What is the advantage of the Kolmogorov complexity prior? 2012-02-16T01:51:26.001Z


Comment by skepsci on What Bayesianism taught me · 2013-09-03T15:16:11.680Z · LW · GW

I think the dichotomy between procedural knowledge and object knowledge is overblown, at least in the area of science. Scientific object knowledge is (or at least should be) procedural knowledge: it should enable you to A) predict what will happen in a given situation (e.g. if someone drops a mento into a bottle of diet coke) and B) predict how to set up a situation to achieve a desired result (e.g. produce pure L-glucose).

Comment by skepsci on Reality is weirdly normal · 2013-09-03T14:55:31.792Z · LW · GW

Humans have a preference for simple laws because those are the ones we can understand and reason about. The history of physics is a history of coming up with gradually more complex laws that are better approximations to reality.

Why not expect this trend to continue with our best model of reality becoming more and more complex?

Comment by skepsci on Reality is weirdly normal · 2013-09-03T14:51:56.511Z · LW · GW

This is trivially false. Imagine, for the sake of argument, that there is a short, simple set of rules for building a life permitting observable universe. Now add an arbitrary, small, highly complex perturbation to that set of rules. Voila, infinitely many high complexity algorithms which can be well-approximated by low complexity algorithms.

Comment by skepsci on To what degree do you model people as agents? · 2013-09-03T14:45:46.064Z · LW · GW

I model basically everyone I interact with as an agent. This is useful when trying to get help from people who don't want to help you, such as customer service or bureaucrats. By giving the agent agency, it's easy to identify the problem: the agent in question wants to get rid of you with the least amount of effort so they can go back to chatting with their coworkers/browsing the internet/listening to the radio. The solution is generally to make it seem like less effort to get rid of you by helping you with your problem (which is their job after all) than something else. This can be done by simply insisting on being helped, making a ruckus, or asking for a manager, depending on the situation.

Comment by skepsci on To what degree do you model people as agents? · 2013-09-03T14:37:30.953Z · LW · GW

I do the same sort of thinking about the motivations of other drivers, but it seems strange to me to phrase the question as "what does he know that I don't?" More often than not, the cause of strange driving behaviors is lack of knowledge, confusion, or just being an asshole.

Some examples of this I saw recently include 1) a guy who immediately cut across two lanes of traffic to get in the exit lane, then just as quickly darted out of it at the beginning of the offramp; 2) A guy on the freeway who slowed to a crawl despite traffic moving quickly all around him; 3) That guy who constantly changes lanes in order to move just slightly faster than the flow of traffic.

I'm more likely to ask "what do they know that I don't?" when I see several people ahead of me act in the same way that I can't explain (e.g. many people changing lanes in the same direction).

Comment by skepsci on Open Problems Related to Solomonoff Induction · 2013-08-18T16:56:25.039Z · LW · GW

If there's some uncomputable physics that would allow someone to build such a device, we ought to redefine what we mean by computable to include whatever the device outputs. After all, said device falsifies the Church-Turing thesis, which forms the basis for our definition of "computable".

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-15T05:14:34.440Z · LW · GW

Perhaps it terminates in the time required proving that A defects and B cooperates, even though the axioms were inconsistent, and one could also have proved that A cooperates and B defects.

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-14T14:21:55.541Z · LW · GW

How will you know? The set of consistent axiom systems is undecidable. (Though the set of inconsistent axioms systems is computably enumerable.)

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-14T05:10:51.604Z · LW · GW

What happens if the two sets of axioms are individually consistent, but together are inconsistent?

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-14T04:57:43.862Z · LW · GW

Your source code is your name. Having an additional name would be irrelevant. It is certainly possible for bots to prove they cooperate with a given bot, by looking at that particular bot's source. It would, as you say, be much harder for a bot to prove it cooperates with every bot equivalent to a given bot (in the sense of making the same cooperate/defect decisions vs. every opponent).

Rice's theorem may not be as much of an obstruction as you seem to indicate. For example, Rice's theorem doesn't prohibit a bot which proves that it defects against all defectbots, and cooperates with all cooperatebots. Indeed, you can construct an example of such a bot. (Rice's theorem would, however, prevent constructing a bot which cooperates with cooperatebots and defects against everyone else.)

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-13T20:04:43.038Z · LW · GW

What's wrong with "I will cooperate with anyone who verifiably asserts that they cooperate with me". A program could verifiably assert that by being, e.g., cooperatebot. A program could be written that cooperates with any opponent that provides it with a proof that it will cooperate.

Comment by skepsci on Open Thread, February 1-14, 2013 · 2013-07-12T05:44:40.433Z · LW · GW

Thanks. The logic the board uses to determine posts you've read seems strange.

