You can envision the team at CBS’s Person Of Interest pushing their chairs back from the table and saying, “Okay, our work is done here.”

Person’s fifth and final season starts Tuesday (5/3) at 10 p.m. ET and it has a high-speed run to the finish line. Starting next week, CBS will run the show both Monday and Tuesday nights at 10, so its 13-episode season will wrap up on June 21.

There’s certainly no time to waste. The last season starts with our characters in jeopardy and the fate of the world hanging in the balance.

Adding its own weird dimension to those crises is that we may or may not get closure on perhaps the strangest relationship on television, between Harold Finch (Michael Emerson, top, middle left) and his computer.

For what it’s worth, this is no ordinary computer.

The guiding premise of Person is that with advanced surveillance, Internet data, and other technological developments, all of us are being watched pretty much every minute.

It’s a notion that has measurably less of a sci-fi aura now than it did even when Person debuted in September 2011.

In any event, Finch created a computer called The Machine that aggregates all this data. It’s so advanced that it doesn’t only report what’s going on now, but can predict things that will happen in the future, like crimes.

The caveat is that The Machine can’t specify exactly what the crime will be, or whether the person involved with be a victim or a perp.

Since The Machine is a clandestine operation, Finch’s initial dilemma was what to do with the information. Then he got together with former soldier John Reese (Jim Caviezel, left), a resourceful and incredibly skilled albeit troubled operative, and they worked out a system. Finch would try to track down potential perpetrators and Reese would try to stop them.

That’s a benign use for the scary power of The Machine. Others could clearly find more sinister possibilities, and over the years The Machine has become an increasingly coveted target.

As we enter this final season, a powerful criminal organization called Samaritan is determined to appropriate it with potential consequences Finch fears could include the end of human civilization.

Without the option of calling in the cops, the small team that must try to stop Samaritan largely comes down to Reese, Finch and Root (Amy Acker, top left), a mysterious woman who signed on with the good guys.

They continue to get quiet help from Detective Lionel Fusco (Kevin Chapman, top right), their inside man on the police force. But they’re largely on their own – outnumbered and outgunned, though perhaps not yet out-computed.

Some of the computer talk has been getting denser as the show has moved along, but one thing all viewers will notice is the relationship Finch has developed with The Machine.

From the beginning, Finch’s biggest concern was that by developing a machine with artificial intelligence, he was courting the possibility that the machine would advance beyond humans and take over, like the computer Hal in 2001: A Space Odyssey.

But as Finch has worked with The Machine over the years, he has also developed an emotional relationship with it. In many ways, it’s become a friend.

So he’s dealing with some complicated emotional crosscurrents as his team tries to fend off Samaritan in the final season’s presumably final showdown.

Person Of Interest has been eerily prescient over the last few years about our real-life contemporary concerns over our vanishing privacy. In the process, frankly, it has sometimes drifted toward the weird side. But its parting message isn’t hard to decipher: Even when CBS hits the “shut down” button on the show, the issues it has raised will only intensify.