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pianoforte611 comments on On immortality - Less Wrong Discussion
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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.
This. This matters.
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?
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.
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.
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?'
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.
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.
It's called a counterexample.
If you agree that an eternal universe doesn't guarantee infinite minds, then that's all I was arguing.
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.