On immortality
10ChaosMote
4Kindly
2ChaosMote
7DanielLC
2TheAncientGeek
0DanielLC
2TheAncientGeek
2Algon
0theseus
5Shmi
0Algon
2Shmi
0Algon
0Shmi
4buybuydandavis
0Algon
0buybuydandavis
0[anonymous]
0Algon
3spxtr
1Jiro
3Ander
0Algon
1avturchin
1Toggle
1RowanE
0Algon
1pianoforte611
0Algon
1pianoforte611
0Algon
0pianoforte611
0Algon
1pianoforte611
0Algon
1pianoforte611
0Algon
0pianoforte611
0Algon
0pianoforte611
0Algon
0wadavis
-1wadavis
0arisen
0Algon
0advancedatheist
0Vladimir_Nesov
1Algon
0Vladimir_Nesov
New Comment
Mathematician here. I wanted to agree with @pianoforte611 - just because you have infinite time doesn't mean that every event will repeat over and over.
For those interested in some reading, the general question is basically the question of Transience in Markov Chains; I also have some examples. :)
Let us say that we have a particle moving along a line. In each unit of time, it moves a unit of distance either left or right, with probability 1/10 of the former and 9/10 of the latter. How often can we expect the particle to have returned to its starting point? Well, to return to the origin, we must have moved left and right an equal number of times. At odd times, this is impossible; at time 2n, the probability of this is %5En%20\cdot%20\left(\frac9{10}\right)%5En%20\cdot%20\binom{2n}{n}) (this is not difficult to derive, and a simple explanation is given here). Summing this over all n, we get that the expected number of returns is one in four - in other words, we have no guarantee of returning even once, much less an infinite number times!
If this example strikes you as somewhat asymmetric, worry not - if the point was moving in three dimensions instead of one (so it could up, down, forward, or back as well as left or right), then a weighing of 1/6 to each direction means that you won't return to the starting point infinitely often. If you don't like having a fixed origin, use two particles, and have them moving independently in 3 dimensions. They will meet after time zero with less-than-unit-probability (actually, the same probability as in the previous problem, since the problems are equivalent after you apply a transformation).
I hope this helps!
What if we assume a finite universe instead? Contrary to what the post we're discussing might suggest, this actually makes recurrence more reasonable. To show that every state of a finite universe recurs infinitely often, we only need to know one thing: that every state of the universe can be eventually reached from every other state.
Is this plausible? I'm not sure. The first objection that comes to mind is entropy: if entropy always increases, then we can never get back to where we started. But I seem to recall a claim that entropy is a statistical law: it's not that it cannot decrease, but that it is extremely unlikely to do so. Extremely low probabilities do not frighten us here: if the universe is finite, then all such probabilities can be lower-bounded by some extremely tiny constant, which will eventually be defeated by infinite time.
But if the universe is infinite, this does not work: not even if the universe is merely potentially infinite, by which I mean that it can grow to an arbitrarily large finite size. This is already enough for the Markov chain in question to have infinitely many states, and my intuition tells me that in such a case it is almost certainly transient.
You are absolutely correct. If the number of states of the universe is finite, then as long as any state is reachable from any other state, then every state will be reached arbitrarily often if you wait long enough.
This sounds like quantum immortality. The problem is that the probability measure of survival goes down. The further future yous don't exist nearly as much as the present yous, so they don't matter as much.
Every universe existing explains everything. Its simplicity is matched by its lack of explanatory power, so it's not particularly likely.
The problem is something-to-do-with-measure, but no one quite knows what, since no one knows much about measure.
Many World believers have to believe low measure worlds don't matter much, because they'd go nuts otherwise, but that doesn't make it a fact. It's not as physics is apt to tell people what matters.
It's more likely to be someone in a world with higher measure. If this wasn't the case, then people would all be Boltzmann brains, and remembering evidence for quantum physics would be no more likely than chance. Given that, it seems odd to care about all of the worlds equally.
There is .no non-odd solution to caring and many worlds, The body is a survival machine that is primordially programmed to prefer surviving to dying. Throw in the assumption that dying isnt incompatible with surviving, and that just fritzes.
