Just a quick author's note: I imagine this takes place right after the Last Christmas for 12 and somewhere early in series 6 for 11.
As much as the Doctor liked to brag to Amy and Rory about how advanced Time Lords were, sleep was still something that he (rather unfortunately) required. He didn't need anywhere near as much as eight hours a day. The Doctor couldn't even imagine staying still that long, asleep or not.
He would sleep only when at the point of extreme exhaustion. He would sleep only when nodding off would be in mere seconds of closing his eyes.
"So how did I get here?" He wondered, blowing stray hair from his eyes. His head felt heavy, like his mind was filled with cobwebs.
He remembered sitting on the seat in the control room, intending just to rest his eyes. The next time he thought he opened them he was in a small square room. The room was covered floor to ceiling in vibrant orange paint. It lacked any furniture, decoration, windows or doors.
On the opposite end of the room he saw there was an older man crouched down with his ear pressed to the wall. His curly grey hair, and his black clothes made him look like an ink blot in the middle of all the orange.
"Hello?" The Doctor asked.
The older man turned just enough to acknowledge his presence and let out an irritated sign. "Oh. You. Well, what do you want? I'm a bit busy right now."
He tried to place the man's accent to somewhere other than Scotland and failed. He was trapped in an orange room with an angry Scotsman. The Doctor wasn't quite sure what to say him. "Where are we?" He ventured.
"Me? Well I can't really say, can I?" The other man replied distractedly and then pointed at the Doctor. "You? You probably fell asleep during repairs again."
"I'm still asleep?" The Doctor questioned. He brought the palm of his hand to his forehead with a loud smack. "That would explain things. Oh, of course I'm asleep. How stupid of me." He squinted. The room was starting to look more and more familiar. "I've been here before, haven't I? I've dreamed this place…"
"Lots of times. Not in a while, no other strong telepathic species to get pulled in by, no other Time Lords to share with. " The other man replied tapping on the wall again. "Now, shut up. I'm busy."
"You're the one who is busy? In my dream?" The Doctor snorted. "All right, this is my dream… this is where… we're sharing a dream." He concluded, the fog starting to clear from his mind. "We're linked, telepathically. That's why this room is familiar, it's a telepathic dream…"
"We've probably crossed too close in the time vortex." The man replied, removing his ear from the wall. "Same as the other time but this time… Hey! Stop distracting me!" He stood up and brushed his hands off on his long black coat.
The Doctor frowned and crossed his arms over his chest. "Other time?"
"Yes, yes, I thought you were supposed to be clever. You're making me look bad." The other man prattled on as he then pushed passed the Doctor to examine the opposite wall. "We didn't physically crash in to each other this time, just our dreams, now if you could please shut up… No! Wait! Un-shut up! What was the last adventure you had? Last thing you did? Where were you?"
"Amy and Rory and I were just- Wait, crash-" He ran over to the other man. "You're- you're me?" He asked in confusion "I crashed in to my own mind? How is that even possible?"
"Of course I'm you." The other Doctor replied, looking confused as to why he had to ask. "Who else would I be?"
"No, no, you- you cannot be me. You are not possible, you are impossible-" The younger Doctor stumbled over his words as his brain tried to process this new information. "I'm number 12, I'm the last one. I haven't seen you, you'd be 13 or later and that is impossible."
"Impossible? Oh yes," The older man sighed, passing the Doctor again as he went back to the other wall. "You did love that word, didn't you? Impossible this, impossible that, impossible people." His tone became more impatient."Well, spoilers chin boy! Sometimes the impossible becomes possible!"
"Aren't you a cranky one? All scowly and eyebrowed." The younger Doctor crossed his arms over his chest. "You're supposed to be impossible!"
"What did you expect an impossible person to be like?"
"I don't know?" He threw his hands up. "Cheery? You could at least try a smile."
The older Doctor forced a wide smile that showed his teeth. "Better?"
The younger Doctor suppressed a shudder. "Ooh, oh, no, no, that does not work on that face. Don't, don't smile… ever, please."
The younger Doctor examined his newer incarnation a bit closer. "And you're Scottish! Brilliant! Never been Scottish. Were you ginger before it went all-" he gestured to the other's grey hair.
The older Doctor's face fell. "I'm not telling you… and neither of those are words by the way, eyebrowed and scowly…" He pointed out, then clapped his hands together. "Now, where are you in your timeline? No-wait, you said Amy and Rory, that gives me a rough idea." He tapped his index finger to his chin. "Long before where we are…hmmm, it should be safe. Unless you're just a dream or memory…" He walked over to stop in front of the younger Doctor, eyeing him critically, looking for anything to indicate he was a dream.
"I'm not 'just a memory'." The younger Doctor protested then sighed. "Which is of course what a dream would say, wouldn't it? I'm with Amy and Rory right now, but that could be something you're remembering… Wait, how do I know you're not a dream? Me, just making up a new regeneration?"
"Well it doesn't matter if you're dreaming, does it?" The older Doctor snorted. "Worst case for you, you're in the TARDIS. Worst case for me, brain is getting digested. I'm rather fond of my brain not being treated as edible. All right then, how do I know you're not a dream?"
"Digested?" The younger Doctor asked in disbelief.
"Yes, digested." He repeated impatiently. "Time may be of the essence here."
"Okay, fine then, ask me I question I couldn't know the answer to. Something… big that has happened, something a dream wouldn't be likely to forget." The younger Doctor insisted.
The older Doctor paused. "You're still pretty early in your timeline I think… Okay, River. Yes, River Song."
"Who is River Song? What is she to you?"
"Ha, ha, so funny." He deadpanned. "Obviously not what I meant."
"I have guesses," the younger Doctor admitted, letting his arms fall to his sides. "but no, I'm not certain yet exactly who she is."
The older Doctor muttered something under his breath, but seemed pleased with the answer. "Okay, okay…" He wandered and pressed his ear to the wall again.
"You're testing if you're really dreaming." The younger Doctor observed, determined not to be outdone by himself. "You're trying to trigger something. You've probably got someone with a scanner over you right now or you're hooked up to machine and you're trying to give it different readings. You're… monitoring yourself dreaming? To see if you're brain is being eaten?"
"Don't think about it!" the older man hissed. "I just need to see the readings of when I'm asleep and when I'm awake to make sure they're proper."
"Make sure they're proper?" The younger Doctor echoed before he could stop himself.
The other Doctor gave him a weary sigh. "Let's just say it's been a rough night and leave it at that, hmmm? We'll probably forget this whole conversation soon as we wake up but best not to chance it. If you do remember it, you'll figure it out in time."
"Course I will, I always do."
The room started to shake, causing the older Doctor to smack his forehead in to the wall before tumbling to the floor.
"I think we're waking up." The younger Doctor called out as he tried to steady himself. "Or we're drifting too far apart to keep the connection."
"Then I guess you'll be seeing me around in your further, Doctor." The older Doctor said, scrambling to his feet.
"Only if you're not impossible."
The older Doctor gave a small smile in reply.
The younger Doctor wrinkled his nose. "Oh no, not with the smiling thing. Don't-don't do that."