Raised as a Catholic, Appaden told me that he discovered Randi in 2010, when he watched the magician in an online TED talk discussing homeopathy. At the time Appaden was a student at a Christian college, struggling with his faith; two years later, during Randi’s first visit to India, he took a 13-hour bus ride across the country to see Randi in person. “It literally changed my life,” he told me, and explained that he now hopes to help teach skepticism in Indian schools.

The magician looked small and frail, lost in the folds of his striped dress shirt, leaning on his cane, but he mugged gamely for every acolyte. For many of his most zealous followers, the opportunity to meet Randi at TAM may be as close as they will ever come to a religious experience. “It’s an obligation, it’s a very heavy obligation,” he said. “I can’t stand one person being turned away and not being given the same attention that others have been given.”

A few days before the conference, I visited Randi at his home, in Plantation, Fla. The modest octagonal house was almost hidden from the street by a lush garden of finger palms, elephant ears and paperbark trees. As we sat upstairs, surrounded by some 4,000 books — arranged alphabetically by subject, from alchemy, astrology, Atlantis and the Bermuda Triangle to tarot, U.F.O.s and witchcraft — he said that he disliked being called a debunker. He prefers to describe himself as a scientific investigator. He elaborated: “Because if I were to start out saying, ‘This is not true, and I’m going to prove it’s not true,’ that means I’ve made up my mind in advance. So every project that comes to my attention, I say, ‘I just don’t know what I’m going to find out.’ That may end up — and usually it does end up — as a complete debunking. But I don’t set out to debunk it.”

Born Randall James Zwinge in 1928, Randi began performing as a teenager in the 1940s, touring with a carnival and working table to table in the nightclubs of his native Toronto. Billed as The Great Randall: Telepath, he had a mind-reading act, and also specialized in telling the future. In 1949 he made local headlines for a trick in which he appeared to predict the outcome of the World Series a week before it happened, writing the result down, sealing it an envelope and giving it to a lawyer who opened and read it to the press after the series concluded. But no matter how many times he assured his audiences that such stunts were a result of subterfuge and legerdemain, he found there were always believers. They came up to him in the street and asked him for stock tips; when he insisted that he was just a magician, they nodded — but winked and whispered that they knew he was truly psychic. Once he understood the power he had over his audience, and how easily he could exploit their belief in the supernatural to make money, it frightened him: “To have deceived people like that . . . that’s a terrible feeling,” he said.

He turned instead to escapology — as The Amazing Randi: The Man No Jail Can Hold — and feats of endurance. He broke a record for his 55-minute stint encased in ice, and bested the time his hero Houdini had spent trapped in a coffin on the bottom of the swimming pool at the Hotel Shelton in Manhattan. But Randi never forgot the believers, and how susceptible they were to exploitation by those who lacked his scruples. And so, as his reputation as a magician grew, he also began to campaign against spiritualists and psychics. In 1964, as a guest on a radio talk show, he offered $1,000 of his own money in a challenge to anyone who could show scientific evidence of supernatural powers. Soon afterward, he began broadcasting his own national radio show dedicated to discussion of the paranormal. He bought a small house in Rumson, N.J., and installed a sign outside that announced randi — charlatan. He lived there alone, with a pair of talking birds and a kinkajou named Sam. Although Randi had known he was gay since he was a teenager, he kept that to himself. “I had to conceal it, you know,” he told me. “They wouldn’t have had a known homosexual working in the radio station. This was a day when you had to keep it completely hidden.”

During the late ’60s and early ’70s, popular interest in the paranormal grew: There was a fascination with extrasensory perception and the Bermuda Triangle and best sellers like “Chariots of the Gods,” which claimed Earth’s ancient civilizations were visited by aliens. There were mystics, mind-readers and psychic surgeons, who were said to be able to extract tumors from their patients using only their bare hands — and without leaving a mark. Randi continued on his crusade. Few of his fellow illusionists were interested in exposing the way that conjuring tricks were used to dupe gullible audiences into believing in psychic abilities. “Everybody else just kind of rolled their eyes,” Penn Jillette, a good friend of Randi’s, told me. “'Why is Randi spending all this time doing this? We all know there is no ESP. It’s just stupid people believe it, and that’s fine.’ ”