I see what you're saying, but I don't think that the two situations are equivalent. I'm not going by the many worlds interpretation, but the Copenhagen one. In a finite universe, I understand that one is not guaranteed immortality, and even in the many worlds interpretation, immortality is iffy as Tegrmark has explained. Though I do see the point of your second objection, I think that it is not illogical to go either way on this point. I act under a coherence theory of Truth, so my attempt at grasping Truth may lead me down a different path to your attempt, but we will eventually meet up somewhere, given enough time.
Thanks for taking a time to reply! By the way, why do you think I got down voted? Was it the tone, my saying something obvious or something else entirely? I'd be much obliged if you could critique my post a little more.
My guess is the mostly the tone and the overly strong conclusion.
The topic is certainly one that is close to home for a lot of LWers and it seems to me we've heard almost all the variations. Then the tone, of a kind of artistic revelatory piece introducing lots of ideas only to dismiss them soon after, seems much more appropriate for a journalistic piece than the kind of deep logical thinking strived for here. Putting arguments in the reader's mouth and talking very patronizingly ("you're a picky one... my friend... this probably isn't going where you expect it to...Algon's recipe for immortality") also doesn't work great in my opinion.
The conclusion is also a point of contention, as people here tend to like calibration and it seems a little too overconfident. Reductionists don't necessarily believe that another copy of you springing into existence later will be the same consciousness, and many readers have commented that they don't. For one example, Scott Aaronson proposes an interesting possibility. Similarly, issues about the universe being infinitely long and infinitely recurring, etc., are very much debatable, with most evidence coming out against you. Then to not treat any of these other possibilities, but whisk through each as if one narrow interpretation did it, seems to me not to be a helpful discussion of the topic so much as a narrow attempt at showing wit.
On the plus side, it's cool that you asked for constructive help and were willing to engage, and I think more research into and consideration of these ideas could lead somewhere good.
Wild speculations on quantum physics aside, I would like to use the regular pedestrian definition of immortality that is distinguishable from this and any other version of afterlife being discussed:
Immortality is eternal life or the ability to live forever
By this definition, a friend of mine who has recently and unexpectedly died from lung cancer is quite dead and in no way immortal. I can visit her grave, or see the grief of her friends and relatives, religious or otherwise. Reading about Boltzmann brains, Infinite multiverses or the Second Coming of the Messiah is not in any way comforting, because I still cannot undo her death.
From that point of view, and the only one that matters to me, Algon's recipe of doing "nothing" is admitting defeat.
I'm sorry about your friend. But before I say anything, could you say why exactly my speculations are wild? I'm just running with an idea that many more knowledgeable people than I (many physicists) think is a descent possibility.
why exactly my speculations are wild?
- we do not know how large the universe is (there are no infinities in physics, only in math)
- Boltzmann brains most likely do not exist
- And even if they did, they would not be conscious
- And even if they were, it does not alleviate your mother's grief in our little corner of the universe when you are run over by a drunk driver, because her identity is not connected to all those other potential copies of you and her.
In general, conflating reductionism with a certain set of pop-sci ideas is probably not very smart.
1) A universe that does not undergo a Big Crunch would necessarily last for an infinite amount of time. THough there is one caveat, which is the paper that the very same blogger you linked to wrote (Its in the page) 2) I think a Copenhagen interpretation is more likely. But I will have to mull that article over for a while. 3) I am not actually saying that all will re-appear is your brain, but the entirety of you and the rest of the world and so on, with exactly the same happenings going on. So yes, you would be conscious, and it would be you. 4) Here is a lecture by Leonard Suskind, which may help clear things up a bit. Either way, its fairly enjoyable https://www.youtube.com/watch?v=jhnKBKZvb_U 5) The problem with your example of a mother grieving is this: the same situation would inevitably occur again, but this time, you would survive, or would be miraculously revived or etc. And since a person is just a structure, if that structure re occurs, it will be the same person. It will be the mother, and she will see her son alive. Now, since there are two seperate paths going on here, the mother in situation A 10 years later will not be the same as mother in situation B 10 years later. But, there are various paths that could where the mother in situation A sees her son again, and so everything will be fine. And there will be some world where mother A suddenly wakes up on a grassy field and sees here supposedly dead son next to her, and all will be well. And such a world is possible i.e. the configuration of the atoms is possible, and so it will happen in a universe that has no 'end'.
