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Originally Posted by Ken G
What external information? All the species are identical. Think of them as all the possible ways humanity could have gone, if a butterfly had flapped its wings.
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Well, you originally suggested we look at:
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... the other 10 billionth borns in their own similar intelligent species
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That certainly seemed like you were looking for external information about the likely lifespan of intelligent races.
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Originally Posted by Ken G
You are clinging to the 95% confidence without recognizing that being the 10 billionth changes that confidence irreparably, even if you don't know how it changes it.
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Clinging"? Nice choice of word.
But 95% confidence here doesn't require all those other imaginary species in their crowded restaurant - just us humans.
Let's say everyone who ever lived announced at some time in their lives: "I'm one of the last 95% of people who'll ever lived." 95% of them would be right. If they were statistically astute, they'd have better phrased it "I'm 95% confident I'm one of the last 95% of people who'll ever lived." The 10-billionth person might be one of those in the top 95% or one of those in the bottom 5%: it
doesn't matter, his/her statement is still valid.
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Originally Posted by Ken G
Where is your idealized set, all who conclude their species won't outlive 200 million, and only 5% are wrong? That is the set you have not produced.
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There is no such set. The 200 million figure is the product of a
single person, the 10-billionth, who may be right (with 95% probability) or may be wrong (with 5% probability). His rightness or wrongness is not a function of the figure 200 million, but of his/her
actual position in the total number of humans, something which (s)he cannot know, but can certainly estimate with 95% confidence.
In some of your collection of species, the person who predicts 200 million will be correct; in others, that person will be wrong. We have no way of estimating the proportion of rights and wrongs in that set, but that proportion has no mathematical linkage to the first 5% of humans who ever lived, or whether there were more or less than 10 billion of them.
I think you're confusing
within species probability and
across species probability.
Grant Hutchison