dankane

Karma: 244

dankane Mar 13, 2014, 6:20 AM
0 points
on: The Problem with AIXI
So what happens when AIXI determines that there’s this large computer, call it BRAIN whose outputs tend to exactly correlate with its outputs? AIXI may then discover the hypothesis that the observed effects of AIXI’s outputs on the world are really caused by BRAIN’s outputs. It may attempt to test this hypothesis by making some trivial modification to BRAIN so that it’s outputs differ from AIXI’s at some inconsequential time (not by dropping an anvil on BRAIN, because this would be very costly if the hypothesis is true). After verifying this, AIXI may then determine that various hardware improvements to BRAIN will cause its outputs to more closely match the theoretical Solomonoff Inductor, thus improving AIXI’s long term payoff.

I mean, AIXI is waaaay too complicated for me to actually properly predict, but is this scenario actually so unreasonable?

dankane Jan 1, 2014, 7:10 PM
0 points
in reply to: Liron’s comment on: A proposed inefficiency in the Bitcoin markets
Well, rather then modelling the price at time t by exp(B t) were B is a Brownian motion, you could model it by exp(B t—c*t) for some constant c.

On a more basic level instead of saying that after a day the price will be multiplied by either 0.9 or 1.111 with equal probability, you could have the price multiplied by either 0.9 or 1.1 with equal probability. In the later case, the expected value tomorrow is exactly the value today. On the other hand, because 0.9*1.1 < 1, this later process will end up at 0 in the long run almost surely. Then again, this model would probably only work as a first order approximation to the behavior anyway. If bitcoin ever does manage to become a competitive major currency, its volatility would almost have to decrease drastically.

dankane Dec 30, 2013, 4:39 AM
0 points
on: A proposed inefficiency in the Bitcoin markets
Given that it sounds like nobody has actually run the numbers, is there a reason to suspect that bitcoin prices are best modeled by a uniform random walk on the log scale? If it is modeled instead by a weighted random walk with an appropriate negative drift term the expected value of a BTC tomorrow could be exactly equal to today’s expected value (or more exactly today’s value adjusted for inflation).

dankane Nov 30, 2013, 7:28 AM
0 points
in reply to: PeterisP’s comment on: The dangers of zero and one
Yes. I agree. I am certainly not trying to say that 99.99% confidence in the primality status of a four digit number is not achievable.

dankane Nov 22, 2013, 8:31 AM
50 points
on: 2013 Less Wrong Census/Survey
Took the survey. Note: “average” is not a very precise term. For one, “average person” is probably a mediocre stand-in for “typical person” (since there isn’t actually a commonly accepted way to take averages of people). Furthermore, questions like “How long, in approximate number of minutes, do you spend on Less Wrong in the average day?” are actually highly ambiguous. The arithmetic mean of times that I spend on Less Wrong over days is substantially different from the median time.

dankane Nov 22, 2013, 8:04 AM
0 points
in reply to: gjm’s comment on: The dangers of zero and one
OK. I agree. Checking the output on numbers less than 100 vastly decreases the probability of error, especially after enumerating simple errors and realizing that none of them would return anything remotely correct on those numbers.

dankane Nov 20, 2013, 5:27 AM
1 point
in reply to: gjm’s comment on: The dangers of zero and one
Can you really be sure that a program that you write has at least a 99.9% chance of being correct without performing moderately extensive testing? Personally, I’d probably put significantly more confidence in (b).

dankane Nov 3, 2013, 7:10 PM
1 point
in reply to: Eliezer Yudkowsky’s comment on: Lone Genius Bias and Returns on Additional Researchers
OK. Granted. Even a belief that the AMF is better at affecting intelligence explosions is unlikely to justify the claim that it is the best, and thus not justify the behavior described.

dankane Nov 2, 2013, 6:07 PM
5 points
in reply to: lukeprog’s comment on: Lone Genius Bias and Returns on Additional Researchers
They could also reasonably believe that marginal donations to the organizations listed would not reliably influence an intelligence explosion in a way that would have significant positive impact on the value of the far future. They might also believe that AMF donations would have a greater impact on potential intelligence explosions (for example, because an intelligence explosion is so far into the future that the best way to help is to ensure human prosperity up to the point where GAI research actually becomes useful).

dankane Jun 23, 2013, 3:19 PM
0 points
in reply to: Will_Sawin’s comment on: Robust Cooperation in the Prisoner’s Dilemma
If you do that, you’re back in the same situation that you started with and are cooperating with CooperateBot again.

dankane Jun 20, 2013, 9:24 PM
0 points
in reply to: Will_Sawin’s comment on: Robust Cooperation in the Prisoner’s Dilemma
Proposal 1 runs into the problem that it does not cooperate with itself if the two copies have slightly different bounds on proof lengths. Since if A cooperates, you can (with a not too long proof) show that B did not find a contradiction. But this contradicts the bounded version of the incompleteness theorem.

A similar problem holds for Proposal 2.

dankane Jun 8, 2013, 7:34 PM
2 points
in reply to: dankane’s comment on: Robust Cooperation in the Prisoner’s Dilemma
Ah, never mind I see it. You just need to modify the proof of Lob’s Theorem. Instead of using L = (there exists a proof of L) → S you instead use L = (there exists a proof of L of length at most Ackermann(10)) → S and the rest of the proof of Lob’s Theorem still works.

dankane Jun 8, 2013, 7:25 PM
0 points
on: Robust Cooperation in the Prisoner’s Dilemma
I’m not convinced that FairBot cooperates with itself. If we call the statement that FairBot self-cooperates S, then it is not the case that we know that (There exists a proof of S) → S [which would imply S by Lob’s Theorem]. Instead, what we know is (There exists a proof of S of length at most Ackermann(20)) → S. I’m not convinced that this is enough to conclude S. In fact, I am somewhat doubtful that S is true.