Now, I think that your first link holds the strongest objection, but I am in no real position to argue with the author. So, in several years time when I've finished undergrad, gotten a PhD in Physics and am ready to answer you, I'll come calling. Then we can have a nice discussion as two rationalists where I can try and convince you that the would is infinite, and quite possibly horrific,.
A universe that does not undergo a Big Crunch would necessarily last for an infinite amount of time.
False. I'll let you do your own research on other options.
2) I think a Copenhagen interpretation is more likely.
Objective collapse is a very unlikely case, it is contradicted by gravitational measurements.
3) I am not actually saying that all will re-appear is your brain, but the entirety of you and the rest of the world and so on, with exactly the same happenings going on. So yes, you would be conscious, and it would be you.
The question of consciousness and identity is way too deep to be dismissed with one argument.
5) [... ]
sounds like meaningless rambling to me
I am in no real position to argue with the author. So, in several years time when I've finished undergrad, gotten a PhD in Physics and am ready to answer you, I'll come calling.
Very smart of you. I hope that it works out for you the way you intend to. And that I will still remember enough Physics from my own PhD years to hold a useful discussion.
Yay, the Eternal Recurrence Lives!
Not so much.
Identity as intertemporal solidarity with any other being is a choice, whether the being has "identical" structure or not. It's a choice for your attitude toward the "you" of tomorrow morning. Or your attitude toward a parakeet 3000 years ago.
But going back to a recurrence of "the same" structure, the notion of a low probability of a being with "the same" structure popping into existence is based on an ultra extreme tail end extrapolation from our current models. Have you validated those models to the gazillionth decimal point? Me neither.
Also, the math is just wrong. An infinite number of chances (let's make them independent, but not necessarily equal) need not sum to a certainty.
Alright, what about the whole transporter thing? That is, if you were suddenly went into a star-trek like transporter, you would be disassembled, and reassembled on the other side of the solar system. Would that still be you? Now, I could try and convince you that that is the case from a reductionist point of view, but I think that the arguments themselves are pretty clear, and I don't have much time. If you want me to though, I can, just message me.
Anyway, if you do accept that this other you is still the same you, because it has the same thoughts, the same memories, the same outlook on life, the same propensity to do such and such, then you should be okay with this whole thing. Because what I'm talking about is pretty much the same as the transported scenario, just with a much longer time gap in between. And in these cases, the whole universe itself gets recreated, along with you. Sure, you could pop up alone, or missing five organs, but there is still a chance that it will occur. And could you clarify your last point? Because I was under the impression that the expected number of an events with probability P happening in a time T (which is infinite) is p*T. Which is infinite, and so not P approaches zero as T approaches zero. The whole limits thing. If I'm wrong, then please show me, so that I can learn why I'm wrong, and stop wasting people's time.
Alright, what about the whole transporter thing?
I wrote:
Identity as intertemporal solidarity with any other being is a choice, whether the being has "identical" structure or not. It's a choice for your attitude toward the "you" of tomorrow morning. Or your attitude toward a parakeet 3000 years ago.
Or your attitude toward the whole transporter thing.
Some will consider a "transporter" a mode of transportation, and some will consider it a disintegrator/creator.
I don't accept the transported person is me, also from reductionist grounds. Incidentally I wonder what you would think if the machine was not destructive, or if it got stuck in a loop and kept outputting copies, etc.
I consider a person to be a certain structure extending throughout space time. So, if two structures are identical, as in the loop scenario, I'd say that they were the same person. Of course, that's only if these accidental clones have the structure, which they will not, as one clone will be in position A, and the other will be in position B, and so be different people, albeit very similar ones. The same goes for the first scenario, they are going to be different people since they will be in different situations. In the case where they have the same experiences for the rest of their lives, and so the same structures in space time, they will be the same person. But that could only happen in two universal configurations which were the exact same... which is what will happen in an infinite universe. But might I ask, why do you not think that they shall be the same person?
