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92 To be a prophet!? The Copernican principle

Suggested Reading:
Gott, J. (1993). Implications of the Copernican principle for our future prospects. Nature, 363(6427), pp.315-319.
Carlton M. Caves (2000). Predicting future duration from present age: A critical assessment, Contemporary Physics, 41:3, 143-153.

It is always useful if we can make predictions about the future. It could be a frivolous question like “when will Girls’ Generation disband” or something more deep like “when will be the end of the human being?” There are no concrete answers to these questions for sure, but can we make some educated guesses somehow? 

In 1993, John Richard Gott III proposed a simple framework called the Copernican principle to solve this problem. He reasoned that, it is not legitimate to assume we live in a special place or in a special period of time without solid reasons. Earth is not the center of the universe, and human being is not a privileged species. I was born in 1994, but it does not mean 1994 is a special year in history. Based on the assumption of a random observer, he derived a formula that he claimed to predict how long something will last in the future, and he claimed that the results are readily applicable to various situations. 

Let’s see an example. Ray, our random observer, is a big fan of Girls’ Generation, a legendary K-pop girl group. After the departure of some members, he really wonders how long this girl group will last in the future. He therefore drew a diagram like this: Girls’ Generation debuted in 2007(t_begin) and will eventually disband someday(t_end). The first time Ray happened to know Girls’ Generation is in 2011(t_now). Since Ray and other fans are just unremarkable observers, who happened to know the group in some unremarkable time points, if we calculate the ratio r = t_past/(t_past + t_future) for all the Girls’ Generation fans, Gott claimed that it is reasonable to assume that r follows a uniform distribution from 0 to 1.

After obtaining the distribution of r, Gott said that we can calculate the confidence interval of t_future from that. Since r is uniformly distributed from 0 to 1, the 95% confidence interval of r would be  0.025 < r < 0.975, and the 95% confidence interval of t_future would then be 1/39*t_past < t_future < 39*t_past. So from Ray’s experience, he will estimate that Girls’ Generation should last at least 4/39 years from 2011, but probably not longer than 156 years from 2011. If we narrow the confidence interval, we can calculate that there will only be a 25% chance that Girls’ Generation will continue after 2023. 

This may sound stupid as this gave us some unreasonably huge range of prediction, but the author gave us some other examples of greater scale. The history of human being is about 200,000 years. From the same equation, we can predict the 95% confidence interval of human being’s future will be 5,100 years < t_future < 7.8x10^6 years. This translates to a total longevity between 0.205 million and 8 million years for our species, and it is comparable to the average longevity of other species (between 1 and 11 million years). Gott then moved on to show that how this equation could be derived from exponential distribution, and then discuss how his principle can be used to explain why we never receive a radio signal from extraterrestrial lives, and why we are unlikely to colonize the galaxy. 

The bimodal distribution of the lifespan of K-pop idol groups. The raw data is obtained from Wikipedia.

However, it is important to note that we cannot apply Copernican principle to any situations as Gott claimed. A great example will be the exponential decay, in which the future life time has nothing to do with the past — it is memoryless. For a deterministic process, such as a bomb set to explode after an hour, the Copernican principle is not applicable as well. It is also not a good idea to predict the longevity of a K-pop girl group. the K-pop entertainment companies usually sign a 5-to-7-year contract with their artists, so the longevity of a K-pop idol group follows a bimodal distribution: most of the groups are either so unsuccessful that they cannot survive in the first few years, or they manage to live beyond the contract yet soon disband. In fact, the derivations proposed by Gott is flawed and hidden assumptions were not properly addressed: the t_end should be regarded as a random variable rather than a fixed number, and the possibilities of making an observation before the event begins or after it ends already were not addressed.

That being said, Gott’s method does make a huge cultural impact and it does offer some back-of-the-envelope estimates for some processes that we have totally no ideas. However, it is important to keep in mind that it is simply a naive estimate, and we should spend more time analyzing the underlying mechanisms to reach a more reasonable guess.

Reference about the K-pop idol groups:
Wikipedia pages: List of South Korean idol groups (1990s), List of South Korean idol groups (2000s), List of South Korean idol groups (2010s).
The figure of Girls' Generation is obtained from Wikipedia: https://en.wikipedia.org/wiki/File:LG_%EC%8B%9C%EB%84%A4%EB%A7%88_3D_TV_%EC%83%88_%EB%AA%A8%EB%8D%B8_%E2%80%98%EC%86%8C%EB%85%80%EC%8B%9C%EB%8C%80%E2%80%99_%EC%98%81%EC%9E%85.jpg