In particular, I can also prove (There exists a proof of (not S) of length at most Ackermann(20)) → (not S). This is by case analysis:
1. If S is false: By simulating FairBot, I can prove not S, and thus the statement
2. If S is true: Since the axioms are consistent, there is no proof of (not S). Thus, by enumerating all proofs of length at most Ackermann(20), I can prove that there is no proof of (not S) of at most this length, thus proving the above statement. Then again, it is likely that any proof of this implication would need to be longer than Ackermann(20)...
On the other hand, you do need more than Lob’s Theorem to prove that FairBot self-cooperates. Anybody know enough logic to resolve this issue?

dankane May 6, 2013, 11:47 PM
2 points
on: Pascal’s Muggle: Infinitesimal Priors and Strong Evidence
This system does seem to lead to the odd effect that you would probably be more willing to pay Pascal’s Mugger to save 10^10^100 people than you would be willing to pay to save 10^10^101 people, since the leverage penalties make them about equal, but the latter has a higher complexity cost. In fact the leverage penalty effectively means that you cannot distinguish between events providing more utility than you can provide an appropriate amount of evidence to match.

dankane Jan 16, 2013, 7:33 PM
0 points
in reply to: dankane’s comment on: Second-Order Logic: The Controversy
Actually, here’s maybe a better way of saying what I’m trying to get at here: What evidence would actually convince you that we lived in a universe given by a non-standard model of the natural numbers?

Before you say “I run a computer program which returns a proof of 0=1 in PA”, think about it for a while. Ignoring the fact that in practice, you would probably suspect that the proof is wrong, might you instead take this as evidence that PA is actually inconsistent. After all, Godel tells us that we can’t really be sure about that. In fact, if you did live in a nonstandard model of PA, and found a nonstandard proof of 0=1, wouldn’t it feel from the inside like you found an inconsistency in PA rather than that you found a nonstandard number?

dankane Jan 9, 2013, 7:29 PM
1 point
in reply to: Rob Bensinger’s comment on: Second-Order Logic: The Controversy

Even though there are more complicated universes that perfectly generate our observations to date than there are simple universes that do so, given proper subsets of our universe, assuming a structurally simple universe tends to yield more accurate predictions than does assuming a structurally complex universe.

But when we are talking about which model of set theory to use to model our experiences, all of the non-standard models give exactly the same predictions to date (and will continue to do so until we reach non-standard times). And not all of these models are horribly complicated. There’s the model of constructable set theory, where you only have the sets absolutely guaranteed you by the axioms. This gives you a countable model of set theory (and hence not the standard one), but it is still easily describable.

dankane Jan 9, 2013, 7:33 AM
1 point
in reply to: Rob Bensinger’s comment on: Second-Order Logic: The Controversy
I guess here’s my point. We would not expect to have seen any empirical differences between standard and non-standard models of spacetime yet. There would not be any observable differences until we reach supernatural times. I suppose you might discount the nonstandard models based on their not being computable or something, but I’m not convinced that this is the right thing to do. I also agree that the standard model should be given more weight (due to its conceptual simplicity to pin down) than any particular nonstandard model, but I don’t see why it should be given more weight than all of them put together. The even more concise (or at least less potentially problematic) theory would be to say that we are living in some model of these axioms and not bother to specify which.

dankane Jan 9, 2013, 1:08 AM
2 points
on: Second-Order Logic: The Controversy
Eliezer—why is it that you seem to adamant that our physical reality is better modeled by the standard natural numbers rather than some supernatural model? If we try to see whether a physical implementation of a Turing machine provides an inconsistency in PA, then of course it won’t because it will run for fewer than Ackermann(20) iterations, and all number theories say that it won’t halt by then. If we instead lived in something that looked like the game of life and we did expect it to last infinitely long why exactly would we expect time steps to be indexed by some particular model of the natural numbers when we haven’t yet seen more than finitely many of them (and those finitely many are predicted in all models). Claiming that we don’t expect the Turing machine to ever halt because it hasn’t yet seems a little like saying that all times I’ve seen come before 2014, and therefore I expect that all times ever will have this property.

dankane Nov 5, 2012, 4:24 AM
4 points
in reply to: juliawise’s comment on: Voting is like donating thousands of dollars to charity
On the other hand, it seems to me like the differences between the foreign policies of the two candidates don’t seem nearly as significant as the differences in their domestic policies. Furthermore, problems like malaria would be best dealt with through foreign aid budgets, which really aren’t that big to begin with. In any case, I think my point stands that the value of an “altruistic dollar” in this context is significantly less than the value of an actual dollar donated to an optimal charity.

dankane Nov 5, 2012, 2:38 AM
13 points
on: Voting is like donating thousands of dollars to charity
On the other hand, if you want to strictly adhere to utilitarian principles, you would probably have to note that the “altruistic dollars” obtained through selection of the better candidate probably produce much less utility per dollar than a dollar donated to one of givewell.org’s top rated charities. Standards of living in the US are already so high that a marginal dollar is worth much less than a marginal dollar in a less developed country. Then again, if you really followed this philosophy and lived in the US, you should probably actually devoting essentially all of your time to earning money to donate to such charities, which is not something that many people are actually willing to do.