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How do we assign zero probability to 0=1 when we can't prove our logic consistent?
Concern trolling in the false flag political operation sense is a thing that happened
An example of this occurred in 2006 when Tad Furtado, a staffer for then-Congressman Charles Bass (R-NH), was caught posing as a "concerned" supporter of Bass' opponent, Democrat Paul Hodes, on several liberal New Hampshire blogs, using the pseudonyms "IndieNH" or "IndyNH". "IndyNH" expressed concern that Democrats might just be wasting their time or money on Hodes, because Bass was unbeatable.[37][38] Hodes eventually won the election.
Does fundamentalist Christianity indicate that the believer would be irrational about issues other than religion?
If yes, what's the difference?
You could spend the tax-evaded income on the black market, since you're hiding contraband from the police anyway.
Since when did epistemic rationality demand making the truth common knowledge? It just means you should know what's true yourself.
Different information about part of nature is not sufficient to change an inference--the probabilities could be independent of the researcher's intentions.
It depends on your priors
One of his "desiderata", his principles of construction, is that the robot gives equal plausibility assignments to logically equivalent statements
I don't see this desiderata. The consistency requirement is that if there are multiple ways of calculating something, then all of them yield the same result. A few minutes of thought didn't lead to any way of leveraging a non 1 or zero probability for Prime(53) into two different results.
If I try to do anything with P(Prime(53)|PA), I get stuff like P(PA|Prime(53)), and I don't have any idea how to interpret that. Since PA is a set of axioms, it doesn't really have a truth value that we can do probability with. Technically speaking, Prime(N) means that the PA axioms imply that 53 has two factors. Since the axioms are in the predicate, any mechanism that forces P(Prime(53)) to be one must do so for all priors.
One final thing: Isn't it wrong to assign a probability of zero to Prime(4), i.e. PA implies that 4 has two factors, since PA could be inconsistent and imply everything?
You can skip this pararaph and the next if you're familiar with the problem. But if you're not, here's an illustration. Suppose your friend has some pennies that she would like to arrange into a rectangle, which of course is impossible if the number of pennies is prime. Let's call the number of pennies N. Your friend would like to use probability theory to guess whether it's worth trying; if there's a 50% chance that Prime(N), she won't bother trying to make the rectangle. You might imagine that if she counts them and finds that there's an odd number, this is evidence of Prime(N); if she furthermore notices that the digits don't sum to a multiple of three, this is further evidence of Prime(N). In general, each test of compositeness that she knows should, if it fails, raise the probability of Prime(N).
But what happens instead is this. Suppose you both count them, and find that N=53. Being a LessWrong reader, you of course recognize from recently posted articles that N=53 implies Prime(N), though she does not. But this means that P(N=53) <= P(Prime(N)). If you're quite sure of N=53—that is, P(N=53) is near 1—then P(Prime(N)) is also near 1. There's no way for her to get a gradient of uncertainty from simple tests of compositeness. The probability is just some number near 1.
I don't understand why this is a problem. You and your friend have different states of knowledge, so you assign different probabilities.
Survey Taken
*I keep seeing probability referred to as an estimation of how certain you are in a belief. And while I guess it could be argued that you should be certain of a belief relative to the number of possible worlds left or whatever, that doesn't necessarily follow. Does the above explanation differ from how other people use probability?
One can ground probability in Cox's Theorem, which uniquely derives probability from a few things we would like our reasoning system to do.
Why should anyone expect a specific kind of word input to be capable of persuading everyone? They're just words, not magic spells.
The specific word sequence is evidence for something or other. It's still unreasonable to expect people to respond to evidence in every domain, but many people do respond to words, and calling them just sounds in air doesn't capture the reasons they do so.
I wouldn't call it orthogonal either. Rationality is about having correct beliefs, and I would label a belief-based litmus test rational to the extent it's correct.
Writing a post about how $political_belief is a litmus test is probably a bad idea because of the reasons you mentioned.
I generally agree with this post, but since people's beliefs are evidence for how they change their beliefs in response to evidence, I would call it bias-inducing and usually tribal cheering instead of totally backwards.
Hash functions map multiple inputs to the same hash, so you would need to limit the input in some other way, and that makes it harder to verify.
The usual formulation of Omega does not lie.
