The Believable Bible
This post arose when I was pondering the Bible and how easy it is to justify. In the process of writing it, I think I've answered the question for myself. Here it is anyway, for the sake of discussion.
Suppose that there's a world very much like this one, except that it doesn't have the religions we know. Instead, there's a book, titled The Omega-Delta Project, that has been around in its current form for hundreds of years. This is known because a hundreds-of-years-old copy of it happens to exist; it has been carefully and precisely compared to other copies of the book, and they're all identical. It would be unreasonable, given the evidence, to suspect that it had been changed recently. This book is notable because it happens to be very well-written and interesting, and scholars agree it's much better than anything Shakespeare ever wrote.
This book also happens to contain 2,000 prophecies. 500 of them are very precise predictions of things that will happen in the year 2011; none of these prophecies could possibly be self-fulfilling, because they're all things that the human race could not bring about voluntarily (e.g. the discovery of a particular artifact, or the birth of a child under very specific circumstances). All of these 500 prophecies are relatively mundane, everyday sorts of things. The remaining 1,500 prophecies are predictions of things that will happen in the year 2021; unlike the first 500, these prophecies predict Book-of-Revelations-esque, magical things that could never happen in the world as we know it, essentially consisting of some sort of supreme being revealing that the world is actually entirely different from how we thought it was.
The year 2011 comes, and every single one of the 500 prophecies comes true. What is the probability that every single one of the remaining 1,500 prophecies will also come true?
For the two examples of the mundane prophecies that you gave it seems possible some on-going conspiracy could have made them true... but it sounds like you're trying to rule that out.
The Open Thread posted at the beginning of the month has gotten really, really big, so I've gone ahead and made another one. Post your new discussions here!
This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.