The Copernican Principle was formulated by physicist J. Richard Gott, who when he visited the Berlin wall in 1969 asked how much longer it was going to divide the city. Assuming that the moment when he visited wasn’t special, he reasoned that his arrival was equally likely to fall before and after the halfway point. Since it had been eight years since it was built, he predicted it would fall in 1977. In fact, it lasted another 20 years. His prediction was somewhat off, but still not bad for such a simple heuristic.
Gott’s approach can be generalized to guessing the duration of any phenomenon when we don’t have a lot of data. For example, as of 2024 the United States have been around for 248 years, so we can expect them to last until the year 2272.
Restaurants are another example. When I first came to San Francisco was for a few months in late 2008 I stayed at a friend’s apartment in the Inner Sunset which he didn’t use as he was moving in with his girlfriend. There were several restaurants in the neighborhood I went to because they were cheap. When I returned to San Francisco in 2014, this time for the long term, I kept visiting the Inner Sunset every once in a while, and I saw many restaurants come and go. Nowadays, many of the ones that opened since 2014 are gone, but most of those that I knew from 2008 are still around. This proves the Copernican Principle: Restaurants that have been around for a long time are most likely to be around for many years to come, while those that opened recently are also those that are most likely to close soon.
A real-life application of the Copernican Principle that I find useful is to help decisions on how long to wait for something. The other day, I decided to get ice cream at one of those places in the Sunset that has been around forever. Since it was a hot day, there was a line of people also getting ice cream. After waiting for five minutes, I realized that the servers were slower than I had anticipated and that I might be there for some time, but how much longer? Applying the Copernican Principle, I reasoned that it’d most likely be another five minutes, which would be acceptable. This turned out to be a correct estimate, and a little over four minutes later I had my taro ice cream cone.
If the lifespan of something can be estimated using the Copernican Principle depends on the underlying distribution. For example, we know that there’s an upper bound to how old people can get, so it’d be silly to apply the Copernican Principle to life expectancy. The Copernican Principle holds if the underlying distribution is an Erlang distribution, which results in the predicted time remaining for a given phenomenon is independent from how long the phenomenon has already lasted.
The Copernican Principle is related to the concept of Reversion to the Mean. Both assume that things even out over time, but in different ways. Reversion to the Mean assumes that if we observe something unusual, the next event is going to be more average and less unusual. The Copernican Principle assumes that there’s nothing unusual about the present moment.
Nehaveigur 