Dr. Who and the Birthday Paradox...

So today I thought I’d just jump off the ledge of sanity and take a look at one of my personal favorite shows…Dr. Who.  Obviously there is a lot going on in that show and if you have never seen it before, I highly recommend you stop reading right now and give it a chance.  When you get back we can begin.

Or are we ending?  Or are we somewhere in the middle?  See, that’s something that happens when you watch Dr. Who…you lose a little bit of your sense of reality as we know it.  So what, in all of space and time, could we possibly talk about in reference to Dr. Who? Well let’s talk about how old he is.

Depending on where you are at in the series, he’s either around 900, over 4.5 billion, or just over 950.  The problem with any of those numbers is, they aren’t in chronological order within the series itself.

Let’s take a beat here and explain something.  The Doctor is a time traveling alien from the planet Gallifrey.  Occasionally he dies and regenerates into a new incarnation.  That’s a plot device the show uses to justify changing out actors every so often and allowing the series to move forward with new storylines.  Now, the Doctor’s 7^th incarnation states in an episode that he’s 953 years old, but his 9^th incarnation explicitly states that he’s just 900 years old.  Now if you follow the Doctor’s incarnations, the years should follow suit.  The higher the numbers in incarnation, the higher numbers in age, right?  Oh to be young and old again.

So let’s look at exactly what I’m talking about:  The 1^st Doctor quotes his age as being somewhere in the range of 236 years old towards the beginning of his adventures, and when he regenerates into his second incarnation, he’s 450.  That’s pretty straight forward.  That implies that during the course of his adventures he lived about 226 years on and off screen.  Okay, cool.

The second incarnation says towards the end of his run that he’s 500 years old which is also fine.  That means during the course of his adventures he lived 50 years.  It’s the 3^rd incarnation where things get a little sticky, he states that his life has covered many thousands of years.  We’re going to come back to that because that language is very important.

The Fourth incarnation, and fan favorite, says his age is 748, but then throughout the run of this incarnation he claims to be anywhere between 400 and 1000.  Another Time Lord mentions in the series that after the first 200 years most tend to loose count.

Later the 6^th incarnation says he’s 953, then the 9^th incarnation says he’s 900.  You really see how it all jumps around, but why does it jump around?  Is this just evidence of bad writing, a lack of continuity within the series itself?

Actually, no, when you take into count how we calculate age cannot work for the Doctor.  The Doctor spends a fair amount of time separated from the time stream, so his life is not aligned with ours.  Lets look at the situation from our perspective.  We are born, we live so many years, then we die.  It’s a very straight line from cause to effect, beginning middle and end.  If you were born in 1979 and died in 2079, you lived exactly 100 years.  End of story.

Now let’s look at that from a time traveler’s point of view.  You are born in 1979.  In 2009 you get into the TARDIS and are taken back to 1879.  The way you calculate your age has effectively halted, and you are stuck at 30 years old.  You cannot go in reverse; you can’t suddenly be negative 100 or 130 year old.  You’re measuring tool for time has literally come to a screeching halt.  Now the TARDIS takes you to 2179.  Are you 30 or 200 years old now?  Technically speaking you are both.  If you measure your age by when you were born to what year it is right now for you, then you are in fact 200 years old.  But you are also only 30 years old because you haven’t aged a year since 2009, you weren’t present in the time stream for all 200 years.  So you’re sitting there in a little café in 2179 and someone comes up to you and asks how old you are, what is your answer? If you answered “Somewhere between 30 and 200…” you now look like a lunatic.

If we try to track the Doctor’s back and forth movement through time from the point of his birth, then we might be able to get some sense of how old he actually is, but we can never nail it down because he spends different lengths of time in different years.  The 12^th Doctor spends 4.5 billion years stuck in a box at one point.  Or does he?  That too is a little difficult to gauge because that takes place on Gallifrey which has a different sense of time than Earth does.  Time is a mutable thing for Time Lords, and while the Doctor may have spent 4.5 billion years in the box, it may have only been a month for Gallifrey.  It might have only been a few minutes for that matter.  Or maybe he just got in the box right then and there.

So much about physics affects how we understand time.  The twin example is a good one, where one twin goes into space at light speed while the other stays on earth.  The twin in space is travels for 40 years but doesn’t age because time is halted for him, while the one on earth ages 40 years.  When space-twin gets back, he’s still the same age, while the one on earth is 40 years older…but they’re still twins, and still the same age.

Ultimately it’s the show’s producers who have the final say on how old the Doctor is supposed to be and they have a very interesting answer:

“The thing I keep banging on about is that he doesn't know what age he is. He's lying. How could he know, unless he's marking it on a wall? He could be 8,000 years old, he could be a million. He has no clue. The calendar will give him no clues.” Steven Moffatt

Hopefully you now have a better understanding of why that is.  Anyway, thanks for reading and we’ll see you next…time.