Then there was another unknown known: the likely consequences of an invasion. Shortly before it began, Mr. Blair met President Jacques Chirac of France. As well as reiterating his opposition to the coming war, Mr. Chirac offered the prime minister specific warnings. Mr. Blair and his friends in Washington seemed to think that they would be welcomed with open arms in Iraq, Mr. Chirac said, but that they shouldn’t count on it. It was foolish to think of creating a modern democracy in an artificial country with a divided society like Iraq. And Mr. Chirac asked whether Mr. Blair realized that, by invading Iraq, they might yet precipitate a civil war.

This has been described in a BBC documentary by someone present, Sir Stephen Wall, a Foreign Office man then attached to Downing Street. As the British team was leaving, Mr. Blair turned and said, “Poor old Jacques, he just doesn’t get it,” to which Sir Stephen now adds dryly that he turned out to get it rather better than “we” did.

At that time, Mr. Chirac was reviled in America, and his career has just ended in disgrace, with a court conviction for embezzlement. But who was right about Iraq? All the calamities that followed the invasion were not only foreseeable, they were foreseen. And yet for Mr. Blair, as well as Washington, they were unknown knowns.

One more such, bitter as it is to say so when many people have been ruined, was the Bernard L. Madoff fraud. For years, his investors gratefully and unquestioningly accepted returns that were strictly incredible. Loud warning voices sounded. Harry Markopolos, a former investment officer, exhaustively back-analyzed Mr. Madoff’s supposed figures by computer. He spent nearly nine years repeatedly trying to explain to the Securities and Exchange Commission that these figures were not merely incredible but mathematically impossible. And still the S.E.C. chose to unknow it. Leos Janacek wrote a harrowing opera called “The Makropulos Affair”; Peter Gelb at the Met should commission someone to write “The Markopolos Affair” as a fable for our times.

In a very different kind of scandal, not everyone at Penn State, and certainly not every fan, knew what had happened in the showers. But quite enough was known by people who could have acted. They chose instead to unknow. And so to another classic unknown known, the euro. The recent summit in Brussels turned into a silly melodrama, with a British prime minister, David Cameron this time, once more playing the pantomime villain. But Mr. Cameron was right, if for the wrong reasons, to oppose the European Union’s latest frantic (and doomed) plan to prop up the euro.

If truth be told (but it so rarely is!), the euro cannot work and could never have worked. That is, a single currency embracing countries as diverse in social culture, productivity, work practices and taxation as Germany and Greece, or the Netherlands and Portugal, is economically impossible without much closer fiscal and financial union — which is politically impossible. Anyone could have known that at the time the euro was introduced, but for the rulers of the European Union it was their very own unknown known.

“The Cloud of Unknowing” is a medieval classic of mystical writing, and unknowing still hangs over us. It will be a happier new year if we can dispel some of that cloud, try to unknow less, and know a little more.