Coperican principle in "Welcome to the Universe"

My atheist group is reading "Welcome to the Universe" by N.dG. Tyson, Gott, and Strauss, we'll discuss it on Sunday, so I need replies quickly.

J. Richard Gott uses a mathematical formulation of the Copernican principle to estimate how long humans will survive, resting on the assumption that one's place or position (temporally or spatially) is not likely to be special (thus, "Copernican" principle).

But the mathematical formulation of this appears flawed because it rests on an arbitrary choice of which 50% likelihood is chosen. Gott says:

"If you are located randomly between the beginning and the end of whatever you are observing, there is a probability of 50% that you are located in the middle two quarters [between 25% of the way along, and 75% of the way along].

If you are at the very beginning of the middle two quarters [at 25% along], it's future is 3 times as long as its past [0 to 25% x 3 = 25% to 100%].

But if you are at the very end of the middle two quarters, it's future is 1/3rd as long as its past [0 to 75% = 3 x 75% to 100%].

There is a 50% chance that you lie between these two extremes and that it's future is between 1/3rd and 3 times as long as its past."

This means that if you know the beginning (the past) you can predict the future to a 50% likelihood. He visited the Berlin Wall when it was 8 years old, so the predicted a 50% likelihood that its length (at being torn down) would be between 2.66 years and 24 years. It was torn down 20 years after his visit.

However, looks what happens when I make the exact same calculation, but starting with in a different place:

If you are located randomly between the beginning and the end of whatever you are observing, there is a probability of 50% that you are located in the 10th to 60th percentiles [between 10% of the way along, and 60% of the way along].

If you are at the very beginning of the 10th to 60th percentiles [at 10% along], it's future is 9 times as long as its past [0 to 10% x 9 = 10% to 100%].

But if you are at the very end of the 10th to 60th percentiles, it's future is 2/3rd as long as its past [0 to 60% x 2 = 3 x 60% to 100%].

There is a 50% chance that you lie between these two extremes and that it's future is between 2/3rd and 9 times as long as its past.

This calculation will give a different probability of the lifespan of, say, the Berlin Wall, merely because I chose a different 50% to work with. It seems which 50% you choose is arbitrary.

Am I missing something?

via International Skeptics Forum http://ift.tt/2m0TppN