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?”
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.
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”?
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?
“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.
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.
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.
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.
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?
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.
I still don’t see. Can you be even more direct?
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.
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.
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.