Predicting Future Using The Copernican Principle

“Prediction is difficult, especially if it involves the future” - Niels Bohr

Richard Gott, an astrophysics professor, visited Germany in 1969. Upon visiting the Berlin Wall, the first thought that came to his mind was “How long is this going to last”. This is very similar to what Nicolaus Copernicus asked several years back. Copernicus questioned “Where are we?” in relation to where Earth is in the entire Universe and thus stated “Earth is not the center of the universe; and it’s not really special.

Gott quickly reasoned out his own question by using referencing back to what Copernicus stated and said to himself “ There’s nothing special about this visit. I’m just travelling to Europe and happened to visit this place because it happens to be here. This makes my visit random in time. So this makes any moment to be equally likely to make a prediction and I should’ve come precisely at the halfway point ( as there’s a 50% chance for fall before halfway and 50% chance for fall post halfway ) and if I am at the halfway then this shall last for another x years where x is it’s age right now; When Gott visited, the Berlin Wall was 8 years old and he predicted that it’ll last for another 8 years giving it a total lifespan of 16 years. The prediction was quite close as the wall collapsed after standing tall for 20 years.

When I first thought about and tried applying this in real life, it felt pretty pointless. Let’s assume that Gott visits a baby of 2 years old, would he predict that the baby will live merely for another 2 years? Also, if he visits an elderly person of say 75 years old, would he predict that this person will live till 150 ? I also observed a bit of irony to this entire logic as assuming that our arrival is not any special makes us to be located in the center of all which contradicts to the entirety of the Copernican Principle. So I started reading more on this and understood why my understanding of it failed by applying just as it is. That brings us to the famous “Bayes Principle”.

Copernicus x Bayes :

Bayes’ rule requires us to input our prior expectations so as to compute future probability but what if we don’t necessarily have one. In situations of choosing a raffle (gambling competition), we assume a “uniform prior” which considers every portion of winning tickets to be equally likely. But for examples such as that of the Berlin wall, we don’t really have a uniform prior but rather an uninformative prior. This means saying that we don’t really know anything about the time span we’re going to predict. The only piece of data that we can give to Bayes’s is the fact that we’ve visited Berlin Wall when it’s eight years old. Hence, with having only one information in hand the safe bet is to use Copernican Principle. If we want to predict something that will last and have no knowledge on the subject whatsoever, then the best guess we can make is to settle for “it will last just as much as it did earlier” with respect to the current instance of time.

This principle is essentially just another Bayes’ Rule with an uninformative prior. In fact, there’s been examples of this principle being used by different situations.

Harold Jeffreys, a Bayesian Statistician determined the total number of tramcars in a city. Given only one serial number of a tramcar, he’d simply doubled it. A similar technique was used in World War II, when an estimate of the number of German tanks resulted in 246. Using extremely difficult reconnaissance techniques, the Allies guessed 1400+ but the post war count shows 245, the true figure.

There are situations where this principle works just about right and it doesn’t in other situations. As stated earlier, it works best if we have no information about the subject in prior but fails in cases where we predict a human lifespan as we already know the average lifespan of a human. Hence it doesn’t make sense to say that a 75 year old will live till 150 years.

The more prior information we can get to Bayes’ the better the prediction or else just double the numerical value we already posses in hand.

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