...Or we could realize that we've been using an inappropriate mathematical model and then everything adds up back to normality.
I disagree with argument of your article in this context.
I didn't wrote it explicitly, but if peoples of future spend 0.01% of their time in simulation of the Earth of 21st century, most of peoples, who think they are living in 21st century are wrong.
It's like you have 2 bag of numbered pieces of paper, in the first one there are 1 million of them, and 1% of them have number 6. An other bag have 10 pieces of paper and they are numbered correctly. Each piece of paper have equal chance to be taken. You take one, and you see 6. From which bag did you take the paper?
if peoples of future spend 0.01% of their time in simulation of the Earth of 21st century, most of peoples, who think they are living in 21st century are wrong.
Granted.
Therefore, if you were a randomly sampled person from all people who has ever thought or will be thinking that they live in 21st century you should think that there is only a small chance that you indeed live in 21st century.
But, as you are not, in fact, a randomly sampled person, this whole reasoning is unsound.
It's like you have 2 bag of numbered pieces of paper, in the first one there are 1 million of them, and 1% of them have number 6. An other bag have 10 pieces of paper and they are numbered correctly. Each piece of paper have equal chance to be taken. You take one, and you see 6. From which bag did you take the paper?
Likewise here without the "Each piece of paper have equal chance to be taken" condition your reasoning doesn't work. It's a crucial assumption, and you are not justified to make it in anthropic scenario.
But, as you are not, in fact, a randomly sampled person, this whole reasoning is unsound.
Why I am not a randomly sampled person?
≈all peoples who believe they live in 21st century actually don't. I believe that I live in 21nd century, so I don't live in the 21st century. It sounds like perfect logic.
In be honest, I don't understand your counterargument right now.
Likewise here without the "Each piece of paper have equal chance to be taken"
I have simply forgot to mention this condition, but I did mean it.
Why I am not a randomly sampled person?
≈all peoples who believe they live in 21st century actually don't. I believe that I live in 21nd century, so I don't live in the 21st century. It sounds like perfect logic.
In be honest, I don't understand your counterargument right now.
Okay, let's start from the beginning. What does it mean to be randomly sampled? How do we know that some things are randomly sampled from some set of things and why this set of things in particular?
Suppose you have a bag of stones. When you blindly pick a stone from this bag why are we justified to assume that it's a random sample from all the stones from this particular bag at this particular moment and not from some completely different bag? Or from this bag but from two months in the future when it may be filled with different stones instead? Or a random sample from all the stones that exists in the universe? Or even multiverse?
There is some kind of rational principle here, that allows to systematically make maps representing the territory, whether we are talking about stones or people.
There is some kind of rational principle here
Maybe you have to consider all the info you have, so you can't use all the stones in the multiverse as a reference class if you already know what's in the bag?
And the stones in this bag strongly influence the chance of picking one, unlike stones in a different bag.
Maybe you have to consider all the info you have, so you can't use all the stones in the multiverse as a reference class if you already know what's in the bag?
Consider the information you have:
And yet from all this information about stones - mind you, we haven't even begun talking about all information you have - what is relevant to the problem of blindly picking a stone from a particular bag is specifically the information about composition of stones inside it at the moment of picking and not anywhere and anywhen else in space and time.
But how do we know what is relevant? What is the principle that determines it? And is this principle solely about your knowledge state - in the map - or does it have something to do with the territory that your map is trying to approximate?
And the stones in this bag strongly influence the chance of picking one, unlike stones in a different bag.
Good, I think you are looking in the right direction. Now let's taboo the words "influence" and "chance". Try to formulate the same idea in terms of physical laws of the universe and processes that go accoding to these laws.
But how do we know what is relevant?
There is no such thing as The One Truly Perfect Class. All of these are rough estimations; some are better than others. It's better to use "all stones in the multiverse" than to use nothing, but if you have a choice between all stones in the multiverse and all stones on Earth, use the latter as the reference class.
Probabilities are in the mind, and you use a reference class because you can't calculate the trajectories of stones in the bag — and you have good reasons to believe there is an equal probability for each stone to be chosen (since they're all in the bag).
It was a fun exercise, thanks.
(I’m repeating it just to make sure you’ve understood my argument. If you have, ignore the next paragraph.)
However, I still don't understand how this proves that we are not in a simulation: all I know is that my memory claims I live in the 21st century, but I think most people who believe they live in the 21st century are wrong. I can't see any priors that distinguish between the two universes, so I just use a priori probabilities.
There is no such thing as The One Truly Perfect Class. All of these are rough estimations; some are better than others. It's better to use "all stones in the multiverse" than to use nothing, but if you have a choice between all stones in the multiverse and all stones on Earth, use the latter as the reference class.
But why is one reference class more preferable than the other? What does determine it? How do we know that it's better to use "all the stones on Earth" than "all the stones in the multiverse"? And even better still to use "all the stones in this particular bag in this particular moment"? But not better to use "two specific stones from the bag"?
Probabilities are in the mind, and you use a reference class because you can't calculate the trajectories of stones in the bag — and you have good reasons to believe there is an equal probability for each stone to be chosen (since they're all in the bag).
True. Probability is in the map. Which is an approximation of the territory. And yet some maps are more accurate than the others. Some do correspond to the territory - approximate it correctly to the degree that they claim to, and some do not. How do we know whether a particular map corresponds to the particular territory? And what is the territory for probability theory, to begin with?
But why is one reference class more preferable than the other?
"Stones" is not a good class with clearly defined boundaries (like humans or potatoes), but we know about the stone that it is from Earth, so we must use this information.
Reference class "all stones in the bag" use all information we have, so it's the best. In fact, reference class should be the space of possibilities.
Your second question leads to the same answer, isn't it?
