No, it's not external information, it's internal information. The point is, you cannot use the number 10 billion anywhere in your longevity calculation, and also say that there is a 5% chance you are in the first 5% of your population. The distribution I gave as an example proves this. There has to be some probability distribution, it's not external information until you specify it. But no matter what it is, Carter would not be correct in his 5% probability, except under specially chosen conditions.

You understand what I'm saying, yes, but follow up your reasoning. As a function of birth number, given the distribution I assumed, the actual probability of being in the first 5% is completely a variable. For some it's less than 5%, for some more. This is my point-- there is automatically correlation between birth number and longevity probability. Carter thinks that because you don't know this correlation, you can ignore it and still use both the 10 billion number and the 5% number in the same calculation. In fact, you may only use one or the other, not both, even if you don't know the correlation between them. There are many other examples of this phenomenon in probability. I'll start a new thread about two envelopes containing money to demonstrate the point. It is very subtle, and I think it is the real reason that the Carter reasoning is not just of limited value, as I argued before, but it's downright wrong. The other arguments are working from an intuitive place where Carter can't be right, but they haven't really hit the mark because correlations in probability have a very subtle effect sometimes.