An exact copy of me may be "me" from an identity perspective, but it is a separate entity from a utilitarian perspective. The death of one is still a tragedy, even if the other survives.
You should know this intuitively. If a rogue trolley is careening toward an unsuspecting birthday cake, you'll snatch it out of the way. You won't just say, "eh, in another time that cake will survive," and then watch it squish. Unless you're some sort of monster.
Suppose some wizard casts a spell to make your neurons twice as thick, with everything still functioning normally. Suppose furthermore that for some reason the counterspell involves being hit by a trolley. Did the trolley kill someone?
Now ask the same question where the neurons are duplicated and each neuron is replaced by a pair of two running in parallel.
Now ask the same question where the parallel sets are running in physically separated brains....
This seems significantly shakier than even the idea of quantum immortality.
Lets call your idea "Boltzmann Brain Immortality". That is, the idea that "because a Boltzmann Brain version of me might possibly pop into existence somewhere in the multiverse at some point in time, ever, I am immortal".
I have two main objections to this: 1) Boltzmann Brains are generally considered a problem in theories of physics which allow them. That is, if a model of physics allows Boltzmann Brains to be possible, with non vanishing probability in comparison to 'real' intelligent life, this is considered generally considered a flaw in the theory.
2) I wouldn't consider a Boltzmann Brain version of me to qualify as 'life' or 'immortality', since there si no continuity of experience - the Boltzmann Brain just vanishes again an instant later.
1) I get that the whole idea of Boltzmann brains is unwanted in physics, but that is just because it potentially invalidates a lot of our knowledge. Now, if we could find out that the universe has only existed for a finite time because otherwise something would have Changed in a major way in it, and we have some sort of multi verse theory going on, then its no longer a problem. But besides that, I don't think that it is as huge a problem as everyone thinks. Sure, its undesirable in one way, but it may well be true, like moral relativism.
and 2) I don't think that you quite got what I was saying. Yes, that is what happens to a Boltzmann Brain, but the point I'm trying to make, which is the same thing that physicists find troubling, is that in an infinite looking universe, every state of the universe would be recreated. The whole thing, including the galaxy we live in. Say if something went wrong, and you died in five minutes. This infinite world would require that happening countless times, as well as the universe in which you did not die, or survived happening an infinite number of times.
A new article on the topic:
Boltzmannian Immortality* Christian Loew†
Hysteresis exists. Complex models are often time-dependent, and initial states may not always be retrievable under any circumstances.
In the immediate sense, the world we experience obviously has the quality of irreversible change. On a larger scale, our cosmos could easily be such a system- even without ChaosMote's excellent statistical treatment, we can't be sure that, just because things in general continue to happen, an event like the big bang could happen an infinite number of times. No matter how wide the scope of your analysis, it may be that the 'final answer' is that we are indeed working within a single time-dependent system.
I think that the most reasonable thing to assume is that every possible kind of reality exists. Why? Well, there seems to be no good reason for it not to. To assume that the universe is the sole reality is one assumption too many for me, and I say the fewer assumptions there are, the better.
If I'm not mistaken, this is the strong assumption underlying the whole post. And I would encourage you to consider this claim in probabilistic terms, rather than just working within a believe/disbelieve binary. What is your degree of confidence in this proposition, and why?
I think Yvain did it better, and went a more interesting direction with it. Good try though, I think this issue doesn't get discussed enough.
I think that his post as a whole was better. In fact, I suppose my post would better serve as an side to Yvain's. Also, I think I ran with the whole immortality thing more than he did. I believe I addressed more potential issues, or at least blabbered on for longer about them. I do think it is an important issue, because a world like this has serious consequences. Namely, utilitarian like theories break down. Nick Bostrom wrought a good paper on this sort of thing (ethics in an infinite universe), though he didn't present a viable solution. SO on the one hand you have proper immortality,and on the other you don't have a decent ethical system. Frankly, I'm not sure I would even want a world like this, if it doesn't allow ethics.
