Robinson, I could try to nitpick all the things wrong with your post, but it’s probably better to try to guess at what is leading your intuition (and the intuition of others) astray.
Here’s what I think you think:
Either the laws of physics are such that the LHC would destroy the world, or not.
Given our survival, it is guaranteed that the LHC failed if the universe is such that it would destroy the world, whereas if the universe is not like that, failure of the LHC is not any more likely than one would expect normally.
Thus, failure of the LHC is evidence for the laws of physics being such that the LHC would destroy the world.
This line of argument fails because when you condition on survival, you need to take into account the different probabilities of survival given the different possibilities for the laws of the universe. As an analogy, imagine a quantum suicide apparatus. The apparatus has a 1⁄2 chance of killing you each time you run it and you run it 1000 times. But, while the apparatus is very reliable, it has a one in a googol chance of being broken in such a way that every time it will be guaranteed not to kill you, but appear to have operated successfully and by chance not killed you. Then, if you survive running it 1000 times, the chance of it being broken in that way is over a googol squared times more likely than the chance of it having operated successfully.
Here’s what that means for improving intuition: one should feel surprised at surviving a quantum suicide experiment, instead of thinking “well, of course I would experience survival”.
Finally a note about the anthropic principle: it is simply the application of normal probability theory to situtations where there are observer selection effects, not a special separate rule.
Robinson, I could try to nitpick all the things wrong with your post, but it’s probably better to try to guess at what is leading your intuition (and the intuition of others) astray.
Here’s what I think you think:
Either the laws of physics are such that the LHC would destroy the world, or not.
Given our survival, it is guaranteed that the LHC failed if the universe is such that it would destroy the world, whereas if the universe is not like that, failure of the LHC is not any more likely than one would expect normally.
Thus, failure of the LHC is evidence for the laws of physics being such that the LHC would destroy the world.
This line of argument fails because when you condition on survival, you need to take into account the different probabilities of survival given the different possibilities for the laws of the universe. As an analogy, imagine a quantum suicide apparatus. The apparatus has a 1⁄2 chance of killing you each time you run it and you run it 1000 times. But, while the apparatus is very reliable, it has a one in a googol chance of being broken in such a way that every time it will be guaranteed not to kill you, but appear to have operated successfully and by chance not killed you. Then, if you survive running it 1000 times, the chance of it being broken in that way is over a googol squared times more likely than the chance of it having operated successfully.
Here’s what that means for improving intuition: one should feel surprised at surviving a quantum suicide experiment, instead of thinking “well, of course I would experience survival”.
Finally a note about the anthropic principle: it is simply the application of normal probability theory to situtations where there are observer selection effects, not a special separate rule.