In front of you are two boxes.
Box A contains $1000.
If Omega predicted you would just take Box B, Box B contains $1,000,000.
If Omega predicted you would take both boxes, Box B contains nothing. Omega will also go back in time and kill your grandfather.
Nobody has any idea how accurate Omega’s predictions are.
Does the fact that you exist prove that Omega thought you would just take one box, so Box B definitely contains the million dollars, and if you took both boxes it would imply that Omega was a terrible predictor so you might as well just take both boxes and run?
[Question] Newcomb’s Grandfather
Luke takes both boxes. The box A contains $1000. The box B is empty.
Omega appears in a flash of light.
Luke: “You killed my grandfather!”
Omega: “No, I am your grandfather.”
Omega, continues: “Because of your stupid choice, I had to travel back in time and kill myself. Luckily, I was signed up for cryonics. In 2048, the year of Singularity, I was revived by uploading into a robotic body. By lucky coincidence, I got my hands on an unfinished time-travel research, which I succeeded to complete. I devised a clever plan that involved traveling to the past and providing you with $1000000, so that you could found the company that will develop the technology which will eventually bring the Singularity, which would make our family the undisputed masters of the post-Singularity world.”
Omega, continues: “For technical reasons, to avoid certain paradoxes related to time travel, it was necessary to implement this plan as an acausal decision, where the wrong choice would doom the whole project and revert the world to its original timeline. I trusted your rationality, Luke, but apparently, my expectations were too high.”
Luke: “But how can I exist if you killed my grandfather… uh, yourself? Isn’t that a paradox? I remember my grandfather still living when I was a small child...”
Omega: “I never said I would kill your grandfather before you were born. Or before your parents were born. Apparently, you were not even paying attention to the problem in front of you, Luke. I am so disappointed.”
Luke: “Wait, we still have some hope! You said that a wrong choice would restore the original timeline. But I still have the extra $1000 from the box A! Not enough to found my own company, but perhaps I could still buy a share of the company that will bring the Singularity, and we could still own a fraction of the future world.”
Omega snatches the money out of Luke’s hand.
Omega: “Nope. I have no more trust in you. I am putting this money into my savings account. In 2048, this, plus the interest, will be barely enough to pay for this high-tech robotic body. I need enough processing power to do the time-travel research. This is the original timeline, Luke.”
Omega disappears.
Omega will also go back in time and kill your grandfather.
sounds like a meaningful sentence, but it isn’t, except in movies. Don’t use it for something like a decision theory. Or, better yet, at all, ever, outside of a literary device in sci fi.
Are we talking about closed timelike curves? Then you cannot enter or exit those, as per general relativity, so the whole point is moot. Are we talking about Omega spawning a whole new timeline, expending a universe-worth amount of energy in the process? Then it doesn’t affect you in this timeline. You can also go down the rabbit hole of “but which you is really you?”, but that angle has already been covered in the analysis of the regular Newcomb’s when discussing whether you are an “actual” person or a simulation of one by Omega.
In the vicinity of closed timelike curves tend to be non-closed curves which could provide useful delivery. Blackholes may not be exited either but the concept of extracting energy from the ergosphere is still a useful thing.
No, there is no such thing as a “vicinity” of closed timelike curves. They are causally isolated from the rest of the spacetime.
As I understand the presence of closed timelikie curves is a classification that marks out those spacetimes that are in danger of featuring time travel. Like the coffee mug is an example of the topology that has a hole.
I think the situation is analogous in that you can draw a path on a coffemug that closes on itself but it doesn’t mean that it is impossible to make a path that enters and exits the handle. Such a path is possible and need not be closed (within the handle).
