The first question we have to ask is, why does Santa do what he does?
Seriously, who goes to that level of trouble to give gifts to people with nothing in return? Well, if we look at The Doctor's track record, he's dedicated his entire life to helping people. He's particularly fond of humans and basically exists to make people feel safe and happy.
We also know the Doctor is more or less incapable of standing still. In 'The Slow Invasion' we saw The Doctor go almost literally insane when he had to sit and wait for a couple of hours.
Finally, there's the challenge involved. The Doctor's MO is to jump at the chance of an impossible challenge and always manages to pull it off.
So, think of Santa's job. He has to do the impossible in a single night, something that will make him impossibly busy and the result is he makes people feel safe and happy.
Basically, doing Santa's job is something that fits with everything we know about The Doctor.
Then we come to the logistics.
There are approximately 2.18 billion Christians on the planet. If we divide that by the average members of a family (two parents and two kids), that's roughly 545 million homes he has to visit in a single night.
If Santa starts at most westerly tip of Alaska at GMT+12 and works his way east, finishing in Russia at GMT+12, he can guarantee himself 24 hours of darkness on Christmas Eve. That means, in order to deliver presents to every person who celebrates Christmas, Santa has to visit roughly 22708333 homes every hour...or six thousand three hundred and seven homes every second.
Now, even if Santa could move that fast, we know that Santa doesn't just arrive, drop presents and leave. He eats the mince pie/cookies and milk you've left for him, and he can't do each house in the most efficient order because he has to avoid the houses of the kids who are waiting up to try and catch a glimpse of him.
Basically, the only way he can do it is if he has more time than is available. Long story short, he needs a TARDIS, or at least a Vortex Manipulator to allow himself to travel in time. That way, he can visit a house, drop off the gifts, eat his cookie, then travel to the next house and arrive there at the same time he's at the first one.
Of course, this leads to problems. If he's in every house simultaneously, he's likely to meet himself, which means crossing his own timeline, leading to timey-wimey problems, and that much time travel in a single location will tear so many holes in the time-space continuum, that he'd likely leave all of Earth time-locked...just like the Last Great Time War became time-locked due to over-use of time travel.
So, it's likely he'd do maybe on street or a few streets at a time. This explains why you can hear Santa on the roof of your house sometimes. He has to walk, rather than just land the TARDIS in your living room.
This, however answers a long time question. Now that very few houses have chimneys, how does Santa get into the house? Well, the answer is obviously that Santa has a Sonic Screwdriver to let himself into houses.
But, of course, this raises another question: If Santa is delivering presents in a TARDIS, why is Santa always depicted in a sleigh rather than a Police Box?
The answer to that is obviously simple. The TARDIS isn't a Police Box, It's a TARDIS and, as such, has a chameleon circuit....a camouflage system designed to automatically blend in with it's environment.
Well, Santa, in his modern form, has been around since 1773...and what vehicle would fit most seamlessly into pre-Victorian England? A sleigh, of course...and while The Doctor doesn't experience time in a linear fashion, we know the TARDIS only got 'stuck' as a Police Box due to the faulty Chameleon Circuit in the 1960's....meaning it's entirely probable that in the 1700's, the TARDIS could indeed have been disguised as a Sleigh.
Also, as a Time Traveller, we know The Doctor wouldn't necessarily wait a year between deliveries. In fact, it would make far more sense to 'do' multiple Christmases at a time. You might as well deliver a present, hop forward in time and do next year's while you are there. So, perhaps, up to this point, The Doctor has only delivered presents when the Chameleon Circuit is working.
Of course, there's the final option. The Doctor is a genius, who literally saved the universe by jump-starting a second Big Bang. It's unlikely that he couldn't fix the Chameleon Circuit if he really wanted to. All evidence points to the fact that the TARDIS is a Police Box simply because The Doctor likes it that way.
Finally, we come to the most conclusive piece of evidence: Santa's Sack. In a single bag, he can carry enough presents for 2 billion people, and this bag can fit on a regular sized sleigh. The only way this can work is if his sack is bigger on the inside, and the Time-Lords of Gallifrey are the only known people in the known universes to have mastered this technology.
