So if the Tenth Doctor met his idol why shouldn't the Eleventh Doctor?
The Doctor ran around the central console of the TARDIS and frantically played about with all the dials and buttons. He didn't know what any of them did but it was better than doing nothing in a crisis like this. The time machine was shaking violently and making an extremely not very good and not very quiet sound. The Doctor decided to use a trick perfected by his tenth incarnation and began hitting the console with a hammer.
"Sorry about this old girl!" He yelled over the noise.
After the fourteenth or fifteenth (the Doctor had lost count) whack, the TARDIS stopped shaking and threw the Time Lord to the glass floor in a painful heap.
"Eyes, nose, chin, bowtie, Stetson." The Doctor said as he checked for any damage. "I'm fine." He leaped to his feet with his usual youthful vigour and began checking the TARDIS's console.
"Oh good the time rotor has recalibrated." He said.
"The briode nebuliser is still on the fritz though." Said the other man in the control room.
"Oh don't worry; it's been like that for ages."
"Don't you take any pride in your TARDIS? Call yourself a Time Lord?"
"Oi! I love my TARDIS!"
"Doesn't look that way to me."
The Doctor suddenly realised the logical impossibility. The other man seemed to have come to the same conclusion at the same time. Both men slowly made their way towards each other until they were face to face.
The Doctor would recognise that mop-like hair and nifty bowtie anywhere. It was his second incarnation.
"No." The Doctor said quietly.
"What?" The other Doctor said.
"No." The Doctor said again, this time with a huge grin slowly making its way onto his face.
"What?" The other Doctor said again.
"No." The Doctor said for a third and final time. The huge grin had now taken permanent residence on his face.
"What?"
"Oh this is just so cool!" The Doctor said with barely contained glee. "Look at you! The bowtie, the checked trousers, the hair! Brave choice that hairstyle. At lot of people think it looks silly but I think it looks cool!"
"Oh thank you. Your choice of neckwear is very nice too."
"Oh this is amazing! Oh. Actually it's very, very not good. The universe might collapse in on itself within the next minute. But still, it would be worth it!"
"Look I'm very flattered that you're such a big fan of mine but I think you may be taking it a bit far."
"Wait, fan, what?"
"You've clearly styled yourself after me and that's very nice but there was no need to leave Gallifrey just to stalk me."
"No, wait, I'm not a fan. I'm you from the future!"
"Oh don't be silly! I would never regenerate into someone so young!"
The Doctor chuckled. "Just wait until you see number five and number ten."
"What was that?"
"Oh, nothing. Ah, I can prove that I'm you." The Doctor produced the sonic screwdriver from the inside pocket of his green military jacket.
The other Doctor was taken aback for a few moments. "But's that's…that's the mark seven sonic screwdriver. I drew up the blueprints back on Gallifrey. I never showed them to anyone. I never built it because I thought it wouldn't work."
"Oh it works. It's the best screwdriver I've ever had!"
"Really? Well I'll certainly have to build it now won't I?"
"You'll have to wait until your me I'm afraid."
"Ah yes, we don't want any of those nasty time paradoxes do we?"
"Wibbly wobbly timey wimey!" The Doctor said with a massive grin.
"Oh that's a very nice phrase! I think I'll use that at some point."
"You'd better not until our tenth incarnation."
"We should try to stop creating these paradoxes shouldn't we?"
A beeping noise sounded from the TARDIS's console. The Doctor immediately began adjusting the many dials.
"It's nice to see I still have such good taste." The other Doctor said as he gestured at the Doctor's bowtie. He then gestured at the Stetson. "And I would like a hat like that."
"Yes it is very nice isn't it?" The Doctor said as he admired the hat atop his head. "Craig gave it to me."
"Craig?"
"Let's not go there again."
"So this is my TARDIS is it?" The other Doctor said as looked around the control room. "This is the Everything But The Kitchen Sink theme isn't it?"
"Let me guess; you don't like it?" The Doctor said as he finished tinkering with the console.
"Oh no, I rather like it! But I'll have to wait until I'm you to use it won't I? Oh dear."
"It's much better than the Coral theme number nine and number ten used. That one was awful! Oh. Oh, I just created another paradox. You'll have to use it now. Oh dear."
"Time for me to go home before we punch a Belgium-sized hole in the time vortex I think."
"I hit some time turbulence you see. The ensuring chaos is properly what brought you here. I've reset the time controls; you should be going home soon. Geronimo!"
"Goodbye Doctor. It was a pleasure to meet you."
"Thank you."
"For what?"
"For being so brilliant!"
The other Doctor faded away. The Doctor laughed to himself until he suddenly remembered something and soniced the console. The other Doctor reappeared.
"One last thing." The Doctor said to his younger self. "If you ever have the urge to throw the TARDIS's manual into a supernova because you disagreed with it, don't. There's been a few times since where it would have been really handy."
With that, he soniced the console and the other Doctor disappeared again. The Doctor laughed to himself as he dashed to the TARDIS's storage room. He searched the warehouse sized room until he found the TARDIS's user manual. He opened it and saw a note scribbled onto the inside cover:
I remembered!