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A random distribution means that you have the same chance of hearing it in year 1 as you do in year 6k, right?

Until there is a second one, there is nothing to statistically distinguish this from random noise.

This is something philosophers debate, right? Similar to the Doomsday Argument asking whether it's reasonable to assume our lives are in the middle of the human species timeline rather than at the end:

https://en.m.wikipedia.org/wiki/Doomsday_argument

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