(Rob Griffith/AP)

Jeff Flake is a Republican U.S. senator from Arizona. Martin Heinrich is a Democratic U.S. senator from New Mexico.

So two U.S. senators, a Republican and a Democrat, are marooned for a week on a deserted island.. . .

Sounds like a lead-in to a political joke, right? Well, it actually happened. We know, because we are those two senators.

Why did we do it? Why on earth would we travel halfway around the world on our own dime, only to be dropped into the ocean, where we had to swim through shark-infested waters to an uninhabited island, surviving for a week with little more than a machete and the shirts on our backs?

Was it just to get away from it all? There’s plenty of solitude to be had in remote corners of our home states. Was it the allure of an exotic locale? The Marshall Islands are beautiful, but there were no beach chairs or cold drinks where we were.

No, our motivation for taking this extreme measure — filmed by the Discovery Channel for a survival show to be aired Oct. 29 — was the deep, structural dysfunction of the U.S. Senate. We wanted to demonstrate that a Republican senator and a Democratic senator could survive together on a deserted island without retreating to separate red and blue lagoons.

We both know that the Senate, by any objective measure, is broken. It has been years since it passed even one appropriations bill before the end of the fiscal year. Democrats point out that Republicans have filibustered nearly every piece of legislation this session. Republicans counter that Democrats have shut down what was once an open amendment process. The result? We’re on track to have one of the least productive sessions in more than half a century.

Some of the blame can be placed on extreme ideology, encouraged by outside groups bearing score cards and inflamed by cable television and social media. But an even bigger issue is a lack of trust between the parties.

Trust is built when senators know one another. That used to be commonplace. Before the “commuter Congress,” senators and their spouses broke bread in each other’s homes, and in such a setting the concept of party was more verb than noun. Senators didn’t necessarily agree more often then, but they were much better at finding paths forward where both sides could achieve some measure of victory. While we cannot turn back the clock, we must find a way to provide opportunities to forge more productive relationships.

We have a modest proposal, one that doesn’t involve an island and a machete. Currently during a typical workweek, Republicans and Democrats have two or three lunches with the members of their own party, but there are no routine bipartisan events. Those of us who are serving our first six-year term (that includes 45 of the 100 sitting senators) are especially puzzled as to how this came about, and many of us believe it has to change. Meeting as a body at least once a week would be optimal, but scheduling one bipartisan lunch a month would be a good start. We are now petitioning our colleagues to try to make this happen.

The midterm elections may or may not change the Senate majority, but whoever is in control will have a slim margin. What will not change is the necessity for the parties to work together if the Senate is to function again.