Does humanity have a future? Astonishingly, with the help of probability calculus, one can make an arbitrarily precise statement. According to this, between 1 and 2000 billion people will be born after us with 95% certainty.
The end, is it near? Suppose that every person receives a piece of paper with a number on it on the day of their birth, a unique number that is assigned only to them. The first person who ever lived received the "No. 1" a few tens of thousands of years ago, then today, a few hundred generations later, the numbers in the range of around 100 billion are distributed. How many numbers will be distributed in total before humanity dies out? We don't know, but we can try to make a statement about it using probability theory.
This seems absurd at first glance, without further knowledge about the future of mankind, why should we be able to make a statement about the number of people who will come after us? The assumption underlying such a statement is that of the "normality" of our own existence. It is not to be expected (although not impossible) that we were born at a very special ("non-normal") point in time. We would expect most people to be born when there are a lot of people in the world. It's the same with the lottery: the chance of winning the lottery is minimal, and most people lose the lottery. So if you play the lottery, you have to reckon with not winning. A win is not excluded, but very unlikely (otherwise nobody would have to go to work anymore). It's the same with people: it is very unlikely that you belong to the first millionth of all people (or have drawn one of the first "numbers" from the example mentioned above) that are ever born. Likewise, it is unlikely that you belong to the last millionth of all people (or have drawn one of the last numbers that are ever assigned). The closer you get to the “middle numbers”, the more likely this observation becomes. The vast majority of people drew "medium numbers" when they were born.
How many people will be born after us?
Let's try to use this information to determine how many people can be born after us without our own position becoming "extreme" or "non-normal". If we consider an estimate that is 95% certain to be "reliable", then we can now try to make a "reliable" estimate of the people who will be born after us. There is a 95% chance that we are in the middle 95% of all people who have ever been born (we refer to the first 2.5% and last 2.5% of all people who will ever have lived as “non-normal” or "extreme"). This means that depending on where we are within this interval, between 2.5 and 97.5% of all people lived before us, or, the other way around, between 97.5% and 2.5% of all people come after us. With the known number of people who have already lived, this can be converted into concrete numbers. According to this, between 1 and 2000 billion people will be born after us with a probability of 95%. It is quite possible that more than 2000 billion people will be born after us, but the chance of this is only 2.5%. It is also possible that less than 1 billion people will be born after us, the chance for this is only 2.5%.
Let us now imagine a possible future of mankind: in a few decades, the world population will stabilize at a level of 10 billion people, i.e. it will no longer grow and will not shrink either. In this case, the 2000 billion people must already be "consumed" in the year 4000 and humanity will die out with 95% certainty. An alternative would be a comparatively rapid decline to a low, stable population value, for example, 2 billion people on earth, in this case, the 2000 billion people are not "used up" until around the year 12000. Another scenario would be a cyclical commute between high civilization with many billions of people and "Dark Ages" with a world population of less than a billion, in this case, mankind manages to continue to exist for a few 10,000 years. Mind you, these are always the most optimistic numbers that are just about compatible with the statement "95% certainty". The true value is probably much lower, the statement with the greatest probability is "about as many people will be born again as have already lived". So do we have at most a few hundred, maybe a few thousand years left? This is known as the "doomsday argument".
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