Less than a week before he died, McGeorge Bundy, the brilliant Harvard dean who was an architect of John F. Kennedy’s and Lyndon B. Johnson’s Vietnam strategy, met with Gordon M. Goldstein, a young scholar who was helping him prepare a retrospective on the two American presidents most identified with the debacle in Southeast Asia. At their last working lunch, Bundy shared a remarkable insight about the two presidents he served and their motives in prosecuting the war in Vietnam:

“Kennedy didn’t want to be dumb,” he told Goldstein. “Johnson didn’t want to be a coward.”

There are enormous differences between Vietnam and Afghanistan, and this is not the time or place to examine them. History doesn’t repeat itself, though columnists often do.

But there may be startling similarities between the presidents elected in the 1960s and the presidents elected in the first decade of the new century. It is not a stretch to say that in contemplating their strategies for warfare in this new and frightening world, George W. Bush did not want to be known as dumb and Barack Obama did not want to be known as a coward.

A different time

Of course there is almost nothing about our times that resembles the world Kennedy and Johnson occupied and, to an extent we can hardly imagine today, dominated. Indeed, Kennedy and Johnson were arguably more important figures in their times than either Bush or Obama are in ours, though by virtue of his campaign victory only a year ago, Obama will always be a figure of political, cultural and symbolic importance.

That said, our last two presidents fit nicely into the Kennedy-Johnson rubric that Bundy shrewdly set forth at that memorable working lunch. In his speech last week, Obama, careful not to be seen as a coward in the face of the continuing terrorist threat to the world, increased the American commitment in Afghanistan.

The tragedy of George W. Bush was a play in several acts, the most striking of which was his determination not to appear unintelligent. (The word “dumb” is not formally used as a synonym anymore for a person lacking intelligence.)

From the start, Bush was tarred with the reputation of being a lightweight. Those who know the former president are virtually unanimous in their insistence that Bush was more than simply attentive but truly intelligent, if not possessed of a probing mind. The president may not have been innately curious or particularly open to views at odds with his impulses and instincts, but it is a matter of record that his academic performance at Yale was almost identical to that of his 2004 opponent, Sen. John F. Kerry of Massachusetts, nobody’s idea of a dumbo.

Bush sought to look smart

Bush’s determination not to be seen as dumb, as Bundy would have put it, was a curse, warping his outlook and damaging his character. He knew what his critics, merciless and relentless, were saying about him, and as a result he sought to overcompensate.

His political consigliere, Karl Rove, was moved to say that the two of them, the breezy president and the cerebral adviser, were involved in a book-reading contest, heavy on biography and history, that included works by serious-minded authors such as Niall Ferguson, Walter McDougall, Jay Winik and Martin Gilbert — a kind of murderers’ row of your local library.

Theodore Roosevelt, whose consumption of difficult literature in his White House days was nothing short of prodigious — we know this from a fascinating private 1903 letter he wrote to Columbia University President Nicholas Murray Butler, listing about 150 books he had read in a two-year period, including Thucydides, Aeschylus, Sophocles, Euripides and at least four volumes in French — would not have felt the need to have that information distributed.

Obama’s perceived need not to be seen as a weakling surely wasn’t the only, or even the principal, reason he is plunging deeper into Afghanistan, just as Bush’s fears about his perceived intelligence cannot explain fully his actions. Both men face a serious terrorism challenge, one that defies conventional solutions and historical lessons.

No one questions Obama’s intelligence; he was, after all, president of the Harvard Law Review, and he is the author of two thoughtful books. No need to prove anything there. But the great flaw of Obama’s leadership may be his inability to project strength in any realm besides intellectual power.

It is a cliché of Washington that powerful past presidents inspired fear as much as admiration. Lyndon Johnson certainly did, and so did Franklin Roosevelt, and so in his way did the genial Ronald Reagan. (In the Reagan years, only fools doubted the political power of the president, who, while often underestimated, was not often defeated on Capitol Hill.) Many people admire Obama. Hardly anyone fears him.

Obama wants to show courage

Now a president who repeatedly is described as gifted but weak is making a statement about presidential strength even as he increases American strength in Central Asia. There are many legitimate reasons to do so, not least of which is the threat that an al-Qaida sanctuary in Central Asia may present to our freedoms in North America. So Obama’s decision, though troubling to many congressional Democrats, is not outside the mainstream of choices regardless of whether subliminal factors were at work.

During the fevered, almost desperate debate while the Bay of Pigs episode was unfolding in 1961, President Kennedy wondered out loud about the nature of prestige. “What is prestige?” he asked, according to the journals of Arthur M. Schlesinger Jr. “Is it the shadow of power or the substance of power?”

Obama might well ask the same question, not only about the American presence in Afghanistan but also about his own role in the American capital.

One more thought, which brings us back to the Bundy insight about presidents Kennedy and Johnson.

The last thing Kennedy, the most literate president of modern times, needed to worry about was being dumb. The last thing Johnson, whose courage led him to teach the dispossessed in Texas and to fight an outsider’s insurgency in establishment Washington, needed to worry about was being a coward.

There’s a lesson there, and it has nothing to do with Washington’s obsession with what Vietnam might teach us about Afghanistan. It has to do with presidential leadership, and the combination of brains and courage it requires.