You have a bag with a red and a blue ball in it. You pull a ball from the bag, but don’t look at it. What is the probability that it is blue?
Now imagine a counterfactual world. In this other world you drew the red ball from the bag. Now imagine a hippo eating an octopus. What is the probability that you drew the blue ball?
“Why does observational knowledge work in your own possible worlds, but not in counterfactuals?” is the key question here. Perhaps it’s easier to parse like this: “Why isn’t anything you can think of evidence?”
EDIT: Note that although that last question makes my answer to Vladimir’s question obvious, answering the question itself requires, basically, defining what evidence is. I suppose I may as well be helpful: evidence is what you get when an event happens that lets you apply Bayes’ rule to learn something new—not just any old event will do, it has to be an event that gives you different information under different circumstances.
It seems like one answer to “Why isn’t anything you can think of evidence?” might be that “anything you can think of” becomes incomputable very quickly.
Let’s say you were to ask a computer to consider “Anything you can think of” with respect to this problem. Imagine each unique hard drive configuration is a thought, And it can process 1 thought per second per hertz. Let’s make it a 5ghz computer.
It can think of anything on a 32 bit drive in a bit less then 1 second since 2^32 is 4,294,967,296, which is less then 5 billion.
The problem is, in uncompressed Ascii where you would need 8bits for a character, you can’t even fit the thought “32bit” onto a 32 bit harddrive, since it’s 5 bytes/40 bits long.
If we double the harddrive to 64 bits to give ourselves more room for longer thoughts, our 5ghz computer goes from being able to calculate all possible thoughts in less then a second to being able to calculate it in around a human lifetime, because of the exponential growth involved. (At least, assuming I’ve made no math errors.)
We actually have computers do this when we try to have them crack passwords with brute force. A computer trying to brute force a password is essentially trying “Anything it can think of” to open the password protected data.
Consider the following thought experiment
“Why does observational knowledge work in your own possible worlds, but not in counterfactuals?” is the key question here. Perhaps it’s easier to parse like this: “Why isn’t anything you can think of evidence?”
EDIT: Note that although that last question makes my answer to Vladimir’s question obvious, answering the question itself requires, basically, defining what evidence is. I suppose I may as well be helpful: evidence is what you get when an event happens that lets you apply Bayes’ rule to learn something new—not just any old event will do, it has to be an event that gives you different information under different circumstances.
It seems like one answer to “Why isn’t anything you can think of evidence?” might be that “anything you can think of” becomes incomputable very quickly.
Let’s say you were to ask a computer to consider “Anything you can think of” with respect to this problem. Imagine each unique hard drive configuration is a thought, And it can process 1 thought per second per hertz. Let’s make it a 5ghz computer.
It can think of anything on a 32 bit drive in a bit less then 1 second since 2^32 is 4,294,967,296, which is less then 5 billion.
The problem is, in uncompressed Ascii where you would need 8bits for a character, you can’t even fit the thought “32bit” onto a 32 bit harddrive, since it’s 5 bytes/40 bits long.
If we double the harddrive to 64 bits to give ourselves more room for longer thoughts, our 5ghz computer goes from being able to calculate all possible thoughts in less then a second to being able to calculate it in around a human lifetime, because of the exponential growth involved. (At least, assuming I’ve made no math errors.)
We actually have computers do this when we try to have them crack passwords with brute force. A computer trying to brute force a password is essentially trying “Anything it can think of” to open the password protected data.