Let me clarify this point, since it is crucial. If you don't know anything about gravity, you use probabilistic arguments to reason that the Earth's atmosphere should be spread evenly over the whole solar system and beyond. Then someone explains gravity, and suddenly you have it tightly stuck to the surface of our planet. A little information goes a long way when using probability arguments, and the Carter hypothesis is only valid in the absence of any information at all other than birth order. It would be very foolish to use so little information in making a probability argument, along the lines of the 50/50 argument I presented.
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