4 ms·

Oh, and just because you have a infinitely powerful quantum computer simulating infinitely many recursive universes with their own infinitely powerful quantum c

Oh, and just because you have a infinitely powerful quantum computer simulating infinitely many recursive universes with their own infinitely powerful quantum computers, correlation != causation doesn't apply anymore?

benched 13y ago
Actual inter-level causation is not needed for the characters to experience events as they do in the story. The rules that imply that all levels would unfold identically are low-level. Human narrative events that alias as inter-level causation are high-level, sort of emergent effects.
- ben0x539 13y ago
  I agree with that. But I'm questioning the reasoning at the end of the story that they better not shut off the simulation, implied to be for their own sake. The observation that their higher-level reality counterparts will likely choose to shut down the simulation exactly if they do themselves, but the protagonists' choice doesn't influence that.
  - lmkg 13y ago
    IMHO, the entire point of the story is that causality has become twisted into a counterintuitive shape. From a naive literal point of view, no, the universe above theirs is independent. Diane's hypothesis/theorem is that, because their universe is at or near a fixed point, they have in effect invented a way to have unlimited control over their own universe. While there is no causal relationship from their universe the one up the chain, the symmetry implies their actions are mirrored. I've read some of this author's other works. He likes playing with paradoxes like this. It's a twist on causality (and free will), inventing a new way for your actions to have an impact on the universe in the absence of a traditional causal link. It's pretty damn clever.
    - benched 13y ago
      Yes, exactly. It's like a sneaky way of asking if physics is deterministic, alluding to the paradoxical relation between determinism and free will.
      - dllthomas 13y ago
        And a fun way of playing with the notion of fixed points, to boot!
  - prutschman 13y ago
    They are making decisions in the presence of the knowledge that essentially identical "god" agents will be making decisions based on the same information and the same mental states, and that the "god" agents' decisions will impact their own existence. If at any time they were to "choose" to shut down the simulation, it can only be because the total state of the world, including their sense-data and internal mental states, cause them to do so. If that's true for them at time T, then by hypothesis it's true for the "god" agents as well. It may be that, in the sense you have in mind, the protagonists simply do not have choice.
  - vilhelm_s 13y ago
    Ah, but is it really that simple? :) For similar puzzles, you might enjoy Douglas Hofstadter's essay about "super-rationality" (there is a HTML version on gwern's site: http://www.gwern.net/docs/1985-hofstadter http://www.gwern.net/docs/1985-hofstadter), Adam Elga's "Defeating Dr. Evil with self-locating belief" (http://philsci-archive.pitt.edu/1036/ http://philsci-archive.pitt.edu/1036/), and Scott Aaronson's lecture about Newcomb's paradox (http://www.scottaaronson.com/democritus/lec18.html http://www.scottaaronson.com/democritus/lec18.html).
shurcooL 13y ago
If you have an infinitely powerful computer, does that also imply that you necessarily have infinite storage?
- eropple 13y ago
  I don't see why it would; re-computation would be no more meaningfully expensive than a load/store, would it?
- JoshTriplett 13y ago
  Infinite CPU capability does not automatically imply infinite storage, but it does imply that you can compress any storage to an information-theoretic minimum size, by writing a search for an arbitrary program to generate the same data. And that's some absurdly good compression, given the universe simulator assumed in the story: anything that will ever occur as a state of the universe can be compressed to a set of space-time coordinates and an extraction algorithm. With some additional assumptions about the nature of the pseudo-causal loop demonstrated in the story, that compression can also include any arbitrary search parameters you can conceive of, without you having to express them as a program: just search for the data that will be on your hard drive in the future after having executed the search you're currently thinking of.
- polemic 13y ago
  Good question.. I assume its a relatively trivial question for a serious mathematician, but I suspect it's something like: there are classes of problems that, given infinite computation, require infinite storage. In this case it is strongly implied.

benched 13y ago

Actual inter-level causation is not needed for the characters to experience events as they do in the story. The rules that imply that all levels would unfold identically are low-level. Human narrative events that alias as inter-level causation are high-level, sort of emergent effects.

ben0x539 13y ago
I agree with that. But I'm questioning the reasoning at the end of the story that they better not shut off the simulation, implied to be for their own sake. The observation that their higher-level reality counterparts will likely choose to shut down the simulation exactly if they do themselves, but the protagonists' choice doesn't influence that.
- lmkg 13y ago
  IMHO, the entire point of the story is that causality has become twisted into a counterintuitive shape. From a naive literal point of view, no, the universe above theirs is independent. Diane's hypothesis/theorem is that, because their universe is at or near a fixed point, they have in effect invented a way to have unlimited control over their own universe. While there is no causal relationship from their universe the one up the chain, the symmetry implies their actions are mirrored. I've read some of this author's other works. He likes playing with paradoxes like this. It's a twist on causality (and free will), inventing a new way for your actions to have an impact on the universe in the absence of a traditional causal link. It's pretty damn clever.
  - benched 13y ago
    Yes, exactly. It's like a sneaky way of asking if physics is deterministic, alluding to the paradoxical relation between determinism and free will.
    - dllthomas 13y ago
      And a fun way of playing with the notion of fixed points, to boot!
- prutschman 13y ago
  They are making decisions in the presence of the knowledge that essentially identical "god" agents will be making decisions based on the same information and the same mental states, and that the "god" agents' decisions will impact their own existence. If at any time they were to "choose" to shut down the simulation, it can only be because the total state of the world, including their sense-data and internal mental states, cause them to do so. If that's true for them at time T, then by hypothesis it's true for the "god" agents as well. It may be that, in the sense you have in mind, the protagonists simply do not have choice.
- vilhelm_s 13y ago
  Ah, but is it really that simple? :) For similar puzzles, you might enjoy Douglas Hofstadter's essay about "super-rationality" (there is a HTML version on gwern's site: http://www.gwern.net/docs/1985-hofstadter http://www.gwern.net/docs/1985-hofstadter), Adam Elga's "Defeating Dr. Evil with self-locating belief" (http://philsci-archive.pitt.edu/1036/ http://philsci-archive.pitt.edu/1036/), and Scott Aaronson's lecture about Newcomb's paradox (http://www.scottaaronson.com/democritus/lec18.html http://www.scottaaronson.com/democritus/lec18.html).

shurcooL 13y ago

If you have an infinitely powerful computer, does that also imply that you necessarily have infinite storage?

eropple 13y ago
I don't see why it would; re-computation would be no more meaningfully expensive than a load/store, would it?
JoshTriplett 13y ago
Infinite CPU capability does not automatically imply infinite storage, but it does imply that you can compress any storage to an information-theoretic minimum size, by writing a search for an arbitrary program to generate the same data. And that's some absurdly good compression, given the universe simulator assumed in the story: anything that will ever occur as a state of the universe can be compressed to a set of space-time coordinates and an extraction algorithm. With some additional assumptions about the nature of the pseudo-causal loop demonstrated in the story, that compression can also include any arbitrary search parameters you can conceive of, without you having to express them as a program: just search for the data that will be on your hard drive in the future after having executed the search you're currently thinking of.
polemic 13y ago
Good question.. I assume its a relatively trivial question for a serious mathematician, but I suspect it's something like: there are classes of problems that, given infinite computation, require infinite storage. In this case it is strongly implied.