For Wei Dai and everyone else here offering their own tips and tricks: what hard questions have you answered using them, and which tricks helped the most?
The hardest question I’ve answered is “How are probabilities supposed to work in a multiverse where everything that can happen does happen somewhere?” It’s hard to say which tricks helped the most because when I started I didn’t have a list of tips and tricks, so I don’t know how much it would have helped to try to apply them consciously. But here’s what worked in retrospect, in rough order of importance:
Go meta. In this case the meta question was much easier than the object-level question, because I could get the answer from history. Probability theory was created by gamblers, and later formally justified using decision theory, so I knew I should take a decision theory approach to the question.
Don’t stop at the first good answer.Here is the first good answer that I might have stopped at. (The website was created by Hal Finney some years ago.)
marks’s Solve many hard problems at once. Yep, I was also trying to answer “Does quantum immortality/suicide make sense?” and “How are probabilities supposed to work when mind copying is possible?”
Be ready to recognize a good answer when you see it. Apparently several lesswrongers have discovered the same answer independently, but I was the only one who thought it was a big deal and wrote it up. Others shrank from its counter-intuitiveness, or just didn’t realize its significance. I also discussed the idea on my own mailing list, where it failed to make much of a splash.
Explore multiple approaches simultaneously. and Trust your intuitions, but don’t waste too much time arguing for them. The main approaches were “first-person” and “third-person”, and my approach is mostly third-person, but I also spent a lot of time thinking about the first-person approach. (The first-person approach is more concerned about expectations of subjective experiences.) I think there were too many arguments about which is the right approach, when the time could have been better spent actually exploring them.
Sleep on it. Pretty hard to say how much this helped, but I did often go to sleep thinking about the problem.
What’s wrong with UDASSA? If you assume that all possible worlds exist, and that there is a natural measure on them, you can get objective probabilities.
I think your problem with UD (argument 1, in your second link) arises entirely from the way you choose to think about possible worlds. You built on a bad foundation, discovered the foundation was shaky, and so abandoned the original plan. But the problem was just the foundation, not the plan.
Both common sense and physics talk about the world as consisting of things-with-states. This remains true for possible worlds. Possible worlds defined using everyday concepts (e.g. worlds where “McCain defeated Obama in 2008”) or using some exact physical theory (e.g. a billiard-ball world) still have this attribute. If you were to talk about all the possible billiard-ball worlds, there’s no problem telling them apart, and it’s easy to ask whether there’s a natural measure on the set of such worlds.
But at your second link you write
There is an infinite number of universal Turing machines, so there
is an infinite number of UD. If we want to use one UD as an objective
measure, there has to be a universal Turing machine that is somehow uniquely
suitable for this purpose. Why that UTM and not some other? We don’t even
know what that justification might look like.
So you’ve adopted a concept of possible world which is something like “possible program for a universal Turing machine”. But the problem here is arising entirely from your idiosyncratic concept of possible world.
What does a universal Turing machine look like, from the things-with-states perspective? Consider the primordial example of a UTM, Turing’s example of a tape moving back and forth through a read-write head. There are two things with states: the head and the tape. They undergo causal interaction and change states as a result.
Originally Turing was thinking of physical machines like the ones around him, made of metal and electronics and so forth. But suppose we try to take the UTM he described to be a universe in itself. How far can we go in that direction? Again, we can do it, thinking in terms of things-with-states and their interactions. We can think in terms of fundamental entities which have states and which can also be joined to each other in some sense. The tape is a one-dimensional string of entities joined side by side. The head is another entity which interacts with the entities making up the “tape”, and whose join relations are also dynamical—it moves up and down the tape.
This all describes a type of possible world, just as the “billard-ball world” of elastically colliding impenetrable spheres in n-dimensional space is also a meaningful type of possible world. The dynamical rules for the Turing tape are the “laws of physics” for this world, each set of initial conditions gives rise to a possible history, and so on.
Now suppose you consider a different set of laws for the Turing-tape world. It still has the same structure, but the states and how they change are different. Is this mysterious? No, you’ve just defined a different class or subclass of possible worlds. Both classes of world are “computationally universal”, but that doesn’t mean that the world from one class which performs a particular computation is the same world as the world from the other class which performs that computation.
