That is a good point. But bridging laws probably aren’t that complex. At least, not for inferring the basic laws of physics. How many things on the order of Newtonian physics physics do you need? A hundred? A thousand? That could plausibly fit into a few megabytes. So it seems plausible that you could have GR + QFT and a megabyte of briding laws plus some other data to specify local conditions and so on.
And if you disagree with that, then how much data do you think AIXI would need? Let’s say you’re talking about a video of an apple falling in a forest with the sky and ground visible. How much data would you need, then? 1GB? 1TB? 1 PB? I think 1GB is also plausible, and I’d be confused if you said 1TB.
it seems plausible that you could have GR + QFT and a megabyte of briding laws plus some other data to specify local conditions and so on.
How computationally bound variant of AIXI can arrive at QFT? You most likely can’t faithfully simulate a non-trivial quantum system on a classical computer within reasonable time limits. The AIXI is bound to find some computationally feasible approximation of QFT first (Maxwell’s equations and cutoff at some arbitrary energy to prevent ultraviolet catastrophe, maybe). And with no access to experiments it cannot test simpler systems.
A simple strategy when modeling reality is to make effective models which describe what is going and then try to reduce those models to something simpler. So you might view the AI as making some effective modela and going “which simple theory + some bridging laws are equivalent to this effective model”? And then just go over a vast amount of such theories/bridging laws and figure out which is equivalent. It would probably use a lot of heuristics, sure. But QFT (or rather, whatever effective theory we eventually find which is simpler than QFT and GR together) is pretty simple. So going forwards from simple theories and seeing how they bridge to your effective model would probably do the trick.
And remember, we’re talking about an ASI here. It would likely have an extremely large amount of compute. There are approaches that we can’t do today which would become practical with several OoM of more compute worldwide. You can think for a long time, perform big experiments, go through loads of hypothesis etc. And you don’t need to simulate systems to do all of this. Going “Huh, this fundamental theory has a symmetry group. Simple symmetries pop up a bunch in my effective models of the video. Plausibly, symmetry has an important role in the character of physical law? I wonder what I can derive from looking at symmetry groups.”
Anyway, I think some of my cruxes are: 1) How complex are our fundamental theories and bridging laws really? 2) How much incompressible data in terms of bits are there in a couple of frames of a falling apple? 3) Is it physically possible to run something like infra-Bayesianism over poly time hypothesis, with clever heuristics, and use it to do the things I’ve describe in this thread.
Thanks for clearing my confusion. I’ve grown rusty on the topic of AIXI.
So going forwards from simple theories and seeing how they bridge to your effective model would probably do the trick
Assuming that there’s not much fine-tuning to do. Locating our world in the string theory landscape could take quite a few bits if it’s computationally feasible at all.
And remember, we’re talking about an ASI here
It hinges on assumption that ASI of this type is physically realizable. I can’t find it now, but I remember that preprocessing step, where heuristic generation is happening, for one variant of computable AIXI was found to take impractical amount of time. Am I wrong? Are there newer developments?
It hinges on assumption that ASI of this type is physically realizable.
TL;DR I think I’m approaching this conversation in a different way to you. I’m trying to point out an approach to analyzing ASI rather than doing the actual analysis, which would take a lot more effort and require me to grapple with this question.
Thanks for clearing my confusion. I’m grown rusty on the topic of AIXI.
So have I. It is probable that you know more than I do about AIXI right now.
Assuming that there’s not much fine-tuning to do. Locating our world in the string theory landscape could take quite a few bits if it’s computationally feasible at all.
I don’t know how simple string theory actually is, and the bridging laws seem like they’d be even more complex than QFT+GR so I kind of didn’t consider it. But yeah, AIXI would.
I can’t find it now, but I remember that preprocessing step, where heuristic generation is happening, for one variant of computable AIXI was found to take unpractical amount of time.
So I am unsure if AIXI is the right thing to be approximating. And I’m also unsure if AIXI is a fruitful thing to be approximating. But approximating a thing like AIXI, and other mathematical or physical to rationality, seems like the right approach to analyze an ASI. At least, for estimating the things it can’t do. If I had far more time and energy, I would estimate how much data a perfect reasoner would need to figure out the laws of the universe by collecting all of our major theories and estimating their Kolmogorov complexity, their levin complexity etc. Then I’d try and make guesses as to how much incompressible data there is in e.g. a video of a falling apple. Maybe I’d look at whether that data has any bearing on the bridging laws we think exist. After that, I’d look at various approximations of ideal reasoners, whether they’re physically feasible, how various assumptions like e.g. P=NP might affect things and so on.