If Omega maintains a 99.9% accuracy rate against a strategy that changes its decision based on the lottery numbers, it means that Omega can predict the lottery numbers. Therefore, if the lottery number is composite, Omega has multiple choices against an agent that one-boxes when the numbers are different and two-boxes when the numbers are the same: it can pick the same composite number as the lottery, in which case the agent will two-box and earn 2,001,000, or it can pick a different prime number, and have the agent one-box and earn 3,001,000. It seems like the agent that one-boxes all the time does better by eliminating the cases where Omega selects the same number as the lottery, so I would one box.
Above the top-level comment box, there's an option to sort comments by date. Perhaps that should be the default.
But if we're 99.9% confident that a child is going to die (say, they have a very terminal disease), is being cruel to the child 99.99% less bad?
First-years can't cast AK for reasons of raw magical power, so an organization of first-years can't use the Killing Curse as a membership criteria.
Perhaps the only difference between fake gold and real gold is magical--if there's a ritual that permanently transfigures a rock into gold, people can switch that with the gold in vaults. Of course, no one in the magical world would accept transfigured gold as payment.
Dumbledore may be able to overrule the contract, but that would do little to stop the political effects of Harry's statement that Lucius did not kill Hermione. Since it would also reinstate the debt, it doesn't seem like a net benefit to Dumbledore.
Here's a situation where an anecdote should reduce our confidence in a belief:
- A person's beliefs are usually well-supported.
- When he offers supporting evidence, he usually offers the strongest evidence he knows about.
If this person were to offer an anecdote, it should reduce our confidence in his proposition, because it makes it unlikely he knows of stronger supporting evidence.
I don't know how applicable this is to actual people.
I would raise a hypothesis to consideration because someone was arguing for it, but I don't think anecdotes are good evidence in that I would have similar confidence in a hypothesis supported by an anecdote, and a hypothesis that is flatly stated with no justification. The evidence to raise it to consideration comes from the fact that someone took the time to advocate it.
This is more of a heuristic than a rule, because there are anecdotes that are strong evidence ("I ran experiments on this last year and they didn't fit"), but when dealing with murkier issues, they don't count for much.
A related mistake I made was to be impressed by the cleverness of the aphorism "The plural of 'anecdote' is not 'data'." There may be a helpful distinction between scientific evidence and Bayesian evidence. But anecdotal evidence is evidence, and it ought to sway my beliefs.
Anecdotal evidence is filtered evidence. People often cite the anecdote that supports their belief, while not remembering or not mentioning events that contradict them. You can find people saying anecdotes on any side of a debate, and I see no reason the people who are right would cite anecdotes more.
Of course, if you witness an anecdote with your own eyes, that is not filtered, and you should adjust your beliefs accordingly.
I made a hash of that comment; I'm sorry.
If we were to put a bunch of chickens into a room, and on one side of the room was a wolf, and the other side had factory farming cages that protected the chickens from the wolf, I would expect the chickens to run into the cages.
It's true that chickens can comprehend a wolf much better than they can comprehend factory farming, but I'm not quite sure how that affects this thought experiment.
It takes a bit of work to set up, but Tagtime does both the notifications and the logging
There's a bit of a problem with the claim that nobody knows what's what: the usual procedure when someone lacks knowledge is to assign an ignorance prior. The standard methods for generating ignorance priors, usually some formulation of Occam's razor, assign very low probability to claims as complex as common religions.
What do you mean by not rational? People reporting higher satisfaction when they're rich even though they feel less happiness?
Isn't there an irony in belonging to an organisation dedicated to the plight of sentient but cognitively humble beings in the imminent face of vastly superior intelligence and claiming that the plight of sentient but cognitively humble beings in the face of vastly superior intelligence is of no ethical consequence whatsoever. Insofar as we want a benign outcome for humans, I'd have thought that the computational equivalent of Godlike capacity for perspective-taking is precisely what we should be aiming for.
No. Someone who cares about human-level beings but not animals will care about the plight of humans in the face of an AI, but there's no reason they must care about the plight of animals in the face of humans, because they didn't care about animals to begin with.
It may be that the best construction for a friendly AI is some kind of complex perspective taking that lends itself to caring about animals, but this is a fact about the world; it falls on the is side of the is-ought divide.
