Earlier this year, the outspoken American evangelical Harold Camping made an extremely profound prediction: that the world would end on 21st May. The prediction appears to have been incorrect, an unfortunate outcome for Camping and his followers.
Yet as soon as Camping realised his mistake, he hastily revised his prediction. The actual Day of Judgement would be Friday 21st October.
Dicing with the date of the apocalypse is surely the ultimate losing bet. Statisticians are often asked to make predictions based on incomplete information, but in this case it is taken to an extreme. So how might one make a reasonable prediction of when doomsday will occur?
In the absence of any other information, we might believe that each new day has the same extremely small, but non-zero, chance of being the one when the world ends. Let’s call that probability p. So p is the chance that the world will end tomorrow, Friday 21st October.
If Camping is wrong, perhaps we will all be finished instead on Saturday 22nd October. The probability of this occurring is (1-p)p: the world can only end on Saturday if it hasn’t already ended on Friday. Note that (1-p)p is slightly less than p. Similarly, the probability that the world will end on Sunday is (1-p)2p, and so on.
This is an example of the geometric distribution, extremely familiar to statisticians. If we believe all the assumptions, the logical conclusion is that tomorrow is indeed the most likely day for the world to end, or at least, more likely than any other specific day in the future.
Most observers, although apparently not Camping, would of course regard the value of p as almost vanishingly small, so perhaps it’s not worth squandering your life savings just yet. If the arbiters at the Doomsday Clock are to be believed, the current ‘time’ is six minutes to midnight, meaning that 99.58% of the lifetime of the Earth has already elapsed.
If we take the current age of the Earth to be 4.5 billion years – using more scientific estimates than James Ussher’s biblical calculation that the world was created in 4004 BC – then we would expect another 18.8 million years, or 6.9 billion days, until the balloon goes up.
The expected value of the geometric distribution is 1/p, so a simple estimate of the probability that the world will end tomorrow is 1 in 6.9 billion. The estimate of the probability that the world will end in the next year, 1 in 18.8 million, is also extremely small, but of the same order of magnitude as the probability of a single ticket winning the National Lottery in the UK. The odds are not in Camping’s favour.