AFTER tossing out one of those limp politician’s jokes about how its arrival in Brooklyn meant that Shake Shack had finally “hit the big time,” Mayor Michael R. Bloomberg snipped through a green ribbon Dec. 20 to formally open the chain’s location on Fulton Mall.

It is not every day that the mayor serves as midwife at the birth of a hamburger stand, but it is not every hamburger stand that achieves the prominent spot in the city’s consciousness held by Shake Shack. There are 14 of them now, uptown, downtown and out of town (Miami, Washington, Kuwait City). One respectable writer has spoken of the burger as life-changing.

From its origins as a hot-dog cart that the restaurateur Danny Meyer set up as a kind of art project in 2001, Shake Shack has become one of the most influential restaurants of the last decade, studied and copied around the country. Its legacy can be seen not just in the stampede of good, cheap burgers, but in the growing recognition that certain fine-dining values, like caring service and premium ingredients, can be profitably applied outside fine dining all the way down the scale to the most debased restaurant genre of all, the fast-food outlet.

To answer two obvious questions right away:

Yes, I would give stars to a hamburger stand.

No, probably not four stars.

While the mayor was talking, a line had formed. Lines are so central to the Shake Shack experience that they have symbolic overtones. The line is democratic: everybody waits, including Mr. Meyer’s children. It is a signal of freshness: everybody waits, because the food is cooked to order. It is the people’s endorsement: everybody waits, so it must be worth it.