Can the author or somebody else explain what is wrong with Deepseek’s answer to the Kolmogorov complexity question? It seems to give more or less the same answer I’d give, and even correctly notes the major caveat in the last sentence of its output.
I suppose its answer is a bit handwavy (“observer role”?), and some of the minor details of its arguments are wrong or poorly phrased, but the conclusion seems correct. Am I misunderstanding something?
So in general, what DeepSeek says here might align better with intuitive complexity, but the point of asking about Kolmogorov Complexity rather than just Occam’s Razor is that we’re specifically trying to look at formal description length and not intuitive complexity.
Many Worlds does not need extra complexity to explain the branching. The branching happens due to the part of the math that all theories agree on. (In fact, I think a more accurate statement is that the branching is a description of what the math does.)
Then there’s the wavefunction collapse. So first of all, wavefunction collapse is an additional postulate not contianed in the remaining math, so it adds complexity. (… and the lack of the additional postulate does not add complexity, as DeepSeek claimed.) And then there’s a separate issue with KC arguably being unable to model randomness at all. You could argue that this is a failure of the KC formalism and we need KC + randomness oracle to even answer the question. You could also be hardcore about it and argue that any nondeterministic theory is impossible to describe and therefore has KC ∞. In either case, the issue of randomness is something you should probably bring up in response to the question.
And finally there’s the observer role. Iiuc the less stupid versions of Copenhagen do not give a special role to an observer; there’s a special role for something being causally entangled with the experiment’s result, but it doesn’t have to be an agent. This is also not really a separate principle from the wave function collapse I don’t think, it’s what triggers collapse. And then it doesn’t make any sense to list as a strength of Copenhagen because if anything it increases description length.
There are variants of KC that penalize the amount of stuff that are created rather than just the the description length I believe, in which case MW would have very high KC. This is another thing DeepSeek could have brought up.
I am also not a physicist, so perhaps I’ve misunderstood. I’ll outline my reasoning.
An interpretation of quantum mechanics does two things: (1) defines what parts of our theory, if any, are ontically “real” and (2) explains how our conscious observations of measurement results are related to the mathematical formalism of QM.
The Kolmogorov complexity of different interpretations cannot be defined completely objectively, as DeepSeek also notes. But broadly speaking, defining KC “sanely”, it ought to be correlated with a kind of “Occam’s razor for conceptual entities”, or more precisely, “Occam’s razor over defined terms and equations”.
I think Many Worlds is more conceptually complex than Copenhagen. But I view Copenhagen as a catchall term for a category of interpretations that also includes QBism and Rovelli’s RQM. Basically, these are “observer-dependent” interpretations. I myself subscribe to QBism, but I view it as a more rigorous formulation of Copenhagen.
So, why should we think Many Worlds is more conceptually complex? Copenhagen is the closest we can come to a “shut up and calculate” interpretation. Pseudomathematically, we can say
Copenhagen ~= QM + “simple function connecting measurements to conscious experiences”
The reason we can expect Copenhagen-y interpretations to be simpler than other interpretations is because every other interpretation *also* needs a function to connect measurements to conscious experiences, but usually requires some extra machinery in addition to that.
Now I maybe don’t understand MWI correctly. But as I understand it, what QM mathematically gives you is more like a chaotic flux of possibilities, rather than the kind of branching tree of self-consistent worldlines that MWI requires. The way you split up the quantum state into branches constitutes extra structure on top of QM. Thus:
Many Worlds ~= QM + “branching function” + “simple function connecting measurements to conscious experiences”
So it seems that MWI ought to have higher Kolmogorov Complexity than Copenhagen.
I don’t think DeepSeek has argued this point correctly. But I also wouldn’t call its answer nonsense. I would call it a reasonable but superficial answer with a little bit of nonsense mixed in; the kind of answer one might expect a precocious college student to give.
The reason we can expect Copenhagen-y interpretations to be simpler than other interpretations is because every other interpretation also needs a function to connect measurements to conscious experiences, but usually requires some extra machinery in addition to that.
