creating a stumbling block. (E.g.: On several occasions now, I've seen someone on the Internet approximate the number of dust specks from this scenario as being a "billion", since any incomprehensibly large number equals a billion.) Let's try an easier (and way smaller) number instead, and suppose that Pascal's Mugger offers to save a googolplex lives, where a googol is 10100 (a 1 followed by a hundred zeroes) and a googolplex is 10 to the googol power, so 1010100 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 lives saved if you pay Pascal's Mugger five dollars, if the offer is honest.
Pascal's Muggle (short version)
Shortened version of: Pascal's Muggle: Infinitesimal Priors and Strong Evidence
One proposal which has been floated for dealing with Pascal's Mugger is to penalize hypotheses that let you affect a large number of people, in proportion to the number of people affected - what we could call perhaps a "leverage penalty" instead of a "complexity penalty". This isn't just for Pascal's Mugger in particularly, it seems required to have expected utilities in general converge when the 'size' of scenarios can grow much faster than their algorithmic complexity.
Unfortunately this potentially leads us into a different problem, that of Pascal's Muggle.
Suppose a poorly-dressed street person asks you for five dollars in exchange for doing a googolplex's worth of good using his Matrix Lord powers - say, saving the lives of a googolplex other people inside computer simulations they're running.
"Well," you reply, "I think that it would be very improbable that I would be able to affect so many people through my own, personal actions - who am I to have such a great impact upon events? Indeed, I think the probability is somewhere around one over googolplex, maybe a bit less. So no, I won't pay five dollars - it is unthinkably improbable that I could do so much good!"
"I see," says the Mugger.
A wind begins to blow about the alley, whipping the Mugger's loose clothes about him as they shift from ill-fitting shirt and jeans into robes of infinite blackness, within whose depths tiny galaxies and stranger things seem to twinkle. In the sky above, a gap edged by blue fire opens with a horrendous tearing sound - you can hear people on the nearby street yelling in sudden shock and terror, implying that they can see it too - and displays the image of the Mugger himself, wearing the same robes that now adorn his body, seated before a keyboard and a monitor.
"That's not actually me," the Mugger says, "just a conceptual representation, but I don't want to drive you insane. Now give me those five dollars, and I'll save a googolplex lives, just as promised. It's easy enough for me, given the computing power my home universe offers. As for why I'm doing this, there's an ancient debate in philosophy among my people - something about how we ought to sum our expected utilities - and I mean to use the video of this event to make a point at the next decision theory conference I attend. Now will you give me the five dollars, or not?"
"Mm... no," you reply.
"No?" says the Mugger. "I understood earlier when you didn't want to give a random street person five dollars based on a wild story with no evidence behind it whatsoever. But surely I've offered you evidence now."
"Unfortunately, you haven't offered me enough evidence," you explain.
"Seriously?" says the Mugger. "I've opened up a fiery portal in the sky, and that's not enough to persuade you? What do I have to do, then? Rearrange the planets in your solar system, and wait for the observatories to confirm the fact? I suppose I could also explain the true laws of physics in the higher universe in more detail, and let you play around a bit with the computer program that encodes all the universes containing the googolplex people I would save if you just gave me the damn five dollars -"
"Sorry," you say, shaking your head firmly, "there's just no way you can convince me that I'm in a position to affect a googolplex people, because the prior probability of that is one over googolplex. If you wanted to convince me of some fact of merely 2-100 prior probability, a mere decillion to one - like that a coin would come up heads and tails in some particular pattern of a hundred coinflips - then you could just show me 100 bits of evidence, which is within easy reach of my brain's sensory bandwidth. I mean, you could just flip the coin a hundred times, and my eyes, which send my brain a hundred megabits a second or so - though that gets processed down to one megabit or so by the time it goes through the lateral geniculate nucleus - would easily give me enough data to conclude that this decillion-to-one possibility was true. But to conclude something whose prior probability is on the order of one over googolplex, I need on the order of a googol bits of evidence, and you can't present me with a sensory experience containing a googol bits. Indeed, you can't ever present a mortal like me with evidence that has a likelihood ratio of a googolplex to one - evidence I'm a googolplex times more likely to encounter if the hypothesis is true, than if it's false - because the chance of all my neurons spontaneously rearranging themselves to fake the same evidence would always be higher than one over googolplex. You know the old saying about how once you assign something probability one, or probability zero, you can't update that probability regardless of what evidence you see? Well, odds of a googolplex to one, or one to a googolplex, work pretty much the same way."
"So no matter what evidence I show you," the Mugger says - as the blue fire goes on crackling in the torn sky above, and screams and desperate prayers continue from the street beyond - "you can't ever notice that you're in a position to help a googolplex people."
