- In 1969 (8 years after the wall was erected): You'd calculate that there's a 50% chance that the wall will fall between 1972 (8x4/3=11 years) and 1993 (8x4=32 years)

- In 1989 (28 years after the wall was erected): You'd calculate that there's a 50% chance that the wall will fall between 1998 (28x4/3=37 years) and 2073 (28x4=112 years)

- In 1961 (when the wall was, say, 6 months old): You'd calculate that there's a 50% chance that the wall will fall between 1961 (0.5x4/3=0.667 years) and 1963 (0.5x4=2 years)

I found doing the math helped to point out how wide of a range the estimate provides. And 50% of the times you use this estimation method; your estimate will correctly be within this estimated range. It's also worth pointing out that, if your visit was at a random moment between 1961 and 1989, there's only a 3.6% chance that you visited in the final year of its 28 year span, and 1.8% chance that you visited in the first 6 months.

> Well, there’s nothing special about the timing of my visit. I’m just travelling—you know, Europe on five dollars a day—and I’m observing the Wall because it happens to be here.

It's relatively unlikely that you'd visit the Berlin Wall shortly after it's erected or shortly before it falls, and quite likely that you'd visit it somewhere in the middle.

Well 1/3 of the examples you gave were right.

The most likely time to fail is always "right now", i.e. this is the part of the curve with the greatest height.

However, the average expected future lifetime increases as a thing ages, because survival is evidence of robustness.

Both of these statements are true and are derived from:

P(survival) = t_obs / (t_obs + t_more)

There is no contradiction.