I don’t believe this is correct. But I separately think that it being correct would not make DeepSeek’s answer any better. Because that’s not what it said, at all. A bad argument does not improve because there exists a different argument that shares the same conclusion.
Which part do you disagree with? Whether or not every interpretation needs a way to connect measurements to conscious experiences, or whether they need extra machinery?
If the former: you need some way to connect the formalism to conscious experiences, since that’s what an interpretation is largely for. It needs to explain how the classical world of your conscious experience is connected to the mathematical formalism. This is true for any interpretation.
If you’re saying that many worlds does not actually need any extra machinery, I guess the most reasonable way to interpret that in my framework is to say that the branching function is a part of the experience function. I suppose this might correspond to what I’ve heard termed the Many Minds interpretation, but I don’t understand that one in enough detail to say.
A bad argument does not improve because there exists a different argument that shares the same conclusion.
Let an argument A be called “steelmannable” if there exists a better argument S with a similar structure and similar assumptions (according to some metric of similarity) that proves the same conclusion as the original argument A. Then S is called a “steelman” of A.
It is clear that not all bad arguments are steelmannable. I think it is reasonable to say that steelmannable bad arguments are less nonsensical than bad arguments that are not steelmannable.
So the question becomes: can my argument be viewed as a steelman of DeepSeek’s argument? I think so. You probably don’t. However, since everybody understands their own arguments quite well, ceteris paribus it should be expected that I am more likely to be correct about the relationship between my argument and DeepSeek’s in this case.
… Or at least, that would be so if I didn’t have an admitted tendency to be too lenient in interpreting AI outputs. Nonetheless, I am not objecting to the claim that DeepSeek’s argument is weak, but to the claim that it is nonsense.
We can both agree that DeepSeek’s argument is not great. But I see glimmers of intelligence in it. And I fully expect that soon we will have models that will be able to argue the same things with more force.
Whether or not every interpretation needs a way to connect measurements to conscious experiences, or whether they need extra machinery?
If we’re being extremely pedantic, then then KC is about predicting conscious experience (or sensory input data, if you’re an illusionist; one can debate what the right data type is). But this only matters for discussing things like Boltzmann brains. As soon as you assume that there exists an external universe, you can forget about your personal experience just try to estimate the length of the program that runs the universe.
So practically speaking, it’s the first one. I think what quantum physics does with observers falls out of the math and doesn’t require any explicit treatment. I don’t think Copenhagen gets penalized for this, either. The wave function collapse increases complexity because it’s an additional rule that changes how the universe operates, not because it has anything to do with observers. (As I mentioned, I think the ‘good’ version of Copenhagen doesn’t mention observers, anyway.)
If you insist on the point that interpretation relates to an observer, then I’d just say that “interpretation of quantum mechanics” is technically a misnomer. It should just be called “theory of quantum mechanics”. Interpretations don’t have KC; theories do. We’re comparing different source codes for the universe.
steelmanning
I think this argument is analogous to giving white credit for this rook check, which is fact a good move that allows white to win the queen next move—when in actual fact white just didn’t see that the square was protected and blundered a rook. The existence of the queen-winning tactic increases the objective evaluation of the move, but once you know that white didn’t see it, it should not increase your skill estimate of white. You should judge the move as if the tactic didn’t exist.
Similarly, the existence of a way to salvage the argument might make the argument better in the abstract, but should not influence your assessment of DeepSeek’s intelligence, provided we agree that DeepSeek didn’t know it existed. In general, you should never give someone credit for areas of the chess/argument tree that they didn’t search.
Thank you, this has been a very interesting conversation so far.
I originally started writing a much longer reply explaining my position on the interpretation of QM in full, but realized that the explanation would grow so long that it would really need to be its own post. So instead, I’ll just make a few shorter remarks. Sorry if these sound a bit snappy.
As soon as you assume that there exists an external universe, you can forget about your personal experience just try to estimate the length of the program that runs the universe.
And if one assumes an external universe evolving according to classical laws, the Bohmian interpretation has the lowest KC. If you’re going to be baking extra assumptions into your theory, why not go all the way?
Interpretations and Kolmogorov Complexity
An interpretation is still a program. All programs have a KC (although it is usually ill-defined). Ultimately I don’t think it matters whether we call these objects we’re studying theories or interpretations.