Also, 100% certainty can't be impossible, because impossibility implies that it is 0% likely, which would be a self-defeating argument. You may find it highly improbable that I can truly be 100% certain. What probability do you assign to me being able to assign 100% probability?
When I say 100% certainty is impossible, I mean that there are no cases where assigning 100% to something is correct, but I have less than 100% confidence in this claim. It's similar to the claim that it's impossible to travel faster than the speed of light.
I'm already taking insects or nematodes into consideration probabilistically; I think it is highly unlikely that they are sentient, and I think that even if they are sentient, their suffering might not be as intense as that of mammals, but since their numbers are so huge, the well-being of all those small creatures makes up a non-negligible term in my utility function.
A priori, it seems that the moral weight of insects would either be dominated by their massive numbers or by their tiny capacities. It's a narrow space where the two balance and you get a non-negligible but still-not-overwhelming weight for insects in a utility function. How did you decide that this was right?
It's not really fair to call a range of .02 to 65.92 four digit precision just because the upper bound was written with four digits.
In order to bound the states at a number n, it would need to assign probability zero to ever getting an upgrade allowing it to access log n bytes of memory. I don't know how this zero-probability assignment would be justified for any n--there's a non-zero probability that one's model of physics is completely wrong, and once that's gone, there's not much left to make something impossible.
Er, now I see that Eliezer's post is discussing finite sets of physical laws, which rules out the cosmological horizon diagonalization. But, I think this causal models as function mapping fails in another way: we can't predict the n in n-valued future experiential states. Before the camera was switched, B9 would assign low probability to these high n-valued experiences. If B9 can get a camera that allows it to perceive color, it could also get an attachment that allows it to calculate the permittivity constant to arbitrary precision. Since it can't put a bound on the number of values in the L states, the set is uncountable and so is the set of functions.
But the set of causal models is not the set of experience mappings. The model where things disappear after they cross the cosmological horizon is a different model than standard physics, even though they predict the same experiences. We can differentiate between them because Occam's Razor favors one over the other, and our experiences give us ample cause to trust Occam's Razor.
At first glance, it seems this gives us enough to diagonalize models--1 meter outside the horizon is different from model one, two meters is different from model two...
There might be a way to constrain this based on the models we can assign different probabilities to, given our knowledge and experience, which might get it down to countable numbers, but how to do it is not obvious to me.
Causal models are countable? Are irrational constants not part of causal models?
Let's say someone is eating pizza for 20% of their meals. Do you think that replacing pizza with Soylent would result in a worse diet?
That depends on the knowledge that the AI has. If B9 had deduced the existence of different light wavelengths, and knew how blue corresponded to a particular range, and how human eyes see stuff, the probability would be something close to the range of colors that would be considered blue divided by the range of all possible colors. If B9 has no idea what blue is, then it would depend on priors for how often statements end up being true when B9 doesn't know their meaning.
Without knowing what B9's knowledge is, the problem is under-defined.
Anecdotally, I know nobody who has suffered a nutritional deficiency as lethal as zero iron, and the diets in my circle of college students are not very good. I think Soylent will be healthier than my current diet, but I also think the chance of serious nutritional deficiencies is higher.
Edit: To be clear, I'm talking about nutritional deficiencies where one's metabolism starts to fail for want of a crucial element, not deficiencies where someone is consuming marginally less of a nutrient than the optimal amount. I think Soylent will be better than my current diet in the latter category.
Because if something goes wrong, the things you are breaking will be people's well-being. There were two instances where Rob noticed that he was feeling ill and had to correct a nutritional deficiency on the fly. It's less likely that this will happen during large-scale production, but if it does, the people consuming exclusively Soylent will not have all the knowledge Rob did wrt the formula or the symptoms of nutritional deficiency.
I think Soylent is a good idea, and ordered a week's supply, but I'm going to try it slowly; I think the chance that they screw up the production is large enough to merit caution.
"Move fast and break things" is not a good mantra when dealing with nutrition.
Objectivisim includes an ethic that many here dislike.
Or rather, I think that genetics possibly plays a large role now, but that if we raised people better than we could essentially eliminate these issues without focusing on genes.
What model of hereditary intelligence predicts significant hereditary differences in the current environment and negligible differences in an environment where people are raised better?
x + 0 = 0
I think you mean x + 0 = x
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Probability Theory: The logic of science is available in postscript form at