Sorry about posting in the wrong open thread. I followed an "open thread" link, and this looked like it was the most recent open thread.

Comment by skepsci on Open Thread, February 1-14, 2013 · 2013-07-12T04:39:26.717Z · LW · GW

Why do some posts have pink borders?

I can't quite figure it out. I gather it has something to do with being new, since newer posts are more likely to be pink and every reply to a pink post seems to be pink. But it's not purely chronological (since some of the most recent comments do not have pink borders when I view the thread), and it's not purely based on being new since the last time you've viewed a thread (since I've seen pink borders around my own posts).

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-12T03:51:24.101Z · LW · GW

I think a programming language that only allows primitive recursion is a bad idea. One common pattern (which I think we want to allow) was for bots to simulate their opponents, which entails the ability to simulate arbitrary valid code. This would not be possible in a language which restricts to primitive recursion.

Comment by skepsci on Prisoner's dilemma tournament results · 2013-07-10T03:27:17.358Z · LW · GW

Yay, I wasn't last!

Still, I'm not surprised that laziness did not pay off. I wrote a simple bot, then noticed that it cooperated against defectbot and defected against itself. I thought to myself, "This is not a good sign." Then I didn't bother changing it.

Comment by skepsci on Levels of Action · 2013-06-27T18:13:47.342Z · LW · GW

I was going to make this same objection. Your assertion that level 2 tasks are multiplicative with each other is not very plausible. It's obviously false that each typing class improves the typer's ability by 20%, since I can't take 10 typing classes and start typing at 400 words per minute. More likely the gains with multiple typing classes are linear for the first few, and sublinear in the long run.

It is more plausible that level 2 tasks are multiplicative with level 1 tasks. If you get 20% faster at typing, you can transcribe audio 20% faster, and every level 1 transcription task you undertake now pays 20% better.

Comment by skepsci on A Suggested Reading Order for Less Wrong [2011] · 2013-06-24T14:40:54.975Z · LW · GW

After the top 5 or 10 or so, rather than just presenting a list of articles, it may make more sense to split things up by topic. Being presented with a list of 100 articles is kind of intimidating. Being presented with five lists of twenty articles each on five different topics is less so, as it's easier to divide and conquer. Readers may be interested in some topics but not others (at least at first), or may decide to read a few articles on each topic.

Some natural subdivisions might be:

  • Human psychology and biases.
  • Bayesian inference.
  • The scientific method.
  • Quantum mechanics.

Also, others have mentioned sequences. Rather than just ignoring that sequences exist, it would be useful to new readers both to point out the sequences (which would happen more naturally if you broke things up by subject), and to provide the reader with some idea of how important it is to read a given sequence in order.

Comment by skepsci on Prisoner's Dilemma (with visible source code) Tournament · 2013-06-15T04:28:16.206Z · LW · GW

It's not necessarily best to cooperate with everyone with the "AbsolutismBot" wrapper. This guarantees that you and the other program will both cooperate, but without the wrapper it might have been the case that you would defect and the other program would cooperate, which is better for you.

Comment by skepsci on Post ridiculous munchkin ideas! · 2013-05-19T13:59:14.402Z · LW · GW

How do you enforce the 10% salary tithe?

One obvious difficulty in educating children for free and then expecting them to pay you back after they become educated is that, most places, minors cannot enter into legally binding contracts. So the kid graduates, gets a great job (in a country that won't recognize the contract), and says, "I never agreed to pay you 10% of my salary, so I'm keeping it."

Comment by skepsci on Post ridiculous munchkin ideas! · 2013-05-19T05:43:28.668Z · LW · GW

I would worry the effect this may have on your credit rating if anyone catches you at it, together with possibly more serious effects. This could potentially be considered fraud. Altogether it seems much more sensible to simply live within your means and pay off your credit balance each month.

Comment by skepsci on Rationality Quotes May 2013 · 2013-05-07T02:22:37.316Z · LW · GW

Outside of mathematical logic, some familiar examples include:

  • compactness vs. sequential compactness—generalizing from metric to topological spaces
  • product topology vs. box topology—generalizing from finite to infinite product spaces
  • finite-dimensional vs. finitely generated (and related notions, e.g. finitely cogenerated)—generalizing from vector spaces to modules
  • pointwise convergence vs. uniform convergence vs. norm-convergence vs. convergence in the weak topology vs....—generalizing from sequences of numbers to sequences of functions
Comment by skepsci on Rationality Quotes May 2013 · 2013-05-07T02:00:09.559Z · LW · GW

Witty to be sure, but obviously false. The causal connection between baseball and the content (as opposed to the name) of the law is probably fairly tenuous. The number three is ubiquitous in all areas of human culture.

