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Originally Posted by Ken G
There's only one 10 billionth born, let's say it's you. You're either in the corner, or you're not. But whether you are or not, on what are you going to base your conclusion that there was a 5% that you would be?
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The fact that I am declaring with 95% confidence that I'm in the latter 95% of all humans who'll ever live: that
requires that there's a 5% chance I'm in the corner.
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Originally Posted by Ken G
What criterion can you use other than looking at the other 10 billionth borns in their own similar intelligent species?
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OK, that's fine, but that's bringing in a bit of external evidence. I suggested this was what you were doing when you first introduced this argument, and you denied it at that time.
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Originally Posted by Ken G
A probability is a fraction out of many trials that are equally likely. It is fine if those trials are idealized, they don't ever have to actually take place. But what is the set of trials that you are using to say that there is a 5% chance humanity will outnumber 200 billion, if it is not the trials represented by all the species in the "restaurant"?
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I am not performing these trials. The 200 billion result comes only from the 10-billionth human. Other humans perform the same calculation and produce different results. 5% of those various
different human results will be wrong, not 5% of every 10-billionth soul who makes the 200 billion calculation. I've no idea how many of those will be wrong.
If we go back to your restaurant, with the first 5% of every species cluster in one corner: the 10-billionth soul of some species will be in the corner, the 10-billionth soul of other species will still be in the general room. All the folk in the corner will be saying "Oops, we got our calculations wrong - that's 95% confidence for you." All the folk in the general room will be saying "Yep, we were right to assert we were in the last 95%." So some 10-billionth souls will have been right, and some will have been wrong. We can't say what proportion without introducing external information. It doesn't make the calculation invalid at the 95% level for any given population.
Grant Hutchison