The recent unsettling footage of England’s chief medical officer Chris Whitty being grabbed and harassed in a central London park brought to mind many things. There were the similar scenes of BBC journalist Nicholas Watt being pursued, surrounded and abused at a protest in Westminster. Darker still, there was the murder of the MP Jo Cox during the Brexit campaign five years ago.
But I was also reminded of the square root of two.
Two and a half thousand years ago, followers of Pythagoras believed that the constants of the universe were constructed of whole numbers. The Pythagoreans were wrong. One such constant is a simple diagonal across a square — the square root of two. But there are no two whole numbers which, as a fraction, give us the square root of two. 3⁄2 isn’t far off. 10⁄7 is closer. But you can give up on finding the exact fraction.*
None of this should cause much alarm, except perhaps to the long-suffering editors and typesetters of this column. Yet the Pythagoreans were extremely perturbed by the simple demonstration that a basic constant could not be expressed as a fraction of whole numbers. So perturbed, in fact, that it is said the mathematician Hippasus was murdered by being thrown overboard while at sea as a punishment for discovering the ghastly truth.
We don’t know much about Hippasus, and the evidence that he was killed for this little proof is rather patchy. But perhaps the legend has lived on because it serves as a cautionary tale. When a society persecutes people for telling the truth, it is a short step from losing its collective mind.
The totalitarian regimes of the 20th century give us the starkest examples of such insanity. Stalin persecuted genetics researchers in the 1930s and ostentatiously praised the scientist Trofim Lysenko when he claimed that genetics was a “bourgeois perversion” and geneticists were “saboteurs”. The resulting crop failures killed millions. For an encore, Stalin ordered the killing of the statistician in charge of the 1937 census, Olimpiy Kvitkin. Kvitkin’s crime was that his census revealed a fall in population as a result of that famine. Telling that truth could not be forgiven.
In May, the great crop scientist Yuan Longping died at the age of 90. He led the research effort to develop the hybrid rice crops that now feed billions of people. Yet in 1966, he too came very close to being killed as a counter-revolutionary during China’s cultural revolution.
In western democracies we do things differently. Governments do not execute scientists; they sideline them. Late last year, Undark magazine interviewed eight former US government scientists who had left their posts in frustration or protest at the obstacles placed in their way under the presidency of Donald Trump.
Then there are the random acts of hostility on the street and the death threats on social media. I have seen Twitter posts demanding that certain statisticians be silenced or hunted down and destroyed, sometimes for doing no more than publishing graphs of Covid-19 cases and hospitalisations. Even when this remains at the level of ugly intimidation, it is horrible to hear about and must be far worse to experience. It is not something we should expect a civil servant, a vaccine researcher or a journalist to have to endure. And it would be complacent to believe that the threats are always empty.
What can be done? We can demand better from our leaders. Trump never tired of winking his approval at violence against journalists; we can but hope that future presidents refrain. In September 2019, Boris Johnson was dismissive of complaints from MPs who had received death threats. The solution, he said, was Brexit. He has been much quicker to support Whitty, but it seems that his opposition to intimidation and harassment is rather more conditional than one might wish.
While a firmer moral lead from our politicians would help, ultimately the respect for facts — and those who research or report them — has to come from all of us. The facts are sometimes unpleasant: Brexit creates trade barriers between large neighbouring economies. Carbon dioxide emissions are seriously altering the climate. Sars-Cov-2 is much more dangerous than seasonal flu, and cases are rising dramatically in the UK. It would be nice if none of these things were true, but the vast majority of us are adult enough to accept the evidence, the expert judgment of those who gather that evidence and the honesty of those who report it.
The message can be infuriating, but let’s not throw the messenger overboard.
* Prove it, you say? Assume a whole-number fraction, a⁄b, does equal √2. Let’s also assume that a⁄b is the simplest possible fraction, with a and b sharing no common factors. Rearranging a⁄b = √2 gives us 2b2 = a2. That means a2 is an even number, which implies four things: a is also even, and therefore a2⁄2 is also even, and therefore b2 is even, and therefore b is even. Alas, we began by assuming that a⁄b was the simplest possible whole-number fraction, but we’ve just proved that a⁄b is the ratio of two even numbers and therefore the fraction could be simplified by dividing both of them by two. This contradiction shows that our original assumption — that a and b exist at all — must be wrong.
Written for and first published in the Financial Times on 9 July 2021.
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