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Navere comments on Stupid Questions (10/27/2014) - Less Wrong Discussion
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Hi everyone, I have a question related to the possibility that we live in an infinite universe, and the ethical implications that follow. I've been thinking about this a lot lately, and I've looked over Nick Bostrom's paper on infinite ethics which, if I understand it correctly, suggests that in an infinite universe containing infinite positive value (good) and infinite negative value (evil), it appears to be the case that nothing we do can ever really matter ethically because all we can do is a finite amount of good or evil (which has no impact on an infinite value).
But I have seen discussions of multiverse ethics on Less Wrong where commenters are seemingly talking as if they are able to act in an ethically meaningful way in an infinite cosmos, talking about something referred to as their "measure", and of increasing their measure. I'm afraid I do not understand at all what they are talking about.
Can someone please explain in layman's terms what this sort of talk is all about (sometimes the discourse at Less Wrong is over my head, so as simply and clearly as possible please!). What is "your measure" and how can it be that it matters if the amount of positive value and negative value in the universe is infinite? Sorry if I am misunderstanding something basic and this question is stupid. Thanks!
Not sure if infinities really exist. Pretty sure it's important to not be a dick.
You don't have to be sure that infinities exist to explore the possibility. Have you looked at Nick Bostrom's paper? Do you think Bostrom was wasting his time?
In math, "measure" is a way of assigning a "volume" (or length, area, probability) to infinite sets. The "cardinality" of the set of numbers between 0 and 1 is the same infinity as that of the set of numbers between 0 and 2, but the standard "measure" of the latter set is twice as big. You can sum up certain types of functions defined on a continuum by "integrating" those functions values using the appropriate measure.
If there turns out to be a continuum of possible universes created by, say, a particle decay, then there's also a natural physical measure that corresponds to the probabilities we observe; the set of universes in which the particle decays before 1 half-life would be "twice as big" in some sense as the set of universes created in which the decay occurs between one half-life and two half-lifes. If someone offers to do something for you if-and-only-if a particle decays before one half life elapses, you should figure out the expected utility of a 50-50 bet, even if the reality might be that your decision is affecting two different infinities of subsequent universes.
There's a lot I'm glossing over and/or don't understand myself here (why is the probability measure the only ethical measure? lots of different-but-self-consistent measures can always be mathematically well-defined) but hopefully that at least explains the vocabulary a bit.
This is an extremely clear explanation of something I hadn't even realized I didn't understand. Thank you for writing it.
The probability measure is the one that's conserved by physical time-evolution of the system, no? It would be a bit weird to have an ethical system where universe A was worth the same as universe 1 and then a few minutes later it was only worth half as much.
Bostrom suggests the "domain rule" to discount unobservable infinities. Seems pretty reasonable.
It sounds much like a defensive argument for evil behavior. Obviously Good and Evil are just abstractions which only humans can measure, and at the level of the universe these things don't exist and don't matter
If the universe is infinite, then there are infinitely many copies of me, following the same algorithm, so my decisions create infinite amounts of good or evil (through my copies which decide the same way).
Or, to see it from another angle, if the universe is literally infinite, then it is more or less infinitely repetitive. So let's take a part of universe containing a copy of approximately everything, and treat this part as a finite universe, which is just replicated infinitely many times.
Your "measure" is the proportion of your copies to the infinite universe.
Does this follow? The set of computable functions is infinite, but has no duplicate elements.
The measure of simple computable functions is probably larger than the measure of complex computable functions and I probably belong to the simpler end of computable functions.
Ok, I think that helps a bit. But if there are infinite copies, how can you talk of proportions? It's not like anything you do decreases or increases the number of copies, right?
My first thought is that that kind of argument is exactly the kind that even a highly rational person would be wise to respond to with epistemic learned helplessness. It involves putting infinities into a calculation about real-world decisions, and it's an argument that all ethical actions are meaningless.
Also, if one values amount of good accomplished instead of amount of good in the universe, the infinite universe doesn't change anything.
That said, I don't think the multiverse interpretation implies an infinite number of universes unless the universe is also infinite in space or time, so people discussing the multiverse may not believe in an infinite universe.