Statistically speaking around 10.000 years at most
Due to this and the odds of me being born. If humans last millions and millions of years, why would i be born as "one of the pioneers". What would the odds be that i'm born today and not when the galaxy is being fully colonized.
The Doomsday ArgumentThe Doomsday Argument (DA), or Carter catastrophe, is a probabilistic argument that claims to predict the future population of the human species, based on an estimation of the number of humans born to date.
If Leslie's figure is used, then approximately 60 billion humans have been born so far, so it can be estimated that there is a 95% chance that the total number of humans will be less than 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1140 billion humans will be born in 9120 years. Depending on the projection of the world population in the forthcoming centuries, estimates may vary, but the argument states that it is unlikely that more than 1.2 trillion humans will ever live.
If for instance exactly 50% of humans would be born before I were and 50% of humans would be after me, we wouldn't even last longer than few centuries at most.
It can be lengthier in case of drastic population collapse, but even that would imply something bad would happen.
Someone did the same exercise for the Berlin Wall in the 1960s
Doomsday And The Dark Forest: The Fall Of The Berlin Wall And Our Quest For The StarsJ Richard Gott, now an astrophysicist famous for the notion that the universe might have created itself by reaching back through time, visited the Berlin Wall in 1969, while an undergraduate at Harvard. There, he made the following prediction (paraphrased):
The Wall will stand for at least 2 and 2/3 years more, but no longer than 24 years.
On November 9, 1989, a rough twenty years later, his prediction came to fruition, and the Wall came down, precipitating the reunification of East and West Germany.
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An animal species on average last a few million years before we talk about "a new species" through evolution. And given technological evolution and sociological evolution are a thing, and how we've seen society change so much in a short time, it is not unthinkeable that humans would be something completely unrecogniseable much sooner, like cyborgs or robots. Or that artificial intelligence simply takes over.