I've had this thought before, however, is it true that given an infinite amount of time a mind will spontaneously form? I don't think that's necessarily true. Suppose an event E has a probability of occurring at any given time:
P = e ^ (-1- t)
That has a finite probability of occurring given an infinite amount of time. That's sort of cheating, but it illustrates that an infinite amount of time doesn't guarantee that anything that can happen will happen. Maybe the universe does become exponentially less likely to support the existence of a mind over time.
Well, it is necessarily true that anything that can happen, will happen in an infinite, probabilistic world. Of course, there are some issues with this. One, if the mass of the higgs boson falls in a certain area, then the universe will undergo a shift. From what I remember, it is something to do with the vacuum energy/state of the universe, and the laws of physics may well end up changing. Its been a few years since I read that article, so I may not have it completely right. And events that have a probability of an infinitesimal...well, I'm not sure what would happen. I don't know what infinity over infinity is, but I suspect that it will be undefined. Anyway, the expectation of a value is its probability, multiplied by the quantity of cards drawn, or whatever it is you're trying to determine. In this case, how many events with probability P are going to happen in an infinite amount of time? Well, an infinite number. That's just how it works.
If I've been obtuse in some way, don't hesitate to call me out on it. And thanks for reading!
Edit: I just re-read your comment. I don't think that's how the probabilities work in this reality, though I may be wrong... I mean, what sort of probability would this event have in a finite universe? Is it some infinite universe only event? Do those even exist? It should be irrelevant though, because our universe has existed for some time T, and we had some probability P of occurring, and so that would mean we will reoccur in an infinite universe. Same for the other versions of us, though you could provide me with an argument for why that isn't so.
Any event that has a fixed probability will happen in an infinite amount of time, but an event whose probability of happening decreases over time does not necessarily happen given an infinite amount of time. Its possible that thermodynamics will make the universe exponentially more inhospitable to the existence of minds over time. But this is just one way that the an eternal universe could fail to guarantee immortality.
we had some probability P of occurring, and so that would mean we will reoccur in an infinite universe
That P is a function of the state of the universe and therefore a function of time. Its not a constant, we don't know how it is changing.
I'm going to point you down to my reply to Ander, because I think that it might help you see why a universe which is in an inhospitable state does not really matter. Now, your objection would have cleared up the original Boltzmann Brain thing, and the problems therein, but it does not clear up the current one, where we live in a probabilistic universe.
which is in an inhospitable state does not really matter
No it doesn't matter, what matters is that the universe could become increasingly more inhospitable over time. This is not a philosophical point, or a physical point, it is a mathematical one. The statement that "any event with a positive probability of occurring at any point in time will always happen given an infinite amount of time" is mathematically incorrect and I have provided a counterexample.
Ok, so assuming that you have a world where the position of every particle, photon and what have is after a time dt is probabilistic, then there is a possibility that all these particles will go somewhere else, however small. This does change depending on the situation, but each particle has a non-zero probability of being elsewhere. This does not change. Now, it is possible that all these particles will re order themselves so that the entire state of the universe is different, i.e. a state that looks like its 3 billion years after the big bang instead of 13.8 billion. Now, as you were saying the universe may well become more inhospitable over time, reaching a sort of heat death were I believe no minds would be easily able to exist. And in the time it takes the universe to get to that stage, it is exceedingly unlikely that it would have turned into some wholly different stage than was expected. But, given an infinite amount of time, the very arrangment of the universe, not just a few quadrillion atoms, will revert to some other stage. It may become more hospitable, or maybe less. But the next stage could, and would turn into some other state. Eventually, you'll get a universal structure not too different from the current one, and it will be hospitable to life, and will therefore allow the probability of our very beings to re-occur. It may not happen the first time the universe goes to a hospitable state, or the next and so on, but eventually it will.
So I think I've answered your rebuttal, unless you were saying something like 'The universe is inevitably going to be more inhospitable to minds, and will not go back to a more hospitable state, and so the expeceted amount of minds is going to be some finite number as a result of a converging series' If so, then I have nothing to say other then 'Why?'
unless you were saying something like 'The universe is inevitably going to be more inhospitable to minds, and will not go back to a more hospitable state, and so the expeceted amount of minds is going to be some finite number as a result of a converging series' If so, then I have nothing to say other then 'Why?'
