Have you ever felt an invisible presence? Did you ever have the sensation that something unseen was around? Have you ever felt like someone was watching you?

If so, you're hardly alone -- in more than one way.

In fact, there are so many cases that researchers have even studied what they call the "third man factor" -- an expression derived from a headline in 1920 that described the experience of a great Antarctic explorer named Sir Ernest Shackleton, who felt that during a long and racking march over perilous mountains there were more than just the three men in his expedition. "It seemed to me often that we were four," he told a newspaper of the day -- the curious feeling, in the words of a companion, "that there was another person with us."

And so it also has been in more recent headlines.

On September 11, 2001, a man named Ron DiFrancesco who worked for Euro Brokers in the south tower at the World Trade Center found himself in a horrifying  struggle to find his way down and away from the searing flames that would soon collapse the structure after the terrorists' plane struck just below Euro's offices.

Blocked from descending by a collapsed wall, a number of others were stretched face-down on the floor, crying and gasping for air, but something remarkable had occurred to DiFrancesco. "Someone told me to get up," he says. Someone "called" him. The voice was male and insistent but belonged to no human. "Get up!" it said.

Di Francesco did, with the sensation that someone or something was helping him up ("Hey! You can do this," he swears he heard), and this terrified man was led to the stairs -- where he saw a point of light, followed it, fought his way through drywall and other debris, and was directed through flames that normally would have stopped him.

Di Francesco descended to safety moments before the skyscraper fell, one of just four people who survived from the 84th floor or above.

These and other accounts are in a book called The Third Man Factor (by John Geiger with Vincent Lam). An angel? That's what Di Franceso thought -- and he's hardly alone. Often, the "third-man" sensation (perhaps it would be better labeled "another-person" experience) is encountered in extreme conditions, such as one would endure in climbing a mountain like Everest.

In fact, there are a number of historical figures who have claimed precisely this, especially at the brink of death. "I have often felt the presence of a Companion on the mountainside who is not in our earthly party of climbers," wrote a surgeon and Everest climber named Dr. Howard Somervell.

When Charles Lindbergh was making his historic flight, he famously claimed that "phantoms" helped him by "conversing and advising" in the cockpit (he said he actually saw vaguely outlined forms, which were transparent).

Are such accounts the product of delirium -- the imaginative right side of the brain encroaching on the logical left side (when the left side is disabled)? A psychological compensation (for loneliness)?

Or in extreme circumstances, do we glimpse other realities? Have you had such moments? (See today's Mass reading, 6/30).

Some say it was an angel. Others say it was the deceased.

When Joshua Slocum got in trouble during his quest to circumnavigate the world, he claimed a sailor with "an ancient cast of visage" took over and guided the boat through a violent squall to Gibraltar. He said he actually saw the man at the wheel.

In 1967, the American Journal of Psychiatry described a mine disaster in Pennsylvania during which two men -- one a Lutheran, one Roman Catholic -- both claimed to have seen Pope John XXIII in the cave alongside them, dressed in papal garb and leading them to believe they would be saved (despite being entombed nearly 300 feet below the surface for 14 days).

They said they saw the same thing at the same time, and also something else of interest: a woman with long hair who was kneeling at prayer.

Her presence had persisted, they said, for several days.