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’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.
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.