In Mr. Barney’s view, both parties are leading the country in the wrong direction. “Politics is not going to solve the problem,” he said, settling into the third-floor lounge of his Alpine-styled boutique hotel.

That is why he directs his multimillion-dollar contributions not to political candidates or super PACs — but to spreading Ayn Rand’s thinking around the globe. Over the years, he said he had contributed more than $20 million to the Ayn Rand Institute, to create free online courses about her work and other projects. Millions more have gone to other similarly minded groups. “I’m not an altruist, I’m not a do-gooder,” Mr. Barney said. “But I would like to have others experience the understanding and the benefits that I’ve had from philosophy.”

If rationality, hard work and self-interest are fundamental Randian values, so is the pursuit of happiness. And that is what led Mr. Barney to rise early that day — only to have to wait at the front of the ski lift line. Standing there, he mentions to the lift operator his intent to be first down the run.

“You look like you’re first in a lot of things,” the lift operator replies.

Soon enough, Mr. Barney is gliding down the mountain, listening on his earbuds to a favorite Broadway tune, “One Day More,” from “Les Misérables,” with its call to the masses to man the barricades.

An ‘Atlas Shrugged’ Worldview

“The greatest tragedy in all schools today is the ‘D.D.D.’” — a dropout who is in debt and doesn’t get a degree, Mr. Barney said over an artistically arranged dessert plate. The term is one of the many expressions that his staff refers to as “Carl Barneyisms,” the abbreviations, aphorisms, quotations and guidelines that pepper the boss’s daily conversation and fill employee binders.

For years, Mr. Barney worked six-and-a-half-day weeks sending notes to colleagues and friends at all hours about newly discovered enthusiasms — videos, books, middle-of-the-night brainstorms or even gadgets, like the MagicJack, the as-seen-on-TV device to connect a phone to a computer for inexpensive calls.

“If he finds something that he really likes, he’ll send it to 10 of his friends,” said John Allison, the former chief of the bank BB&T and a longtime friend who once received a Keurig coffee maker from him.