One of the more unsettling moments in “Hemingway,” the latest documentary from Ken Burns and Lynn Novick, finds Ernest Hemingway, big-game hunter, chronicler of violence and seeker of danger, doing one thing that terrified him: speaking on television.

It is 1954, and the author, who survived airplane crashes (plural) earlier that year in Africa, had been awarded the Nobel Prize in Literature. He agreed to an interview with NBC on the condition that he receive the questions in advance and read his answers from cue cards.

The rare video clip comes after we’ve spent nearly six hours seeing the author create an image of virile swagger and invent a style of clean, lucid prose. But here Hemingway, an always-anxious public speaker still recuperating from a cerebral injury, is halting and stiff. Asked what he is currently writing about — Africa — his answer includes the punctuation on the card: “the animals comma and the changes in Africa since I was there last period.”

It’s hard to watch. But it is one of many angles from which the expansive, thoughtful “Hemingway” shows us the man in full, contrasting the person and the persona, the triumphs and vulnerabilities, to help us see an old story with new eyes.

Burns, whose survey of American history is interspersed with biographies of figures like Jackie Robinson, Mark Twain and Frank Lloyd Wright, might have taken on Hemingway at any time over the past few decades. But there is an accidentally timely aspect to many of his timeless subjects. His “National Parks” in 2009, for instance, came in time to echo the Obama-era battles over the role of government.

Now “Hemingway,” airing over three nights starting Monday on PBS, comes along as American culture is reconsidering many of its lionized men, from figures on statues to Woody Allen. And there are few authors as associated with masculinity — literary, toxic or otherwise — than the writer who loved it when you called him Papa.