Story highlights Twitter co-founder Jack Dorsey says he wants to move to New York someday, run for mayor

Dorsey lives in San Francisco and also is CEO of Square, the mobile-payments company

Dorsey was the subject of a "60 Minutes" profile on Sunday

Twitter co-founder Jack Dorsey lives in San Francisco, not New York.

But the tech entrepreneur, who also founded mobile-payments company Square, tells "60 Minutes" he wants to move to New York someday and run for mayor.

"What I love about New York is just the electricity I feel right away," he told CBS News' Lara Logan in a segment that aired Sunday . "It's chaos. It's kind of like being in a car in the middle of a thunderstorm. Everything is raging around you, but you're safe inside that car. So New York feels very much to me like that."

With a net worth of more than $1 billion, Dorsey would follow in the footsteps of Michael Bloomberg as a billionaire-turned-New York politician. Moving to the Big Apple also would be a homecoming of sorts for Dorsey, who attended New York University and as a teenager was hired by a New York dispatch company after he hacked into its website.

Dorsey, 36, grew up in St. Louis and spent a lot of time at home playing with computers and studying trains. He also had a police scanner and told CBS the inspiration for Twitter came from listening to the short bursts of chatter from the city's emergency dispatch center.

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"They're always talking about where they're going, what they're doing and where they currently are. And that is where the idea for Twitter came (from) ... ," said Dorsey, who created the code for Twitter's 140-character messages. "And (with cell phones) suddenly we could update where I was, what I'm doing, where I'm going, how I feel. And then it would go out to the entire world."

Dorsey said he is proud of how quickly people adopted Twitter, which launched in 2006, "and used it in a million different ways. They're all over the world. And Twitter enables them to take a $5 cell phone and, wherever they are, communicate with the world for free."

Launched in 2010, Square now has more than 400 employees and has been adopted by Starbucks to help the coffee chain process sales transactions. Dorsey said the idea for Square came from talking to a friend, a glassmaker, who was frustrated that he lost a $2,000 sale because he couldn't accept a credit card.

Dorsey also said that to keep his employees inspired he leads company outings to a place in San Francisco called Lands End , which offers stunning views of the Golden Gate Bridge.

Dorsey says he admires the bridge's utility and elegant design, which he called "this perfect intersection between art and engineering," and believes software should work the same way.