"I'm half human. On my mother's side." ~ The Doctor, Doctor Who (1996 television movie)
"See that? The retinal structure of the eye. The Doctor is half human! No wonder..." ~ The Master, ibid.
Of all the statements made within the long-running BBC science fiction programme Doctor Who, perhaps none is as controversial as the claim that the lead character of the Doctor is half-human. The quotes above come from the 1996 television movie co-produced with the Fox Network, generally considered "canonical" amongst fans despite being one of the most problematical parts of the show's history for this and several other reasons.
The accepted view of the Doctor considers him to be a Time Lord from the planet Gallifrey. Although his race were not named until the end of show's sixth season in 1969 (in The War Games), and his home planet until Season 11 in 1974 (The Time Warrior), it was established as early as the very first episode (An Unearthly Child, 1963) that the character was from a planet other than Earth. The revelation that the Doctor was, in fact, half-human was met with uproar in fan circles, and the fact that the canonicity of the TV movie was in question due to other factors was not helpful.
Nevertheless, the movie is now generally considered canon, and its star - actor Paul McGann - as one of the eleven actors to officially play the lead role, although it is the only time he has played the part on-screen. When Doctor Who returned to the screen in 2005, McGann's Doctor was not referenced directly, but Christopher Eccleston's Doctor was publicised as the "Ninth" (following McGann's Eighth). The likeness of the Eighth Doctor as played by McGann also appeared in the 2007 story Human Nature and the 2008 Christmas special The Next Doctor. That his is a valid incarnation of the character is no longer held in question by the majority of fans.
Yet the claim that the Doctor is half-human is. In fact, it is commonly accepted fan-wisdom that the Doctor is definitely not half-human, whatever may have been stated in the movie. Admittedly, Journey's End, the 2008 series finale, muddied the waters somewhat with its implication that the Doctor did not have any human DNA - but this was not totally unambiguous, and does not necessarily supercede the TV movie's claims in any case. Is there really any definite argument that Journey's End is somehow "more canonical" than the movie - and does the Doctor being half-human really stop that story from working out as it does?
In order to argue that the Doctor is not half-human, and is instead a thoroughbred Gallifreyan, one must fundamentally assert that the TV movie is just plain wrong. Some fans have attempted to argue that the Doctor is joking, or mistaken, but this hardly holds up when we see the Master stating the same thing. Or, perhaps, the Doctor was only half-human in this incarnation - but that, too, is highly questionable, and how do we explain the line "on my mother's side"? No, it seems the best course of action is simply to discard the canonicity of this bit of the film. But this is problematic for a number of reasons. The Doctor's demi-humanity is not just something that appears in a couple of throwaway references - rather, it is a key plot point. If the Doctor is not half-human, the fact that the Eye of Harmony in the TARDIS is set to open upon recognising a human retinal pattern becomes nonsensical, and so in turn does the entire story (more nonsencical than it is already, that is). If the Doctor is not half-human, the story falls apart. If we decide that these lines are not canon, we must decide the whole story is not canon. And, because this is the Eighth Doctor's only onscreen appearance, this would involve discarding the entire television run of one whole incarnation. To me, that hardly seems fair.
There is, however, a solution. It is simple: the TV movie got it right. The Doctor really is half-human. After all, the Doctor has never definitively stated in thirty seasons that he isn't half-human, and even the implications of Journey's End can be explained away satisfactorily if one puts one's mnd to it (though this will not be focused on further here). When he claims to be a "Time Lord", this can be seen as a title as much as a race - the unmade season 27 would have seen the very definitely human companion Ace become a Time Lord, for goodness' sake, although to be fair even I think that's silly. The Doctor says as much himself in the 2008 story The Doctor's Daughter: "A Time Lord is so much more. A sum of knowledge. A code. A shared history. A shared suffering." The stories The Deadly Assassin (1976) and The Invasion of Time (1978) imply that not all Gallifreyans are Time Lords. (If the Doctor does claim to be "Gallifreyan", this can be seen again as referencing his cultural identity - after all, Gallifrey was the planet on which he was born and raised, even if he is not 100% genetically Gallifreyan. It is similar to a child with English and French parents claiming to be "English" because they have lived in England all their life and feel no strong ties to France.)
What about those times when the Doctor denies being human? I do not think these pose much of a problem. After all, he does not necessarily fill the criteria for humanity - and he certainly is not fully human. Perhaps, for much the same reasons as he might consider himself "Gallifreyan", he does not consider himself "human" - he was not born on Earth and did not grow up in a human society. Even the TV movie itself has the Doctor directly deny his humanity - "I am not human!" the Seventh Doctor exclaims repeatedly on the operation table, and these are in fact close to being his final words. "I love humans," the Eighth Doctor says, perhaps rather implying that he isn't one himself. Despite the fact that he is indeed partly human, he doesn't consider himself to be one, and is perhaps slightly embarrassed by the idea - maybe explaining why he doesn't mention it very often.
But the idea that the Doctor really is half-human goes beyond the fact that he is never clearly stated to be anything else. It is something that I believe fundamentally makes sense. The premise of a show is a man who can travel anywhere in space and time - yet, he seems to concentrate overwhelmingly on Earth and humans. At a rough count, of 201 stories to date, 62% are set at least partially on Earth - even ignoring the Pertwee era where the Doctor was stranded on Earth against his wishes, more than half of all serials occur partly or wholly on our planet. A staggering 83% of stories feature humans in some way, not counting the regular cast. (Only two stories, 1964's The Edge of the Destruction and 1965's The Web Planet, fail to feature any characters aside from the regulars who aren't at least humanoid - and the former has no guest cast members at all.) Even if these are not totally indicative of all the Doctor's adventures, it still seems he likes our planet and our species one hell of a lot. Perhaps he has just grown a fondness for humanity - but even in the very first story, there is a reference to a further Earth-based adventure around the time of the French Revolution, and it is implied he and his granddaughter Susan may have visited Britain at some time post-decimalisation (i.e. after 1971). This is not to mention the fact that the Doctor and Susan make their stay on Earth unusually long - some six months, in fact. All this is before the Doctor encounters what are commonly accepted to be his first human companions, schoolteachers Ian and Barbara, who do undoubtedly have a profound effect on his character in other ways. What better reason for the Doctor to like Earth so much (or, at the very least, for the TARDIS to be drawn there so frequently) than the fact that it is the home of his ancestors?
