The Copernican Principle and How to Use Statistics to Figure Out How Long Anything Will Last

In “Implications of the Copernican principle for our future prospects” ($200 here or free through the questionably legal SciHub here), Gott explained that if we assume we don’t occupy a unique moment in history, we can use a basic equation to predict the lifetime of any phenomenon.The Copernican Lifetime EquationThe equation, in its simple brilliance (derivation at the end of article) is:Where t_current is the amount of time something has already been around, t_future is the expected amount of time it will last from now, and confidence interval expresses how certain we are in the estimate..This equation is based on a simple idea: we don’t exist at a unique moment in time and therefore, when we observe an event, we are most likely watching the middle and not the beginning or the conclusion.You are most likely not at the beginning or end of an event but in the middle (Source).As with any equation, the best way to figure out how it works is to input some numbers..Let's apply this to something simple, say the lifetime of the human species..We’ll use a 95% confidence interval and assume modern humans have been around for 200,000 years..Plugging in the numbers, we get:The answer to the classic dinner-party question (okay, only the dinner parties I go to) of how long humans will be around is 5130 to 7.8 million years with 95% confidence..This is in close agreement with actual evidence that shows the mean duration of a mammal species is about 2 million years with the Neanderthals making it 300,000 years and Homo erectus 1.6 million years.The neat part about this equation is it can be applied to anything while relying only on statistics instead of trying to untangle a complex underlying web of causes..How long a television show runs for, the lifetime of a technology, or the length of time a company exists are all subject to numerous factors that are impossible to tease apart..Rather than digging through all the causes, we can take advantage of the temporal (a fancy word for time) Copernican Principle and arrive at a decent estimate for the lifetime of any phenomenon.To apply the equation to something closer to home, data science, we first need to find the current lifetime of the field, which we’ll put at 6 years based on when the Harvard Business Review released the article “Data Scientist: The Sexiest Job of the 21st Century”..Then, we use the equation to find we can expect, with 95% confidence, data science will be around for at least another 8 weeks, and at most, 234 years.If we want a narrower estimate, we reduce our confidence interval: at 50%, we get from 2 to 18 years.This illustrates an important point in statistics: if we want to increase the precision, we have to sacrifice accuracy..A smaller confidence interval is less likely to be correct, but it gives us a narrower range for our answer.If you want to play around with the numbers, here’s a Jupyter Notebook.Being Right, Atomic Bombs, and TakeawaysYou might object the answers from this equation are ridiculously wide, a point I’ll concede..However, the objective is not to get a single number — there are almost no situations, even when using the best algorithm, that we can find the one number guaranteed to be spot on — but to find a plausible range.I like to think of the Copernican Lifetime Equation as a Fermi estimate, a back of the envelope style calculation named for the physicist Enrico Fermi..In 1945, with nothing more than some scraps of paper, Fermi estimated the yield of the Trinity atomic bomb test to within a factor of 2!. More details

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