P. S.: can you just write your argument directly? It took too much time to ask questions, so it's inefficient.
"Stones" is not a good class with clearly defined boundaries (like humans or potatoes)
Nothing is. We are dealing with abstractions and approximations of reality, in probability theory especially. And yet some approximations are correct while others are not.
Reference class "all stones in the bag" use all information we have, so it's the best.
We've been through that already. We have all kind of information, but still truly take in account only some of it, while constructing our mathematical models.
In fact, reference class should be the space of possibilities.
I fully agree. The whole term "reference class" is very misleading with its apparent arbitrariness. What we actually need to be talking about is the sample space, consisting of mutually exclusive and collectively exhaustive outcomes of a probability experiment.
P. S.: can you just write your argument directly? It took too much time to ask questions, so it's inefficient.
My apologies. From now on I'm going to be direct.
Probability is in the map but this map has to correspond to the territory. And the only way to have a relation of map territory correspondence also known as "truth" is to go and check.
So how do we know which outcomes are possible in a particular real world situation? We conduct an experiment. We blindly pick a stone from the bag multiple times and notice that every time this is a stone from the bag and not a stone from somewhere else on the planet Earth. This isn't just a fact about our knowledge state. It's the way reality actually works. If physics was different, say there was a portal in the bag leading to stones in some far away place, then your experiment would produce different results. On the other hand, if you simply believed very very strongly that there is a portal, while in fact there were none, you would still simply get one of the stones from the bag.
So when we say that something is a random sample from something or that something is a possible outcome, we mean, that reality actually works this way. That there is a certain causal process that leads to you getting a stone from the bag and not from somewhere else when you follow a particular experimental procedure. And you are describing this behavior of reality, to a certain approximation, with math. Here I talk about it in more details.
With that in mind, do you see why you are not a random sample from all people who has ever thought or will be thinking that they live in 21st century, while a stone blindly picked from the bag is a random sample from all the stones in the bag?
And the only way to have a relation of map territory correspondence also known as "truth" is to go and check.
Disagree. For example, if you have a dice that is symmetric by form and by weight with 4 sides, you are sure that if you roll it 100 times you will have around 25 results for each side.
I don't see which direct experiment you can use to figure out whether we are in a simulation or not that isn't extremely dangerous (searching for bugs in the simulation? Suicide?), so we should use other methods.
"With that in mind, do you see why you are not a random sample from all people who have ever thought or will be thinking that they live in the 21st century, while a stone blindly picked from the bag is a random sample from all the stones in the bag?"
I still don't see. Can you be even more direct?
Disagree. For example, if you have a dice that is symmetric by form and by weight with 4 sides, you are sure that if you roll it 100 times you will have around 25 results for each side.
And this belief of mine is grounded in actual behavior of dice in our physical reality, which I would never be able to get without going and checking the way reality works. I don't think we actually have any disagreement here.
I don't see which direct experiment you can use to figure out whether we are in a simulation or not that isn't extremely dangerous (searching for bugs in the simulation? Suicide?), so we should use other methods.
The point isn't that we can perform some kind of experiment to distinguish between simulation/no simulation conditionally on its result. The point is what kind of prior one should use - what mathematical model is appropriate for the situation that we are talking about. And the answer is: the kind of model that approximate the behavior of the universe.
I still don't see. Can you be even more direct?
The reason why we can say that picking a stone from a bag is a random sample from all the stones in a bag is because there is an actual causal process determining which stone will be picked from the stones in the bag, which we approximate to the level of our knowledge.
But there is no such process for your being alive in simulation or no simulation. There is no God, who from beyond time considered whether creating you in actual 21st century or its future simulation based on the total number of people there. That's not how our universe works to the best of our knowledge. The existence of such process would contradict relativity as it would be sending information back in time. And so we can't assume a random sample from all the people.
There are two axes along which the anthropic principle can be applied: time and universes.
The first one- time- is simple: let's suppose, there is 3 epochs: before humanity, before the 22nd century and after the 22nd century. Before 22nd century, 10^11 humans had lived. After we will colonize universe so there will be 10^28 humans (according to my own rough estimate). So what's the probability of being born in a particular epoch, assuming you are born as a human?
It's clear out that you could not have been born before epoch of humanity, and the probability that you have been born before 22nd century is extremely low.
Nick Bostrom ends his reflexions here and say: "humanity will extinct in the 21st century, because, otherwise, probability that you and me will born after and the 22nd century ≈1 but we have not".
But there's an other axe: universes.
Imagine, that you are trying to determine whether you are in universe A or universe B. At the start, your probabilities are 1 to 1. Than you discover that there's 100 times more humans in universe A than in B. After doing bayesian update, now your probabilities are 100 to 1.
Let's suppose there are two possible universes: one in which humanity goes extinct in the 21st century, and one in which humanity colonizes the universe. Considering, that >99.99999% of all peoples life in the universe where humanity won and after 22nd century, the only conclusion can be made: humanity have won and now we are in the simulation of 21st century, because there is much more.
... but if this argument is truth, why not push it to its limits? What if there is a universe where there is no the law of conservation of energy and there is infinity space, so there is an infinite number of intelligent beings (and some of them enjoy simulations)?
Infinity is infinitively greater than 10^28, so the probability that our simulation was launched in the universe with infinite energy is 1-1/∞, so ≈1
At this point, you might think: but what if there is just no universe with infinite energy?
Do you remember example with universes A and B?
The fact that universe A might not exist change nothing- you exist, so, there's 100 to 1 that universe A exist.
Cogito, ergo we are in a simulation launched in a universe with infinite energy and space- where there are so many intelligent beings that, if you tried to write down their number in decimal system of measurement, the stars would burn out before you finishes writing even 1/100 digits of this number.