Kurros

• KurrosFeb 5, 2014, 3:25 AM

  7 points

  in reply to: VipulNaik’s comment on: Knigh­tian Uncer­tainty from a Bayesian perspective

  “Jonah was looking at probability distributions over estimates of an unknown probability (such as the probability of a coin coming up heads)”

  It sounds like you are just confusing epistemic probabilities with propensities, or frequencies. I.e, due to physics, the shape of the coin, and your style of flipping, a particular set of coin flips will have certain frequency properties that you can characterise by a bias parameter p, which you call “the probability of landing on heads”. This is just a parameter of a stochastic model, not a degree of belief.

  However, you can have a degree of belief about what p is no problem. So you are talking about your degree of belief that a set of coin flips has certain frequentist properties, i.e. your degree of belief in a particular model for the coin flips.

  edit: I could add that GIVEN a stochastic model you then have degrees of belief about whether a given coin flip will result in heads. But this is a conditional probability: see my other comment in reply to Vanvier. This is not, however, “beliefs about beliefs”. It is just standard Bayesian modelling.

• KurrosFeb 5, 2014, 1:17 AM

  0 points

  in reply to: Vaniver’s comment on: Knigh­tian Uncer­tainty from a Bayesian perspective

  “I view these sorts of distributions over distributions as that- there’s some continuous parameter potentially in the world (the proportion of white and black balls in the urn), and that continuous parameter may determine my subjective probability about binary events (whether ball #1001 is white or black).”

  To me this just sounds like standard conditional probability. E.g. let p(x|I) be your subjective probability distribution over the parameter x (fraction of white balls in urn), given prior information I. Then

  p(“ball 1001 is white”|I) = integral_x { p(“ball 1001 is white”|x,I)*p(x|I) } dx

  So your belief in “ball 1001 is white” gets modulated by your belief distributions over x, sure. But I wouldn’t call this a “distribution over a distribution”. Yes, there is a set of likelihoods p(“ball 1001 is white”|x,I) which specify your subjective degree of belief in “ball 1001 is white” GIVEN various x, but in then end you want your degree of belief in “ball 1001 is white” considering ALL values that x might have and their relative plausibilities, i.e. you want the marginal likelihood to make your predictions.

  (my marginalisation here ignores hypotheses outside the domain implied by there being a fraction of balls in the urn...)

• KurrosFeb 3, 2014, 4:30 AM

  0 points

  in reply to: Manfred’s comment on: Foun­da­tions of Probability

  Lol ok, so long as I get my answer eventually :p.

• KurrosFeb 3, 2014, 3:19 AM

  0 points

  in reply to: Manfred’s comment on: Foun­da­tions of Probability

  Was the “Putting in the Numbers” post the one you were referring to? You didn’t post that on Saturday, but now it is Monday and there doesn’t seem be a third post. Anyway I did not see this question answered anywhere in “Putting in the Numbers”...

• KurrosJan 31, 2014, 8:24 AM

  1 point

  in reply to: Manfred’s comment on: Put­ting in the Numbers

  Yeah I think integral( p*log(p) ) is it. The simplest problem is that if I have some parameter x to which I want to assign a prior (perhaps not over the whole real set, so it can be proper as you say—the boundaries can be part of the maxent condition set), then via the maxent method I will get a different prior depending on whether I happen to assign the distribution over x, or x^2, or log(x) etc. That is, the prior pdf obtained for one parameterisation is not related to the one obtained for a different parameterisation by the correct transformation rule for probability density functions; that is, they contain logically different information. This is upsetting if you have no reason to prefer one parameterisation or another.

  In the simplest case where you have no constraints except the boundaries, and maybe expect to get a flat prior (I don’t remember if you do when there are boundaries… I think you do in 1D at least) then it is most obvious that a prior flat in x contains very different information to one flat in x^2 or log(x).

• KurrosJan 30, 2014, 11:54 PM

  2 points

  on: Put­ting in the Numbers

  Refering to this:

  “Simply knowing the fact that the entropy is concave down tells us that to maximize entropy we should split it up as evenly as possible—each side has a ¹⁄₄ chance of showing.”

