Looks like I almost missed a very interesting discussion. Hope I’m not too late in joining it.
As far as I can tell, you still need the Solomonoff prior for decision making. Kevin T. Kelly’s Ockham Efficiency Theorem says that by using Ockham’s Razor you minimize reversals of opinion prior to finding the true theory, but that seems irrelevant when you have to bet on something, especially since even after you’ve found the truth using Ockham’s Razor, you don’t know that you’ve found it.
Also, I think there’s a flaw in Shalizi’s argument:
Suppose one of these rules correctly classifies all the data.
But if you’re working with a sparse random subset of the rules, why would any of them correctly classify all the data? In algorithmic information theory, the set of rules is universal so one of them is guaranteed to fit the data (assuming the input is computable, which may not be a good assumption but that’s a separate issue).
All good points if the universe has important aspects that are computable, which seems uncontroversial to me. Thanks for the link, I’d lost it sometime ago, that thread is pretty epic.
Looks like I almost missed a very interesting discussion. Hope I’m not too late in joining it.
As far as I can tell, you still need the Solomonoff prior for decision making. Kevin T. Kelly’s Ockham Efficiency Theorem says that by using Ockham’s Razor you minimize reversals of opinion prior to finding the true theory, but that seems irrelevant when you have to bet on something, especially since even after you’ve found the truth using Ockham’s Razor, you don’t know that you’ve found it.
Also, I think there’s a flaw in Shalizi’s argument:
But if you’re working with a sparse random subset of the rules, why would any of them correctly classify all the data? In algorithmic information theory, the set of rules is universal so one of them is guaranteed to fit the data (assuming the input is computable, which may not be a good assumption but that’s a separate issue).
All good points if the universe has important aspects that are computable, which seems uncontroversial to me. Thanks for the link, I’d lost it sometime ago, that thread is pretty epic.