Sorry for being out of topic, but has that 3^^^^3 problem been solved already? I just read the posts and, frankly, I fail to see why this caused so much problems.
Among the things that Jaynes repeats a lot in his book is that the sum of all probabilities must be 1. Hence, if you put probabilities somewhere, you must remove elsewhere. What is the prior probability for “me being able to simulate/kill 3^^^^3 persons/pigs”? Let’s call that nonzero number “epsilon”. Now, I guess that the (3^^^^3)-1 case should have a probability greater or equal than epsilon, same for (3^^^^3)-2 etc. Even with a “cap” at 3^^^^3, this makes epsilon ⇐ 1/(3^^^^3). And this doesn’t consider the case “I fail to fulfill my threat and suddenly change into a sofa”, let alone all the >=42^^^^^^^42 possible statements in that meta-multiverse. The integral should be one.
Now, the fact that I make said statement should raise the posterior probability to something larger than epsilon, depending on your trust in me etc, but the order of magnitude is at least small enough to cancel out the “immenseness” of 3^^^^3. Is it that simple or am I missing something?
Sorry for being out of topic, but has that 3^^^^3 problem been solved already? I just read the posts and, frankly, I fail to see why this caused so much problems.
Among the things that Jaynes repeats a lot in his book is that the sum of all probabilities must be 1. Hence, if you put probabilities somewhere, you must remove elsewhere. What is the prior probability for “me being able to simulate/kill 3^^^^3 persons/pigs”? Let’s call that nonzero number “epsilon”. Now, I guess that the (3^^^^3)-1 case should have a probability greater or equal than epsilon, same for (3^^^^3)-2 etc. Even with a “cap” at 3^^^^3, this makes epsilon ⇐ 1/(3^^^^3). And this doesn’t consider the case “I fail to fulfill my threat and suddenly change into a sofa”, let alone all the >=42^^^^^^^42 possible statements in that meta-multiverse. The integral should be one.
Now, the fact that I make said statement should raise the posterior probability to something larger than epsilon, depending on your trust in me etc, but the order of magnitude is at least small enough to cancel out the “immenseness” of 3^^^^3. Is it that simple or am I missing something?