Could it be predicted in 1969 how long the Berlin Wall will exist? We all know now that it came down in 1989, and is by now gone longer than it had existed. But this very question was the one that American physicist John Richard Gott asked himself, when he visited Berlin one year after the clampdown of the Prague Spring.
As nobody could predict when the Berlin Wall – if at all – would fall, not even John Richard Gott, he postulated that one should use the Copernican Principle, when nothing is known. The Copernican Principle, named after the 16th-century astronomer Nikolaus Kopernikus, stated that humans have no special status in the Cosmos.
Adopted for the Berlin Wall in 1969 this means that there is a 75 percent possibility that the wall right at that moment had a quarter of its total duration of existence already behind. That means that the wall’s age of 8 years would mean that with a 75 percent confidence interval, the wall would last for 32 years, and thus cease to exist in 1993. And we can say now with hindsight that Gott was right. The wall fell even four years earlier in 1989.
He named the method Copernican Method and applied to other fields such as the expectancy of how long humans will exist. This ‚Doomsday-argument‘ would give us a result of an expected additional existence of humans between 5,100 and 7.8 million years with a 95 percent confidence interval. Considering this, we have no need to panic.
As Gott’s method raised some criticism about its effect and the way it works, he approached ‚The New Yorker‘ to apply the method on the expected runtimes of Broadway shows. Poring over the data and applying the method he could predict 95 percent of the shows runtimes with a 95 percent confidence interval.
Why was Gott right? Because the Copernican Method is an instance of Bayes’ theorem. This theorem estimates the probability of the appearance of an event by making it dependent on the probability of the appearance of another event.
With that we can calculate that the internet search giant Google will exist until 2032 and the United States as a nation until 2255. The new relationship of your best friend that he started a month ago on the other hand will be over in a month.
The best estimate to how long something will exist without knowing something about it is to know how long it has been existing. Any additional information, such as the age of a person, gives us clues and we know from experience that a 90-year-old person won’t live to the age of 180.
We recognize that there must be two categories of objects in the world. Those that have a limited lifespan, and those that have an unlimited lifespan. From a mathematically stand point the lifespan for the first category hass a Pareto-distribution, and the latter one a normal distribution.
If we have the feeling for which distribution we are dealing with, then we have the basic building block for a forecast. And as it turns out, the Bayes’ theorem several rules of thumbs for forecasts that can help us.
The multiplicative rule takes past measures multiplied with a constant factor. Without prior knowledge this value is set at 2.
For expected movie revenue the value 1.4 is used. If a movie has gained 10 million dollars, then the total revenue is forecast to be 14 million.
If we want to forecast the life expectancy of a young person that younger than the average of the rest of the population – without further knowledge on the person’s health status, life style, situation it the home country and similar influencing factors – then we are to the safe side to use the average life expectancy.
If the person gets older and comes closer to the average life expectancy, then we can – with high confidence – add years to the average. For a 90-year-old and a 6-year-old with an average life expectancy of 76 years, we could set it to 94 and 77 years respectively (the 6-year-old gets one bonus year, because he has survived child mortality).
The additive rule forecasts that things will be constant for a constant time. It’s based on an Erlang-distribution.
Whatever rule is applied, the results become better the more information we have. The average governing time of Egyptian Pharaos is difficult to forecast if we don’t have additional information.
This article was also published in German.