"Right!" you say. "I can believe that you're a Matrix Lord. I mean, I'm not a total Muggle, I'm psychologically capable of responding in some fashion to that giant hole in the sky. But it's just completely forbidden for me to assign any significant probability whatsoever that you will actually save a googolplex people after I give you five dollars. You're lying, and I am absolutely, absolutely, absolutely confident of that."
"So you weren't just invoking the leverage penalty as a plausible-sounding way of getting out of paying me the five dollars earlier," the Mugger says thoughtfully. "I mean, I'd understand if that was just a rationalization of your discomfort at forking over five dollars for what seemed like a tiny probability, when I hadn't done my duty to present you with a corresponding amount of evidence before demanding payment. But you... you're acting like an AI would if it was actually programmed with a leverage penalty on hypotheses!"
"Exactly," you say. "I'm forbidden a priori to believe I can ever do that much good."
"Why?" the Mugger says curiously. "I mean, all I have to do is press this button here and a googolplex lives will be saved." The figure within the blazing portal above points to a green button on the console before it.
"Like I said," you explain again, "the prior probability is just too infinitesimal for the massive evidence you're showing me to overcome it -"
The Mugger shrugs, and vanishes in a puff of purple mist.
The portal in the sky above closes, taking with the console and the green button.
(The screams go on from the street outside.)
A few days later, you're sitting in your office at the physics institute where you work, when one of your colleagues bursts in through your door, seeming highly excited. "I've got it!" she cries. "I've figured out that whole dark energy thing! Look, these simple equations retrodict it exactly, there's no way that could be a coincidence!"
At first you're also excited, but as you pore over the equations, your face configures itself into a frown. "No..." you say slowly. "These equations may look extremely simple so far as computational complexity goes - and they do exactly fit the petabytes of evidence our telescopes have gathered so far - but I'm afraid they're far too improbable to ever believe."
"What?" she says. "Why?"
"Well," you say reasonably, "if these equations are actually true, then our descendants will be able to exploit dark energy to do computations, and according to my back-of-the-envelope calculations here, we'd be able to create around a googolplex people that way. But that would mean that we, here on Earth, are in a position to affect a googolplex people - since, if we blow ourselves up via a nanotechnological war or (cough) make certain other errors, those googolplex people will never come into existence. The prior probability of us being in a position to impact a googolplex people is on the order of one over googolplex, so your equations must be wrong."
"Hmm..." she says. "I hadn't thought of that. But what if these equations are right, and yet somehow, everything I do is exactly balanced, down to the googolth decimal point or so, with respect to how it impacts the chance of modern-day Earth participating in a chain of events that leads to creating an intergalactic civilization?"
"How would that work?" you say. "There's only seven billion people on today's Earth - there's probably been only a hundred billion people who ever existed total, or will exist before we go through the intelligence explosion or whatever - so even before analyzing your exact position, it seems like your leverage on future affairs couldn't reasonably be less than one in a ten trillion part of the future or so."
"But then given this physical theory which seems obviously true, my acts might imply expected utility differentials on the order of 1010100-13," she explains, "and I'm not allowed to believe that no matter how much evidence you show me."
This problem may not be as bad as it looks; a leverage penalty may lead to more reasonable behavior than depicted above, after taking into account Bayesian updating:
Mugger: "Give me five dollars, and I'll save 3↑↑↑3 lives using my Matrix Powers."
You: "Nope."
Mugger: "Why not? It's a really large impact."
You: "Yes, and I assign a probability on the order of 1 in 3↑↑↑3 that I would be in a unique position to affect 3↑↑↑3 people."
Mugger: "Oh, is that really the probability that you assign? Behold!"
(A gap opens in the sky, edged with blue fire.)
Mugger: "Now what do you think, eh?"
You: "Well... I can't actually say this has a likelihood ratio of 3↑↑↑3 to 1. No stream of evidence that can enter a human brain over the course of a century is ever going to have a likelihood ratio larger than, say, 101026 to 1 at the absurdly most, assuming one megabit per second of sensory data, for a century, each bit of which has at least a 1-in-a-trillion error probability. You'd probably start to be dominated by Boltzmann brains or other exotic minds well before then."
Mugger: "So you're not convinced."
You: "Indeed not. The probability that you're telling the truth is so tiny that God couldn't find it with an electron microscope. Here's the five dollars."
Mugger: "Done! You've saved 3↑↑↑3 lives! Congratulations, you're never going to top that, your peak life accomplishment will now always lie in your past. But why'd you give me the five dollars if you think I'm lying?"
You: "Well, because the evidence you did present me with had a likelihood ratio of at least a billion to one - I would've assigned less than 10-9 prior probability of seeing this when I woke up this morning - so in accordance with Bayes's Theorem I promoted the probability from 1/3↑↑↑3 to at least 109/3↑↑↑3, which when multiplied by an impact of 3↑↑↑3, yields an expected value of at least a billion lives saved for giving you five dollars."