  Ok, that’s fine for discrete events, but what about continuous ones? That is, how do I choose a prior for real-valued parameters that I want to know about? As far as I am aware, MAXENT doesn’t help me at all here, particularly as soon as I have several parameters, and no preferred parameterisation of the problem. I know Jaynes goes on about how continuous distributions make no sense unless you know the sequence whose limit you took to get there, in which case problem solved, but I have found this most unhelpful in solving real problems where I have no preference for any particular sequence, such as in models of fundamental physics.

• KurrosJan 30, 2014, 11:36 PM

  5 points

  in reply to: So8res’s comment on: On sav­ing the world

  It would have been kind of impossible to work on AI in 1850, before even modern set theory was developed. Unless by work on AI, you mean work on mathematical logic in general.

• KurrosJan 30, 2014, 8:10 AM

  0 points

  in reply to: Manfred’s comment on: Foun­da­tions of Probability

  Ok, but do you really mean that sentence how it is written? To me it means the same thing as saying that assigning probability to anything is logically equivalent to assigning probability to 0=1 (which I am perfectly happy to do so if that is the point then fine, but that doesn’t seem to be your implication)

• KurrosJan 30, 2014, 4:19 AM

  0 points

  on: Foun­da­tions of Probability

  “But to assign some probability to the wrong answer is logically equivalent to assigning probability to 0=1.”

  Only if you know it is the wrong answer. You say the robot doesn’t know, so what’s the problem? We assign probabilities to propositions which are wrong all the time, before we know if they are wrong or not.

• KurrosDec 10, 2013, 10:37 PM

  2 points

  in reply to: A1987dM’s comment on: The Statis­ti­cian’s Fallacy

  The statistics also remains important at the frontier of high energy physics. Trying to do reasoning about what models are likely to replace the Standard Model is plagued by every issue in the philosophy of statistics that you can imagine. And the arguments about this affect where billions of dollars worth of research funding end up (build bigger colliders? more dark matter detectors? satellites?)

• KurrosNov 27, 2013, 10:49 PM

  1 point

  in reply to: hyporational’s comment on: 2013 Less Wrong Cen­sus/​Survey

  I can’t disagree with that :p. I will concede that the survey question needs some refinement.

• KurrosNov 27, 2013, 10:43 PM

  1 point

  in reply to: scav’s comment on: 2013 Less Wrong Cen­sus/​Survey

  Hmm, I couldn’t agree with that later definition. Physics is just the “map” after all, and we are always improving it. Mathematics (or some future “completed” mathematics) seems to me the space of things that are possible. I am not certain, but this might be along the lines of what Wittgenstein means when he says things like

  “In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.

  If things can occur in atomic facts, this possibility must already lie in them.

  (A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)” (from the Tractatus—possibly he undoes all this in his later work, which I have yet to read...)

  This is a tricky nest of definitions to unravel of course. I prefer to not call anything supernatural unless it lies outside the “true” order of reality, not just if it isn’t on our map yet. I am a physicist though, and it is hard for me to see the logical possibility of anything outside the “true” order of the universe. Nevertheless, it seems to me like this is what people intend when they talk about God. But then they also try to prove that He must exist from logical arguments. These goals seem contradictory to me, but I guess that’s why I’m an athiest :p.

  I don’t know where less “transcendant” supernatural entities fit into this scheme of course. Magic powers and vampires etc need not neccessarily defy logical description, they just don’t seem to exist.

  I agree that in the end, banishing the word supernatural is probably the easiest way to go :p.

• KurrosNov 27, 2013, 9:02 AM

  1 point

  in reply to: ialdabaoth’s comment on: 2013 Less Wrong Cen­sus/​Survey

  But don’t you think there is an important distinction between events that defy logical description of any kind, and those that merely require an outlandish multi-layered reality to explain? I admit I can’t think of anything that could occur in our world that cannot be explained by the simulation hypothesis, but assuming that some world DOES exist outside the layers of nested simulation I can (loosely speaking) imagine that some things really are logically impossible there. And that if the inhabitants of that world observe such impossible events, well, they will wrongly concluded that they are in a simulation, but actually there will be truly supernatural happenings afoot.

