Recently the Large Hadron Collider was damaged by a mechanical failure. This requires the collider to be warmed up, repaired, and then cooled down again, so we're looking at a two-month delay.
Inevitably, many commenters said, "Anthropic principle! If the LHC had worked, it would have produced a black hole or strangelet or vacuum failure, and we wouldn't be here!"
This remark may be somewhat premature, since I don't think we're yet at the point in time when the LHC would have started producing collisions if not for this malfunction. However, a few weeks(?) from now, the "Anthropic!" hypothesis will start to make sense, assuming it can make sense at all. (Does this mean we can foresee executing a future probability update, but can't go ahead and update now?)
As you know, I don't spend much time worrying about the Large Hadron Collider when I've got much larger existential-risk-fish to fry. However, there's an exercise in probability theory (which I first picked up from E.T. Jaynes) along the lines of, "How many times does a coin have to come up heads before you believe the coin is fixed?" This tells you how low your prior probability is for the hypothesis. If a coin comes up heads only twice, that's definitely not a good reason to believe it's fixed, unless you already suspected from the beginning. But if it comes up heads 100 times, it's taking you too long to notice.
So - taking into account the previous cancellation of the Superconducting Supercollider (SSC) - how many times does the LHC have to fail before you'll start considering an anthropic explanation? 10? 20? 50?
After observing empirically that the LHC had failed 100 times in a row, would you endorse a policy of keeping the LHC powered up, but trying to fire it again only in the event of, say, nuclear terrorism or a global economic crash?
Okay, it scares me when I realize that I've been getting probability theory wrong, even though I seemed to be on perfectly firm ground. But I'm finding that it's even more scary that even our hosts and most commenters here seem to be getting it backwards -- at least Robin; given that the last question in the post seems so obviously wrong for the reasons pointed out already, I'm starting to wonder whether the post is meant as a test of reasoning about probabilities, leading up to a post about how Nature Does Not Grade You On A Curve (grumble :)). Thanks to simon for pointing out the flaw -- I didn't see it myself.
Since simon's explanation is apparently failing to convince most other people here, let me try my own:
As Robinson points out, there are two underlying events. (A): The laws of physics either mean that a working LHC would destroy the world, or that it wouldn't; let p_destroyer denote our subjective prior probability that it would destroy the world. (B): Either something random happens that prevents the LHC from working, or it doesn't. There is an objective Born probability here that a randomly chosen Everett branch of future Earth at date X will have had a string of failures that kept the LHC from working. We should really consider a subjective probability distribution over these objective probabilities, but let us just consider the resulting subjective probability that a randomly chosen Everett branch will not have had a string of failures preventing LHC from working -- call it p_works.
Now, at date X, in a randomly chosen Everett branch, there are four possibilities:
Now, we cannot directly observe whether he LHC would destroy Earth if turned on; what we actually can "observe" in a randomly chosen Everett branch at date X is which of the following three events is true:
i. The LHC is turned on and working fine. (Aka "case 4") ii. The LHC is not turned on, because there has been a string of random failures. (Aka "case 1 OR case 3") iii. Earth is gone. (Aka "case 2")
Of course, in case iii aka 2, we are not actually around to observe -- thus the scare quotes around "observe."
simon's argument is that if we observe case ii aka "1 OR 3" aka "a string of random failures has prevented the LHC from working up to date X", then our posterior probability of "The LHC would destroy Earth if turned on" is equal to our prior probability of that proposition (i.e., to p_destroyer):
p(case 1 OR case 3) = p(case 1) + p(case 3) = p_destroyer (1 - p_works) + (1 - p_destroyer) (1 - p_works) = 1 - p_works
p(case 1 | the LHC would destroy Earth) = p(the LHC would destroy Earth AND it fails to operate | the LHC would destroy Earth) = 1 - p_works p(case 3 | the LHC would destroy Earth) = p(the LHC would NOT destroy Earth AND it fails to operate | the LHC WOULD destroy Earth) = 0 p(case 1 OR case 3 | the LHC would destroy Earth) = p(case 1 | the LHC would destroy Earth) + p(case 3 | the LHC would destroy Earth) = (1 - p_works + 0) = 1 - p_works
p(the LHC would destroy Earth | case 1 OR case 3) = p(case 1 OR case 3 | the LHC would destroy Earth) p(the LHC would destroy Earth) / p(case 1 OR case 3) = (1 - p_works) p_destroyer / (1 - p_works) = p_destroyer