"The purpose of your being here, as I understand it, is prayer without distraction?" Simon asked.
"I'm not being distracted now," Father Iakovos replied, laughing.
"Why are you laughing? First, tell me why you're laughing?" Simon asked.
"Why am I laughing? Because Saint Paul says, 'We're to pray unceasingly,'" he replied.
Asked what's funny about that, Father Iakovos said, "That's not what's funny about it. What's funny is, how you think I can stop praying."
He told Simon he's praying every minute of the day, even while they were conducting their interview.
You don't see Father Iakovos praying while he's talking, but when you look at other monks, you can see that their lips never stop moving. Not for a second.
They just keep reciting the Jesus prayer day and night: Lord Jesus have mercy on me.
It becomes like breathing. Some monks say they can pray when they sleep, and they get no more than three hours sleep a night.
But Mount Athos gets more applicants than it can handle - it's harder to get into than Harvard. A man comes as a novice. He's free to leave if he doesn't like it, and the monks can tell him to leave if they don't like him.
"When a novice arrives here, can you tell whether he's going to make it or not? Can you tell whether he's going to qualify to be a monk?" Simon asked Father Serapion.
"After a while, it becomes pretty obvious whether or not someone is cut out for it, which is why we have a trial period which can last up to three years," he explained.
"I bet you know a lot sooner than three years," Simon remarked.
"Certainly," he replied.
Once a novice is accepted into the community, it's a lifetime commitment. And life never changes there. Never.
Every day at three in the morning a single bell rings, informing the brothers that it's time to stop praying on their own, and start praying in church. On a typical day - and every day is a typical day - the services last eight hours.
The monks say it's an eight hour conversation with God, a dress rehearsal for eternity. And remember: this doesn't only happen on Sundays - it happens every day, 365 days a year. A monk never gets a day off.
"60 Minutes" was able to film the brotherhood at Simonospetras celebrating the Divine Liturgy, the life of Christ, observed by men whose only passion is to move closer to Christ every day. The depth of their devotion defies description.
They didn't look like the same monks we had met in the gardens and the workshops - they were utterly transformed with a concentration so profound, they were immune from distraction. There were occasional flashes of ecstasy.
There are no musical instruments in the church, just the monks' voices, chanting without end. Many of the voices, the basses in particular, could have made it at the Metropolitan Opera.
We didn't understand the words; we didn't really have to. One phrase we did know: "Kyrie Eleison" - "Lord have mercy."
The most miraculous thing about Mount Athos may simply be the fact that it's still there. Over the centuries, it has been invaded by crusaders, Ottomans, mercenaries, pirates and Franks. The Nazis had their eyes on it, too.