That was an interesting read, thanks again: you’ve researched the thinking on this at depth. Seriously, there are hundreds of articles confused by this stuff? Wow, what a waste of intellectual effort…
As you say:
We also show that DA becomes strongest if it is based on the idea of the “natural reference class” of observers, that is, the observers who know about the DA (i.e. a Self-Referenced DA).
So the meta move predates my joke — people have actually had that level of confusion as well: I wasn’t the first to invent Scientist 3, they already exist.
At the risk of belaboring what, sadly, seems not to been obvious to many past writers, the “natural reference class” defined above is also an invalid prior. It’s extremely easy to construct random distributions over time whose criteria break causality: the concept of a random uniformly-selected second in some predefined range is actually well formed, and so is “whenever this radioactive atom ends up decaying”, but the concept of a random uniformly-selected second drawn from all of those seconds in which any variable property X happens to be true breaks causality (unless you do this in retrospect): to determine the correct rate for the earlier seconds you need to have precognition about the state of X at times in in the future. The question you need to ask yourself is: “part way through this period, could I accurately construct the probability distribution up to this point, and tell you how much probability mass is then left over for the future rest of the distribution, without needing any information from the future?” If the answer is ”No” then you’re requiring precognition in the assumptions of your argument, and are going to get weird results. To do a worked example, for the radioactive atom: if it has already decayed, then the distribution so far is a Dirac delta function at the instant that it decayed, with 0 probability-mass remaining; otherwise the distribution so far is all 0, with all 1 of the probability-mass left over.
That was an interesting read, thanks again: you’ve researched the thinking on this at depth. Seriously, there are hundreds of articles confused by this stuff? Wow, what a waste of intellectual effort…
As you say:
So the meta move predates my joke — people have actually had that level of confusion as well: I wasn’t the first to invent Scientist 3, they already exist.
At the risk of belaboring what, sadly, seems not to been obvious to many past writers, the “natural reference class” defined above is also an invalid prior. It’s extremely easy to construct random distributions over time whose criteria break causality: the concept of a random uniformly-selected second in some predefined range is actually well formed, and so is “whenever this radioactive atom ends up decaying”, but the concept of a random uniformly-selected second drawn from all of those seconds in which any variable property X happens to be true breaks causality (unless you do this in retrospect): to determine the correct rate for the earlier seconds you need to have precognition about the state of X at times in in the future. The question you need to ask yourself is: “part way through this period, could I accurately construct the probability distribution up to this point, and tell you how much probability mass is then left over for the future rest of the distribution, without needing any information from the future?” If the answer is ”No” then you’re requiring precognition in the assumptions of your argument, and are going to get weird results. To do a worked example, for the radioactive atom: if it has already decayed, then the distribution so far is a Dirac delta function at the instant that it decayed, with 0 probability-mass remaining; otherwise the distribution so far is all 0, with all 1 of the probability-mass left over.