Okay, I think our crux comes from the slight ambiguity from the term “anthropic shadow”.
I would not consider that anthropic shadow, because the reasoning has nothing to do with anthropics. Your analysis is correct, but so is the following:
Suppose you have N coins. If all N coins come up 1, you find a diamond in a box. For each coin, you have 50:50 credence about whether it always comes up 0, or if it can also come up 1.
For N>1, you get a diamond shadow, which means that even if you’ve had a bunch of flips where you didn’t find a diamond, you might actually have to conclude that you’ve got a 1-in-4 chance of finding one on your next flip.
The “ghosts are as good as gone” principle implies that death has no special significance when it becomes to bayesian reasoning.
Going back to the LHC example, if the argument worked for vacuum collapse, it would also work for the LHC doing harmless things (like discovering the Higg’s boson or permanently changing the color of the sky or getting a bunch of physics nerds stoked or granting us all immortality or what not) because of this principle (or just directly adapting the argument for vacuum collapse to other uncertain consequences of the LHC).
In the bird example, why would the baguette dropping birds be evidence of “LHC causes vacuum collapse” instead of, say, “LHC does not cause vacuum collapse”? What are the probabilities for the four possible combinations?
I think we basically agree now. I think my original comments were somewhat confused, but also the deadly coin model was somewhat confused. I think the best model is a variant of the N-coin model where one or more of the coins are obscured, and I think in this model your proof goes through to show that you should independently perform Bayesian updates on each coin, and that since you don’t get information about the obscured coin, you should not update on it in a anthropic shadow style way.
Okay, I think our crux comes from the slight ambiguity from the term “anthropic shadow”.
I would not consider that anthropic shadow, because the reasoning has nothing to do with anthropics. Your analysis is correct, but so is the following:
The “ghosts are as good as gone” principle implies that death has no special significance when it becomes to bayesian reasoning.
Going back to the LHC example, if the argument worked for vacuum collapse, it would also work for the LHC doing harmless things (like discovering the Higg’s boson or permanently changing the color of the sky or getting a bunch of physics nerds stoked or granting us all immortality or what not) because of this principle (or just directly adapting the argument for vacuum collapse to other uncertain consequences of the LHC).
In the bird example, why would the baguette dropping birds be evidence of “LHC causes vacuum collapse” instead of, say, “LHC does not cause vacuum collapse”? What are the probabilities for the four possible combinations?
I think we basically agree now. I think my original comments were somewhat confused, but also the deadly coin model was somewhat confused. I think the best model is a variant of the N-coin model where one or more of the coins are obscured, and I think in this model your proof goes through to show that you should independently perform Bayesian updates on each coin, and that since you don’t get information about the obscured coin, you should not update on it in a anthropic shadow style way.