NEW YORK (AP) -- George Washington, first president, said this: "It is our true policy to steer clear of permanent alliances with any portion of the foreign world."
Eldridge Cleaver, civil rights leader, said this: "Americans think of themselves collectively as a huge rescue squad on 24-hour call."
Toby Keith, populist country singer, said this: "This big dog will fight when you rattle his cage - and you'll be sorry that you messed with the U.S. of A."
Now: Place those three divergent sentiments in a large bowl. Whip vigorously until blended. There you'll have, in one curious, often contradictory recipe, the world-changing, world-shaking world view of the quixotic species known as the American people.
When 21st-century Americans contemplate their place on the planet, they confront a complex history of isolationism and engagement, a deep instinct to live and let live that coexists with an equally fervent desire to be a robust beacon of freedom - sometimes by any means necessary.
That means that, while a presidential transition offers many limbos, none is quite so stark as the expected change in the approach, method and technique of foreign policy that will come with the inauguration of Barack Obama on Tuesday.
"It's a very plastic moment," says Eric Rauchway, author of "Blessed Among Nations: How the World Made America."
The arrival of Obama and his secretary of state designate, Hillary Rodham Clinton, represents a baton-passing between two distinct versions of the American world view - George W. Bush's interventionist, we-know-best foreign policy and Obama's vow to "restore our moral standing."
Both of those outlooks have their merits and their supporters. In the era after 9/11, particularly, Americans' hunger for security in the "homeland" is fervent - enough so that we re-elected Bush in 2004 more than a year after he ordered the invasion of Iraq on a false premise.
Nevertheless, polls show an increasing dissatisfaction with how America plays with others in the international sandbox, and the neoconservatives who pushed a more aggressive American position toward the world - men such as Donald Rumsfeld, John Bolton and Paul Wolfowitz - left the Bush administration years ago.
But when a new president gazes out upon the republic and looks for clues to consider the American mood toward the world and craft policy accordingly, sometimes it's all quite difficult to figure out.
We are a welcoming people who have embraced waves of immigrants who have changed us - and keep changing us - in productive ways. Yet ours is a suspicious land where accusations of Frenchness helped sour voters against John Kerry and, days after 9/11, anti-Muslim sentiment claimed the life of an Indian Sikh - the cultural equivalent of mistaking a pine tree for a chrysanthemum bush.
This is a country where ordering Chinese takeout has become a fundamentally American activity, yet also where legions of non-passport-holders who devour the mediated experiences of "Morocco" and "Japan" at Walt Disney World's Epcot Center would never dream of visiting the real thing.
And this is a nation where festivals celebrating faraway cultures are held in the smallest, least diverse of communities - but where an average senior citizen in Frederick, Md., will issue whispered warnings about black helicopters and the one-world government that's surely going to usurp our sovereignty.
"We need others and others need us. And we don't like that," says Schuyler Foerster, president of the World Affairs Council of Pittsburgh, one of many such groups that work with their regions to facilitate American engagement with the world.
Jack Holmes, a political scientist at Hope College in Holland, Mich., studies long-term foreign policy trends. He says American attitudes typically pinball every couple of decades between two phases, "introvert" and "extrovert," and are approaching the end of an extrovert phase.
He doesn't expect an introverted Obama administration but thinks the public is ready for changes in strategy, tactics and tone.
"Americans are never quite happy with what their role is in the world. Either they want to show the world how to do it, or sit back and set an example that the world can follow," Holmes says. But with a sharp change in policy and attitude potentially at hand, he says, "The American public is at a very important moment when it comes to how this country sees itself."
Evidence is everywhere, and has been for many generations, that this country sees itself as a "shining city upon a hill," as one of its earliest leaders, John Winthrop, put it - a metaphor that Ronald Reagan reintroduced effectively in the 1980s.
"Inspiration is our export," says Ted Widmer, author of "Ark of the Liberties: America and the World."
That tendency to be a model for humanity created a magnificent society built on ideas and ideals - and also got a lot of people killed.
It is the instinct that makes Americans the most philanthropic people in the world. It also makes them a wellspring of resentment by nations that bristle at what they call U.S. arrogance - something that perplexes many good Americans who say they are only trying to help.
"I think we do underestimate the degree that our actions are considered by people of other countries," Widmer says.
In fact, when foreigners actually visit America they seem to come away charmed. U.S. Travel, the leading industry group for the travel sector, surveyed more than 2,000 foreign nationals and found those who had visited the United States were 74 percent more likely to have a favorable opinion about Americans than those who had not.
"When the American people are being themselves, it is proven to work," says Geoff Freeman, U.S. Travel's senior vice president for public affairs.
"There's been a healthy debate in this country as to, `Does it matter what the world thinks of us?'" he says. "And I think that the past eight years have turned much of that debate toward, `Yes, it does matter.'"
It matters because, like it or not, the domino effect isn't just about communism anymore. Markets fail in Asia, and Americans convulse. Jobs shed in Dubuque show up in Dubai. And, most dramatically, foreign-policy decisions executed in far-off lands can have direct security effects at home.
At the same time, engaging Americans in the nuances of foreign affairs has often proven difficult. Not only does geography keep most things far away in concept if not in fact, but many of the 21st century's diffuse global realities are difficult to wrangle because they lack visual, Hollywood-style iconography.
Instead of dust bowls and bread lines, we have intricate financial networks that connect us with the world but are impossible for all but experts to visualize. Instead of menacing footage of Nazi rallies or Nikita Khrushchev banging his shoe, we have an undefined enemy who roams the globe surreptitiously and hides in plain sight. And instead of the movie ending with a climax - an Iraq invasion, say - the aftermath trickles on and the mission is not, in fact, yet accomplished.
For eight years of Bush foreign policy, the Democrats have insisted, quite vociferously, that they understand America's place in the world better than their rivals. On Tuesday, they get to show us if they're right.
"We must use what has been called `smart power,'" Clinton told the Senate Foreign Relations Committee at her confirmation hearing last week. That, she said, means deploying "the full range of tools at our disposal - diplomatic, economic, military, political, legal, and cultural - picking the right tool or combination of tools for each situation."
Is that the wariness of permanent alliances? The huge rescue squad? The big dog unleashed? From isolationism to Manifest Destiny, from emergence as a major power to post-World War II consensus to neoconservative activism, American history is replete with all three options.
And the American people of the 21st century, part of a connected world for better and worse, face the same challenge their leaders do: understanding that, when it comes to reaching a hand into the complex toolbox of world affairs, you'd better know how to use the implement you grab.
Ted Anthony covers politics and culture for The Associated Press. Comments about Measure of a Nation can be sent to measure(at)ap.org.