Comment by skepsci on Rationality Quotes April 2013 · 2013-04-19T19:45:43.698Z · LW · GW

Exactly. In fact, it was well known at the time that the Earth is round, and most educated people even knew the approximate size (which was calculated by Eratosthenes in the third century BCE). Columbus, on the other hand, used a much less accurate figure, which was off by a factor of 2.

The popular myth that Columbus was right and his contemporaries were wrong is the exact opposite of the truth.

Comment by skepsci on Rationality Quotes April 2013 · 2013-04-19T19:25:05.433Z · LW · GW

Wouldn't explaining why the statement is misleading be more productive than suppressing the misleading statement?

Comment by skepsci on Questions for Moral Realists · 2013-02-23T03:09:59.614Z · LW · GW

If a person somehow loses the associated good feelings, ice cream also ceases to be desirable. I still don't see the difference between Monday and Tuesday.

I think I might have some idea what you mean about masochists not liking pain. Let me tell a different story, and you can tell me whether you agree...

Masochists like pain, but only in very specific environments, such as roleplaying fantasies. Within that environment, masochists like pain because of how it affects the overall experience of the fantasy. Outside that environment, masochists are just as pain-averse as the rest of the world.

Does that story jibe with your understanding?

Comment by skepsci on The Curve of Capability · 2012-02-29T07:19:41.028Z · LW · GW

The difference is between amateur and professional ratings. Amateur dan ratings, just like kyu ratings, are designed so that a difference of n ranks corresponds to suitability of a n-stone handicap, but pro dan ratings are more bunched together.

See Wikipedia:Go pro.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-28T21:09:50.975Z · LW · GW

I would be very interested if anyone has good examples of this phenomenon.

There are a few "triads" mentioned in the intellectual hipster article, but the only one that really seems to me like a good example of this phenomenon is the "don't care about Africa / give aid to Africa / don't give aid to Africa" triad.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-28T20:47:11.759Z · LW · GW

This advice is worse than useless. But coming from someone who was instrumental in the "Physicists have figured a way to efficiently eradicate humanity; let's tell the politicians so they may facilitate!" movement, it's not surprising.

Protip: the maxim "That which can be destroyed by the truth, should be" does not mean we should publish secrets that have a chance of ending global civilization.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-28T20:32:32.817Z · LW · GW

So I should interpret Will's "Omega = objective morality" comment as meaning "sufficiently wise agents sometimes cooperate, when cooperation is the best way to achieve their ends"? I don't think so.

Comment by skepsci on Test Your Calibration! · 2012-02-28T05:48:53.831Z · LW · GW

It's also completely ridiculous, with a sample size of ~10 questions, to give the success rate and probability of being well calibrated as percentages with 12 decimals. Since the uncertainty in such a small sample is on the order of several percent, just round to the nearest percentage.

Comment by skepsci on Harry Potter and the Methods of Rationality discussion thread, part 9 · 2012-02-27T20:17:49.755Z · LW · GW

No, it's an annual rate. You quote it as an annual rate, and it matches the annual rate I found by repeating your search. So you need to multiply by seven to get the rate of people committing suicide during the years they would, if a Hogwarts student, be attending Hogwarts.

Comment by skepsci on Harry Potter and the Methods of Rationality discussion thread, part 9 · 2012-02-27T08:49:27.015Z · LW · GW

Except that students stay at Hogwarts for 7 years, not one, which would put the suicide rate at Hogwarts at one per 14 years, not one per century (if wizards commit suicide at the same rate as muggles). If you assumed that Wizarding suicide attempts were 5 times as likely to be successful, that would put the rate at one suicide every 3 years.

Of course, it's entirely possible that the wizarding resilience to illness and injury also makes them more resilient to mental illness, and that's why suicide rates are lower.

Comment by skepsci on Harry Potter and the Methods of Rationality discussion thread, part 9 · 2012-02-27T08:24:01.248Z · LW · GW


Comment by skepsci on Rationality Quotes February 2012 · 2012-02-26T09:23:20.466Z · LW · GW

It is trivial* to see that this game reduces to equivalent to a simple two party prisoners dilemma with full mutual information.

It only reduces to/is equivalent to a prisoner's dilemma for certain utility functions (what you're calling "values"). The prisoners' dilemma is characterized by the fact that there is a dominant strategy equilibrium which is not Pareto optimal. But if the utility functions of the agents are such that the game is zero-sum, then this can't be the case, as every outcome is Pareto optimal in a zero-sum game.

