I think you might be taking my attempt at wry humor too seriously. I don’t actually agree with Scientist 3: I just think they’re marginally less wrong than Scientist 2, who is marginally less wrong than Scientist 1. They’re all Frequentists, and as a result they’re all confused. Scientists 2 and 3 are just each cumulatively conditioning on one more chosen piece of information.
My actual opinion is implied by the line from the joke “…you should include everything you already know about the situation in your priors. That’s kind of obvious, once you stop and think about it.” and is then reprised in the punchline “…the clue they forgot to include in their priors…”— which I then expanded on in the serious footnote to the joke, since I assumed many frequentists would still not get it.
Questions as reference class is underexposed topic which can be presented as a joke: “Why this table is green?”—“Because if it were red, you would ask: “Why it is red?”″
That’s also a good one. Basically the Look-Elsewhere Effect.
Sadly the problem with fallacy humor is that people too stuck in the fallacy rarely get it (and may get upset) — but it can be very helpful to any who do.
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.
I think you might be taking my attempt at wry humor too seriously. I don’t actually agree with Scientist 3: I just think they’re marginally less wrong than Scientist 2, who is marginally less wrong than Scientist 1. They’re all Frequentists, and as a result they’re all confused. Scientists 2 and 3 are just each cumulatively conditioning on one more chosen piece of information.
My actual opinion is implied by the line from the joke “…you should include everything you already know about the situation in your priors. That’s kind of obvious, once you stop and think about it.” and is then reprised in the punchline “…the clue they forgot to include in their priors…”— which I then expanded on in the serious footnote to the joke, since I assumed many frequentists would still not get it.
Thanks for the link, I’ll go read it.
Questions as reference class is underexposed topic which can be presented as a joke: “Why this table is green?”—“Because if it were red, you would ask: “Why it is red?”″
That’s also a good one. Basically the Look-Elsewhere Effect.
Sadly the problem with fallacy humor is that people too stuck in the fallacy rarely get it (and may get upset) — but it can be very helpful to any who do.
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.