Yet this is what you’re assuming, more or less, when you talk about having to pick a UTM as the UTM, in terms of which possible worlds will be defined. You’re treating a possible world as a second-order abstraction (equivalence class of computations) and trying to do without a thing-with-states foundation. If you insist on having such a foundation, this problem goes away. You still have the very formidable problem of trying to enumerate all possible forms of interactions among things-with-states. There is still the even larger problem of identifying and justifying the broadest notion of possible world you are willing to consider. What about worlds where there’s no time? What about worlds where there’s no “physical law”—changes happen, but for no reason? But your particular problem is an artefact of computational idealism, where reality is supposed to consist of computational or mathematical “entities” which exist independently of anything like “things” or “substances”.
I wonder why my answer to cousin_it’s question is sitting at 0 points, while his question is at 5 (3 when I posted my reply). Is it not the kind of answer people are looking for?
Another sample problem domain is crossword puzzles:
Don’t stop at the first good answer—You can’t write in the first word that seems to fit, you need to see if it is going to let you build the other words.
Explore multiple approaches simultaneously—Same idea, you often can think of a few different possible words that could work in a particular area of the puzzle, and you need to keep them all in mind as you work to solve the other words.
Trust your intuitions, but don’t waste too much time arguing for them—This one doesn’t apply much because usually people don’t fight over crossword puzzles.
Go meta—This is a big one, because usually crossword puzzles have a theme, often quite subtle, and if you look carefully you can see how your answers are building as part of a whole. This then gives you another direction to get ideas for possible answers, as things that would go with the theme, rather than just taking the clues literally.
Dissolve the question—Well, I don’t know about this, but I suppose if you get frustrated enough you could throw the puzzle into the trash.
Sleep on it—This works well for this kind of puzzle, I find. Coming back to it in the morning you will often make more progress.
Be ready to recognize a good answer when you see it—Once you have enough crossing words in mind you can have good confidence that you are on the right track and go ahead and write those in, even if you don’t have good ideas for some of the linked words. You need to recognize that when enough parts come together and your solution makes them fit, that is a strong clue that you are making progress, even if there are still unanswered aspects.
Most of my “hard” questions are programming designs that need to work around a weakness in the system. They probably don’t compare well to the big nasties. “Sleep on it” is probably the most valuable of the ones I have seen listed here. “Transform it” also applies to design well.
For Wei Dai and everyone else here offering their own tips and tricks: what hard questions have you answered using them, and which tricks helped the most?
The hardest question I’ve answered is “How are probabilities supposed to work in a multiverse where everything that can happen does happen somewhere?” It’s hard to say which tricks helped the most because when I started I didn’t have a list of tips and tricks, so I don’t know how much it would have helped to try to apply them consciously. But here’s what worked in retrospect, in rough order of importance:
Go meta. In this case the meta question was much easier than the object-level question, because I could get the answer from history. Probability theory was created by gamblers, and later formally justified using decision theory, so I knew I should take a decision theory approach to the question.
Don’t stop at the first good answer. Here is the first good answer that I might have stopped at. (The website was created by Hal Finney some years ago.)
marks’s Solve many hard problems at once. Yep, I was also trying to answer “Does quantum immortality/suicide make sense?” and “How are probabilities supposed to work when mind copying is possible?”
Be ready to recognize a good answer when you see it. Apparently several lesswrongers have discovered the same answer independently, but I was the only one who thought it was a big deal and wrote it up. Others shrank from its counter-intuitiveness, or just didn’t realize its significance. I also discussed the idea on my own mailing list, where it failed to make much of a splash.
Explore multiple approaches simultaneously. and Trust your intuitions, but don’t waste too much time arguing for them. The main approaches were “first-person” and “third-person”, and my approach is mostly third-person, but I also spent a lot of time thinking about the first-person approach. (The first-person approach is more concerned about expectations of subjective experiences.) I think there were too many arguments about which is the right approach, when the time could have been better spent actually exploring them.
Sleep on it. Pretty hard to say how much this helped, but I did often go to sleep thinking about the problem.
Link to the solution?
See my posts tagged with udt. (Start with the top one in that link.)
What’s wrong with UDASSA? If you assume that all possible worlds exist, and that there is a natural measure on them, you can get objective probabilities.
I answered that at against UD+ASSA, part 1 and against UD+ASSA, part 2. See also the additional argument in indexical uncertainty and the Axiom of Independence.
I think your problem with UD (argument 1, in your second link) arises entirely from the way you choose to think about possible worlds. You built on a bad foundation, discovered the foundation was shaky, and so abandoned the original plan. But the problem was just the foundation, not the plan.
