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I have an analogy, it might be wrong or hard to follow. However, I believe it shows why the article's argument is pretty nonsensical. Suppose there were two p

I have an analogy, it might be wrong or hard to follow. However, I believe it shows why the article's argument is pretty nonsensical. Suppose there were two possible universes - God had a choice when creating the world - and we're living in one of them. We have no idea about His choice, or what other possible universe there might be. How could we learn anything about another universe? Obviously we can't. Can we have a better than even chance of guessing whether we're living in the better or the worse of the two possible universes? Per the article, we can! Mimicking the protocol described in the article: * Step 1: We choose a random number, setting this aside. I don't specify how we choose this. * Step 2: Then we evaluate the universe we're living in, which we do have access to, via whatever fitness function we want, as to how good it is. We arrive at a numerical score. Edit: This corresponds to opening the envelope to see what number is inside. Note that we don't have any information about the number in the other envelope! (The other possible universe.) None whatsoever. If the numerical score is higher than the random number we had guessed, congratulations, we're probably living in the better of the possible universes! if the numerical score is lower than the random number we had chosen, odds are we're not living in the better possible universe! But this method of gaining a bit of information is just so patently absurd on its face. Obviously we haven't actually learned anything at all. I hope this little exercise shows how ridiculous the steps outlined are. It is clear we cannot actually gain any insight whatsoever into the philosophical question proposed, through this method. we don't actually learn whether we're probably living in the better of two possible universes, where we have absolutely no idea as to what the two might differ in (what number the other universe might have.)

dllthomas 11y ago
"Can we decide if we're living in the better or the worse of the two possible universes? Per the article, we can!" No, per the article you'll have a marginally better chance than picking without assessing at all. I don't think your framing shows anything at all about whether that's sense or nonsense.
- deleted 11y ago
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- logicallee 11y ago
  (edited) In my analogy, assessing the universe numerically = opening the envelope to see what number is inside. I think it's a pretty close analogy, and obviously leads to an absurd, nonsensical result: that we can learn something about whether we 'probably' (>50%) are in the better universe, without knowing anything about the value of the other one.
  - dllthomas 11y ago
    I still don't see why your analogy does anything but introduce additional complication. To me, the result appears no more nonsensical than in the original formulation - where it appears correct. So long as X and Y are chosen in advance - and independently - of my guessing, if I draw my reference R from any continuous distribution, there is some nonzero chance that it will fall between X and Y, letting me distinguish them in that case.
    - logicallee 11y ago
      you have no idea what possible values X and Y can have. It's like an alternative universe, or guessing a number first and then finding a function to numerically evaluate the universe whose range you don't know in advance. I find it nonsensical that this can yield any information.
level3 11y ago
Your analogy is clouded by emotion, since it appeals to the notion that we shouldn't be able to pick some arbitrary number and then be able to compare the quality of universes. Comparison of universes is multifaceted, so it seems nonsensical, but it actually becomes very possible when you reduce the universes to a single number, and thus make it a question about a probability space. Let's use your protocol. We arbitrarily choose a number R. Then we find out our universe's number A. So now our question is, what is the probability that B is further away from A than R (and in the same direction)? This might seem intractable because we don't know anything about the way A and B were chosen. But in fact, we don't need to. We're not actually trying to calculate the probability; we just want to know whether it's greater than zero. As initially posed, the problem is, "Out of all the possible distributions for A and B, and all the possible As and Bs for each distribution, is there a nonzero probability that B is further away from A than R (and in the same direction)?" Intuition might tell you no, since the interval [A,B] is always finite over a seemingly infinite range. But that doesn't account for the fact that "most" distributions are just as finite. And it's also easy to envision that there are an infinite number of distributions that will permit a B that meets that condition (especially given that there are just as many Bs on "that side" of R as there are on "this side"). Still, you may argue that we don't have an easy way to sum the probabilities over all the distributions. So we solve the problem by re-framing it in simpler terms. Instead of fixing R while varying A and B, we transform the problem by fixing A and B and varying R (which is completely under our control). And it turns out, if our distribution of R is positive everywhere, then regardless of A and B, there's a nonzero probability of R falling between them. We still need to sum over all possible distributions of A and B, but we've already shown that every term of the sum is positive. In the end, we might not know the exact value of that probability, but that's irrelevant to the problem.
- logicallee 11y ago
  You don't seem to have a problem with the protocol itself, by the way. What do you say regarding what all the people in this thread state that you can't chose a random number to begin with? (there is no way to pick an integer uniformly at random)?
  - 11y ago

dllthomas 11y ago

"Can we decide if we're living in the better or the worse of the two possible universes? Per the article, we can!" No, per the article you'll have a marginally better chance than picking without assessing at all. I don't think your framing shows anything at all about whether that's sense or nonsense.

deleted 11y ago
[deleted]
logicallee 11y ago
(edited) In my analogy, assessing the universe numerically = opening the envelope to see what number is inside. I think it's a pretty close analogy, and obviously leads to an absurd, nonsensical result: that we can learn something about whether we 'probably' (>50%) are in the better universe, without knowing anything about the value of the other one.
- dllthomas 11y ago
  I still don't see why your analogy does anything but introduce additional complication. To me, the result appears no more nonsensical than in the original formulation - where it appears correct. So long as X and Y are chosen in advance - and independently - of my guessing, if I draw my reference R from any continuous distribution, there is some nonzero chance that it will fall between X and Y, letting me distinguish them in that case.
  - logicallee 11y ago
    you have no idea what possible values X and Y can have. It's like an alternative universe, or guessing a number first and then finding a function to numerically evaluate the universe whose range you don't know in advance. I find it nonsensical that this can yield any information.

level3 11y ago

Your analogy is clouded by emotion, since it appeals to the notion that we shouldn't be able to pick some arbitrary number and then be able to compare the quality of universes. Comparison of universes is multifaceted, so it seems nonsensical, but it actually becomes very possible when you reduce the universes to a single number, and thus make it a question about a probability space. Let's use your protocol. We arbitrarily choose a number R. Then we find out our universe's number A. So now our question is, what is the probability that B is further away from A than R (and in the same direction)? This might seem intractable because we don't know anything about the way A and B were chosen. But in fact, we don't need to. We're not actually trying to calculate the probability; we just want to know whether it's greater than zero. As initially posed, the problem is, "Out of all the possible distributions for A and B, and all the possible As and Bs for each distribution, is there a nonzero probability that B is further away from A than R (and in the same direction)?" Intuition might tell you no, since the interval [A,B] is always finite over a seemingly infinite range. But that doesn't account for the fact that "most" distributions are just as finite. And it's also easy to envision that there are an infinite number of distributions that will permit a B that meets that condition (especially given that there are just as many Bs on "that side" of R as there are on "this side"). Still, you may argue that we don't have an easy way to sum the probabilities over all the distributions. So we solve the problem by re-framing it in simpler terms. Instead of fixing R while varying A and B, we transform the problem by fixing A and B and varying R (which is completely under our control). And it turns out, if our distribution of R is positive everywhere, then regardless of A and B, there's a nonzero probability of R falling between them. We still need to sum over all possible distributions of A and B, but we've already shown that every term of the sum is positive. In the end, we might not know the exact value of that probability, but that's irrelevant to the problem.

logicallee 11y ago
You don't seem to have a problem with the protocol itself, by the way. What do you say regarding what all the people in this thread state that you can't chose a random number to begin with? (there is no way to pick an integer uniformly at random)?
- 11y ago