I’ve only talked to Fable about it, so I don’t have a favorite explanation. (and I can’t say I actually understand it).
Schmidhuber is the other guy (other than Tegmark) that influenced the everything-list people and Wei Dai, to my understanding. But he eventually switched from a simplicity prior to a simplicity+speed prior. It seems interesting and underexplored on LessWrong. But it also seems, at first glance, less motivated than a pure beautiful Solomonoff induction thing. So I don’t know.
Staring at the Schmidhuber paper for a while now, I don’t think the speed prior helps much here. My understanding is that instead of using the length of a program that produces a string, it uses the length of the program plus the logarithm of the runtime of the output string being computed. But I don’t think this helps much: we will be a bit envious of the aliens who lived 6 billion years after the Big Bang (they have 1 bit advantage over us), but we can still easily outcompete them by building a bigger obelisk. And I think world summoning by writing also works: in the thought experiment, the new world’s program code already encodes full brain-uploads and everything, so people can immediately start living happy lives in the new world; pointing to their experiences doesn’t take much more computation the amount of computation that happened in the outside world leading up to the moment of writing down the new world’s program code.
So I don’t think the speed prior fixes any of the problems described here, and meanwhile it seems to make various unintuitive predictions (at least according to Shmidhuber’s paper, I haven’t thought through if these are fixable), so altogether I’m not very excited about it.
Cool, thanks for looking into it! But wouldn’t the program that locates our obelisk / the world summoning text also take a while? If it’s one of the natural short description length programs like “find the largest obelisk” or “find the most common string”, then it might take extremely long since you’d have to run the universe very far into the future. (I may be missing something obvious).
Sure, but normal hypotheses like “I’m a flesh-and-blood human on Earth, a tiny planet 13 billion years after the Big Bang” also take a lot of computation. My current guess is that logarithm of runtime is not that big of a penalty, and the Schmidhuber prior will give you something similar to the Solomonoff-prior. But if I’m wrong about this, and the runtime penalty is stronger than I imagine, that’s even worse news for the Schmidhuber prior because then you need to make up exotic hypotheses about how the world was born yesterday.
Coming back to this again—still really useful, thank you. The obelisk and world-summoning points are quite strong.
Have you looked into Schmidhuber’s speed prior at all? It seems to at least ward off those. (although other problems remain, of course).
Thanks! No, I haven’t really heard of the Schmidhuber speed prior. Do you have a link to your favorite explanation of it?
I’ve only talked to Fable about it, so I don’t have a favorite explanation. (and I can’t say I actually understand it).
Schmidhuber is the other guy (other than Tegmark) that influenced the everything-list people and Wei Dai, to my understanding. But he eventually switched from a simplicity prior to a simplicity+speed prior. It seems interesting and underexplored on LessWrong. But it also seems, at first glance, less motivated than a pure beautiful Solomonoff induction thing. So I don’t know.
Staring at the Schmidhuber paper for a while now, I don’t think the speed prior helps much here. My understanding is that instead of using the length of a program that produces a string, it uses the length of the program plus the logarithm of the runtime of the output string being computed. But I don’t think this helps much: we will be a bit envious of the aliens who lived 6 billion years after the Big Bang (they have 1 bit advantage over us), but we can still easily outcompete them by building a bigger obelisk. And I think world summoning by writing also works: in the thought experiment, the new world’s program code already encodes full brain-uploads and everything, so people can immediately start living happy lives in the new world; pointing to their experiences doesn’t take much more computation the amount of computation that happened in the outside world leading up to the moment of writing down the new world’s program code.
So I don’t think the speed prior fixes any of the problems described here, and meanwhile it seems to make various unintuitive predictions (at least according to Shmidhuber’s paper, I haven’t thought through if these are fixable), so altogether I’m not very excited about it.
Cool, thanks for looking into it! But wouldn’t the program that locates our obelisk / the world summoning text also take a while? If it’s one of the natural short description length programs like “find the largest obelisk” or “find the most common string”, then it might take extremely long since you’d have to run the universe very far into the future. (I may be missing something obvious).
Sure, but normal hypotheses like “I’m a flesh-and-blood human on Earth, a tiny planet 13 billion years after the Big Bang” also take a lot of computation. My current guess is that logarithm of runtime is not that big of a penalty, and the Schmidhuber prior will give you something similar to the Solomonoff-prior. But if I’m wrong about this, and the runtime penalty is stronger than I imagine, that’s even worse news for the Schmidhuber prior because then you need to make up exotic hypotheses about how the world was born yesterday.
That makes sense to me at first glance, thanks.