Ladies and Gentlemen. I think this is conclusive proof that Santa is a Time Lord...and most likely to be The Doctor
Seriously, who goes to that level of trouble to give gifts to people with nothing in return? Well, if we look at The Doctor's track record, he's dedicated his entire life to helping people. He's particularly fond of humans and basically exists to make people feel safe and happy.
We also know the Doctor is more or less incapable of standing still. In 'The Slow Invasion' we saw The Doctor go almost literally insane when he had to sit and wait for a couple of hours.
Finally, there's the challenge involved. The Doctor's MO is to jump at the chance of an impossible challenge and always manages to pull it off.
So, think of Santa's job. He has to do the impossible in a single night, something that will make him impossibly busy and the result is he makes people feel safe and happy.
Basically, doing Santa's job is something that fits with everything we know about The Doctor.
Then we come to the logistics.
There are approximately 2.18 billion Christians on the planet. If we divide that by the average members of a family (two parents and two kids), that's roughly 545 million homes he has to visit in a single night.
If Santa starts at most westerly tip of Alaska at GMT+12 and works his way east, finishing in Russia at GMT+12, he can guarantee himself 24 hours of darkness on Christmas Eve. That means, in order to deliver presents to every person who celebrates Christmas, Santa has to visit roughly 22708333 homes every hour...or six thousand three hundred and seven homes every second.
Now, even if Santa could move that fast, we know that Santa doesn't just arrive, drop presents and leave. He eats the mince pie/cookies and milk you've left for him, and he can't do each house in the most efficient order because he has to avoid the houses of the kids who are waiting up to try and catch a glimpse of him.
Basically, the only way he can do it is if he has more time than is available. Long story short, he needs a TARDIS, or at least a Vortex Manipulator to allow himself to travel in time. That way, he can visit a house, drop off the gifts, eat his cookie, then travel to the next house and arrive there at the same time he's at the first one.
Of course, this leads to problems. If he's in every house simultaneously, he's likely to meet himself, which means crossing his own timeline, leading to timey-wimey problems, and that much time travel in a single location will tear so many holes in the time-space continuum, that he'd likely leave all of Earth time-locked...just like the Last Great Time War became time-locked due to over-use of time travel.
So, it's likely he'd do maybe on street or a few streets at a time. This explains why you can hear Santa on the roof of your house sometimes. He has to walk, rather than just land the TARDIS in your living room.
This, however answers a long time question. Now that very few houses have chimneys, how does Santa get into the house? Well, the answer is obviously that Santa has a Sonic Screwdriver to let himself into houses.
But, of course, this raises another question: If Santa is delivering presents in a TARDIS, why is Santa always depicted in a sleigh rather than a Police Box?
The answer to that is obviously simple. The TARDIS isn't a Police Box, It's a TARDIS and, as such, has a chameleon circuit....a camouflage system designed to automatically blend in with it's environment.
Well, Santa, in his modern form, has been around since 1773...and what vehicle would fit most seamlessly into pre-Victorian England? A sleigh, of course...and while The Doctor doesn't experience time in a linear fashion, we know the TARDIS only got 'stuck' as a Police Box due to the faulty Chameleon Circuit in the 1960's....meaning it's entirely probable that in the 1700's, the TARDIS could indeed have been disguised as a Sleigh.
Also, as a Time Traveller, we know The Doctor wouldn't necessarily wait a year between deliveries. In fact, it would make far more sense to 'do' multiple Christmases at a time. You might as well deliver a present, hop forward in time and do next year's while you are there. So, perhaps, up to this point, The Doctor has only delivered presents when the Chameleon Circuit is working.
Of course, there's the final option. The Doctor is a genius, who literally saved the universe by jump-starting a second Big Bang. It's unlikely that he couldn't fix the Chameleon Circuit if he really wanted to. All evidence points to the fact that the TARDIS is a Police Box simply because The Doctor likes it that way.
Finally, we come to the most conclusive piece of evidence: Santa's Sack. In a single bag, he can carry enough presents for 2 billion people, and this bag can fit on a regular sized sleigh. The only way this can work is if his sack is bigger on the inside, and the Time-Lords of Gallifrey are the only known people in the known universes to have mastered this technology.
Ladies and Gentlemen. I think this is conclusive proof that Santa is a Time Lord...and most likely to be The Doctor