I have a dozen directions I could take this. I haven't decided where yet. It takes place in 2373 during the Dominion War, after the events of First Contact
but before the Second Battle of Deep Space Nine.
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Will Riker looked out the viewscreen. "This sucks," he commented.
Picard snorted. "My grandfather used to say that. For much the same reasons."
"If it's all the same to Starfleet Command, if the Federation is at war, we should be shooting Dominion warships."
"I concur, Number One. But you know the theory."
"That doesn't make it any less aggravating."
The boffins in Starfleet Intelligence had coughed up this brilliant (by their own humble admission) theory. They calculated that the Starfleet Flagship would be targeted by Dominion intelligence forces, so they sent the powerful Sovereign-class starship to low-priority areas to rendezvous with assorted ships. This would give the Dominion false information about Starfleet movements and priorities. After a while, the Dominion would figure it out and begin ignoring the Enterprise, then Starfleet would form a battlegroup around it and use it in a flanking assault.
Both Picard and Riker thought Starfleet Intelligence was suffering from Impacted Brain Syndrome. But they were loyal officers and followed legal and proper orders, even stupid ones. And having broken orders once this war by diving into the Battle of Sector 001 - even though they did save Earth, the Federation, and the integrity of history itself in the process - their leeway with the upper echelons was near the breaking point.
So they sailed in dull space between Cardassia and the quasi-isolationist First Federation, listened to the war through official dispatches, and got annoyed.
Tactical Officer Lieutenant Gormenghast remarked, "Captain? Commander? You're ... wearing hats."
The two officers reached up and found that the Lieutenant was correct. They pulled them off and saw that they were pastel-colored, reflective, and cone-shaped - children's party hats.
The bridge vanished and the Starfleet officers found themselves in a tent with a band playing and revelers wearing pastel cone-shaped party hats were dancing. In a flash of light, Picard and Riker found two figures standing by them, blowing noise-makers.
"Hey, Jean-Luc! Great party! Who invited you?" Q and his companion laughed.
"Q!" Picard protested. "As if this war wasn't unpleasant enough!"
They were all abruptly on the bridge again. Data got up from the helm in alarm and Gormenghast pulled a phaser.
"And here I came to -" He looked up at Gormenghast. "Hey, a Scalosian! You idiots finally fixed your little whizzing problem, eh?"
Picard got up and gestured at Gormenghast. "At ease, Lieutenant."
Q's companion shrugged. "Go ahead and shoot if it makes you feel any better. It's not like it'll do any good."
Gormenghast seemed to contemplate it, then lowered his phaser.
Q brightened up. "Oh! Jean-Luc, this is -" Q grinned. "- My Boy!"
"Dad!" Q the Younger whined.
Riker shook his head in disbelief. "Q has spawned. I am disgusted."
Q the Elder snorted. "Well, unlike you, I actually keep track of my offspring! Granted, I just have the one. Unlike you."
Q the Younger laughed. "You don't even know that you became a grandfather two weeks ago! What a moron!"
Riker was stunned, then Picard interrupted. "If you're here just to teach your child how to be annoying, go away. Go do something useful, like bothering the Changelings."
"Them?! Ew! They have no sense of humor!" Q smirked.
"Changelings? Dad, aren't you the one who took away their genders and made it impossible for them to - ?"
"I admit nothing. Mind you, it was funnier at the time. Anyway, we're here on business." He sat down, a Victorian plush chair materializing in time for him to sit comfortably. "I came for your inestimable assistance, Jean-Luc."
Riker sat down. "Now what?"
"It's simple," Q the Elder explained. "My boy here was doing some light reading - everything ever written by any human ever -"
"Which killed a whole picosecond. Amazing amounts of pornography."
"Hush. Well, he came across this pre-spaceflight fiction that talked about a humanoid species in a very non-standard environment. We got into a debate as to whether or not such a species could actually exist and remain humanoid - evolution and all, you know. So we decided to test it."
