In contrast with the title, you did not show that the MWI is falsifiable nor testable.
I agree that he didn’t show testable, but rather the possibility of it (and the formalization of it).
You just showed that MWI is “better” according to your “goodness” index, but that index is not so good
There’s a problem with choosing the language for Solomonoff/MML, so the index’s goodness can be debated. However, I think in general index is sound.
You calculate the probability of a theory and use this as an index of the “truthness” of it, but that’s confusing the reality with the model of it.
I don’t think he’s saying that theories fundamentally have probabilities. Rather, as a Bayesian, he gives some priors to each theory. As more evidences accumulate, the right theory will update and its probability approaches 1.
The reason human understanding can’t be part of the equations is, as EY says, shorter “programs” are more likely to govern the universe than longer “programs,” essentially because these “programs” are more likely to be written if you throw down some random bits to make a program that governs the universe.
So I don’t buy your arguments in the next section.
But that argument is not valid: we rejected the hypothesis that nebulae are not distant galaxies not because the Occam’s Razor is irrelevant, but because we measured their distance and found that they are inside our galaxy; without this information, the simpler hypothesis would be that they are distant galaxies.
EY is comparing the angel explanation with the galaxies explanation; you are supposed to reject the angels and usher in the galaxies. In that case, the anticipations are truly the same. You can’t really prove whether there are angels.
But how often does the Occam’s Razor induce you to neglect a good model, as opposed to how often it let us neglect bad models?
What do you mean by “good”? Which one is “better” out of 2 models that give the same prediction? (By “model” I assume you mean “theory”)
but indeed it is useful to represent effectively what are the results of the typical educational experiments, where the difference between “big” and “small” is in no way ambiguous, and allows you to familiarize fast with the bra-ket math.
You admit that Copenhagen is unsatisfactory but it is useful for education. I don’t see any reason not to teach MWI in the same vein.
Now imagine Einstein did not develop the General Relativity, but we anyway developed the tools to measure the precession of Mercury and we have to face the inconsistency with our predictions through Newton’s Laws: the analogous of the CI would be “the orbit of Mercury is not the one anticipated by Newton’s Laws but this other one, now if you want to calculate the transits of Mercury as seen from the Earth for the next million years you gotta do THIS math and shut up”; the analogous of the MWI would be something like “we expect the orbit of Mercury to precede at this rate X but we observe this rate Y; well, there is another parallel universe in which the preceding rate of Mercury is Z such that the average between Y and Z is the expected X due to our beautiful indefeasible Newton’s Law”.
If indeed the expectation value of observable V of mercury is X but we observe Y with Y not= X (that is to say that the variance of V is nonzero), then there isn’t a determinate formula for predict V exactly in your first Newton/random formula scenario. At the same time, someone who has the Copenhagen interpretation would have the same expectation value X, but instead of saying there’s another world he says there’s a wave function collapse. I still think that the parallel world is a deduced result from universal wave function, superposition, decoherence, and etc that Copenhagen also recognizes. So the Copenhagen view essentially say “actually, even though the equations say there’s another world, there is none, and on top of that we are gonna tell you how this collapsing business works”. This extra sentence is what causes the Razor to favor MWI.
Much of what you are arguing seems to stem from your dissatisfaction of the formalization of Occam’s Razor. Do you still feel that we should favor something like human understanding of a theory over the probability of a theory being true based on its length?
You admit that Copenhagen is unsatisfactory but it is useful for education. I don’t see any reason not to teach MWI in the same vein.
Because it sets people up to think that QM can be understood in terms of wavefunctions that exist and contain parallel realities; yet when the time comes to calculate anything, you have to go back to Copenhagen and employ the Born rule.
Also, real physics is about operator algebras of observables. Again, this is something you don’t get from pure Schrodinger dynamics.
QM should be taught in the Copenhagen framework, and then there should be some review of proposed ontologies and their problems.
There’s a problem with choosing the language for Solomonoff/MML, so the index’s goodness can be debated. However, I think in general index is sound.
When I hear about Solomonoff Induction, I reach for my gun :)
The point is that you can’t use Solomonoff Induction or MML to discriminate between interpretations of quantum mechanics: these are formal frameworks for inductive inference, but they are underspecified and, in the case of Solomonoff Induction, uncomputable.
Yudkowsky and other people here seem to use the terms informally, which is an usage I object to: it’s just a fancy way of saying Occam’s razor, and it’s an attempt to make their arguments more compelling that they actually are by dressing them in pseudomathematics.
The reason human understanding can’t be part of the equations is, as EY says, shorter “programs” are more likely to govern the universe than longer “programs,” essentially because these “programs” are more likely to be written if you throw down some random bits to make a program that governs the universe.