Collapse postulate
Has nothing to do with how the universe operates, as I see it. If you’d like, I think we can cast Copenhagen into a more Many Worlds -like framework by considering Many Imaginary Worlds. This is an interpretation, in my opinion functionally equivalent to Copenhagen, where the worlds of MWI are assumed to represent imaginary possibilities rather than real universes. The collapse postulate, then, corresponds to observing that you inhabit a particular imaginary world—observing that that world is real for you at the moment. By contrast, in ordinary MWI, all worlds are real, and observation simply reduces your uncertainty as to which observer (and in which world) you are.
If we accept the functional equivalence between Copenhagen and MIWI, this gives us an upper bound on the KC of Copenhagen. It is at most as complex as MWI. I would argue less.
Chess
I think we need to distinguish between “playing skill” and “positional evaluation skill”. It could be said that DeepBlue is dumber than Kasparov in the sense of being worse at evaluating any given board position than him, while at the same time being a vastly better player than Kasparov simply because it evaluates exponentially more positions.
If you know that a player has made the right move for the wrong reasons, that should still increase your estimate of their playing skill, but not their positional evaluation skill.
Of course, in the case of chess, the two skills will be strongly correlated, and your estimate of the player’s playing skill will still go down as you observe them making blunders in other positions. But this is not always so. In some fields, it is possible to reach a relatively high level of performance using relatively dumb heuristics.
Moving onto the case of logical arguments, playing skill corresponds to “getting the right answers” and positional evaluation skill corresponds to “using the right arguments”.
In many cases it is much easier to find the right answers than to find correct proofs for those answers. For example, most proofs that Euler and Newton gave for their mathematical results are, technically, wrong by today’s standards of rigor. Even worse, even today’s proofs are not completely airtight, since they are not usually machine-verifiable.
And yet we “know” that the results are right. How can that be, if we also know that our arguments aren’t 100% correct? Many reasons, but one is that we can see that our current proofs could be made more rigorous. We can see that they are steelmannable. And in fact, our current proofs were often reached by effectively steelmanning Euler’s and Newton’s proofs.
If we see DeepSeek making arguments that are steelmannable, that should increase our expectation that future models will, in fact, be able to steelman those arguments.
Can the author or somebody else explain what is wrong with Deepseek’s answer to the Kolmogorov complexity question? It seems to give more or less the same answer I’d give, and even correctly notes the major caveat in the last sentence of its output.
I suppose its answer is a bit handwavy (“observer role”?), and some of the minor details of its arguments are wrong or poorly phrased, but the conclusion seems correct. Am I misunderstanding something?
Here’s my take; not a physicist.
So in general, what DeepSeek says here might align better with intuitive complexity, but the point of asking about Kolmogorov Complexity rather than just Occam’s Razor is that we’re specifically trying to look at formal description length and not intuitive complexity.
Many Worlds does not need extra complexity to explain the branching. The branching happens due to the part of the math that all theories agree on. (In fact, I think a more accurate statement is that the branching is a description of what the math does.)
Then there’s the wavefunction collapse. So first of all, wavefunction collapse is an additional postulate not contianed in the remaining math, so it adds complexity. (… and the lack of the additional postulate does not add complexity, as DeepSeek claimed.) And then there’s a separate issue with KC arguably being unable to model randomness at all. You could argue that this is a failure of the KC formalism and we need KC + randomness oracle to even answer the question. You could also be hardcore about it and argue that any nondeterministic theory is impossible to describe and therefore has KC ∞. In either case, the issue of randomness is something you should probably bring up in response to the question.
And finally there’s the observer role. Iiuc the less stupid versions of Copenhagen do not give a special role to an observer; there’s a special role for something being causally entangled with the experiment’s result, but it doesn’t have to be an agent. This is also not really a separate principle from the wave function collapse I don’t think, it’s what triggers collapse. And then it doesn’t make any sense to list as a strength of Copenhagen because if anything it increases description length.