I confess that I find this line of reasoning a bit suspicious - it seems overly clever - but at least on the level of intuitive-virtues-of-rationality it doesn't seem completely stupid in the same way as Pascal's Muggle. This muggee is at least behaviorally reacting to the evidence. In fact, they're reacting in a way exactly proportional to the evidence - they would've assigned the same net importance to handing over the five dollars if the Mugger had offered 3↑↑↑4 lives, so long as the strength of the evidence seemed the same.
But I still feel a bit nervous about the idea that Pascal's Muggee, after the sky splits open, is handing over five dollars while claiming to assign probability on the order of 109/3↑↑↑3 that it's doing any good. My own reaction would probably be more like this:
Mugger: "Give me five dollars, and I'll save 3↑↑↑3 lives using my Matrix Powers."
Me: "Nope."
Mugger: "So then, you think the probability I'm telling the truth is on the order of 1/3↑↑↑3?"
Me: "Yeah... that probably has to follow. I don't see any way around that revealed belief, given that I'm not actually giving you the five dollars. I've heard some people try to claim silly things like, the probability that you're telling the truth is counterbalanced by the probability that you'll kill 3↑↑↑3 people instead, or something else with a conveniently exactly equal and opposite utility. But there's no way that things would balance out that neatly in practice, if there was no a priori mathematical requirement that they balance. Even if the prior probability of your saving 3↑↑↑3 people and killing 3↑↑↑3 people, conditional on my giving you five dollars, exactly balanced down to the log(3↑↑↑3) decimal place, the likelihood ratio for your telling me that you would "save" 3↑↑↑3 people would not be exactly 1:1 for the two hypotheses down to the log(3↑↑↑3) decimal place. So if I assigned probabilities much greater than 1/3↑↑↑3 to your doing something that affected 3↑↑↑3 people, my actions would be overwhelmingly dominated by even a tiny difference in likelihood ratio elevating the probability that you saved 3↑↑↑3 people over the probability that you did something equally and oppositely bad to them. The only way this hypothesis can't dominate my actions - really, the only way my expected utility sums can converge at all - is if I assign probability on the order of 1/3↑↑↑3 or less. I don't see any way of escaping that part."
Mugger: "But can you, in your mortal uncertainty, truly assign a probability as low as 1 in 3↑↑↑3 to any proposition whatever? Can you truly believe, with your error-prone neural brain, that you could make 3↑↑↑3 statements of any kind one after another, and be wrong, on average, about once?"
Me: "Nope."
Mugger: "So give me five dollars!"
Me: "Nope."
Mugger: "Why not?"
Me: "Because even though I, in my mortal uncertainty, will eventually be wrong about all sorts of things if I make enough statements one after another, this fact can't be used to increase the probability of arbitrary statements beyond what my prior says they should be, because then my prior would sum to more than 1. There must be some kind of required condition for taking a hypothesis seriously enough to worry that I might be overconfident about it -"
Mugger: "Then behold!"
(A gap opens in the sky, edged with blue fire.)
Mugger: "Now what do you think, eh?"
Me (staring up at the sky): "...whoa." (Pause.) "You turned into a cat."
Mugger: "What?"
Me: "Private joke. Okay, I think I'm going to have to rethink a lot of things. But if you want to tell me about how I was wrong to assign a prior probability on the order of 1/3↑↑↑3 to your scenario, I will shut up and listen very carefully to what you have to say about it. Oh, and here's the five dollars, can I pay an extra twenty and make some other requests?"
(The thought bubble pops, and we return to two people standing in an alley, the sky above perfectly normal.)
Mugger: "Now, in this scenario we've just imagined, you were taking my case seriously, right? But the evidence there couldn't have had a likelihood ratio of more than 101026 to 1, and probably much less. So by the method of imaginary updates, you must assign probability at least 10-1026 to my scenario, which when multiplied by a benefit on the order of 3↑↑↑3, yields an unimaginable bonanza in exchange for just five dollars -"
Me: "Nope."
Mugger: "How can you possibly say that? You're not being logically coherent!"