No, I am merely pointing out the the expected number of minds is not necessarily infinite given an eternal universe. It could be finite. You are arguing that it must be infinite. I don't have to prove that it must be finite to refute this, all I have to do is point out that it is possible for it to be finite.
But the next stage could, and would turn into some other state. Eventually, you'll get a universal structure not too different from the current one, and it will be hospitable to life.
This is subject to the same problem. Given an infinite amount of time, it is not the case that the universe must return to a state like the current one. That is a math error.
Look, you can't just make up probabilities out of thin air like that. I accept that such a thing may be possible, but I have not heard or seen anything like it. If you can give an example of such an event, of any kind, that would greatly bolster my propensity to accept your argument.
As to your second point, it is necessarily true. The universe would have some finite possibility of changing to some other state, including this one. It is not, as far as I can see, subject to the same problem. If you can explain, in full detail, why this is the case, then I'll be happy to accept your argument. An infinite universe isn't just good news. In fact, it may be worse than a finite one with no hope of true immortality.
Look, you can't just make up probabilities out of thin air like that
It's called a counterexample.
I accept that such a thing may be possible, but I have not heard or seen anything like it.
If you agree that an eternal universe doesn't guarantee infinite minds, then that's all I was arguing.
The universe would have some finite possibility of changing to some other state, including this one.
That probability is not a fixed number, you cannot rule out that it is a decreasing function with an integral that sums to less than one. If you think it is a constant, you have to demonstrate why.
I was saying that 'I may be wrong, and not know of any probabilities like this'. Secondly. you should give an example instead of just defining such an event. As far as I can see, what you essentially said was 'Suppose that an infinite amount of minds will not occur, thought that's cheating a bit. Then what do you say?' Well, I can't say anything, because that whole things is presupposing that I'm wrong. It really is cheating.
Also, the point I'm trying to make is that each configuration of the universe has a set probability to go to any other state. The manner in which you work out the probabilities for each configuration of the universe does not change.
'Suppose that an infinite amount of minds will not occur, thought that's cheating a bit. Then what do you say?' Well, I can't say anything, because that whole things is presupposing that I'm wrong. It really is cheating.
I won't engage further if you continue to straw man me. That isn't even a reasonably close straw man.
If you want an example of something that has an exponentially decreasing probability of happening* then consider a point in space with four paths branching out of it. Each of those paths has four pathways branching out of it and so on (the number of points and paths is infinite). If you start at one pathways and choose paths at random, what is the probability that you will eventually choose lets say the first of the four paths given an infinite number of walks? Backtracking is of course allowed. That probability is less than one.
What might resemble that in reality? The configuration space of the universe could fit the bill. But this is just an example of how the idea that "given an infinite amount of time, anything that can happen will happen" could fail.
*not quite a clean exponential function, but it has the important property that the probabilities are all greater than zero, but sum to less than one given an infinite number of steps.
Ok, now that I've had a chance to think about it, I have an objection to your point. So, what you're saying is that the universe will provide lower and lower probabilities for sentient beings to form as time goes by. This would have to include solar systems as well, since if the probabilities of solar systems spontaneously arising was constant, then life would also have a constant chance of forming each moment of time the usual way i.e. by self-replicating chemicals happening to form cells and evolution kicking in. So we must rule that and other things out for your objection to hold. And that is not inherently problematic.
But, the universe is expanding at an accelerating rate, and the gap between atoms will eventually become huge. Finally, space would be expanding faster than the speed of light, and no atoms could communicate with each other past a certain point in time, as information travels at the speed of light. Now, the atoms have nothing to interfere with them, and will have eventually spent up as much energy as they possibly can and be in their lowest energy states. This means that the probabilities of all the atoms doing certain things, moving in certain ways is fixed, because they are in a fixed state; nothing can interfere with them. And this would have solved the problem if it was not for the fact that the probabilities of the atoms still allow for huge structures to be formed. I can't remember the exact details, but I can link you to a source: https://www.youtube.com/watch?v=jhnKBKZvb_U This is a video in which Leonard Suskind explains the whole Boltzmann brain issue, and why it is still an issue in our current understanding of the universe.