  I mention this somewhat pointless story just because religious philosophers would generally not accept that God is merely supernatural in your sense, I think they would insist on something closer to my sense, nonsense though it may be.

• KurrosNov 27, 2013, 8:49 AM

  1 point

  in reply to: scav’s comment on: 2013 Less Wrong Cen­sus/​Survey

  I’m no theologian, but it seems to me that this view of the supernatural does not conform to the usual picture of God philosophers put forward, in terms of being the “prime mover” and so on. They are usually trying to solve the “first cause” problem, among other things, which doesn’t really mesh with God as the super-scientist, since one is still left wondering about where the world external to the simulation comes from.

  I agree that my definition of the supernatural is not very useful in practice, but I think it is necessary if one is talking about God at all :p. What other word should we use? I quite like your suggested “extra-natural” for things not of this world, which leaves supernatural for things that indeed transcend the constraints of logic.

• KurrosNov 26, 2013, 12:40 AM

  3 points

  in reply to: hyporational’s comment on: 2013 Less Wrong Cen­sus/​Survey

  To me, the simulation hypothesis definitely does not imply a supernatural creator. ‘Supernatural’ implies ‘unconstrained by natural laws’, at least to me, and I see no reason to expect that the simulation creators are free from such constraints. Sure, it means that supernatural-seeming events can in principle occur inside the simulation, and the creators need not be constrained by the laws of the simulation since they are outside of it, but I fully expect that some laws or other would govern their behaviour.

• KurrosNov 26, 2013, 12:27 AM

  2 points

  in reply to: aspera’s comment on: 2013 Less Wrong Cen­sus/​Survey

  You don’t think people here have a term for their survey-completing comrades in their cost function? Since I probably won’t win either way this term dominated my own cost function, so I cooperated. An isolated defection can help only me, whereas an isolated cooperation helps everyone else and so gets a large numerical boost for that reason.

• KurrosNov 26, 2013, 12:08 AM

  2 points

  in reply to: Ander’s comment on: 2013 Less Wrong Cen­sus/​Survey

  Lol, I cooperated because $60 was not a large enough sum of money for me to really care about trying to win it, and in the calibration I assumed most people would feel similarly. Reading your reasoning here, however, it is possible I should have accounted more strongly for people who like to win just for the sake of winning, a group that may be larger here than in the general population :p.

  Edit: actually that’s not really what I mean. I mean people who want to make a rational choice to maximum the probability of winning for its own sake, even if they don’t actually care about the prize. I prefer someone gets $60 and is pleasantly surprised to have won, than I get $1. I predict that overall happiness is increased more this way, at negligible cost to myself. Even if the person who wins defected.

• KurrosNov 26, 2013, 12:02 AM

  3 points

  in reply to: jpet’s comment on: 2013 Less Wrong Cen­sus/​Survey

  It defined “God” as supernatural didn’t it? In what sense is someone running a simulation supernatural? Unless you think for some reason that the real external world is not constrained by natural laws?

• KurrosNov 23, 2013, 10:34 PM

  2 points

  in reply to: CronoDAS’s comment on: [Tran­script] Richard Feyn­man on Why Questions

  In this case, Feynman is worth listening to slowly. There is something about the way he explains this that the transcript does not do justice to.

• KurrosNov 15, 2013, 11:51 PM

  3 points

  in reply to: jockocampbell’s comment on: The dan­gers of zero and one

  When you prove something in mathematics, at very least you implicitly assume you have made no mistakes anywhere, are not hallucinating, etc. Your “real” subjective degree of belief in some mathematical proposition, on the other hand, must take all these things into account.

  For practical purposes the probability of hallucinations etc. may be very small and so you can usually ignore them. But the OP is right to demonstrate that in some cases this is a bad approximation to make.

  Deductive logic is just the special limiting case of probability theory where you allow yourself the luxury of an idealised box of thought isolated from “real world” small probabilities.

  edit: Perhaps I could say it a different way. It may be reasonable for certain conditional probabilities to be zero or one, so long as they are conditioned on enough assumptions, e.g. P(“51 is a prime” given “I did my math correctly, I am not hallucinating, the external world is real, etc...”)=1 might be achievable. But if you try to remove the conditional on all that other stuff you cannot keep this certainty.