That last would be the one thing that can cure the headache brought on by a temporal displacement of the kind experienced by Agent J (Smith) when a hostile alien, Boris the Beast (Jemaine Clement as a gnarly stentorian) escapes from his lunar prison and gets a do-over, as it were, thanks to an illegal time machine. In order to save the planet, and his laconic partner, K (Tommy Lee Jones), J has to go back in time 40 years to head off Boris, who doesn’t care for his epithet of “Beast”, before he can fix what went wrong for him back in 1969. There are, of course, rules, the most important one being that under no circumstances can J contact the younger K (Josh Brolin doing a Tommy Lee Jones impression that is nothing short of uncanny). This means, further of course, that that is exactly what happens. Added to the mix is Agent O (Emma Thompson in the present, Alice Eve in the past), the new head honcho who may or may not know more about K than either of them lets on.

There are the usual gags about which celebrities are actually aliens, and a clever one about which celebrity isn’t. The fact that the younger K is supposed to be 29, despite Brolin’s appearance to the contrary, is taken care of with a facile bit of dialogue that acknowledges the problem and invites the audience to then move on. There are also the usual aliens hiding in plain sight that suddenly reveal themselves to be far more complicated that they would seem. Heading that list is Boris himself, with ingeniously spiny detachable parts that do his nefarious bidding. A trip to a Chinese restaurant, provides more along those lines, and culminates with J doing a diverting battle with a giant carp using only his wits, a metal tray, and an uncertain understanding of the creatures anatomy. For sheer inventiveness, though, there is Griff (Michael Stuhlbarg), a creature of the fifth dimension who can see all the possible timelines on the verge of coalescing in the present, and the story does a tidy job of exploiting those multiple timelines. As for Griff, he’s a delightfully upbeat alien with an aura of elfin innocence that, even as he’s expounding the probability of the more unfortunate possibilities in possible timelines, holds its own against J’s cockiness and K’s timeless deadpan.

Special effects, always a high point of these films, are not wanting, particularly the retro-gadgets from 1969 that manage to be quaint and futuristic at the same time. The best one, though, is the one Griff manifests, and though it is one of the quietist, it’s also the most beautiful in both the aesthetic and cosmic sense, as it puts Griff, and his peculiar sartorial choices in perspective, as well as putting in perspective on Griff’s peculiar place in the MEN IN BLACK universe.

It all culminates in the launching of Apollo 11 on its way to landing the first men on the moon, around which the fate the future buzzes, as well as the answers to a few mysteries from the past while introducing a few more, no doubt to keep the franchise going. High action, slick humor, raucous fun, MIB 3 is also a surprisingly thoughtful paean to higher implications of pie, and to the miracle of chance that makes up the unified fabric of the past, present, and the future.