Me: "I agree that I'm being incoherent in a sense, but I think that's acceptable in this case, since I don't have infinite computing power. In the scenario you're asking me to imagine, you're presenting me with evidence which I currently think Can't Happen. And if that actually does happen, the sensible way for me to react is by questioning my prior assumptions and reasoning which led me to believe I shouldn't see it happen. One way that I handle my lack of logical omniscience - my finite, error-prone reasoning capabilities - is by being willing to assign infinitesimal probabilities to non-privileged hypotheses so that my prior over all possibilities can sum to 1. But if I actually see strong evidence for something I previously thought was super-improbable, I don't just do a Bayesian update, I should also question whether I was right to assign such a tiny probability in the first place - whether the scenario was really as complex, or unnatural, as I thought. In real life, you are not ever supposed to have a prior improbability of 10-100 for some fact distinguished enough to be written down, and yet encounter strong evidence, say 1010 to 1, that the thing has actually happened. If something like that happens, you don't do a Bayesian update to a posterior of 10-90. Instead you question both whether the evidence might be weaker than it seems, and whether your estimate of prior improbability might have been poorly calibrated, because rational agents who actually have well-calibrated priors should not encounter situations like that until they are ten billion days old. Now, this may mean that I end up doing some non-Bayesian updates: I say some hypothesis has a prior probability of a quadrillion to one, you show me evidence with a likelihood ratio of a billion to one, and I say 'Guess I was wrong about that quadrillion to one thing' rather than being a Muggle about it. And then I shut up and listen to what you have to say about how to estimate probabilities, because on my worldview, I wasn't expecting to see you turn into a cat. But for me to make a super-update like that - reflecting a posterior belief that I was logically incorrect about the prior probability - you have to really actually show me the evidence, you can't just ask me to imagine it. This is something that only logically incoherent agents ever say, but that's all right because I'm not logically omniscient."
When I add up a complexity penalty, a leverage penalty, and the "You turned into a cat!" logical non-omniscience clause, I get the best candidate I have so far for the correct decision-theoretic way to handle these sorts of possibilities while still having expected utilities converge.
As mentioned in the longer version, this has very little in the way of relevance for optimal philanthropy, because we don't really need to consider these sorts of rules for handling small large numbers on the order of a universe containing 1080 atoms, and because most of the improbable leverage associated with x-risk charities is associated with discovering yourself to be an Ancient Earthling from before the intelligence explosion, which improbability (for universes the size of 1080 atoms) is easily overcome by the sensory experiences which tell you you're an Earthling. For more on this see the original long-form post. The main FAI issue at stake is what sort of prior to program into an AI.
New report: Intelligence Explosion Microeconomics
Summary: Intelligence Explosion Microeconomics (pdf) is 40,000 words taking some initial steps toward tackling the key quantitative issue in the intelligence explosion, "reinvestable returns on cognitive investments": what kind of returns can you get from an investment in cognition, can you reinvest it to make yourself even smarter, and does this process die out or blow up? This can be thought of as the compact and hopefully more coherent successor to the AI Foom Debate of a few years back.
(Sample idea you haven't heard before: The increase in hominid brain size over evolutionary time should be interpreted as evidence about increasing marginal fitness returns on brain size, presumably due to improved brain wiring algorithms; not as direct evidence about an intelligence scaling factor from brain size.)
I hope that the open problems posed therein inspire further work by economists or economically literate modelers, interested specifically in the intelligence explosion qua cognitive intelligence rather than non-cognitive 'technological acceleration'. MIRI has an intended-to-be-small-and-technical mailing list for such discussion. In case it's not clear from context, I (Yudkowsky) am the author of the paper.
Abstract:
I. J. Good's thesis of the 'intelligence explosion' is that a sufficiently advanced machine intelligence could build a smarter version of itself, which could in turn build an even smarter version of itself, and that this process could continue enough to vastly exceed human intelligence. As Sandberg (2010) correctly notes, there are several attempts to lay down return-on-investment formulas intended to represent sharp speedups in economic or technological growth, but very little attempt has been made to deal formally with I. J. Good's intelligence explosion thesis as such.
I identify the key issue as returns on cognitive reinvestment - the ability to invest more computing power, faster computers, or improved cognitive algorithms to yield cognitive labor which produces larger brains, faster brains, or better mind designs. There are many phenomena in the world which have been argued as evidentially relevant to this question, from the observed course of hominid evolution, to Moore's Law, to the competence over time of machine chess-playing systems, and many more. I go into some depth on the sort of debates which then arise on how to interpret such evidence. I propose that the next step forward in analyzing positions on the intelligence explosion would be to formalize return-on-investment curves, so that each stance can say formally which possible microfoundations they hold to be falsified by historical observations already made. More generally, I pose multiple open questions of 'returns on cognitive reinvestment' or 'intelligence explosion microeconomics'. Although such questions have received little attention thus far, they seem highly relevant to policy choices affecting the outcomes for Earth-originating intelligent life.
The dedicated mailing list will be small and restricted to technical discussants.
Being Half-Rational About Pascal's Wager is Even Worse
For so long as I can remember, I have rejected Pascal's Wager in all its forms on sheerly practical grounds: anyone who tries to plan out their life by chasing a 1 in 10,000 chance of a huge payoff is almost certainly doomed in practice. This kind of clever reasoning never pays off in real life...
...unless you have also underestimated the allegedly tiny chance of the large impact.