(say if one consider the bottom of the mug to be deep past and the top of it to be deep future, the time trallers path would be open but the possib lity of such paths is conected to the existence of the “handle” but the actual travel doesn’t actually take place on the round going part of it)
No, it is literally impossible to enter or exit a CTC, at least in classical GR. All CTCs are shrouded by a Cauchy horizon, meaning that you cannot “push” the evolution of a spatial slice into a CTC region. Or out of it, if you apply the same logic in reverse. The issue most people forget is that the spacetime in GR is not a background on which matter exists, the spacetime metric is unique (up to diffeomorphisms) and it uniquely determines the stress energy tensor at every point in spacetime, which means it determines its matter content almost completely. Thus one cannot have one loop of a CTC without something being there, and another with it. Anyway, it’s getting a bit technical. My original comment was that the OP setup breaks physics as we know it, and so it’s kind of pointless to discuss.
Is this meaningfully different from saying Omega just doesn’t give you the boxes in the first place if Omega predicted you would two-box?
I like the version you’re implying with this comment:
You have an imaginary thought experiment where a being has unrealistic abilities to predict your behaviors. You haven’t yet been presented with two boxes, but you’re speculating on what you’d choose. What should you do?
A strange game. The only winning move is not to play.
Rules and mechanics about time travel in the real world are not really known. Scenarios like these are kind of thought pumps about what even could happen atm.
One issue is whether you identify with your genes. Would a person born in the same time and place but for different parents be you?
One issue is also whether you care about different possibilities of yourself. Imagine a kind of russian roulette where you can choose to get your grandfather killed but double your current net worth (or maybe you literally go murder-rob another iteration of you). If you only care about “your branch” or “you standing here” this can seem and under some timetravel rules is upside with neglible downsides. If you care about your “multiverse average happiness” and under some other kind of rules this can seems to give an expected net worth of (0+2x)/2 = 1x
What about your grandfather?
Yeah I guess regular intuition only cover affecting the present and future. With time travel it might not be taken for guarantee that the past “is in the bank”. I mostly took the role of the grandfather to be your causal support. One can consider whether things would change if “kill grandfather” is changed to “kill you just after having been born” (or to the more extreme end “snuff out sun before life develops on earth”).
Time travel is impossible. Therefore, Omega’s “going back in time” to kill your grandfather was actually just it predicting you taking both boxes and killing him based on that prediction. Or, if Omega comes from outside of spacetime and just interacts with our universe by manipulating the universal wavefunction, it could at most kill your grandfather from another Everett branch, since the one from yours definitely survived.
In the former case, yes, your existence is evidence that Omega predicted you would just take box B. In the latter case, it’s best to act as if that’s what Omega predicted anyway.
It’s reasonable to note when a premise is ridiculous. That said, what would you do if the premise was true?
It’s not that the premise is false, it’s not well defined, borderline on incoherent, like existence of God.
How is the “existence of God” a “borderline on incoherent” premise?
If you don’t specify a particular range of meanings for “God” then it’s not well-defined. (Suppose the ancient Romans were right, so e.g. Zeus and Venus exist. Does that mean that “God exists”? Suppose the deists are right: there is a single in-some-sense-supreme being, but it doesn’t actually interact with our world in any interesting way. Does that mean that “God exists”? Suppose all the historical interventions ascribed by, say, the Christian tradition to God did in fact happen and were the doings of a super-powerful being, but that being is nothing like omnipotent and nothing like unique but is merely the only such being that happens to have taken an interest in our planet. Does that mean that “God exists”? Suppose our world is a simulation inside some tremendously powerful computer. Does that mean that “God exists”? What if the simulation is run by a team of people, not just one? What if they have no idea that intelligent life has appeared inside their universe-simulation at all? Etc.)
If you do specify a particular range of meanings for “God” then it may be well-defined. For instance, you could say that “God” means precisely what the median present-day evangelical Anglican Christian believes, or something like that. But the beliefs of typical religious believers, or whole religious traditions, aren’t necessarily very coherent. For instance, the median present-day evangelical Anglican Christian believes in “the Trinity” but (1) the m.p-d.e.A.C. quite likely couldn’t tell you very exactly what that means, and (2) it’s somewhat debatable how much sense it can be made to make. Or, many religious people believe (1) God is good, (2) God’s goodness at least somewhat resembles the best imaginable human goodness, (3) God is something like omnipotent, and in particular can easily do anything that the human race could, (4) God is intimately aware of all of us and our concerns, (5) God loves us (in, again, some sense somewhat resembling the best human love) and (6) it is bad for a human to leave someone else they love suffering horribly when they could easily do something about it; but it’s at least arguable that (1-6) are not mutually consistent given how many people are suffering how horribly at any given moment.