Q the Younger blurted, "I built the planet myself! It's not in your classification system - it probably can't exist in nature. Think of it as a mix of Class H and Class Y. The tricky part was -"
"Q! please." Q the Elder continued. "To be sure of results, we popped the new planet backwards in time about a hundred thousand years in an area where it wouldn't be bothered. Then we began looking around humanoid-inhabited planets of the time and found small groups of technological primitives - animal skins, chipped flint tools, simple electronics - "
"Real grunters. Make you look advanced."
"All about to be wiped out in natural disasters. We scooped them up, made the necessary modifications to survive on the new world, and dropped them off."
"Interesting," Data said. "As well as morally ambiguous."
"Pooh on you," Q the Elder said. "'Morally ambiguous' my omnipotent and shapely ass! They lived and got to evolve! Without us they would have just died and been forgotten!"
Picard shook his head. "Get to the point, Q."
"The point is that our little father-and-son art project has hatched. They've developed first-generation interstellar travel and have begun to snoop around the stars. Got a couple of colonies going and have already contacted aliens. Not far from here, in fact. I thought that they came out okay. Junior here doesn't."
"Really snooty types," Q the Younger said. "All social order and intellectual development. Not to mention really full of themselves. You know what they call their interstellar society? 'The Great Inquiry'. Not even 'The Bla-Bla Empire' or 'The United Federation of Doody-Heads'."
"So we thought to get the unbiased opinion of someone with great experience in being judgmental about other cultures. Namely you."
"No," Riker said. "Now go away."
"Actually that doesn't sound bad," Picard said. "You said they were near here?"
Q snapped his fingers. "Your computers - which inexplicably haven't taken over yet - now have the coordinates."
Picard looked at the Q's, who gave him big innocent smiles. "What's the catch?"
"Nothing!" the Q's said.
"Bull!" Riker said. "You're up to something!"
Q the Younger raised his hand. "We aren't going to do a thing. I swear on my mother's grave."
"Is your mother dead?" Riker asked.
"I wish," Q the Elder said. "She's such a complete and utter bi-"
A sixteen-ton weight dropped on top of the elder Q.
The younger Q yelled at the ceiling, "I don't listen to him! I wuv oo, Mommy!" He seemed embarrassed to be there. "I'll just take Dad home." He shook his head. "Damn it, Dad, do you have to get smashed in front of the humans?" They disappeared in a flash, restoring the bridge to it's original state.
Data looked at the helm controls. "There is a course laid in, Captain. It leads to a world twenty-six light-years from our current location. None of the stars in that cluster have ever been visited." He accessed the sensors. "There are neutrino emissions and subspace disturbances indicative of interstellar technology. They are rather faint. If I had not been looking, I might have missed them."
Picard and Riker smirked at each other. "Well, our mandate is exploration and contact. And since Starfleet deems us more useful doing non-war-related activities -" Picard sat down and pointed forward. "Set course for the Great Inquiry. Warp Seven." He grinned. "I have to admit that I am curious. And the name is promising."
Riker mentioned, "I don't remember any pre-spaceflight science fiction about a civilization called 'The Great Inquiry'. Data?"
"The name is not familiar, Commander. But a great deal of fiction about alien races is written by any developing society prior to First Contact. And not all of Earth's literature survived to the present day. If it was in a book that has no surviving copies, it is likely that only a Q or similarly resourceful entity could discover it."
"Knowing Q, they probably communicate by throwing grenades in people's faces or something."
The Q's looked on as the Enterprise went into warp. When the ship vanished, they began laughing.
"He fell for it!" Q the Younger said. "I can't believe he fell for it!"
"I know!" Q the Elder said, gasping in laughter. "All the things I've pulled on him, and he still couldn't resist! Even a frog can learn to be afraid of the flashlight!"
"Wait until they get a load of these guys!"
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For those who do not know about the Great Inquiry, here's a hint