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So let me see if I've got this straight.
Computer Scientists: For some problems, there are random algorithms with the property that they succeed with high probability for any possible input. No deterministic algorithm for these problems has this property. Therefore, random algorithms are superior.
Eliezer: But if we knew the probability distribution over possible inputs, we could create a deterministic algorithm with the property.
Computer Scientists: But we do not know the probability distribution over possible inputs.
Eliezer: Never say "I don't know"! If you are in a state of ignorance, use an ignorance prior.
Now of course the key question is what sort of ignorance prior we should use. In Jaynes's book, usually ignorance priors with some sort of nice invariance properties are used, which makes calculations simpler. For example if the input is a bit stream then we could assume that the bits are independent coinflips. However, in real life this does not correspond to a state of ignorance, but rather to a state of knowledge where we know that the bit stream does not contain predictable correlations. For example, the probability of 1000 zeros in a row according to this ignorance prior is 10^{-300}, which is not even remotely close to the intuitive probability.
The next step is to try to create an ignorance prior which somehow formalizes Occam's razor. As anyone familiar with MIRI's work on the problem of logical priors should know, this is more difficult than it sounds. Essentially, the best solution so far (see "Logical Induction", Garrabrant et al. 2016) is to create a list of all of the ways the environment could contain predictable correlations (or in the language of this post, resemble an "adversarial telepath"), and then trade them off of each other to get a final probability. One of the main downsides of the algorithm is that it is not possible to list all of the possible ways the environment could be correlated (since there are infinitely many), so you have to limit yourself to taking a feasible sample.
Now, it is worth noting that the above paper is concerned with an "environment" which is really just the truth-values of mathematical statements! It is hard to see how this environment resembles any sort of "adversarial telepath". But if we want to maintain the ethos of this post, it seems that we are forced to this conclusion. Otherwise, an environment with logical uncertainty could constitute a counterexample to the claim that randomness never helps.
To be precise, let f be a mathematical formula with one free variable representing an integer, and suppose we are given access to an oracle which can tell us the truth-values of the statements f(1),...,f(N). The problem is to compute (up to a fixed accuracy) the proportion of statements which are true, with the restriction that we can only make n queries, where n << N. Monte Carlo methods succeed with failure probability exponential in n, regardless of what f is.
Now suppose that f is determined by choosing m bits randomly, where m << n, and interpreting them as a mathematical formula (throwing out the results and trying again if it is impossible to do so). Then if the minimum failure probability is nonzero, it is exponential in m, not n, and therefore bigger than the failure probability for Monte Carlo methods. However, any algorithm which can be encoded in less than ~m bits fails with nonzero probability for diagonalization reasons.
In fact, the diagonalization failure is one of the least important ones, the main point is that you just don't know enough about the environment to justify writing any particular algorithm. Any deterministically chosen sequence has a good chance of being correlated with the environment, just because the environment is math and math things are often correlated. Now, we can call this an "adversarial telepath" if we want, but it seems to occur often enough in real life that this designation hardly seems to "carve reality at its joints".
TL;DR: If even math can be called an "adversarial telepath", the term seems to have lost all its meaning.
Never a good idea. Unless you win. Ask the recipient of $100m tax-free whether or not it was a good idea to buy a ticket.
I don't buy lottery tickets, but as much as the chance is so ridiculously small that you might as well burn the ticket as soon as you buy it, that doesn't stop people from winning.
In what sense is this place a graveyard?
A quiet place from which most souls have departed, but which references a lot of accomplishments in days past.
I, too, think the SSC's comment format is unfortunate, but it's up to Scott to do something about it. In fact, I think he treats it as a feature to avoid comment overload.
Oh, good.
You're a bit late, though, LessWrong is mostly a graveyard now. A lot of people from here moved over to the Scott Alexander's blog which is highly recommended.
I'm unlikely to remain in academia after getting the degree. While I was coming to terms with the problems I'd face in academia, I was delighted to learn that there's a non-trivial demand in private industry for people who know how to quantify psychological constructs in a way that produces actionable information.
Hello everyone,
I'm a PhD student in social psychology focusing my time mainly on applied statistics and quantitative methods for the study of brain and behavior. My research focuses on the way that people's goals influence the way they reason and form judgments, but I've also dabbled a bit in self-regulation/self-control.
Perhaps my attraction to this community is based on the fact that I feel that my field is an unfriendly environment for the free exploration of novel or uncommon ideas. Specifically, I suspect that many of the models of human decision-making being put forth by our field over-estimate the tendency for biases/heuristics to lead to errors or poor judgments. For example, few (if any) of my colleagues are aware that our stereotypes of other groups tend to be highly accurate and this effect is one of the largest effects in all of social psychology. It appears that, in many cases, our biases tend to improve accuracy and decision-making quality. However, to utter phrases like "stereotype accuracy" around most social psychologists is to invite suspicion about one's underlying motives. I'm here not because I want to talk about stereotype accuracy in particular, but because I'd like to be able to consider such an idea without the threat of damaging my reputation and career.
I also like thinking about AI and how an (accurate) understanding of human reasoning in information-starved contexts could help us design AI responsibly, but that's just whipped cream.
Wouldn't having three deities instead of one be more complex by their interactions with one another? Even if they existed on separate planes of existence, they would have to all be exerting some kind of influence for them to be gods, no? And in their shared application of influence, would they not be interacting?
I actually don't quite agree (this is the first time I found something new to criticize on one of the sequence posts).
To me, it seems like humility as discussed here is inherently a distortion, that when applied, shifts a conclusion in some way. The reason why it can be a good thing is simply that, if a conclusion is flawed, it can shift it into a better place, sort of a counter-measure to existing biases. it is as if I do a bunch of physical measurements and realize that the value I observe is usually a bit too small, so I just add a certain value to my number every time, hoping to move it closer to the correct one.
However, once I fix my measurement tools, that distortion then becomes negative. Similarly, once I actually get my rationality correct, humility will become negative. In this case, there also seems to be a general tool to get your conclusion fixed, which is to use the outside view rather than the inside view. Applying that to the engineer example:
What about the engineer who humbly designs fail-safe mechanisms into machinery, even though he's damn sure the machinery won't fail? This seems like a good kind of humility to me.
If the engineer used the outside view, he should know that humans are fallible and already conclude that he should spend an appropriate amount of time on fail-safe mechanics. If he then applied humility on top of it, thus downplaying his efforts despite having used the outside-view, it should lead him to worry/work on it more than necessary.
Of course, you could reason that in my example, applying the outside view is itself a form of applying humility. My point is simply that even proper humility doesn't seem to cover any new ground. It's not "part of rationality," so to speak. It's simply a useful tool, practically speaking, to apply when you haven't conquered your biases yet. In that sense, I would argue that, ultimately, the correct way to use humility is not at all / automatically without doing anything.
Again, people sometimes use idiomatic English to describe subjective states of high confidence that do not literally correspond to probabilities greater than 0.999! (Why that specific threshold, anyway?)
You know, I take it back; I actually can't see how this might be confusing.
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