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: i...
Edit: Hello again. After a fair bit of discussion with some of you, I can say with great relief my belief in an infinite universe with infinite minds in it has gone down. Now, that is not to say that I think that it won't rear its ugly head once more, but it seems to have been beaten back for a while. If you're wondering why I sound relieved, well, that because an infinite, mind hospitable universe is a terrible place. Though some have presented me with some arguments against the whole immortality thing to do with consciousness, well that's a little harder to discuss.I don't think the path I'm taking on the philosophy of mind thing is wrong, but there's a ways to go yet. But I've seen the groundwork, and it looks good to me. Anywho, I've got about 40 -50% belief that its right in the argument I presented below, whereas before it was a little under 70%. Now, I think I'll make another one of these in a few years, because this is an important topic. This whole thing, or something like it may well be right, and utilitarian ethics is going down in that case. And that's bad news for a lot of people, including me. So I'll see you a few years down the line, when I've learnt some more physics, and have brushed up on my arguments.
Hello there,
This is my first time writing a LessWrong post (welcome thread aside), and I thought I'd start with something that has occupied most people's minds at one point or another: death. Essentially, I am reasonably sure that immortality already exists from a reductionist point of view, albeit with one assumption that some may not agree with. And depending on whether or not the universe will last forever, then immortality is guaranteed for everyone, throughout all time. it is I think I'd be correct in saying that many people on this site are familiar with the whole Boltzmann brain idea, but I'll go through it anyway, to set the stage.
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. The idea was originally conceived Boltzmann for a deterministic, infinite world, but it works just as well for a probabilistic one. According to the laws of probability, it is possible that any structure could spontaneously form at random points in the universe. The expected time it would take for that to happen would be far vaster than the length of the universe. A brain could also appear in the midst of space at any time whatsoever, existing for a brief moment in the starry void before fading away. And, in a universe that lasts for an infinite amount of time, it will happen. An infinite amount of times. And so will every other possible combination of atoms. So, doesn't that mean that we would reappear? Well, yes. A structure the same as the universe is right now, with you perfectly recreated would form an infinite amount of times. So, I say to you, is this not immortality? Is this person appearing an infinite amount of times, the very same you that now exists?
Well, I think so. This is just a simplification, but its a decent example. Suppose two books could be made, which are identical in structure, and we would call them the same book, despite there being two of them. There is no special stuff that makes any of these objects unique, only their structure, which represents how they(people) have changed due to their interactions with the world from a given starting point. So, if we exist for an infinite period, are we not immortal?
But there are still some problems. Just because the same life is repeating over and over again, it doesn't mean that you'll be living forever. To live you need some change, different thoughts, ideas and so on. If you have the same ones over and over again, and cannot even remember the full past, then you're no truly immortal. Well, not so fast. That idea is dependant upon the world being deterministic in nature. Your future actions could go down any number of paths, though they're not 'up to you' in the traditional sense. So the future you is not determined, you're structure from this point in time could take any number of paths, and in an infinite universe, it will take all possible paths. But the problem is still there. 50 years from now, when I'm dead and gone, my particular branch of life will be over. I will have died and that will be the end of this incarnation of me.
After you die, and have whatever thoughts come to the dying, that will be the end, no? Well, what if your body, just after your last thought, was reassembled straight after? This too is possible, so would you not be carrying on with your life? And you happen to live a few more years, and in this world, someone invents the an immortality pill, and you go on to life forever?
So, death is trounced, is it not? Our woes are for nought, and we need not truly worry about death. But hang on, this whole thing was based on an infinite universe. So death is still in play! Well, here's where things start to get a little more iffy. Now, I wholly believe in this, and I think it perfectly reasonable, but others may baulk at this. So, why does our universe exist? Better yet, why does anything exist at all? Wait a minute, don't leave just yet, this probably isn't going where you think it is. Now, some have proposed multi verse theories, which may circumvent this whole problem, and provide an infinite number of universes. But I don't think that's necessary. Its reasonable to keep your assumptions to a minimum, so I think assuming that our reality is the only one should also go.
So there you have it. What do you think?.