There are variants of KC that penalize the amount of stuff that are created rather than just the the description length I believe, in which case MW would have very high KC. This is another thing DeepSeek could have brought up.
I am also not a physicist, so perhaps I’ve misunderstood. I’ll outline my reasoning.
An interpretation of quantum mechanics does two things: (1) defines what parts of our theory, if any, are ontically “real” and (2) explains how our conscious observations of measurement results are related to the mathematical formalism of QM.
The Kolmogorov complexity of different interpretations cannot be defined completely objectively, as DeepSeek also notes. But broadly speaking, defining KC “sanely”, it ought to be correlated with a kind of “Occam’s razor for conceptual entities”, or more precisely, “Occam’s razor over defined terms and equations”.
I think Many Worlds is more conceptually complex than Copenhagen. But I view Copenhagen as a catchall term for a category of interpretations that also includes QBism and Rovelli’s RQM. Basically, these are “observer-dependent” interpretations. I myself subscribe to QBism, but I view it as a more rigorous formulation of Copenhagen.
So, why should we think Many Worlds is more conceptually complex? Copenhagen is the closest we can come to a “shut up and calculate” interpretation. Pseudomathematically, we can say
Copenhagen ~= QM + “simple function connecting measurements to conscious experiences”
The reason we can expect Copenhagen-y interpretations to be simpler than other interpretations is because every other interpretation *also* needs a function to connect measurements to conscious experiences, but usually requires some extra machinery in addition to that.
Now I maybe don’t understand MWI correctly. But as I understand it, what QM mathematically gives you is more like a chaotic flux of possibilities, rather than the kind of branching tree of self-consistent worldlines that MWI requires. The way you split up the quantum state into branches constitutes extra structure on top of QM. Thus:
Many Worlds ~= QM + “branching function” + “simple function connecting measurements to conscious experiences”
So it seems that MWI ought to have higher Kolmogorov Complexity than Copenhagen.
I don’t think DeepSeek has argued this point correctly. But I also wouldn’t call its answer nonsense. I would call it a reasonable but superficial answer with a little bit of nonsense mixed in; the kind of answer one might expect a precocious college student to give.
But again, I might be wrong.
I don’t believe this is correct. But I separately think that it being correct would not make DeepSeek’s answer any better. Because that’s not what it said, at all. A bad argument does not improve because there exists a different argument that shares the same conclusion.
Which part do you disagree with? Whether or not every interpretation needs a way to connect measurements to conscious experiences, or whether they need extra machinery?
If the former: you need some way to connect the formalism to conscious experiences, since that’s what an interpretation is largely for. It needs to explain how the classical world of your conscious experience is connected to the mathematical formalism. This is true for any interpretation.
If you’re saying that many worlds does not actually need any extra machinery, I guess the most reasonable way to interpret that in my framework is to say that the branching function is a part of the experience function. I suppose this might correspond to what I’ve heard termed the Many Minds interpretation, but I don’t understand that one in enough detail to say.
Let an argument A be called “steelmannable” if there exists a better argument S with a similar structure and similar assumptions (according to some metric of similarity) that proves the same conclusion as the original argument A. Then S is called a “steelman” of A.
It is clear that not all bad arguments are steelmannable. I think it is reasonable to say that steelmannable bad arguments are less nonsensical than bad arguments that are not steelmannable.
So the question becomes: can my argument be viewed as a steelman of DeepSeek’s argument? I think so. You probably don’t. However, since everybody understands their own arguments quite well, ceteris paribus it should be expected that I am more likely to be correct about the relationship between my argument and DeepSeek’s in this case.
… Or at least, that would be so if I didn’t have an admitted tendency to be too lenient in interpreting AI outputs. Nonetheless, I am not objecting to the claim that DeepSeek’s argument is weak, but to the claim that it is nonsense.
We can both agree that DeepSeek’s argument is not great. But I see glimmers of intelligence in it. And I fully expect that soon we will have models that will be able to argue the same things with more force.
If we’re being extremely pedantic, then then KC is about predicting conscious experience (or sensory input data, if you’re an illusionist; one can debate what the right data type is). But this only matters for discussing things like Boltzmann brains. As soon as you assume that there exists an external universe, you can forget about your personal experience just try to estimate the length of the program that runs the universe.
