In 1969, could anyone predict how long the Berlin Wall would stand? We know it fell in 1989, and it has now fallen longer than it ever stood. But that was the question American physicist John Richard Gott asked himself during a visit to Berlin a year after the Prague Spring was crushed.
Since no one could predict when the Berlin Wall would fall, if ever, including John Richard Gott, Gott postulated that the Copernican Principle should be applied in cases where nothing is known. The Copernican Principle, named after 16th century astronomer Nicolaus Copernicus, describes how humans have no special place in the cosmos.
Applied to the Berlin Wall in 1969, this meant that there was a 75 percent probability that he saw the Berlin Wall at a time when it had already passed the first quarter of its total existence. That is, from the age of eight in 1969, with a 75 percent confidence interval, it would no longer be standing in 1993. The calculation would thus stop from the year of the establishment 1961 8 times 4 quarters. That would be 32 years, thus 1993. And he was to be right, the Wall fell four years earlier.
He christened this method the ‘Copernicus Method’ and at the same time applied it to the life expectancy of mankind. Between 5,100 and 7.8 million years we should still have as a species in front of us with this ‘doomsday argument‘ with 95 percent confidence interval, so no reason for us or our children to panic.
Since the method drew heavy criticism about its effect and operation, Gott with ‘The New Yorker’ magazine also applied this method to test against the expected running time of Broadway shows. In doing so, he was 95 percent correct with his predictions, with a 95 percent confidence interval.
Why was God right? Because the Copernican principle is an instance of the ‘Bayes theorem‘. In this theorem, the probability of one event occurring is made dependent on the probability of another event occurring.
This can be used to calculate that Google will be around until about 2032, and the USA will endure as a nation until the year 2255. However, your best friend’s new relationship that he entered into a month ago will be over in just a month.
The best estimate of how long something will last without even knowing anything is that it will last as long as it already existed. However, if one has further information, for example 90 years is not the age of a wall, but of a person, then we have the knowledge that such a person will not become 180 years old.
From this we see that there must be two categories of objects in the world. Those that have a naturally limited life span, and others that do not. Mathematically, the life span of the first category is distributed on a Pareto distribution, and the latter on a normal distribution.
If we have a sense of what kind of distribution we’re dealing with, then we’ve already laid a foundation for making a good prediction. And as it turns out, Bayes’ theorem provides several rules of thumb for prediction that help us do this.
With the multiplicative rule, you take the past unit of measurement, multiply it by a constant factor. Without prior knowledge, the factor has the value 2.
For expected film revenues, for example, the factor 1.4 is taken. So if a film has generated 10 million euros in revenues to date, then total revenues of 14 million can be expected.
Rule of Averages
If, for example, we want to determine the life expectancy of a young person who is still younger than the average age of the population – without having any further information on health, lifestyle, situation in the home country and the like – then we are on the safe side if we specify the average life expectancy as the life expectancy.
If the person gets older and comes closer and closer to the average life expectancy, then we can set the concrete life expectancy of this person with a sufficiently large confidence interval with a few years above the average. For a 90 year old and a 6 year old, with an average life expectancy of 76 years, we would thus arrive at 94 and 77 years of life expectancy (the 6 year old gets an additional bonus year here because he has already survived infant mortality).
The additive rule predicts that things will continue to go that way for a constant time. It is based on an Erlang or left-skewed distribution.
Whichever rule is used, the results get better when you have more information. However, predicting the average length of reigns of Egyptian pharaohs is difficult without more information.