Hillary Rodham Clinton seems hung up on smart and stupid.

During her term as secretary of state, Clinton talked a lot about "smart power" — elevating diplomacy and development alongside military might. Now, she is distancing herself from the foreign policy of the president she served, telling the Atlantic's Jeffrey Goldberg that "great nations need organizing principles, and 'Don't do stupid stuff' is not an organizing principle."

But what if she had been the one in the Oval Office since 2009? How different would her foreign policy be from President Obama's? These questions are clearly more than a thought experiment. If she runs in 2016, potentially the first secretary of state since James Buchanan to ascend to the White House, voters will want to know the answers.

There would certainly be stylistic differences between Clinton and Obama. Even on the campaign trail, Clinton seemed more passionate about foreign policy than Obama, more enthusiastic about creating relationships with world leaders and playing the politics of diplomacy. She is more sensitive to America's image as an indispensable power. And though she's no reckless warrior, she is perhaps more inclined to consider using force under carefully tailored circumstances.

But on substance, Clinton's policies would probably not have diverged fundamentally from the ones the president pursued while she was his secretary of state or those he has embraced subsequently. Indeed, Clinton could never have become Obama's top diplomat and functioned so well in that job had they not been largely on the same page in terms of how they saw the world and what America should do about it. They both are transactors, not ideological transformers — smart, pragmatic centrists largely coloring inside the lines in a world of long shots and bad options. In other words, there's no need for them to "hug it out" on foreign policy.

Iran

Obama and Clinton were never the Bobbsey twins when it came to Iran. Clinton has pressed for tough sanctions since she was a senator from New York. During the presidential debates, she jumped on candidate Obama's idea to engage with the Iranians without preconditions. She says in her memoir "Hard Choices" that she regretted the president's refusal to take a harder line with the mullahs in response to their crackdown on the Green Revolution in 2009. And in the Atlantic interview, she was adamantly against the idea that Iran has a right to enrich uranium: "The preference would be no enrichment. The potential fallback position would be such little enrichment that they could not break out." The U.S. team currently negotiating with Tehran has conceded some enrichment as a practical matter, with limits to be negotiated.

But if Clinton had been president, she probably would have struck the same deal and followed a similar approach, first seeking an interim accord and then testing the possibilities through another year of negotiations before getting to a final agreement. After all, it was she who set the current talks in motion. She and Obama had agreed on a dual-track strategy of pressure and engagement. That meant sustained and tougher sanctions, with the door left open for diplomacy. After the sultan of Oman offered Clinton a back channel for secret bilateral diplomacy, it was her State Department, specifically Bill Burns and Jake Sullivan, that staffed it on the U.S. side.

A President Clinton, understanding that the alternative to a deal might be war — either an Israeli military strike or even a U.S. one — would probably have gone to great lengths to make sure that every possibility had been explored before resorting to force. Negotiators get attached to their negotiations and don't want to fail. And so Clinton would have probably authorized the same concessions to Iran as the current negotiating team has.

Arab-Israeli peace

Clinton, perhaps with 2016 in mind, has been less critical than Obama of Israeli policies, especially the military response to Hamas. And unlike Obama, she has long-established relationships with the players in the peace process. I accompanied her, when she was first lady, to Leah Rabin's funeral and watched her charm and magnetic impact on Israelis regardless of party. She also has a better sense than Obama of how to deal with Benjamin Netanyahu — learned in part from watching her husband. "Who's the f — -ing superpower here?" President Bill Clinton exploded to aides after his initial encounter with the Israeli prime minister. And still, Bill Clinton reached two agreements with the Likud leader. A President Hillary Clinton might have tried harder than Obama has to cement a bond with Netanyahu. And there might not have been so much broken crockery in the U.S.-Israeli relationship.

Still, it's hard to imagine that Clinton would have taken a different course in pursuing a two-state solution — or achieved different results. Given the lack of trust between Netanyahu and Palestinian President Mahmoud Abbas, the wide gaps on the core issues and the impossibility of pursuing a more modest interim deal, the only option available was the one Obama authorized John Kerry to take: try to mediate a "framework agreement" that leaves many of the details on core issues such as Jerusalem unresolved. And even then, failure was virtually guaranteed.

