Fifty years ago this summer, with Americans riveted by a presidential contest pitting John F. Kennedy against Richard M. Nixon, Dwight D. Eisenhower contemplated his departure from the White House. As he prepared to retire from public life, Ike sketched out the ideas that would inform his celebrated farewell address, presciently warning against the dangers of a military-industrial complex. Simultaneously, he was plotting ways to overthrow the Cuban government.

Eisenhower did not remain in office long enough to implement the plan that his minions hatched. Instead, he bequeathed it to JFK, who promptly and naively allowed it to proceed. We remember the ensuing debacle by the place where it occurred: the Bay of Pigs.

Although Kennedy took the fall for the bungled, CIA-engineered invasion by Cuban exiles, his predecessor deserves a share of the blame. Without Eisenhower, the Bay of Pigs would never have occurred. How could such a careful and seasoned statesman have concocted such a crackpot scheme? The apparent contradiction — wisdom and folly coexisting in a single figure — forms a recurring theme in presidential politics, one that persists today.

What was true then, when the ostensible threat posed by Fidel Castro loomed large, remains true now, when the issue has become Afghanistan: The formulation of American statecraft rests on three widely accepted fictions. Presidents, we are led to believe, know things the rest of us can’t know, or at least can’t be allowed to know. Armed with secret knowledge and abetted by sophisticated advisors, presidents are by extension uniquely positioned to discern the dangers facing the nation. The surest way to address those dangers, therefore, is for citizens to defer to the Oval Office. Call it the Trust Daddy principle.

Yet there are at least two problems. First, presidential judgment has repeatedly proved to be fallible; Ike’s reckless campaign to unseat Castro providing a case in point. Perhaps worse, presidential claims of being able to connect the dots, thereby revealing the big picture, have turned out to be bogus. Eisenhower (and Kennedy) viewed Castro’s revolution as an intolerable affront — tiny Cuba placing the entire Western Hemisphere in jeopardy. The Cuban dictator had to go. Yet half a century later, Castro survives and his revolution wheezes along. Who cares? It’s difficult to recall exactly what all the fuss was about.

Pretending to navigate by some sort of acutely accurate presidential GPS, the man in the White House actually flies blind. Whether it’s Lyndon B. Johnson plunging into Vietnam, Jimmy Carter unleashing the CIA in Soviet-occupied Afghanistan, Ronald Reagan dispatching U.S. “peacekeepers” to Beirut, George H.W. Bush setting out to feed starving Somalis or Bush’s son, George W., invading Iraq, the man ostensibly in charge quite literally doesn’t know what’s coming next. Hence, the frequency with which events catch presidents (or their unwary successors) by surprise.

No one in Washington will acknowledge this, of course. After all, maintaining an aura of omniscience is necessary to sustain illusions of omnipotence, which in turn justify the vast prerogatives to which the White House lays claim. Once it’s admitted that presidents and their “wise men” rely mostly on guesswork and are no smarter than the geezers meeting over coffee down at the corner cafe, the mystique enveloping the nation’s capital — all those important people busily making important decisions — will vanish in thin air. Plain folk might get restive.

This describes the predicament that President Obama will soon encounter in Afghanistan. In time-honored presidential fashion, Obama has issued any number of pronouncements regarding Afghans, their problems and aspirations. He has invested Afghanistan’s fate with historic importance: Americans dare not flinch from their obligation to fix that distant land. Our president knows what Afghans need. And he has articulated a strategy — winning Afghan hearts and minds — that will assure our success, all between now and July 2011, when U.S. troops will begin coming home.

Yet that strategy is not working, even as the clock keeps ticking. Time is running out. So for the president, a great opportunity is about to present itself. He can admit the obvious: Afghanistan’s fate is not his (or ours) to decide. Or he can recycle the standard guff about persevering in the promotion of freedom, with American soldiers (as usual) paying the price for presidential unwillingness to acknowledge error.

Eisenhower has much to teach Obama. During his two terms in office, Ike did some things right and more than a few things wrong. Where he most disappointed his admirers, however, was in waiting until the eve of his departure from office before speaking the truth. Here’s hoping that Barack Obama won’t wait that long.

Andrew J. Bacevich is a professor of history and international relations at Boston University. His new book, “Washington Rules: America’s Path to Permanent War,” has just been published.