Mr. Romer’s logic is connected in a roundabout way to the work that won him the Nobel. Macroeconomists used to think about the world by tallying up quantifiable stuff: capital, labor, natural resources. They weren’t sure how to account for ideas. But Mr. Romer, in a seminal 1990 paper, showed that ideas were central to progress. His model of economic growth incorporating them enabled economists to ask entirely new questions about the modern “knowledge economy”: Where do ideas come from? How do they spread? Why are cities such hotbeds for creating them?

By the late aughts, Mr. Romer was sure that cities were the urgent subject of the 21st century. He had a new idea: “charter cities” that would be built in the developing world but governed by nations with more advanced economies and more rules protecting, say, property rights and independent judges. He was picturing British-era Hong Kong, replicated 50 times over.

Some developing-world politicians were intrigued. Critics cried neocolonialism. Libertarians largely misread Mr. Romer’s intentions: They saw new territory where capitalists could shrug off government rules. To Mr. Romer, the idea was about seeding the right government rules.

The proposal forced Mr. Romer to learn the mechanics of cities. He persuaded N.Y.U. to create a new institute devoted to them, and two planning experts gave him an education. Shlomo Angel taught him the foundation of good street grids. Alain Bertaud gave him a framework: Urban planners design too much, while economists cede too much to the market. The answer lies in between — in drawing the street grid on the desert.

“The beauty of the mind of Paul is that he sees patterns where we don’t see them, because he sees patterns across examples which have nothing to do with each other,” Mr. Bertaud said.

Mr. Romer looked at the Manhattan street grid, the imagined charter city, Black Rock City. He was doing this even in his short tenure at the World Bank, where he worked from 2016 to early 2018. He took the job quietly hoping to persuade the institution to back a new city. (It did not.)

In all of this, Mr. Romer has been creeping further from the economists toward the urban planners. By the time he got to Burning Man in August, he was thinking of himself as a University of Chicago-trained economist, once indoctrinated in the almighty free market, now in open revolt against his roots.