The planet boasts several examples of a capital city that is so important to its nation, across the range of human activities, that it dwarfs all other cities in the country.

Paris certainly is one of those, and perhaps the ultimate example (though London is in the running). When France’s “second city” is gritty Marseille or bucolic Lyon … well, that’s a mighty big drop from Paris, and not just in matters chic or moderne.

Practically everything that matters in France is in Paris. All arms of the government, big businesses, the stock exchange, the news and entertainment industries.

(There even is a vineyard to be found inside the peripherique, along with just about everything else that matters to France.)

Which leads us to our Paris Observation of the day: You can bump into someone important just walking down the street, in this town.

Paris, remember, is not a particularly big town. It’s a huge sprawl, when you include the suburbs, but “inside the peripherique” (the ring road which circles the 20 arrondisements) holds only about 2 million people. That isn’t a lot for a city of such importance across the spectrum of human endeavor.

Also, the movers and shakers tend to cluster in a few upscale areas.

My sister, brother-in-law and niece saw “Harry Potter” (Daniel Radcliffe) in a restaurant on the tony Ile St-Louis. (My niece got his autograph.)

If you happen to find yourself near the American Embassy, at the end of the Champs, you also are close to the Elysee Palace — which is where the president of the republique lives. At any moment you could see Nicolas Sarkozy rolling past (probably on his way to a meeting with Angela Merkel) or even Carla Bruni.

The prime minister lives in a crowded neighborhood in the 7th, and I’ve been walking past when the gates have flown open, and a convoy has materialized.

It is not at all uncommon to see police cars leading foreign dignitaries on the Boulevard des Invalides. (Recognizing flags helps identify the president/king/tyrant in the limousine.)

A friend of ours last night was at a dinner that included the former head of the European Central Bank, the editor of the New York Times and the U.S. ambassador to France.

A week ago, two people we know were in the apartment of the editor of a major Paris-based newspaper and a well-known Russian composer.

Some relatives for years lived only a few doors from the actress Catherine Deneuve.

Walk into the lobby of any of the five-star hotels … and no telling whom you might see arriving or leaving. Princess Di and Dodi Fayed walked out of the Ritz on the Right Bank just moments before the fatal accident in 1997. Someone else we know just missed Mick Jagger at the George V a few years back.

And this sense of “important people all around us” has been going on a long time. In the 1920s and 1930s, to drop by Brasserie Lippe or Deux Magots, a cafe, might mean a sighting of Hemingway, Fitzgerald, Sartre, Camus or Picasso.

Things are quite different in the U.S., where power and influence are spread around the country. The focal point of government (Washington D.C.) is neither the nexus of big business (New York) nor of popular culture (Los Angeles) nor of agribusiness (Chicago).

It is possible to bump into Larry David or Ben Stiller at a Starbucks in Hollywood, or sight Andy Warhol (were he still alive) in New York, or encounter a senator while touring D.C.

But those cities are thousands of miles apart. None boast the concentration of celebrity and power to be found in Paris, heart of the realm.

In France, anyone who doesn’t live in Paris is “provincial.”

Sounds harsh, but it’s true. This is where it all happens.