That’s what I think the right approach to examining what an ASI can do in this particular case looks like. As compared to what the OP did, which I think is misguided. I’ve been trying to point at that approach in this thread, rather than actually do it. Because that would take too much effort to be worth it. I’d have to got over the literature for computably feasible AIXI variants and all sorts of other stuff.
That is a good point. But bridging laws probably aren’t that complex. At least, not for inferring the basic laws of physics. How many things on the order of Newtonian physics physics do you need? A hundred? A thousand? That could plausibly fit into a few megabytes. So it seems plausible that you could have GR + QFT and a megabyte of briding laws plus some other data to specify local conditions and so on.
And if you disagree with that, then how much data do you think AIXI would need? Let’s say you’re talking about a video of an apple falling in a forest with the sky and ground visible. How much data would you need, then? 1GB? 1TB? 1 PB? I think 1GB is also plausible, and I’d be confused if you said 1TB.
How computationally bound variant of AIXI can arrive at QFT? You most likely can’t faithfully simulate a non-trivial quantum system on a classical computer within reasonable time limits. The AIXI is bound to find some computationally feasible approximation of QFT first (Maxwell’s equations and cutoff at some arbitrary energy to prevent ultraviolet catastrophe, maybe). And with no access to experiments it cannot test simpler systems.
A simple strategy when modeling reality is to make effective models which describe what is going and then try to reduce those models to something simpler. So you might view the AI as making some effective modela and going “which simple theory + some bridging laws are equivalent to this effective model”? And then just go over a vast amount of such theories/bridging laws and figure out which is equivalent. It would probably use a lot of heuristics, sure. But QFT (or rather, whatever effective theory we eventually find which is simpler than QFT and GR together) is pretty simple. So going forwards from simple theories and seeing how they bridge to your effective model would probably do the trick.
And remember, we’re talking about an ASI here. It would likely have an extremely large amount of compute. There are approaches that we can’t do today which would become practical with several OoM of more compute worldwide. You can think for a long time, perform big experiments, go through loads of hypothesis etc. And you don’t need to simulate systems to do all of this. Going “Huh, this fundamental theory has a symmetry group. Simple symmetries pop up a bunch in my effective models of the video. Plausibly, symmetry has an important role in the character of physical law? I wonder what I can derive from looking at symmetry groups.”
Anyway, I think some of my cruxes are: 1) How complex are our fundamental theories and bridging laws really? 2) How much incompressible data in terms of bits are there in a couple of frames of a falling apple? 3) Is it physically possible to run something like infra-Bayesianism over poly time hypothesis, with clever heuristics, and use it to do the things I’ve describe in this thread.
Thanks for clearing my confusion. I’ve grown rusty on the topic of AIXI.
Assuming that there’s not much fine-tuning to do. Locating our world in the string theory landscape could take quite a few bits if it’s computationally feasible at all.
It hinges on assumption that ASI of this type is physically realizable. I can’t find it now, but I remember that preprocessing step, where heuristic generation is happening, for one variant of computable AIXI was found to take impractical amount of time. Am I wrong? Are there newer developments?
TL;DR I think I’m approaching this conversation in a different way to you. I’m trying to point out an approach to analyzing ASI rather than doing the actual analysis, which would take a lot more effort and require me to grapple with this question.
So have I. It is probable that you know more than I do about AIXI right now.
I don’t know how simple string theory actually is, and the bridging laws seem like they’d be even more complex than QFT+GR so I kind of didn’t consider it. But yeah, AIXI would.
So I am unsure if AIXI is the right thing to be approximating. And I’m also unsure if AIXI is a fruitful thing to be approximating. But approximating a thing like AIXI, and other mathematical or physical to rationality, seems like the right approach to analyze an ASI. At least, for estimating the things it can’t do. If I had far more time and energy, I would estimate how much data a perfect reasoner would need to figure out the laws of the universe by collecting all of our major theories and estimating their Kolmogorov complexity, their levin complexity etc. Then I’d try and make guesses as to how much incompressible data there is in e.g. a video of a falling apple. Maybe I’d look at whether that data has any bearing on the bridging laws we think exist. After that, I’d look at various approximations of ideal reasoners, whether they’re physically feasible, how various assumptions like e.g. P=NP might affect things and so on.
That’s what I think the right approach to examining what an ASI can do in this particular case looks like. As compared to what the OP did, which I think is misguided. I’ve been trying to point at that approach in this thread, rather than actually do it. Because that would take too much effort to be worth it. I’d have to got over the literature for computably feasible AIXI variants and all sorts of other stuff.