To delve into the darkest mystery of an all-powerful secret brotherhood, the first step, as any reader of Dan Brown knows, is to enlist the aid of a humanities professor. Fortunately, James Twitchell, an English professor at the University of Florida, was available for detective work.

We went to Alexandria, Va., and ventured into the high temple of American Freemasonry — 333 feet high, to be exact, which probably makes it even bigger than the Masons’ crypt discovered by Nicolas Cage in “National Treasure.”

We studied the 17-foot bronze statue of George Washington and a mural of him in a Masonic apron as he laid the cornerstone of the Capitol. We saw stained-glass windows of Masons like Benjamin Franklin and heard how President Truman had gone there to meet with his brothers.

We visited the lodge room where Masons convene today, a hall said to be modeled on the Temple of Solomon, although it reminded us more of the House of Lords. It had seats for hundreds. But a member of the brotherhood, Jim Williams, told us that only 15 or 20 show up for a typical meeting, most of them men past retirement age, like himself.

“My son likes to say that the average age of a Mason today is comatose,” he told us.

So apparently they won’t be taking over the world. What happened to them? That’s one of the mysteries investigated by Twitchell in his book, “Where Men Hide.” Why, when the baby boomers came of age, did American males lose interest in joining the Masons or the Elks or the other fraternal clubs of their fathers?

Some of the boomers were too busy at home with new responsibilities like housework and child care, and some considered the male lodges hopelessly retrograde after the advent of feminism. But Twitchell doesn’t think that feminism was the main reason for the clubs’ decline. Men still indulged their desires to escape from their families, but they had new options.

They escaped into their computers and sank into Barcaloungers to watch sports on TV. They went out with the guys to play golf or ride motorcycles. They found strip clubs more entertaining than lodge meetings.

When they sought moral self-improvement, they joined men’s groups at megachurches instead of lodges offering Masonic theosophy. They weren’t interested in learning, for instance, that the cement being applied by Washington to the Capitol cornerstone was a symbol of universal brotherhood.

As membership in the Masons declined (from more than 4 million in the 1960’s to less than half that today), the lodges tried coaxing new members by loosening their requirements. It became possible to progress from a first-degree Mason to a 32nd-degree Mason in as little as eight hours of instruction — a gimmick known as “all the way in one day.”

The brotherhood that invented the concept of the blackball even tried marketing itself to outsiders, with predictable results. Who wants to join a secret organization that’s open to anyone?

Lately some lodges have reverted to the traditional Masonic rules and mystique, and they’ve managed to attract some younger members (including Generation Xers intrigued by Dan Brown’s conspiracy theories). The age of the average Mason in America has fallen slightly, although it’s still in the 60’s, and the old members have been dying faster than new ones have been joining.

Twitchell is not a nostalgist for the days of sexual segregation, but he recognizes that the old fraternal organizations served a need that still exists — and isn’t being met in most of the alternate hiding places used by men.

“There’s no real fraternalism in hanging out with the guys at a strip club,” he said. “Individual escapes like TV and the Internet don’t provide the sense of community and nurturing that men got at lodge meetings. Not for nothing did they call it the mother lodge.”

One reason women outlive men is probably because they’re so much better at maintaining social networks — staying in touch with other women through phone calls, lunches, book clubs, shopping expeditions. Men are more apt to end up lonely. They need an excuse to seek out one another.

They need to be doing something like initiating blindfolded brothers or electing the Most Worshipful Grand Master. The great secret of the Masons, the explanation for the funny hats and the handshakes and the code words, was that they wanted to get together and couldn’t figure out any other way.