Both common sense and physics talk about the world as consisting of things-with-states. This remains true for possible worlds. Possible worlds defined using everyday concepts (e.g. worlds where “McCain defeated Obama in 2008”) or using some exact physical theory (e.g. a billiard-ball world) still have this attribute. If you were to talk about all the possible billiard-ball worlds, there’s no problem telling them apart, and it’s easy to ask whether there’s a natural measure on the set of such worlds.
But at your second link you write
So you’ve adopted a concept of possible world which is something like “possible program for a universal Turing machine”. But the problem here is arising entirely from your idiosyncratic concept of possible world.
What does a universal Turing machine look like, from the things-with-states perspective? Consider the primordial example of a UTM, Turing’s example of a tape moving back and forth through a read-write head. There are two things with states: the head and the tape. They undergo causal interaction and change states as a result.
Originally Turing was thinking of physical machines like the ones around him, made of metal and electronics and so forth. But suppose we try to take the UTM he described to be a universe in itself. How far can we go in that direction? Again, we can do it, thinking in terms of things-with-states and their interactions. We can think in terms of fundamental entities which have states and which can also be joined to each other in some sense. The tape is a one-dimensional string of entities joined side by side. The head is another entity which interacts with the entities making up the “tape”, and whose join relations are also dynamical—it moves up and down the tape.
This all describes a type of possible world, just as the “billard-ball world” of elastically colliding impenetrable spheres in n-dimensional space is also a meaningful type of possible world. The dynamical rules for the Turing tape are the “laws of physics” for this world, each set of initial conditions gives rise to a possible history, and so on.
Now suppose you consider a different set of laws for the Turing-tape world. It still has the same structure, but the states and how they change are different. Is this mysterious? No, you’ve just defined a different class or subclass of possible worlds. Both classes of world are “computationally universal”, but that doesn’t mean that the world from one class which performs a particular computation is the same world as the world from the other class which performs that computation.
Yet this is what you’re assuming, more or less, when you talk about having to pick a UTM as the UTM, in terms of which possible worlds will be defined. You’re treating a possible world as a second-order abstraction (equivalence class of computations) and trying to do without a thing-with-states foundation. If you insist on having such a foundation, this problem goes away. You still have the very formidable problem of trying to enumerate all possible forms of interactions among things-with-states. There is still the even larger problem of identifying and justifying the broadest notion of possible world you are willing to consider. What about worlds where there’s no time? What about worlds where there’s no “physical law”—changes happen, but for no reason? But your particular problem is an artefact of computational idealism, where reality is supposed to consist of computational or mathematical “entities” which exist independently of anything like “things” or “substances”.
I wonder why my answer to cousin_it’s question is sitting at 0 points, while his question is at 5 (3 when I posted my reply). Is it not the kind of answer people are looking for?
For my part, I was distracted trying to find where you wrote up your answer. For that, I apologize.
Another sample problem domain is crossword puzzles:
Don’t stop at the first good answer—You can’t write in the first word that seems to fit, you need to see if it is going to let you build the other words.
Explore multiple approaches simultaneously—Same idea, you often can think of a few different possible words that could work in a particular area of the puzzle, and you need to keep them all in mind as you work to solve the other words.
Trust your intuitions, but don’t waste too much time arguing for them—This one doesn’t apply much because usually people don’t fight over crossword puzzles.
Go meta—This is a big one, because usually crossword puzzles have a theme, often quite subtle, and if you look carefully you can see how your answers are building as part of a whole. This then gives you another direction to get ideas for possible answers, as things that would go with the theme, rather than just taking the clues literally.
Dissolve the question—Well, I don’t know about this, but I suppose if you get frustrated enough you could throw the puzzle into the trash.
Sleep on it—This works well for this kind of puzzle, I find. Coming back to it in the morning you will often make more progress.
Be ready to recognize a good answer when you see it—Once you have enough crossing words in mind you can have good confidence that you are on the right track and go ahead and write those in, even if you don’t have good ideas for some of the linked words. You need to recognize that when enough parts come together and your solution makes them fit, that is a strong clue that you are making progress, even if there are still unanswered aspects.
Most of my “hard” questions are programming designs that need to work around a weakness in the system. They probably don’t compare well to the big nasties. “Sleep on it” is probably the most valuable of the ones I have seen listed here. “Transform it” also applies to design well.
Also, what kinds of questions qualify as hard, for the purpose of this thread?
(I do have a couple of tricks, but my questions are nowhere near as hard as some of the philosophy / AI theory problems discussed here on LW.)
Let’s say anything that takes more than a few hours to answer.
That’s a good question. I can’t actually think of any particularly hard questions I’ve had to attack strategically to answer.