For example. At one critical junction in history, Leo Szilard, the first physicist to see the possibility of fission chain reactions and hence practical nuclear weapons, was trying to persuade Enrico Fermi to take the issue seriously, in the company of a more prestigious friend, Isidor Rabi:
I said to him: "Did you talk to Fermi?" Rabi said, "Yes, I did." I said, "What did Fermi say?" Rabi said, "Fermi said 'Nuts!'" So I said, "Why did he say 'Nuts!'?" and Rabi said, "Well, I don't know, but he is in and we can ask him." So we went over to Fermi's office, and Rabi said to Fermi, "Look, Fermi, I told you what Szilard thought and you said ‘Nuts!' and Szilard wants to know why you said ‘Nuts!'" So Fermi said, "Well… there is the remote possibility that neutrons may be emitted in the fission of uranium and then of course perhaps a chain reaction can be made." Rabi said, "What do you mean by ‘remote possibility'?" and Fermi said, "Well, ten per cent." Rabi said, "Ten per cent is not a remote possibility if it means that we may die of it. If I have pneumonia and the doctor tells me that there is a remote possibility that I might die, and it's ten percent, I get excited about it." (Quoted in 'The Making of the Atomic Bomb' by Richard Rhodes.)
This might look at first like a successful application of "multiplying a low probability by a high impact", but I would reject that this was really going on. Where the heck did Fermi get that 10% figure for his 'remote possibility', especially considering that fission chain reactions did in fact turn out to be possible? If some sort of reasoning had told us that a fission chain reaction was improbable, then after it turned out to be reality, good procedure would have us go back and check our reasoning to see what went wrong, and figure out how to adjust our way of thinking so as to not make the same mistake again. So far as I know, there was no physical reason whatsoever to think a fission chain reaction was only a ten percent probability. They had not been demonstrated experimentally, to be sure; but they were still the default projection from what was already known. If you'd been told in the 1930s that fission chain reactions were impossible, you would've been told something that implied new physical facts unknown to current science (and indeed, no such facts existed). After reading enough historical instances of famous scientists dismissing things as impossible when there was no physical logic to say that it was even improbable, one cynically suspects that some prestigious scientists perhaps came to conceive of themselves as senior people who ought to be skeptical about things, and that Fermi was just reacting emotionally. The lesson I draw from this historical case is not that it's a good idea to go around multiplying ten percent probabilities by large impacts, but that Fermi should not have pulled out a number as low as ten percent.
Having seen enough conversations involving made-up probabilities to become cynical, I also strongly suspect that if Fermi had foreseen how Rabi would reply, Fermi would've said "One percent". If Fermi had expected Rabi to say "One percent is not small if..." then Fermi would've said "One in ten thousand" or "Too small to consider" - whatever he thought would get him off the hook. Perhaps I am being too unkind to Fermi, who was a famously great estimator; Fermi may well have performed some sort of lawful probability estimate on the spot. But Fermi is also the one who said that nuclear energy was fifty years off in the unlikely event it could be done at all, two years (IIRC) before Fermi himself oversaw the construction of the first nuclear pile. Where did Fermi get that fifty-year number from? This sort of thing does make me more likely to believe that Fermi, in playing the role of the solemn doubter, was just Making Things Up; and this is no less a sin when you make up skeptical things. And if this cynicism is right, then we cannot learn the lesson that it is wise to multiply small probabilities by large impacts because this is what saved Fermi - if Fermi had known the rule, if he had seen it coming, he would have just Made Up an even smaller probability to get himself off the hook. It would have been so very easy and convenient to say, "One in ten thousand, there's no experimental proof and most ideas like that are wrong! Think of all the conjunctive probabilities that have to be true before we actually get nuclear weapons and our own efforts actually made a difference in that!" followed shortly by "But it's not practical to be worried about such tiny probabilities!" Or maybe Fermi would've known better, but even so I have never been a fan of trying to have two mistakes cancel each other out.
I mention all this because it is dangerous to be half a rationalist, and only stop making one of the two mistakes. If you are going to reject impractical 'clever arguments' that would never work in real life, and henceforth not try to multiply tiny probabilities by huge payoffs, then you had also better reject all the clever arguments that would've led Fermi or Szilard to assign probabilities much smaller than ten percent. (Listing out a group of conjunctive probabilities leading up to taking an important action, and not listing any disjunctive probabilities, is one widely popular way of driving down the apparent probability of just about anything.) Or if you would've tried to put fission chain reactions into a reference class of 'amazing new energy sources' and then assigned it a tiny probability, or put Szilard into the reference class of 'people who think the fate of the world depends on them', or pontificated about the lack of any positive experimental evidence proving that a chain reaction was possible, blah blah blah etcetera - then your error here can perhaps be compensated for by the opposite error of then trying to multiply the resulting tiny probability by a large impact. I don't like making clever mistakes that cancel each other out - I consider that idea to also be clever - but making clever mistakes that don't cancel out is worse.