How would Clinton have handled the latest confrontation in Gaza? In 2012, she played an important role in facilitating a cease-fire there, though it was then-Egyptian President Mohammed Morsi who delivered Hamas. More than likely, this time around she would have found herself — like Kerry — without a win. She might have had more influence over Netanyahu. But with Hamas willing to continue the fight, the odds of a U.S.-brokered success would still have been low.

(It's also worth noting on Egypt that as secretary of state, Clinton was wary of Obama's efforts to force Hosni Mubarak out too quickly. But in the wake of Morsi's disastrous presidency, as president she would have almost certainly backed the Obama/Kerry decision to improve relations with the new Egyptian president, the former supreme military commander.)

Russia and Ukraine

Clinton has a reputation for being tough on Russia. Indeed, Putin accused her of orchestrating the 2012 demonstrations against him.

And yet, it's hard to believe that, as president, the pragmatic Clinton would have initially pursued something other than a reset policy. U.S. relations with Russia were at rock bottom after the Georgia war and the preceding squabbles over Kosovo, missile defense and NATO expansion. With the ascendance of the seemingly forthcoming Dmitry Medvedev, any American president would have tried to identify issues on which the United States and Russia might cooperate — and would have shown resolve if the Russians pushed back on others.

As president, Clinton might have pivoted sooner to a hard line when it became clear in 2011 that the reset had run its course. She told the New York Times' John Harwood as much.

But it's unlikely that would have made much difference. None of the recommendations on Russia contained in her parting memo to Obama — including rejecting Putin's invitation to a presidential summit and avoiding flattering him with high-level attention — would have changed Putin's strategy. He simply has more cards and the will to play them.

As for Ukraine, put Clinton in Obama's shoes during the past several months of Putin's adventurism in Crimea and his meddling in eastern Ukraine, and it's hard to see what she might have done differently to impose greater costs on Russia, let alone to counter and reverse Putin's support for pro-Russia separatists. Military force isn't an option. So Clinton, like Obama, would have fallen back on some package of steps, including marshaling the Europeans, nonlethal military assistance to Ukraine, tough rhetoric and sustained sanctions.

Syria

In the Atlantic interview, Clinton asserted that the "failure to help build up a credible fighting force [in opposition to Bashar Assad] left a big vacuum, which the jihadists have now filled." Clinton called Obama afterward to say that she didn't mean to attack his policies. But the two have long had differences in how to approach the Syrian civil war. As early as 2012, Clinton wanted to do more to weaken Assad. But more — training and equipping carefully vetted elements of a dysfunctional and divided opposition — wasn't all that far from what Obama eventually came to accept in 2013.

To change the balance on the battlefield, a President Clinton would have had to win backing for a more comprehensive military strategy involving not just arming rebels but also creating no-fly zones and authorizing direct U.S. military strikes against Syrian regime targets. It's by no means clear that she would have gone that far, let alone whether the risk-averse Pentagon would have supported it.

On the question of chemical weapons, Clinton's policies would probably have been very much in line with Obama's. As secretary of state, she echoed Obama's red line. And although she had stepped down by the time of the Assad regime's August 2013 attack that killed 1,400 people, she publicly supported Obama's decision to seek a congressional vote before launching a strike. If she'd been president, she might have been more reluctant to go to Congress and more skeptical that a deal brokered by the Russians would successfully eliminate Syria's chemicals. But as Clinton rightly describes in her memoir, Syria was a "wicked problem." I'm not at all sure that as president she would have done much better in trying to deal with it, let alone resolve it.

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This is not in any way to undermine her talents and capacities when it comes to foreign policy. It is, however, to underscore a critical point these days when it comes to America's role in the world. To paraphrase Marx, men and women make history. But they rarely do so as they please. No matter how determined she may have been to assert U.S. leadership or to push her concept of smart power, the cruel and unforgiving nature of the world would have imposed the same severe constraints. Not every problem today has a solution that is amenable to U.S. military or diplomatic power — or to Clinton magic.

Aaron David Miller, a vice president at the Woodrow Wilson International Center for Scholars, has served as a Middle East adviser for Republican and Democratic secretaries of state. He is the author of the forthcoming "The End of Greatness: Why America Can't Have (and Doesn't Want) Another Great President." He wrote this article for the Washington Post.