Nostradamus game

Let’s predict how much more, at least, there is left to live mask mode, The Internet or Habru? Let’s figure it out on our fingers, not knowing anything, except for how long these phenomena have already been with us, and justify our predictions with simple tricks from statistics and the Copernican principle…

Copernicus principle

Doomsday theorem, literally claims that with 95% certainty we can assume that the human race will disappear within 9120 years. The exact date is not precisely defined, but what will disappear is almost certainly… The theorem was discovered and popularized by a professor of astrophysics John Gott…

Gott based his reasoning on the fact that people living now are in a random place throughout the chronology of human history. It is pure coincidence that we are now living in 2021, and this year is not preferable to any other – 20,000 BC, 1315 or 1917. As the position of the Earth in the solar system is not central, so is our year 2021. Gott called this statement the Copernican principle…

The conjecture visited the future famous scientist in 1969 after a tourist visit to Berlin, where he saw The Berlin wall… At that time, the wall had already stood for 8 years. After some simple calculations in his mind, he told a friend that the wall would stand for at least 2 and no more than 24 years. That’s why.

Let be $$ – the time of existence of the phenomenon to the present moment, and $$ – how much remains to him until the end. Assuming that hitting the time point t of the time interval of complete existence $$ randomly and equally probable, we have a random variable

distributed on the segment [0, 1] evenly… In this case confidence intervalwith which the random variable $$ with probability $$ is inside the segment is

Let us express $$ through $$ and $$ and we get the interval for the time of further existence $$

With odds one to one ($$) Gott estimated how much remains of the Berlin Wall:

Multiplied the random number 8 by 3 and got that no more than 24 years. In any case, having such an estimate, you can already accept bets.

Predictions

Inspired by his discovery, Gott made many predictions. The most famous of them is the one Doomsday theorem, published in the journal Nature in 1993… The principle is the same, except that $$, so to speak, to be sure, with an error probability of no more than 1/20. In the role of a uniformly distributed random variable, the ratio $$where $$ – the approximate number of people who have already lived and are living in this world, and $$ – the final number of all who will live for all time. It will be no more $$, i.e, if we assume that 60 billion people have been born up to the present moment (Leslie’s estimate), then we can say that with 95% certainty the total number of people N will be less than 20 * 60 billion = 1.2 trillion. Assuming that the world’s population stabilizes at 10 billion people and the average life expectancy is 80 years, it is not hard to calculate how long it will take for the remaining 1,140 billion people to be born. Namely, this reasoning means that with 95% certainty we can say that the human race will disappear within 9120 years. This is what Wikipedia says.

Follow Gott, come on and I’ll pretend Nostradamus and I will predict that

• mask mode (already lasting more than 500 days) is unlikely to disappear in the next 10 days,
• Habr will live in no less than another five months,
• and the Internet will not disappear for at least a year.

Seriously? Let’s bet!

In his book JR Gott III, Time Travel in Einstein’s Universe (Houghton Mifflin, Boston, 2001), Ch. five. John Gott made many predictions about the fate of states, politicians, talk shows. The New Yorker magazine dedicated an article to him – How to Predict Everything… It would seem – a success, but as it happens in science, there were even more critical articles and reviews.

The first obvious objection that comes to mind illustrates comic xkcd

The people of Berlin were not lucky to have seen the dividing wall! Once it was lined up, they could hope that everything goes away – this goes away too. Soon. And closer to its collapse – to consider that their life will end sooner.

A serious analysis, which I will not reproduce here, is given in the article by Carlton M. Caves // Predicting future duration from present age: Revisiting a critical assessment of Gott’s rule, 2008. The bottom line: Gott’s assessment has the right to life, but only if prior probability density looks like:

This kind of distribution is especially so because it time scale invariant… Simply put, the Gott lifetime estimate is applicable only to those objects for which there is no characteristic lifetime.…

Many objects of interest to us have a characteristic time scale. On average, dogs live 10-13 years, people 60-80, butterflies – a day or two, and so on. “Dog years” for dogs, calendar year for humans. The Gott formula is not applicable to them. There are also large-scale invariant probability distributions in life, such as Zipf’s law other rank distributions…

Consistent application Copernicus principle (Gott’s estimates) means the following:

• to take random object,
• see how long it already exists,
• evaluate what rank it belongs to (in order of magnitude)

Everyday experience tells us that if a subject taken at random, say, a researcher, caught the director’s eyes at the wrong time, the tricky question “how long have you been writing your work?” answers – “a month somewhere”, then yes, it is unlikely that he will do everything by tomorrow, but in a couple of years, for sure. Estimated in order of magnitude, everything is fine.

Conclusion

No matter how provocative the content is Doomsday theoremsas well as other forecasts by John Gott, they are all very approximate – in order of magnitude. In addition, not all scientists succeed accidentally pay attention to things people are interested in – the Berlin Wall, politicians, TV series … Not everyone can watch tomorrow.

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