On the other hand, if you want a general heuristic that could've led Fermi to do better, I would suggest reasoning that previous-historical experimental proof of a chain reaction would not be strongly be expected even in worlds where it was possible, and that to discover a chain reaction to be impossible would imply learning some new fact of physical science which was not already known. And this is not just 20-20 hindsight; Szilard and Rabi saw the logic in advance of the fact, not just afterward - though not in those exact terms; they just saw the physical logic, and then didn't adjust it downward for 'absurdity' or with more complicated rationalizations. But then if you are going to take this sort of reasoning at face value, without adjusting it downward, then it's probably not a good idea to panic every time you assign a 0.01% probability to something big - you'll probably run into dozens of things like that, at least, and panicking over them would leave no room to wait until you found something whose face-value probability was large.
I don't believe in multiplying tiny probabilities by huge impacts. But I also believe that Fermi could have done better than saying ten percent, and that it wasn't just random luck mixed with overconfidence that led Szilard and Rabi to assign higher probabilities than that. Or to name a modern issue which is still open, Michael Shermer should not have dismissed the possibility of molecular nanotechnology, and Eric Drexler will not have been randomly lucky when it turns out to work: taking current physical models at face value imply that molecular nanotechnology ought to work, and if it doesn't work we've learned some new fact unknown to present physics, etcetera. Taking the physical logic at face value is fine, and there's no need to adjust it downward for any particular reason; if you say that Eric Drexler should 'adjust' this probability downward for whatever reason, then I think you're giving him rules that predictably give him the wrong answer. Sometimes surface appearances are misleading, but most of the time they're not.
A key test I apply to any supposed rule of reasoning about high-impact scenarios is, "Does this rule screw over the planet if Reality actually hands us a high-impact scenario?" and if the answer is yes, I discard it and move on. The point of rationality is to figure out which world we actually live in and adapt accordingly, not to rule out certain sorts of worlds in advance.
There's a doubly-clever form of the argument wherein everyone in a plausibly high-impact position modestly attributes only a tiny potential possibility that their face-value view of the world is sane, and then they multiply this tiny probability by the large impact, and so they act anyway and on average worlds in trouble are saved. I don't think this works in real life - I don't think I would have wanted Leo Szilard to think like that. I think that if your brain really actually thinks that fission chain reactions have only a tiny probability of being important, you will go off and try to invent better refrigerators or something else that might make you money. And if your brain does not really feel that fission chain reactions have a tiny probability, then your beliefs and aliefs are out of sync and that is not something I want to see in people trying to handle the delicate issue of nuclear weapons. But in any case, I deny the original premise: I do not think the world's niches for heroism must be populated by heroes who are incapable in principle of reasonably distinguishing themselves from a population of crackpots, all of whom have no choice but to continue on the tiny off-chance that they are not crackpots.
I haven't written enough about what I've begun thinking of as 'heroic epistemology' - why, how can you possibly be so overconfident as to dare even try to have a huge positive impact when most people in that reference class blah blah blah - but on reflection, it seems to me that an awful lot of my answer boils down to not trying to be clever about it. I don't multiply tiny probabilities by huge impacts. I also don't get tiny probabilities by putting myself into inescapable reference classes, for this is the sort of reasoning that would screw over planets that actually were in trouble if everyone thought like that. In the course of any workday, on the now very rare occasions I find myself thinking about such meta-level junk instead of the math at hand, I remind myself that it is a wasted motion - where a 'wasted motion' is any thought which will, in retrospect if the problem is in fact solved, not have contributed to having solved the problem. If someday Friendly AI is built, will it have been terribly important that someone have spent a month fretting about what reference class they're in? No. Will it, in retrospect, have been an important step along the pathway to understanding stable self-modification, if we spend time trying to solve the Lobian obstacle? Possibly. So one of these cognitive avenues is predictably a wasted motion in retrospect, and one of them is not. The same would hold if I spent a lot of time trying to convince myself that I was allowed to believe that I could affect anything large, or any other form of angsting about meta. It is predictable that in retrospect I will think this was a waste of time compared to working on a trust criterion between a probability distribution and an improved probability distribution. (Apologies, this is a technical thingy I'm currently working on which has no good English description.)
But if you must apply clever adjustments to things, then for Belldandy's sake don't be one-sidedly clever and have all your cleverness be on the side of arguments for inaction. I think you're better off without all the complicated fretting - but you're definitely not better off eliminating only half of it.
And finally, I once again state that I abjure, refute, and disclaim all forms of Pascalian reasoning and multiplying tiny probabilities by large impacts when it comes to existential risk. We live on a planet with upcoming prospects of, among other things, human intelligence enhancement, molecular nanotechnology, sufficiently advanced biotechnology, brain-computer interfaces, and of course Artificial Intelligence in several guises. If something has only a tiny chance of impacting the fate of the world, there should be something with a larger probability of an equally huge impact to worry about instead. You cannot justifiably trade off tiny probabilities of x-risk improvement against efforts that do not effectuate a happy intergalactic civilization, but there is nonetheless no need to go on tracking tiny probabilities when you'd expect there to be medium-sized probabilities of x-risk reduction. Nonetheless I try to avoid coming up with clever reasons to do stupid things, and one example of a stupid thing would be not working on Friendly AI when it's in blatant need of work. Elaborate complicated reasoning which says we should let the Friendly AI issue just stay on fire and burn merrily away, well, any complicated reasoning which returns an output this silly is automatically suspect.
