The backward link isn’t causal. It’s a logical/Platonic-dependency link, which is indeed how TDT handles counterfactuals (i.e., how it handles the propagation of “surgical alterations” to the decision node C).
My understanding of the link in question, is that the logical value of the digit of pi causes Omega to take the physical action of putting the money in the box.
See Eliezer’s second approach:
2) Treat differently mathematical knowledge that we learn by genuinely mathematical reasoning and by physical observation. In this case we know (D xor E) not by mathematical reasoning, but by physically observing a box whose state we believe to be correlated with D xor E. This may justify constructing a causal DAG with a node descending from D and E, so a counterfactual setting of D won’t affect the setting of E.
My original post addressed Eliezer’s original specification of TDT’s sense of “logical dependency”, as quoted in the post.
I don’t think his two proposals for revising TDT are pinned down enough yet to be able to tell what the revised TDTs would decide in any particular scenario. Or at least, my own understanding of the proposals isn’t pinned down enough yet. :)
The backward link isn’t causal. It’s a logical/Platonic-dependency link, which is indeed how TDT handles counterfactuals (i.e., how it handles the propagation of “surgical alterations” to the decision node C).
My understanding of the link in question, is that the logical value of the digit of pi causes Omega to take the physical action of putting the money in the box.
See Eliezer’s second approach:
My original post addressed Eliezer’s original specification of TDT’s sense of “logical dependency”, as quoted in the post.
I don’t think his two proposals for revising TDT are pinned down enough yet to be able to tell what the revised TDTs would decide in any particular scenario. Or at least, my own understanding of the proposals isn’t pinned down enough yet. :)