= 27d567bc2d48d9f40e9ccc20ea370b15)
Vladimir_Nesov comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (335)
By "can't update" I refer to the problem with marking Thursday "impossible", since you'll encounter Thursday later.
It's not a problem with the model of ontology and preference, it's merely specifics of what kinds of observation events are expected.
If the goal is to identify an event corresponding to observations in the form of a set of possible worlds, and there are different-looking observations that could correspond to the same event (e.g. observed at different time in the same possible world), their difference is pure logical uncertainty. They differ, but only in the same sense as 2+2 and (7-5)*(9-7) differ, where you need but to compute denotation: the agent running on the described model doesn't care about the difference, indeed wants to factor it out.
I humbly apologize for my inability to read (may the Values of Less Wrong be merciful).
Hmm, my argument is summarized in this phrase:
If you update on your knowledge that "it's not Tuesday", it means that you've thrown away the parts of your sample space that contain the territory corresponding to Tuesday, marked them impossible, no longer part of what you can think about, what you can expect to observe again (interpret as implied by observations). Assuming the model is honest, that you really do conceptualize the world through that model, your mind is now blind to the possibility of Tuesday. Come Tuesday, you'll be able to understand your observations in any way but as implying that it's Tuesday, or that the events you observe are the ones that could possibly occur on Tuesday.
This is not a way to treat your mind. (But then again, I'm probably being too direct in applying the consequences of really believing what is being suggested, as in the case of Pascal's Wager, for it to reflect the problem statement you consider.)
In a probability space where you have distinct (non-intersecting) "Monday" and "Tuesday", it is expected (in the informal sense, outside the broken model) that you'll observe Tuesday after observing Monday, that upon observing Monday you rule out Tuesday, and that upon observing Tuesday you won't be able to recognize it as such because it's already ruled out. "Observer-moments" can be located on the same history, and a probability space that distinguishes them will tear down your understanding of the other observer-moments once you've observed one of them and excluded the rest. This model promises you a map disconnected from reality.
It is not the case with a probability space based on possible worlds that after concluding ~X, you expect (in the informal sense) to observe X after that. Possible worlds model is in accordance with this (informal) axiom. Sample space based on "observer-moments" is not.