Beware of the e-prophets

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We have all seen at least one of these disturbing videos, which have gone viral since the start of the Covid-19 pandemic, which show us that five or ten years ago, some people already prophesied it. Before declaring these prophets’ great wizards of the web, it may be useful to remember an elementary result of probability theory: an unlikely event will almost certainly happen, if the situations considered are numerous enough.

Search engines provide a vivid illustration of this result. Take two unrelated words, for example “Covid-19” and “Neolithic,” and open a random web page. It is very unlikely that these two words will appear. But make a request to a search engine and you will see that, among the billions of pages on the web, there are a few where this miracle happened. So, such a request on Google yield more than a million results.

At the end of the 20th century, a challenge was to find a pair of words that did not appear together in any web page, but, with the growth of the web, it became an impossible mission. Advertisements, inserted in unrelated pages, and library catalogs excel in these unlikely reconciliations.

A little probability calculation shows us that, if we repeat n times, independently, a test which has a probability p to give a positive result, the probability that at least one of these tests gives a positive result is 1 – (1 – p)^n. For example, if you attend a concert on a day other than February 29, the probability that you will celebrate your birthday on the same day is very low: 0.00274. But if 1,000 people attend this concert, the probability that at least one of them will celebrate his birthday on this day is 0.936 — almost guaranteed.

As there are more than 5 billion videos on YouTube, if we assume that 0.001% of them, or 50,000, prophesy of a disaster and that there are 10,000 possible disaster scenarios (a fire in Indonesia, an earthquake in Peru, a harsh winter in Canada, a viral pandemic, etc.) and that one of these 10,000 disasters occurs, there is a probability 1 – (1 – 1 in 10,000) 50,000 = 0.993 that it was prophesied on YouTube.

Likewise, everyday dozens of people predict an increase in the price of oil, a fall in the price of oil, a stock market crash, etc. And when such an event occurs, there is always at least one to declare: “I told you so! “Formerly, the exegesis of Nostradamus excelled in finding, in his work, a prophecy which seemed, posteriori, to announce an event that had occurred. It seems that the search engines have now automated this task.

In a society like ours, where information abounds, we should not always trust those whose past predictions are proven, because there are so many people who say anything, that some end up statistically being right. Above all, however, we must ask ourselves about the process that led them to make these forecasts, ask ourselves how they know what they know.