If you’re looking for reasons to puff out your chest and take pride in being American, then take note that the first six Nobel Prize winners announced this week are U.S. citizens.

Here’s something else you should know: Four of those winners were born outside the U.S.

That dynamic neatly summarizes the current state of our innovation economy. We are increasingly dependent on brainpower from overseas that migrates here to drive the research and discoveries we need to power economic growth.

Silicon Valley has been a bigger beneficiary of this influx of brains and talent than perhaps any other region in the U.S. And that means we have more to lose when the debate about immigration turns to demagoguery.

However you feel about the H-1B visas that our tech companies hunger for, or the swarms of bodies crossing our borders to pick our crops, these hot-button topics obscure the reality: We need these immigrants to renew our economy and to prosper. Our demonization of them is shameful.

Instead, we should celebrate the presence of people like Elizabeth Blackburn, professor at the University of California-San Francisco. Blackburn was born in Australia and moved to the U.S. in 1975. On Monday, she and two other researchers learned they would receive the Nobel Prize for medicine and split the $1.4 million it brings.

That money should more than make up for the 5 percent pay cut and furlough Blackburn (and most other University of California employees) received courtesy of the sad, sickly state of California. I wonder how many other Nobel winners took pay cuts just before receiving the award?

When Blackburn came here in the 1970s, it was clear that the U.S. was the undisputed center of the universe when it came to research. But that advantage is slipping away, as Blackburn noted that she sees exciting work being done in many other regions. Given the growing options for new researchers, erecting barriers to them coming to and staying in the U.S. seems ill-advised.

“I’m a big proponent that the flow of intellectual ideas is crucial,” Blackburn said. “To have borders for it seems counterproductive.”

Such walls hurt our country and our economy far in excess of whatever benefits they produce. We need to recognize the enormous contributions immigrants are making to the innovation economy.

According to statistics from the National Science Foundation released in February, foreign-born science and engineering students in 2003 earned one-third of all Ph.D.s awarded in the U.S. And the study noted that “those who do decide to finish advanced study in the United States overwhelmingly choose to stay in the country after earning their advanced degrees.”

Thank goodness. In addition to Blackburn, the other foreign-born Nobel winners over the past two days included:

Charles Kao, who was born in Shanghai, and has both U.K. and U.S. citizenship.

William Boyle, of Bell Laboratories, was born in Nova Scotia and holds dual U.S. and Canadian citizenship.