Optimal eschatology

There’s a group that claims that Judgement Day is May 21st 2011.  Of course, this is doubtless based on research and divine inspiration.  But we can still ask the question – if a group predicts the end of the world, what time should it pick for maximum impact?

You may have heard the joke about the man who listens to an astronomer lecture, and becomes very concerned when she talks about the sun expanding to engulf the Earth.  He says, distraught, “This is terrible!  Is there nothing we can do?”.  “Not really”, she says, “but it is a long way off – about five billion years.”  “Oh thank God!”  he says.  “I thought you had said five million”.

On the other hand, a person predicting the end of the world in ten seconds would find it difficult to assemble a group in such a limited time.

Between these two extremes there must lie a happy medium.  May 21st 2011 seems a little soon, but perhaps it is good to have an early date, to get data quickly.  Mathematical analysis shows that the true optimal date depends on the Bass coefficients of adoption, the equity premium over a riskless asset, and the discount rate – the exact formulation is left as an exercise for the reader.

This analysis assumes that the end of the world date is fixed and announced.  This is often not the case.  Had Christians specified an exact time for the Second Coming, they would be little more than a footnote in ancient history textbooks.  But instead, the Bible tells us in Matthew 24:36 that “But of that day and hour knoweth no man, no, not the angels of heaven…”, a clear reference to a non-degenerate probability distribution.  If the end of the world is specified as a Poisson process, we can ensure that it is always ten years in the future on average, no matter how much time passes.  Until, of course, the end finally comes.

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