Now, since the universe or what have you could reform spontaneously, and would get to the same state where the probabilities are fixed, the whole thing is doomed to repeat. And here is the crux of the thing: An infinite sum the expectation of fixed probabilities will be infinite. That is, they will not converge as in your counterpoint, since there will be some situation in which the probabilities are fixed, and this situation will repeatedly arise. And that's not even mention the fluctuation in the vacuum.
I'm glad you've acknowledged that an eternal probabilistic universe is not sufficient to guarantee immortality and added additional features that the universe needs to posses in order to make that happen. I think you are overconfident though, in your ability to predict how the universe is going to evolve on a very long time span - professional cosmologists are much more humble in positing what the universe might turn out like in the far future.
Alright, now we're getting somewhere. What I wrote down was what I understood of you're argument, and now that you've cleared things up a little, I can try again. What I now understand by your objection is this 'What if the probability of universal configurations is X? How do you respond to this?
Here, I have no clear retort. But I shall try to work on it.
I don't know what infinity over infinity is, but I suspect that it will be undefined.
This. This matters.
Some infinities are bigger than other infinities.
This is more that metaphor. A exponentially larger infinity divided by a small infinity will be infinity. A exponentially small infinity divided by a large infinity will be zero. A division of proportional infinities will be a real number.
So if the chances of a Boltzamann Brain becomes increasingly less likely as enthropy increases. and enthropy increases as time approaches infinity, you have a division of infinities which can equal infinity, a real number, or zero. You won't know which without actually crunching the numbers.
As an aside, arguments that use infinite time come up enough that I'm trying to find a brief graphic or write up that teaches ∞/(2*∞)=1/2 and the ∞/(∞^2)=0. Any pointers?
Your premise is wrong. "So, let's get started with the basic idea. In this universe, things seem to run on probabilistic laws known as quantum mechanics. These allow for very strange consequences, which were previously thought eradicated." It's based on the Copenhagen interpretation of QM! (QED for example does not allow the delayed choice quantum eraser paradox existing in QM).
The problem with the Copenhagen interpretation is: "... that the probability density function from Schroedinger's time-independent equation when averaged over time is just the proportion of the time spent in the allowable states given the dynamics of the system. It is thus the probability of finding the system in any of its allowable states at a randomly chosen time. There are no metaphysical perplexities involved with this probability density function. The time-averaged effect of a particle executing a periodic path is the same as if its generic charge (gravitational mass or electric charge) is spread over its path in proportion to its time spent probability density distribution; i.e., to the proportion of the time it spends at various locations on its path" http://www.sjsu.edu/faculty/watkins/bellth.htm
Yeah, I get the problem(s) now.
Its been over two years. Why'd you bother commenting? I don't mean that in an agressive way.
We need to solve the problem - first - of turning death from a permanent off-state into a temporary and reversible off-state, instead of worrying about "immortality," whatever that means. I keep trying to get cryonicists to adopt this as a new way of explaining the idea, but the older generation of cryonicists apparently can't form the new neural pathways.
See Preference For (Many) Future Worlds (it's linked from Quantum immortality article on LW wiki).
A situation with given structure may matter to different degrees. The familiar special case is probability, when it's uncertain whether the situation will occur. Depending on situation's weight, you'd be willing to trade it for different alternatives, so this measure of situations is relevant for decision making. When a situation weights almost nothing compared to available alternatives, it's irrelevant.
So in the case of quantum immortality or Boltzmann brains, the situations being discussed don't matter compared to our world. They matter only for someone who happens to live in them and know it, to someone who can't affect more. But why care for that guy of measure epsilon?
I'm acting under the Copenhagen interpretation, not many worlds. So I am talking about our world, not any other.
A single world admits many hypothetical situations, abstractions that express the features you care about. Knowledge of the world lets you judge their weight, decisions happen at the level of these abstractions, way above low-level description. So it doesn't matter if the alternatives you are working with also in some sense correspond to things that are physically real. Even in a "many worlds" world, you'd be normally acting at a much coarser level.