The Millennium Falcon is far more maneuverable than the Enterprise, and as such, is literally flying circles around it, looking for a weak spot and turretting away. Which the Enterprise doesn’t really care about, because she has phasers all over the place (and, really, she’s a state-of-the-art flying military base, and the Falcon is basically a small transport vessel). But the Falcon is really hard to hit because it’s so tiny, and also because Han Solo is a certified nutjob and keeps doing crazy maneuvers like bouncing off the Enterprise's shields to rapidly change course, keeping the Enterprise computers from calculating his next move. So they’re at a standoff for a while, both doing space-donuts and occasional Picard Maneuvers and firing off photon torpedoes (seriously, the photon torpedoes arE EVERYWHERE IT’S UNCONTROLLABLE).
Unexpectedly, Serenity drifts by. She’s noted, but largely ignored by both parties.
"Just what the hell is going on there?" Mal asks.
River giggles. “He’s playing.”
"The big ship or the little one?"
"Not them. Him.” She points at the ceiling.
Mal’s eyes go wide as teacup saucers. He swears egregiously in Chinese and FTLs out of there.
Meanwhile, a large blue box has appeared on the Enterprise bridge. The doors open, and the Doctor steps out. “Q, really, how many times," he sighs.
When Q materializes, he’s hiding behind Picard. Picard swats at him until he straightens up. “Hello, Doctor,” Q says. “Please tell the TARDIS to stop shouting at me?”
”No,” the Doctor replies. “I’ve told you before, you are not allowed to use my universe as a playpen. Send them back where they came from.”
"What the devil is going on?" asks a 1701% done Picard. (Like, really, the Insect Ship From Hell, and now Q, and whoever this guy thinks he is. He longs for the days when he was just being cloned or tortured by Cardassians.)
Han Solo is doing sad loop-de-loops, trying to get the Enterprise to notice him again. Briefly, he’s glad it’s not a frigging Death Star, because the loop-de-loops would take a lot longer. (The Death Star couldn’t get involved anyway, because it’s having a hell of a time with those Cylons.)
"I needed an objective set of universal laws," Q protests.
"Go build your own universe, then," the Doctor responds. "I’m not having this here, I’m really not. Someone’s going to recognize these ships, Q."
"But I’m bored,” Q sighs.
"Ohh, you’re bored. Well, that’s completely fine then. As long as you’re only doing it when you’re bored. At least you aren’t teaching the ancient Egyptians to build bloody STARGATES this time.”
He heaves another sigh. It carries with it the inference of fire and ice and rage, the Oncoming Storm, the good wizard in every fairy tale, the weight of aeons — or, well, a fiftieth anniversary, anyway. The Doctor’s been around, objectively, for longer than either of them, and he knows it.
"Q, they’re from fundamentally different genres. Your lot, Star Trek, is science fiction, Star Wars is science fantasy. The universes don’t have remotely compatible physics. It’s a completely pointless question, and any debates are equally pointless due to the lack of objective, scientific information. Besides, if you’re going to do a crossover — and that’s what this is — it should be out of love of the things involved, not some misguided sense of irrational hate or competitiveness.”
There’s a moment of silence as everyone processes the life lesson.
"I’m going to ask you, very politely, to please get off my bridge,” Picard says to the Doctor.
The Doctor peeks around the side of the TARDIS at the viewscreen, where the Millennium Falcon is doing increasingly desperate barrel rolls. Q, grumbling to himself in some untranslatable language, snaps his fingers, and the Falcon disappears in a flash of white light, as all the universes are set back to rights.
There’s an awkward silence.
"What just happened?" Picard asks, having completely forgotten the altercation ever occurred. "Q? What are you doing on my bridge? What’s with the box?"
"Brunch tomorrow?" Q asks the Doctor, defeated.
"Why not now? I’ll put the kettle on." The Doctor steps back into the TARDIS, with in invitational gesture; Q, with a quick grin at Picard, follows.
"Okay, if it’s out of love, can I introduce future Sherlock to past Sherlock?”
"Paradoxes, Q. Paradoxes."
The doors close. The TARDIS dematerializes. All is well with the cosmos.
The Captain’s gone and got himself in trouble.
"Everybody, I want you all to meet Mrs Reynolds."
"Now I did a job, and got nothing but trouble since I did it, not to mention more than a few unkind words as regard to my character. So let me make this abundantly clear. I do the job and then I get paid. Go run your little world.”firefly captain malcolm reynolds
Captain Malcolm Reynolds in 1x01 Serenity
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