The thing that struck me about England's monumental mistake is how rare it is that democracies make the wrong decision, and how remarkable it is that it doesn't happen much more often.
Remarkable, because the outcome is usually finely balanced. Elections and referendums are frequently decided by as little as 2 or 3 per cent of the voting population.
Opinion polls in the weeks and days heading to the vote warn that the result is on a knife edge but long experience has taught us not to worry. Common sense nearly always prevails, if only just.
The polls in Britain were giving Leave a slight lead in the final days but not many believed them, not even the leader of the UK Independence Party, Nigel Farage, who put out a statement on the eve of voting saying its campaign would carry on regardless. I wonder if the outcome of Scotland's independence referendum last year made everyone complacent, not just the young who didn't vote but also many of those who did.
Anyone who has been watching the BBC this week will have witnessed an unusual phenomenon of voting psychology. It has become common to see someone who voted Leave say, "I'm not sure it was the right decision" and even to confess they voted Leave because they thought it wouldn't win.
That is the psychology we used to call "protest voting" in the days when third parties had no chance. It is a vote for the purpose of participating, for registering a sentiment, an affiliation or an identity, rather than making a serious, dull, sensible decision. It is an indulgence that seems harmless when the election seems predictable.
Some English voters clearly did not realise the enormity of their decision last week until the morning after, when their Prime Minister announced he would step down. David Cameron was calm, realistic and even convincingly respectful of a decision he could not have respected. BBC presenters kept referring to his announcement as "emotional" but Cameron's upper lip had been stiff, it was the presenters, and their audience, they knew, who found it emotional.
Cameron had said before the vote he would stay and negotiate Britain's exit if necessary, but then decided it was properly a task for his successor, whoever that might be.
Not Boris Johnson it turns out. Johnson looked as shaken as anybody on the morning after. He read an erudite little speech he had written about his identity with Europe's culture if not its political over-reach. He didn't sound convinced by himself for once. Possibly he had discovered, too late, the difference between amusing himself and newspaper readers with clever pieces of writing, and being responsible for a country's future.
When a democracy regrets its decision at an election it can correct it at the next one. When it regrets a decision of this magnitude at a referendum, there is little prospect of reversing it.
Britain has not just lost an ideal economic position - access to a marketplace of half a billion people without the common currency that carries the only real threat to national sovereignty - it has lost its internal political bearings for the moment.
Its political parties are no longer sure what voters really want. About two thirds of MPs wanted to stay in the European Union. Labour even more than the Tories. Both parties know the country now needs another election to get a clearer sense of what the public wants, but first each party has to elect a leader who might be able to express whatever it is the public wants to do now.
It is a good thing democratic mistakes of this magnitude are so rare because the country, and sometimes the world, lives with them for a long time. The United States made just such a mistake at its presidential election in 2000. But for a few disputed ballot papers in Florida we would not have had George W. Bush and the 2003 invasion of Iraq. That monumental blunder has had such a defining effect on the 21st century so far that we hardly bother wondering how better leadership would have responded to 9/11.
Even Britain's referendum result could be blamed on Bush if the spectre of refugees from the Middle East was really behind it. But France has been protecting Britain from that sort of immigration. Sadly the real resentment behind the Leave vote must have been the mingling of people that comes with the benefits of a bigger market.
Those of us who think of England as a sophisticated, cosmopolitan, culturally confident society are thinking of London, not the England of Nigel Farage. In fact there were always a lot of nauseating Nigels in England. If they are its dominant character now, Europe will be glad to see it go.