Abraham Lincoln said that a house divided against itself cannot stand. He was right about slavery, but the maxim doesn’t apply to much else. In general, the best people are contradictory, and the most enduring institutions are, too.

The Olympics are a good example. The Olympics are a peaceful celebration of our warlike nature.

The opening ceremony represents one side of the Olympic movement. They are a lavish celebration of the cooperative virtues: unity, friendship, equality, compassion and care. In Friday’s ceremony, there’ll be musical tributes to the global community and the Olympic spirit. There will be Pepsi commercial-type images of the people from different backgrounds joyfully coming together. There will be pious speeches about our common humanity and universal ideals.

And there will be a lot of dancing. Because we’re social, semi-herdlike creatures, we take a primordial pleasure in the sight of a large number of people moving in unison. Dance is physical, like sports, but, in many ways, it is the opposite of sports. In dance, the purpose is to blend with and mirror each other; in sport, the purpose is to come out ahead. Dancers perform for the audience and offer a gift of emotion; athletes respond to one another and the spectators are just there to witness and cheer.
Dancers, especially at the opening ceremony, smile in warmth and friendship. No true sport is ever done smiling (this is the problem with figure skating and competitive cheerleading).

After the opening ceremony is over, the Olympics turn into a celebration of the competitive virtues: tenacity, courage, excellence, supremacy, discipline and conflict.

The smiling goes away and the grim-faced games begin. The marathoner struggling against exhaustion, the boxer trying to pummel his foe, the diver resolutely focused on her task. The purpose is to be tougher and better than the people who are seeking the same pinnacle.

If the opening ceremony is win-win, most of the rest of the games are win-lose. If the opening ceremony mimics peace, the competitions mimic warfare. It’s not about the brotherhood of humankind. It’s about making sure our country beats the Chinese in the medal chart.

Through fierce competition, sport separates the elite from the mediocre. It identifies the heroes and standards of excellence that everybody else can emulate (a noble loser can serve as well as a talented winner). The idea is not to win friendship; it’s to win glory. We get to see people experiencing the thrill of victory from the agony of defeat and judge how well they respond.
In sum, the Olympic Games appeal both to our desire for fellowship and our desire for status, to the dreams of community and also supremacy. And, of course, these desires are in tension. But the world is, too. The world isn’t a jigsaw puzzle that fits neatly and logically together. It’s a system of clashing waves that can never be fully reconciled.

The enduring popularity of the Olympics teach the lesson that if you find yourself caught between two competing impulses, you don’t always need to choose between them. You can go for both simultaneously. A single institution can celebrate charitable compassion and military toughness. A three-week festival can be crassly commercial, but also strangely moving.

F. Scott Fitzgerald famously said that the mark of a first rate intelligence is the ability to hold two contradictory thoughts in your mind at the same time. But it’s not really the mark of genius, just the mark of anybody who functions well in the world. It’s the mark of any institution that lasts.

A few years ago, Roger Martin, the dean of the University of Toronto’s management school, wrote a book called “The Opposable Mind,” about business leaders who can embrace the tension between contradictory ideas. One of his examples was A.G. Lafley of Proctor & Gamble.

Some Procter & Gamble executives thought the company needed to cut costs and lower prices to compete with the supermarket store brands. Another group thought the company should invest in innovation to keep their products clearly superior. Lafley embraced both visions, pushing hard in both directions.

The world, unfortunately, has too many monomaniacs — people who pick one side of any creative tension and wish the other would just go away. Some parents and teachers like the cooperative virtues and distrust the competitive ones, so, laughably, they tell their kids that they are going to play sports but nobody is going to keep score.

Politics has become a contest of monomaniacs. One faction champions austerity while another champions growth. One party becomes the party of economic security and the other becomes the party of creative destruction.

The right course is usually to push hard in both directions, to be a house creatively divided against itself, to thrive amid the contradictions. The Olympics are great, but they are not coherent.