If this argument alone is not totally convincing, there are others - for example, the demographics of his companions. The definition of what constitutes a Doctor Who companion is not entirely fixed, but for the purposes of illustration we will consider all those listed by Wikipedia. Of around 42 companions total, 33 have been human - some 79%. Again, we see the Doctor exhibiting a definite preference for humanity. This is somewhat difficult to explain considering he has the run of the entire universe from which to make his choices, but his being half-human himself provides an iron-clad excuse for why this is the case.
Further arguments abound. What, for instance, of the Doctor's marked preference for a human style of dress? In all of his incarnations so far, he has tended to dress in clothing that would not look out of place in twentieth or twenty-first century England - right from the very beginning. Why this odd fashion choice? Other Time Lords do not dress so; even the Master does not bother donning particularly human-style clothing on many of his visits to Earth. (Romana, perhaps, is an exception, but she is heavily influenced by the Doctor.) In fact, the Doctor's preferred style - usually involving a button-up shirt and some sort of necktie, with only a couple of his incarnations breaking this rule - seems in the Whoniverse to be pretty much Earth-exclusive. Again, we have another strong indication that the Doctor feels his ties to Earth very strongly, and has done from the very start. Is not the easiest explanation that he inherited his dress sense from his mother, who presumably was born on Earth some time in the last century or so?
The Doctor shows an incredible knowledge of Earth history and culture. When his TARDIS gets stuck in the form of a terrestrial police box, he chooses to keep it that way - because he likes it. Earth-style items fill his pockets (to give just some examples: a recorder, a yoyo, a Swiss army knife, a cricket ball, a dog whistle and a teaspoon) and he shows a marked liking for jelly babies, not to mention "edible ball-bearings" (The Idiot's Lantern, 2006). He seems intensely attached to Earth, something that might well appear rather peculiar. But if he is half-human, perhaps it makes more sense.
It has long been apparent that the Doctor is not like other Time Lords. Unlike the rest of his race, who for the most part seemed content to sit at home being dull and watching the Universe go on around them, the Doctor's defining trait is that he is a man who must explore time and space for himself, righting wrongs along the way. This need not be because he doesn't totally share his people's DNA - other renegade Time Lords have been seen, though they are rarely anywhere near as heroic as the Doctor - but why shouldn't it be? The final years of the classic series implied the Doctor was "more than just a Time Lord" (a cut line from 1988's Remembrance of the Daleks), and would have gone on to reveal him as the reincarnation of a mysterious being from Gallifrey's past known as the Other. I don't know about anyone else, but I find this far from satisfactory - perhaps because it makes the Doctor too much of a godlike superhero. The idea of the character being half-human is far preferable - perhaps the Doctor is, in a sense, less than just a Time Lord.
Issue 414 of Doctor Who Magazine makes a good point as well - during the series' early years, it was never truly implied that the Doctor was anything but a human being from some advanced civilisation. He may have been in possession of a powerful time-space machine, an enormous intellect great longevity and the ability to rejuvenate, but there wasn't anything much to suggest this wasn't simply how humankind might become in the future. In fact, there are several occasions in 1960s serials - and possibly even later - where the Doctor is referred to as "human" and he doesn't bat an eyelid. It wasn't really until 1969's The War Games, with the revelation of the godlike Time Lords, and much more strongly in 1970's Spearhead in Space where we first learn that the Doctor has two hearts, that he actually begins to be portrayed as someone definitely alien. So perhaps the idea of the character being half-human isn't so very blasphemous after all - there's no strong evidence that the people who worked on the show in its early years necessarily considered him to be an alien being.
Another point which it is interesting to consider is precisely what is meant by "half-human". Could it be that the words are being used to mean "part human" - the Doctor has some human ancestors, but his mother was not necessarily fully human herself? Maybe he had a human grandfather, or great-grandfather, and is otherwise fully Gallifreyan. It's an interesting question, and one which I suspect will never be answered - and indeed, never should be answered. Given the furore that arose over the initial revelation, I wouldn't advise the series addressing the issue of the Doctor's parentage any time soon - and, indeed ever. The character needs to retain his mystery. Personally I prefer to think of the Doctor's mother as human herself, born on Earth in the late nineteenth century or early twentieth, and taken to Gallifrey at some point by the Doctor's father. (Such Time Lord / human relationships are certainly possible, as illustrated by the Doctor's own romances and companion Leela's marriage to Time Lord Andred in The Invasion of Time.) As a result, the Doctor would have suffered something of an ostracisation in his youth, and would have been traumatised by his mother's "early" death - without the saving gift of regeneration, she would simply have passed away of old age like any other human. These events, in my mind, would provide excellent motivations for much of the Doctor's behaviour onscreen. All this is pure speculation on my part, however.
There are doubtless many more minor points that could be made in relation to this topic, but the main argument has already been made. The Doctor has been stated to be half-human in a production that is otherwise regarded as canonical, and disputing the canonicity of this statement only leads to further problems. But, more importantly, the statement actually makes sense in the context of the series as a whole, explaining away many unanswered questions. Fans' strong disdain for this interpretation of the Doctor is, perhaps, unfounded.