Often we think of great leaders as steadfastly sailing a straight course of conviction. Winston Churchill’s declaration in 1940, “We shall not flag or fail. We shall go on to the end,” stands in history as a pivotal moment of this paradigm. The absolute faith — to the point of death — of Mohandas Gandhi and Martin Luther King, Jr. in non-violent revolution will always be symbolic of tremendous heroism. But with Americans’ satisfaction with their government representatives appallingly low, and crucial decisions facing the world community, let us recall three great leaders who set a different example: that the best way forward is sometimes a sharp turn around.

In 1966, an economist and friend of Ayn Rand wrote a scathing essay in The Objectivist in which he blasted the Federal Reserve for being an instrument of tyranny, and called for the restoration of the gold standard. His name was Alan Greenspan. In 1987, he was appointed chairman of the Federal Reserve, the very institution he had condemned years before. Arguably the individual most influential on the global economy, he managed American monetary policy for eighteen years, a tenure during which he oversaw tremendous growth, maintained low inflation and smoothly handled fluctuations until his retirement last week.

History will remember Greenspan as a leader of tremendous genius, praised unanimously by economists of all stripes. His old colleagues from The Objectivist movement continue to condemn him for abandoning his dogmatic principles. But that curb on ideology may in fact have been his greatest strength. As a cover story in last week’s The Wall Street Journal argued, “The essence of Mr. Greenspan is his distrust of any ‘ism’ or rule … his refusal to become invested in any particular model of the economy enabled him to shift gears whenever the prevailing model stopped working.”

On the other side of the globe, Ariel Sharon was a hero of his country since before its creation in 1948. A courageous soldier and commander through many wars, he retired from the Israeli military in 1973 and entered politics, where he became a champion of the settler movement. Although he was an architect of the 1979 peace treaty with Egypt, he opposed the 1993 Oslo Accords with the Palestine Liberation Organization and the subsequent, unreciprocated Israeli attempts at peace, which culminated in the Intifada.

In February 2001, on a ticket that rejected a call for unilateral withdrawal from settlements, he was elected prime minister. The course he then set was revolutionary. Reversing long-held beliefs and years of policy, he recognized that short-term wisdom was leading to long-term disaster. Despite the opposition of his own political base, he held a bitterly divided nation together through painful disengagements from unsustainable territory; he gave voice to a disparate majority in support of his vision; and he changed the world’s perspective on the region’s conflict. The great legacy of Ariel Sharon is not merely his determination. It is his ability to see the world dynamically, to recognize when his own path is failing, and to steer the ship in the opposite course with the same resolve. That is courage.

In the campaign for the 2000 presidential elections, then-Governor George W. Bush called for a more “modest” and “humble” foreign policy. The limited success of President Clinton’s global policing showed that the post-Cold War world needed a new strategy of relative isolationism.

Then one sunny Tuesday morning, the winds of history suddenly shifted. The moment demanded a new course. The president grabbed hold of the nation’s helm and came hard about, sailing directly into the ambiguous storm. Whatever the other failings of the president, his ability in that pivotal moment to change the ideological and strategic direction of his policies in the face of new circumstances, and to unite the people behind him in doing so, was a mark of true leadership.

In last week’s State of the Union address, the president promised to make progress on securing the country’s long-term energy independence. Two days later, Republicans in the House of Representatives elected new majority leader John Boehner over Roy Blunt, in a gesture of rebuke against their corrupt former leader, Tom DeLay. Although Boehner is also known to have close ties with lobbyists, he has called for an end to earmarking, the corrupt practice of dishing out pork which must be eliminated in order for public faith in the legislature to be restored. Now is an opportunity for the government to correct the troubling courses of energy policy and legislative integrity.

Leadership must be about more than blind determination to charge ahead. Ideology is important; ideals give people hope and purpose. But leaders must follow the compass of circumstance, rather than the auto-pilot of dogmatism. Let us hope that the leaders of the world continue to be dynamic as they captain our fleet into the future.