If, however, you are unlucky enough to have been cleverly argued into obeying rules that make it a priori unreachable-in-practice for anyone to end up in an epistemic state where they try to do something about a planet which appears to be on fire - so that there are no more plausible x-risk reduction efforts to fall back on, because you're adjusting all the high-impact probabilities downward from what the surface state of the world suggests...
Well, that would only be a good idea if Reality were not allowed to hand you a planet that was in fact on fire. Or if, given a planet on fire, Reality was prohibited from handing you a chance to put it out. There is no reason to think that Reality must a priori obey such a constraint.
EDIT: To clarify, "Don't multiply tiny probabilities by large impacts" is something that I apply to large-scale projects and lines of historical probability. On a very large scale, if you think FAI stands a serious chance of saving the world, then humanity should dump a bunch of effort into it, and if nobody's dumping effort into it then you should dump more effort than currently into it. On a smaller scale, to compare two x-risk mitigation projects in demand of money, you need to estimate something about marginal impacts of the next added effort (where the common currency of utilons should probably not be lives saved, but "probability of an ok outcome", i.e., the probability of ending up with a happy intergalactic civilization). In this case the average marginal added dollar can only account for a very tiny slice of probability, but this is not Pascal's Wager. Large efforts with a success-or-failure criterion are rightly, justly, and unavoidably going to end up with small marginally increased probabilities of success per added small unit of effort. It would only be Pascal's Wager if the whole route-to-an-OK-outcome were assigned a tiny probability, and then a large payoff used to shut down further discussion of whether the next unit of effort should go there or to a different x-risk.
Reflection in Probabilistic Logic
Paul Christiano has devised a new fundamental approach to the "Löb Problem" wherein Löb's Theorem seems to pose an obstacle to AIs building successor AIs, or adopting successor versions of their own code, that trust the same amount of mathematics as the original. (I am currently writing up a more thorough description of the question this preliminary technical report is working on answering. For now the main online description is in a quick Summit talk I gave. See also Benja Fallenstein's description of the problem in the course of presenting a different angle of attack. Roughly the problem is that mathematical systems can only prove the soundness of, aka 'trust', weaker mathematical systems. If you try to write out an exact description of how AIs would build their successors or successor versions of their code in the most obvious way, it looks like the mathematical strength of the proof system would tend to be stepped down each time, which is undesirable.)
Paul Christiano's approach is inspired by the idea that whereof one cannot prove or disprove, thereof one must assign probabilities: and that although no mathematical system can contain its own truth predicate, a mathematical system might be able to contain a reflectively consistent probability predicate. In particular, it looks like we can have:
∀a, b: (a < P(φ) < b) ⇒ P(a < P('φ') < b) = 1
∀a, b: P(a ≤ P('φ') ≤ b) > 0 ⇒ a ≤ P(φ) ≤ b
Suppose I present you with the human and probabilistic version of a Gödel sentence, the Whitely sentence "You assign this statement a probability less than 30%." If you disbelieve this statement, it is true. If you believe it, it is false. If you assign 30% probability to it, it is false. If you assign 29% probability to it, it is true.
Paul's approach resolves this problem by restricting your belief about your own probability assignment to within epsilon of 30% for any epsilon. So Paul's approach replies, "Well, I assign almost exactly 30% probability to that statement - maybe a little more, maybe a little less - in fact I think there's about a 30% chance that I'm a tiny bit under 0.3 probability and a 70% chance that I'm a tiny bit over 0.3 probability." A standard fixed-point theorem then implies that a consistent assignment like this should exist. If asked if the probability is over 0.2999 or under 0.30001 you will reply with a definite yes.
You only need faith in two things
You only need faith in two things: That "induction works" has a non-super-exponentially-tiny prior probability, and that some single large ordinal is well-ordered. Anything else worth believing in is a deductive consequence of one or both.
(Because being exposed to ordered sensory data will rapidly promote the hypothesis that induction works, even if you started by assigning it very tiny prior probability, so long as that prior probability is not super-exponentially tiny. Then induction on sensory data gives you all empirical facts worth believing in. Believing that a mathematical system has a model usually corresponds to believing that a certain computable ordinal is well-ordered (the proof-theoretic ordinal of that system), and large ordinals imply the well-orderedness of all smaller ordinals. So if you assign non-tiny prior probability to the idea that induction might work, and you believe in the well-orderedness of a single sufficiently large computable ordinal, all of empirical science, and all of the math you will actually believe in, will follow without any further need for faith.)
