The supercomputer complex in Iowa is running a program created by OpenAI, an organization established in late 2015 by a handful of Silicon Valley luminaries, including Elon Musk; Greg Brockman, who until recently had been chief technology officer of the e-payment juggernaut Stripe; and Sam Altman, at the time the president of the start-up incubator Y Combinator.

You must use separate Stripe accounts for projects, websites, or businesses that operate independently from one another.

Patrick’s desk is covered in books. There’s a copy of The Dream Machine, about J.C.R. Licklider, the technologist who conceptualized and funded the early internet. The volume was out of print, but Patrick loves it so much he bought the rights and paid to publish hundreds of copies for employees and guests. The wallpaper on his computer displays a countdown clock for his life: He has 52 years and a few days left. “This is a very coarse estimate, but it’s a reminder that you get old quickly,” he says, a touch of gray now in his red hair. “When you talk to people who are old, some wish they had enjoyed themselves more, but not many wish they had wasted more time.”

Seven years in, however, Stripe’s mission is less to send more books, vacuums, and grooming kits into the world than to “increase the GDP of the internet,” Patrick says. To do this, the company is beginning to move beyond payments by writing software that helps companies retool the way they incorporate, pay workers, and detect fraud. It’s part of an ambitious bid to revamp how online business has been conducted for 20 years and to give anyone with a bright idea a chance to compete. “We think giving two people in a garage the same infrastructure as a 100,000-person ­corporation—the aggregate effects of that will be really good,” Patrick says.