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People will ignore howling plot problems if they like a story enough. Some of the most popular stories make no sense.

I’m not talking about the kind of mystery that can make a work of art intriguing. I enjoy some ambiguity in art. Why does the Mona Lisa smile? What’s Dali evoking by making a clock face hang like a soggy T-shirt? What’s wrong with Citizen Kane’s Charles Foster Kane? People have spent rich careers happily digging into these questions.

No, I’m talking about stuff that just plain unravels — yet people don’t seem to care.

Take Close Encounters of the Third Kind. Spoiler ahead.

Mysterious aliens controlling high technology are visiting Earth. They send to the minds of receptive people a compulsion to draw a distinctive mountain and travel to it.

In addition to telepathy, the aliens communicate via patterns of light and sound, transmissions spelling out longitude and latitude coordinates, and hand gestures. What’s more, they kidnap people who speak a variety of languages.

As these developments pile up, the movie’s human characters — and its audience — wonder: What do the aliens want?

Here’s the spoiler: The aliens want the people most receptive to the telepathically implanted compulsion to show up at the mountain so they can take the most receptive person or persons away.

But why do aliens with advanced science and multiple ways to communicate use indirect, confusing ways?

And whether they use telepathy or kidnapping, why do the aliens take people away?

The movie reveals none of the above. It doesn’t even leave intriguing hints.

You’d think that audiences would find such unanswered questions frustrating, but they don’t. They usually love the movie.

Hell, I love it. The movie’s story is so compelling, its characters so sympathetic, and its visuals so stunning that I didn’t even wonder about these questions until after I’d seen the movie at least twice. I still enjoy it.

But it makes no sense at all.