Furthermore, in a zero-sum game, no cooperation between all of the agents is possible. So it's crazy to believe that an arbitrary set of sufficiently intelligent agents will cooperate to achieve a single "overgoal". Collaboration is only possible if the agents' preferences are such that collaboration can be mutually beneficial.

Comment by skepsci on Get Curious · 2012-02-26T08:19:57.100Z · LW · GW

If you have beliefs about the matter already, push the "reset" button and erase that part of your map. You must feel that you don't already know the answer.

It seems like a bad idea to intentionally blank part of your map. If you already know things, you shouldn't forget what you already know. On the other hand, if you have reason to doubt what you think you know, you should blank the suspect parts of your map when you had reason to doubt them, and not artificially as part of a procedure for generating curiosity.

I think what you may be trying to say is that it is good practice to periodically rethink what you think you know, and make sure that A) you remember how you came to believe what you believe, and B) your conclusions still make sense in light of current evidence. However, when you do this, it is important not to get into the habit of quickly returning to the same conclusions for the same reasons. If you never change your conclusions while rethinking them, that's probably a sign that you are too resistant to changing your mind.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-24T20:27:43.166Z · LW · GW

The decisions produced by any decision theory are not objectively optimal; at best they might be objectively optimal for a specific utility function. A different utility function will produce different "optimal" behavior, such as tiling the universe with paperclips. (Why do you think Eliezer et al are spending so much effort trying to figure out how to design a utility function for an AI?)

I see the connection between omega and decision theories related to Solomonoff induction, but as the choice of utility function is more-or-less arbitrary, it doesn't give you an objective morality.

Comment by skepsci on Hard philosophy problems to test people's intelligence? · 2012-02-24T09:40:27.904Z · LW · GW

The latter.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-24T09:37:11.769Z · LW · GW

I'm very confused* about the alleged relationship between objective morality and Chaitin's omega. Could you please clarify?

*Or rather, if I'm to be honest, I suspect that you may be confused.

Comment by skepsci on Rationality Quotes February 2012 · 2012-02-18T11:18:27.085Z · LW · GW

It is bad luck to be superstitious.

-Andrew W. Mathis

Comment by skepsci on Hearsay, Double Hearsay, and Bayesian Updates · 2012-02-17T20:48:14.330Z · LW · GW

If a bad law is applied in a racist way, surely that's a problem with both the law itself and the justice system's enforcement of it?

Comment by skepsci on Hearsay, Double Hearsay, and Bayesian Updates · 2012-02-17T12:30:26.599Z · LW · GW

Yeah, I was wondering about the downvotes. The welcome thread says that it's perfectly acceptable to ask for an explanation... So, for anyone who downvoted me, why?

Comment by skepsci on The mathematics of reduced impact: help needed · 2012-02-17T08:31:43.539Z · LW · GW

Exactly. If you have determinism in the sense of a function from AI action to result world, you can directly compute some measure of the difference between worlds X and X', where X is the result of AI inaction, and X' is the result of some candidate AI action.

As nerzhin points out, you can run into similar problems even in deterministic universes, including life, if the AI doesn't have perfect knowledge about the initial configuration or laws of the universe, or if the AI cares about differences between configurations that are so far into the future they are beyond the AI's ability to calculate. In this case, the universe might be deterministic, but the AI must reason in probabilities.

Comment by skepsci on Hearsay, Double Hearsay, and Bayesian Updates · 2012-02-16T10:36:16.461Z · LW · GW

An unfriendly legal system might treat being born as a crime. In fact, I'd be surprised if some politician in Arizona hasn't tried to make being born to illegal immigrant parents a crime.

Comment by skepsci on Hard philosophy problems to test people's intelligence? · 2012-02-16T10:09:18.177Z · LW · GW

On a related note, I remember the day when I found out my PhD advisor (a computability theorist!) revealed that he believed the argument against AI from Gödel's incompleteness theorem. It was not reassuring.

Comment by skepsci on Beyond Reasonable Doubt? - Richard Dawkins [link] · 2012-02-16T09:58:01.635Z · LW · GW

Dawkins starts from the premise that there is high uncertainty about the outcome of the case, and concludes that there is high uncertainty about the guilt, which does not follow. Even if it is obvious to everyone that the defendant is very probably guilty, it may be far from obvious exactly how high the jury will estimate the probability of innocence, and where they will set the bar for reasonable doubt.*

*It has never been clear to me where this should be. If I put the credence of guilt at g, should I convict when g>.9? .99? .999? Should I say "to hell with the idea of reasonable doubt anyways, I'm going to estimate myself appropriate relative weights to attach to the outcomes 1) innocent man spends a lifetime in prison, and 2) serial murderer is unleashed upon the public?" I suppose because the lawyers and judge are unlikely to provide me with a credence threshold to use, the most sensible thing to do would be to derive one myself.