(The reason why you need faith for the first case is that although the fact that induction works can be readily observed, there is also some anti-inductive prior which says, 'Well, but since induction has worked all those previous times, it'll probably fail next time!' and 'Anti-induction is bound to work next time, since it's never worked before!' Since anti-induction objectively gets a far lower Bayes-score on any ordered sequence and is then demoted by the logical operation of Bayesian updating, to favor induction over anti-induction it is not necessary to start out believing that induction works better than anti-induction, it is only necessary *not* to start out by being *perfectly* confident that induction won't work.)
(The reason why you need faith for the second case is that although more powerful proof systems - those with larger proof-theoretic ordinals - can prove the consistency of weaker proof systems, or equivalently prove the well-ordering of smaller ordinals, there's no known perfect system for telling which mathematical systems are consistent just as (equivalently!) there's no way of solving the halting problem. So when you reach the strongest math system you can be convinced of and further assumptions seem dangerously fragile, there's some large ordinal that represents all the math you believe in. If this doesn't seem to you like faith, try looking up a Buchholz hydra and then believing that it can always be killed.)
(Work is ongoing on eliminating the requirement for faith in these two remaining propositions. For example, we might be able to describe our increasing confidence in ZFC in terms of logical uncertainty and an inductive prior which is updated as ZFC passes various tests that it would have a substantial subjective probability of failing, even given all other tests it has passed so far, if ZFC were inconsistent.)
(No, this is *not* the "tu quoque!" moral equivalent of starting out by assigning probability 1 that Christ died for your sins.)
MetaMed: Evidence-Based Healthcare
In a world where 85% of doctors can't solve simple Bayesian word problems...
In a world where only 20.9% of reported results that a pharmaceutical company tries to investigate for development purposes, fully replicate...
In a world where "p-values" are anything the author wants them to be...
...and where there are all sorts of amazing technologies and techniques which nobody at your hospital has ever heard of...
...there's also MetaMed. Instead of just having “evidence-based medicine” in journals that doctors don't actually read, MetaMed will provide you with actual evidence-based healthcare. Their Chairman and CTO is Jaan Tallinn (cofounder of Skype, major funder of xrisk-related endeavors), one of their major VCs is Peter Thiel (major funder of MIRI), their management includes some names LWers will find familiar, and their researchers know math and stats and in many cases have also read LessWrong. If you have a sufficiently serious problem and can afford their service, MetaMed will (a) put someone on reading the relevant research literature who understands real statistics and can tell whether the paper is trustworthy; and (b) refer you to a cooperative doctor in their network who can carry out the therapies they find.
MetaMed was partially inspired by the case of a woman who had her fingertip chopped off, was told by the hospital that she was screwed, and then read through an awful lot of literature on her own until she found someone working on an advanced regenerative therapy that let her actually grow the fingertip back. The idea behind MetaMed isn't just that they will scour the literature to find how the best experimentally supported treatment differs from the average wisdom - people who regularly read LW will be aware that this is often a pretty large divergence - but that they will also look for this sort of very recent technology that most hospitals won't have heard about.
This is a new service and it has to interact with the existing medical system, so they are currently expensive, starting at $5,000 for a research report. (Keeping in mind that a basic report involves a lot of work by people who must be good at math.) If you have a sick friend who can afford it - especially if the regular system is failing them, and they want (or you want) their next step to be more science instead of "alternative medicine" or whatever - please do refer them to MetaMed immediately. We can’t all have nice things like this someday unless somebody pays for it while it’s still new and expensive. And the regular healthcare system really is bad enough at science (especially in the US, but science is difficult everywhere) that there's no point in condemning anyone to it when they can afford better.
I also got my hands on a copy of MetaMed's standard list of citations that they use to support points to reporters. What follows isn't nearly everything on MetaMed's list, just the items I found most interesting.
Official LW uncensored thread (on Reddit)
http://www.reddit.com/r/LessWrong/comments/17y819/lw_uncensored_thread/
This is meant as an open discussion thread someplace where I won't censor anything (and in fact can't censor anything, since I don't have mod permissions on this subreddit), in a location where comments aren't going to show up unsolicited in anyone's feed (which is why we're not doing this locally on LW). If I'm wrong about this - i.e. if there's some reason that Reddit LW followers are going to see comments without choosing to click on the post - please let me know and I'll retract the thread and try to find some other forum.
I have been deleting a lot of comments from (self-confessed and publicly designated) trolls recently, most notably Dmytry aka private-messaging and Peterdjones, and I can understand that this disturbs some people. I also know that having an uncensored thread somewhere else is probably not your ideal solution. But I am doing my best to balance considerations, and I hope that having threads like these is, if not your perfect solution, then something that you at least regard as better than nothing.
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