That’s all entirely besides the point though—shminux created the pretense out of nowhere to make fun of it. In this sense, since shminux is making fun of some unspecified “God”, I’d expect them to pick the most reasonable (or most typical) definition to battle, which makes it totally inappropriate to say the problem is underspecified (since underspecifying the opposition’s views and defeating those crippled views isn’t a good way to actually learn from the argument).
I think I disagree with most of that; I think most of “the opposition” (not that I much like that framing) have views that are poorly defined, borderline-incoherent, or both.
(Not because “the opposition” are idiots; I suspect it’s also true that most atheists have rather fuzzy notions of just what “the existence of God” entails.)
Sure, it’s possible (at least, I think it is) to formulate a precisely-defined definition of “God” and debate whether there is any such entity. But that hardly ever happens; when people argue about the topic, what usually happens is that everyone has their own idiosyncratic and tactically-varying idea of what “God” and “God exists” means.
And I don’t think shminux introduced the notion of God in order to make fun of it; I think he thought it was a useful analogy to explain how he feels about the idea of time travel. Something like “it’s a thing lots of people assume is a reasonable idea that one ought to consider the possibility of, but I think it actually doesn’t make sense, and the more closely you look at it the less sense it makes, and bringing it into a discussion usually makes that discussion less useful rather than more”.
That’s exactly how I meant it, a seemingly reasonable concept that doesn’t hold together upon closer examination.
Thanks, this (and the reply confirming this was the meaning) cleared a lot up for me. I misread the original comment pretty poorly and would probably agree with this formulation of it. Thanks for clearing this up for me, I appreciate it.
GIYF, but to borrow from a Quora answer, the concepts of eternal existence, omnipresence, omnipotence, omniscience, omnibenevolence taken together lead to a bunch of contradictions.
If you’re going for some general argument stuff, I have no clue what this had to do with the post above. I was curious if your elaboration would make me read your original comment as anything other than a drive-by attack on religion, but it ended up not doing that. I find the comment as off-putting as if I pointedly ended this comment by claiming something unfavorable about the rhetorical tactics of communists—what would it add besides an insult?
I did not mean to offend you or anyone else here, I was using the analogy in the way gjm explained in the other reply:
I’ll take your word for that. I misread you pretty thoroughly; I’m sorry for that.
Maybe perfect prediction is impossible, too.
Certainly perfect prediction is impossible in some cases. Look at the halting problem in computer science.
Suppose my decision algorithm is: I obtain the source code of Omega and run its prediction algorithm to determine what it predicts I will do, and then do the opposite of that.
This would be kind of like the proof that the halting problem is non-computable.
If you interpret that as a uniform prior between 0% accurate and 100% accurate, then Omega’s “prediction” is a coin toss. If Omega’s predictive accuracy is something you have no other reason to care about, take both boxes.
However, being the sort of person who takes the box makes you less likely to exist in worlds where this prediction is accurate, and more likely to exist in worlds where the prediction is inaccurate. So if you think that Omega’s predictive accuracy on this question is correlated with his predictive accuracy on other questions, and you strongly want future predictions to be accurate, don’t take box A.
It seems odd to describe something as a prediction when you believe it uncorrelated with the outcome. Suppose you think Omega’s predictions are somewhere between 50% and 90% accurate.
Being the sort of person that takes both boxes makes you less likely to exist. So don’t take box A unless you think that the universe you are in is exceptionally bad and want to destroy it.
Omega is almost certainly lying about the going back in time to kill your grandfather, and given that nobody has any evidence of their predictive ability, probably terrible at that too. They’re also the sort of person to openly threaten murder.
On the whole, Omega is probably someone that you want nothing to do with, so just smile without showing your teeth while slowly disengaging until it’s safe to get out of there more rapidly.