Comment by skepsci on Hard philosophy problems to test people's intelligence? · 2012-02-16T09:43:14.701Z · LW · GW

What do you mean by "great (awful)"? Do you mean that the thought experiment itself is an awful argument against AI, but describing the argument is a good way to test how people think?

Comment by skepsci on What is the advantage of the Kolmogorov complexity prior? · 2012-02-16T08:51:40.903Z · LW · GW

Maybe there is some true randomness in the universe

Not a problem.

I know it's not a problem. I explained exactly how to modify Solomonoff induction to handle universes that are generated randomly according to some computable law, as opposed to being generated deterministically according to an algorithm.

Suppose you flip a quantum coin ten times. If you record the output, the K-complexity is ten bits.

Maybe it is, maybe it isn't. Maybe your definition of Kolmogorov complexity is such that the Kolmogorov complexity of every string is at least 3^^^3, because you defined Kolmogorov complexity using a really dumb universal machine. Maybe it's 2, because you programmed a universal machine that was really good at compressing the string 0101110010, because you like it, and it so happens that was what you flipped. If you flip a coin a very large number of times, it's very likely that the Kolmogorov complexity of the output is at least the number of flips, but it could be much smaller due to chance.

As such, there's a 1/1024 prior probability of getting that exact output. This is exactly what you'd get if you assumed it was random.

False, because you don't actually know the complexity was 10.

Basically, K-complexity is treating the very laws of physics as random. Any randomness on top of that works the same way as it would as part of that.

No, it's not doing that at all. Using a complexity-weighted prior is assuming that the universe follows some random computable law, which is more likely to be simple than complex. I suppose this is true to the extent that any probability distribution on a countable set vanishes in the limit (for any enumeration of the countable set!), but I see no reason to bring Kolmogorov complexity into it.

The problem is that it seems that things that are definable but not computable should be above random chance. For example, the K-complexity of a halting oracle is infinite, but it can be defined in finite space. Would the probability of the fine structure constant being a halting oracle be infinitesimal?

I have no idea how to make sense of this question. Are infinitely many bits of fine structure constant even physically meaningful? If beyond a certain point of precision, the fine structure constant can't be measured even in principle because it has no detectable physical effects on accessible time/space scales, it makes no sense to even have an answer to the question "is the fine structure constant a halting oracle?" let alone the probability of such an event.

One reason to use K-complexity is that so far, it's worked far better than anything else. As far as we know, we can fit the laws of physics on a note card, yet the universe contains well over 10^80 particles, and don't get me started on the amount of computing power necessary to run it.

I'll grant you that Occam's razor works well in science. That wasn't the question. The question is what is the advantage, if any, of starting with a Kolmogorov prior for Solomonoff induction, as opposed to any other arbitrary prior. You haven't answered my question.

Comment by skepsci on Hearsay, Double Hearsay, and Bayesian Updates · 2012-02-16T08:25:26.094Z · LW · GW

The assumption was that 80% of defendants are guilty, which is more than 4 of 8. Under this assumption, asking whether p(guilty|convicted) > 80% is just asking whether conviction positively correlates with guilt. Asking if p(innocent|acquitted) > 20% is just asking if acquittal positively correlates with innocence. These are really the same question, because P correlates with Q iff ¬P correlates with ¬Q.

Comment by skepsci on Hearsay, Double Hearsay, and Bayesian Updates · 2012-02-16T07:20:33.961Z · LW · GW

It proves that mistakes have been made, but in the end, no, I don't think it's terribly useful evidence for evaluating the rate of wrongful convictions. Why not? There have been 289 post-conviction DNA exonerations in US history, mostly in the last 15 years. That gives a rate of under 20 per year. Suppose 10,000 people a year are incarcerated for the types of crime that DNA exoneration is most likely to be possible for, namely murder and rape (I couldn't find exact figures, but I suspect the real number is at least this big). Then considering DNA exonerations gives us a lower bound of something like .2% on the error rate of US courts.

That is only useful evidence about the error rate if your prior estimate of the inaccuracy was less than that, and I mean, come on, really? Only one conviction in 500 is a mistake?

Comment by skepsci on Open Thread, February 15-29, 2012 · 2012-02-16T03:04:55.431Z · LW · GW

To me, the entire argument sounds like a rationalization for not signing up for cryo.


Someone who has rationalized a reason for not signing up yet for cryo, and suspects that the real reason is laziness.