What do you suppose McPhee means by “the influence of Ernest Hemingway evidently extended to the Pentagon”?

This is the context this question is referring to:

And inevitably we have come to Ernest Hemingway and the tip of the iceberg—or, how to fashion critical theory from one of the world’s most venerable clichés. “If a writer of prose knows enough about what he is writing about he may omit things that he knows and the reader, if the writer is writing truly enough, will have a feeling of those things as strongly as though the writer had stated them. The dignity of movement of an iceberg is due to only one-eighth of it being above water.” The two sentences are from Death in the Afternoon, a nonfiction book (1932). They apply as readily to fiction. Hemingway sometimes called the concept the Theory of Omission. In 1958, in an “Art of Fiction” interview for The Paris Review, he said to George Plimpton, “Anything you know you can eliminate and it only strengthens your iceberg.” To illustrate, he said, “I’ve seen the marlin mate and know about that. So I leave that out. I’ve seen a school (or pod) of more than fifty sperm whales in that same stretch of water and once harpooned one nearly sixty feet in length and lost him. So I left that out. All the stories I know from the fishing village I leave out. But the knowledge is what makes the underwater part of the iceberg.”

In other words:

There are known knowns—there are things we know we know. We also know there are known unknowns. That is to say, we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know.

Yes, the influence of Ernest Hemingway evidently extended to the Pentagon.

Be that as it might not be, Ernest Hemingway’s Theory of Omission seems to me to be saying to writers, “Back off. Let the reader do the creating.” To cause a reader to see in her mind’s eye an entire autumnal landscape, for example, a writer needs to deliver only a few words and images—such as corn shocks, pheasants, and an early frost. The creative writer leaves white space between chapters or segments of chapters. The creative reader silently articulates the unwritten thought that is present in the white space. Let the reader have the experience. Leave judgment in the eye of the beholder. When you are deciding what to leave out, begin with the author. If you see yourself prancing around between subject and reader, get lost. Give elbow room to the creative reader. In other words, to the extent that this is all about you, leave that out.

I am very confused and do not have an idea of why he is being related to the pentagon. I know he is a very famous poet, but not sure how this relates.

These words were uttered by the Secretary of Defense at The Pentagon. "There are known knowns—there are things we know we know. We also know there are known unknowns. That is to say, we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know."

It's a confused statement, hard to understand (if at all), but he seemed to be saying that the rest of the iceberg can only be imagined and filled in by the beholder/reader.

And Hemingway is not known for his poetry! He was primarily a writer of fiction (novels and short stories) as well as some non-fiction, such as his famous books about bullfighting and big-game hunting in Africa.

In this context, McPhee is using a rhetorical device called irony. By stating that "the influence of Ernest Hemingway evidently extended to the Pentagon," he is suggesting that Hemingway's Theory of Omission, which emphasizes leaving things out to engage the reader's imagination, has somehow influenced the way the Pentagon operates.

However, it's important to note that this statement is meant to be humorous and ironic, rather than a literal connection between Hemingway and the Pentagon. McPhee is drawing a parallel between the idea of omitting information in writing and the concept of classified or restricted information in military operations. Just as Hemingway's theory suggests leaving gaps for the reader to fill in, the Pentagon may also have a tendency to withhold or omit certain information from the public for various reasons.

So, the connection between Hemingway and the Pentagon in this context is not a direct or serious one, but rather a way for McPhee to make a play on words and engage the reader's attention.