I wrote an entry about Stephen Baxter's book MANIFOLD: TIME, where he talks about a statistical argument that we are nearing the end of humanity's existence known as "The Carter Catastrophe". It inherently doesn't make logical sense to me, though I couldn't exactly put my finger on why. It SEEMS to make sense.

Here is the link to the Wikipedia article that talks about it: Doomsday Argument

Baxter gives one example of the argument in his book. Here's another: You have two urns, one with 10 numbered balls, one with 10000 balls, but you don't know which is which. You remove one ball from one of the urns, and it is numbered 7. You can logically infer that it's from the one with 10 balls, because the likelihood of an early ball coming out of the other is pretty low.

Based on that statistical argument, it's argued that since you're here today, it is likely that you are in the last 90% of humans to be born, and less likely that you are in the first 10%. Since humanity's growth is exponential, the last 90% of the people would be born near the "Doomsday" of humanity.

There is an interesting discussion of the argument here.

To me it doesn't make sense, because SOMEONE'S gotta be among those first early humans, and it just so happens that it's the consciousness that is identified as "me". There's nothing special about "me", "I" could have been born at any time.

Someone in the discussion referenced above (which is a couple years old, there may be more current examples out there, but this is the one I found) mentioned that the argument would be able to be made by every single person at almost every single time in "history" (or something like that). Someone else mentions that the sample size in that statistical experiment is exactly 1, and thus is meaningless. If you took out the first 10 balls, and they were 1 through 10, maybe that would mean something...you'd pretty much know with pretty high certainty which urn you were drawing balls from. Conversely, anything higher than 10 on the second draw means with 100% certainty that it's the urn with the much higher number of balls.

It's an interesting thought experiment, and Baxter uses it as an argument given by one of his characters, but doesn't necessarily endorse it as true or as good logic.