That assumes that Solomonoff Induction is the ideal way of performing inductive reasoning, which is debateable.
But even assuming that, and ignoring the fact that Solomonoff Induction is underspecified, there is still a fundamental problem:
The hypotheses considered by Solomonoff Induction are probability distributions on computer programs that generate observations, how do you map them to interpretations of quantum mechanics?
What program corresponds to Everett’s interpretation? What programs correspond to Copenhagen, objective collapse, hidden variable, etc.?
Unless you can answer these questions, any reference to Solomonoff Induction in a discussion about interpretations of quantum mechanics is a red herring.
So the Copenhagen view essentially say “actually, even though the equations say there’s another world, there is none, and on top of that we are gonna tell you how this collapsing business works”. This extra sentence is what causes the Razor to favor MWI.
Actually Copenhagen doesn’t commit to collapse being objective. People here seem to conflate Copenhagen with objective collapse, which is a popular misconception.
Objective collapse intepretations generally predict deviations from standard quantum mechanics in some extreme cases, hence they are in principle testable.
I agree that he didn’t show testable, but rather the possibility of it (and the formalization of it).
There’s a problem with choosing the language for Solomonoff/MML, so the index’s goodness can be debated. However, I think in general index is sound.
I don’t think he’s saying that theories fundamentally have probabilities. Rather, as a Bayesian, he gives some priors to each theory. As more evidences accumulate, the right theory will update and its probability approaches 1.
The reason human understanding can’t be part of the equations is, as EY says, shorter “programs” are more likely to govern the universe than longer “programs,” essentially because these “programs” are more likely to be written if you throw down some random bits to make a program that governs the universe.
So I don’t buy your arguments in the next section.
EY is comparing the angel explanation with the galaxies explanation; you are supposed to reject the angels and usher in the galaxies. In that case, the anticipations are truly the same. You can’t really prove whether there are angels.
What do you mean by “good”? Which one is “better” out of 2 models that give the same prediction? (By “model” I assume you mean “theory”)
You admit that Copenhagen is unsatisfactory but it is useful for education. I don’t see any reason not to teach MWI in the same vein.
If indeed the expectation value of observable V of mercury is X but we observe Y with Y not= X (that is to say that the variance of V is nonzero), then there isn’t a determinate formula for predict V exactly in your first Newton/random formula scenario. At the same time, someone who has the Copenhagen interpretation would have the same expectation value X, but instead of saying there’s another world he says there’s a wave function collapse. I still think that the parallel world is a deduced result from universal wave function, superposition, decoherence, and etc that Copenhagen also recognizes. So the Copenhagen view essentially say “actually, even though the equations say there’s another world, there is none, and on top of that we are gonna tell you how this collapsing business works”. This extra sentence is what causes the Razor to favor MWI.
Much of what you are arguing seems to stem from your dissatisfaction of the formalization of Occam’s Razor. Do you still feel that we should favor something like human understanding of a theory over the probability of a theory being true based on its length?
Because it sets people up to think that QM can be understood in terms of wavefunctions that exist and contain parallel realities; yet when the time comes to calculate anything, you have to go back to Copenhagen and employ the Born rule.
Also, real physics is about operator algebras of observables. Again, this is something you don’t get from pure Schrodinger dynamics.
QM should be taught in the Copenhagen framework, and then there should be some review of proposed ontologies and their problems.
When I hear about Solomonoff Induction, I reach for my gun :)
The point is that you can’t use Solomonoff Induction or MML to discriminate between interpretations of quantum mechanics: these are formal frameworks for inductive inference, but they are underspecified and, in the case of Solomonoff Induction, uncomputable.
Yudkowsky and other people here seem to use the terms informally, which is an usage I object to: it’s just a fancy way of saying Occam’s razor, and it’s an attempt to make their arguments more compelling that they actually are by dressing them in pseudomathematics.
That assumes that Solomonoff Induction is the ideal way of performing inductive reasoning, which is debateable. But even assuming that, and ignoring the fact that Solomonoff Induction is underspecified, there is still a fundamental problem:
The hypotheses considered by Solomonoff Induction are probability distributions on computer programs that generate observations, how do you map them to interpretations of quantum mechanics?
What program corresponds to Everett’s interpretation? What programs correspond to Copenhagen, objective collapse, hidden variable, etc.?
Unless you can answer these questions, any reference to Solomonoff Induction in a discussion about interpretations of quantum mechanics is a red herring.
Actually Copenhagen doesn’t commit to collapse being objective. People here seem to conflate Copenhagen with objective collapse, which is a popular misconception.
Objective collapse intepretations generally predict deviations from standard quantum mechanics in some extreme cases, hence they are in principle testable.