So practically speaking, it’s the first one. I think what quantum physics does with observers falls out of the math and doesn’t require any explicit treatment. I don’t think Copenhagen gets penalized for this, either. The wave function collapse increases complexity because it’s an additional rule that changes how the universe operates, not because it has anything to do with observers. (As I mentioned, I think the ‘good’ version of Copenhagen doesn’t mention observers, anyway.)
If you insist on the point that interpretation relates to an observer, then I’d just say that “interpretation of quantum mechanics” is technically a misnomer. It should just be called “theory of quantum mechanics”. Interpretations don’t have KC; theories do. We’re comparing different source codes for the universe.
I think this argument is analogous to giving white credit for this rook check, which is fact a good move that allows white to win the queen next move—when in actual fact white just didn’t see that the square was protected and blundered a rook. The existence of the queen-winning tactic increases the objective evaluation of the move, but once you know that white didn’t see it, it should not increase your skill estimate of white. You should judge the move as if the tactic didn’t exist.
Similarly, the existence of a way to salvage the argument might make the argument better in the abstract, but should not influence your assessment of DeepSeek’s intelligence, provided we agree that DeepSeek didn’t know it existed. In general, you should never give someone credit for areas of the chess/argument tree that they didn’t search.
Thank you, this has been a very interesting conversation so far.
I originally started writing a much longer reply explaining my position on the interpretation of QM in full, but realized that the explanation would grow so long that it would really need to be its own post. So instead, I’ll just make a few shorter remarks. Sorry if these sound a bit snappy.
And if one assumes an external universe evolving according to classical laws, the Bohmian interpretation has the lowest KC. If you’re going to be baking extra assumptions into your theory, why not go all the way?
An interpretation is still a program. All programs have a KC (although it is usually ill-defined). Ultimately I don’t think it matters whether we call these objects we’re studying theories or interpretations.
Has nothing to do with how the universe operates, as I see it. If you’d like, I think we can cast Copenhagen into a more Many Worlds -like framework by considering Many Imaginary Worlds. This is an interpretation, in my opinion functionally equivalent to Copenhagen, where the worlds of MWI are assumed to represent imaginary possibilities rather than real universes. The collapse postulate, then, corresponds to observing that you inhabit a particular imaginary world—observing that that world is real for you at the moment. By contrast, in ordinary MWI, all worlds are real, and observation simply reduces your uncertainty as to which observer (and in which world) you are.
If we accept the functional equivalence between Copenhagen and MIWI, this gives us an upper bound on the KC of Copenhagen. It is at most as complex as MWI. I would argue less.
I think we need to distinguish between “playing skill” and “positional evaluation skill”. It could be said that DeepBlue is dumber than Kasparov in the sense of being worse at evaluating any given board position than him, while at the same time being a vastly better player than Kasparov simply because it evaluates exponentially more positions.
If you know that a player has made the right move for the wrong reasons, that should still increase your estimate of their playing skill, but not their positional evaluation skill.
Of course, in the case of chess, the two skills will be strongly correlated, and your estimate of the player’s playing skill will still go down as you observe them making blunders in other positions. But this is not always so. In some fields, it is possible to reach a relatively high level of performance using relatively dumb heuristics.
Moving onto the case of logical arguments, playing skill corresponds to “getting the right answers” and positional evaluation skill corresponds to “using the right arguments”.
In many cases it is much easier to find the right answers than to find correct proofs for those answers. For example, most proofs that Euler and Newton gave for their mathematical results are, technically, wrong by today’s standards of rigor. Even worse, even today’s proofs are not completely airtight, since they are not usually machine-verifiable.
And yet we “know” that the results are right. How can that be, if we also know that our arguments aren’t 100% correct? Many reasons, but one is that we can see that our current proofs could be made more rigorous. We can see that they are steelmannable. And in fact, our current proofs were often reached by effectively steelmanning Euler’s and Newton’s proofs.
If we see DeepSeek making arguments that are steelmannable, that should increase our expectation that future models will, in fact, be able to steelman those arguments.