Doctor Who and Philosophy

by Courtland Lewis

  Think of an indispensability argument as consisting of three numbered stages:1. We ought to believe that everything necessarily mentioned, when giving our best scientific account of the universe, exists.

  2. It is necessary to mention numbers when giving our best scientific account of the universe.

  3. Numbers exist.

  If stages #1 and #2 are true, it follows that #3 is true, more surely than trouble follows the Master. So if somebody wants to believe that numbers don’t exist they have to at least deny that either #1 or #2 is true, or they can deny that both are true. Field lays in to #2. He does this by providing an example of how (he thinks) physics can be done without using mathematics. In other words, he does a bit of Carrionite physics.

  Time and Space, but No Relative Dimensions

  As his example, Field takes what’s called the Newtonian theory of gravity, and argues that you don’t need to use mathematics to state the theory. If more proof than the existence of cakes with ball-bearings on top were needed that human beings are ingenious creatures, then Field’s argument would be a good thing to put forward. It’s deeply complex and not for the faint-hearted, but it shows how somebody might go about doing science without doing mathematics. Philosophers think that what Field has done is significant, not just because it allows Krillitane head-teachers the glimmer of hope that they might be able one day to understand everything without force-feeding children oil to make them good at mathematics, but also because it’s a blueprint for how to attack step #2 of the indispensability argument mentioned above.

  But it’s only a blueprint. It’s no more the real thing than Charlotte Abigail Lux lives in a real house. The reason for this is that the Newtonian theory isn’t true. Anyone who told you otherwise—as most science teachers do at most schools—lied. Moral: don’t believe everything you hear. (Especially not from that Mr. Saxon!) While it’s approximately true—you won’t go far wrong using it to help you understand average-sized objects which aren’t moving very quickly, things like robot dogs and Daleks—it’s been replaced in modern physics by Einstein’s famous General Theory of Relativity. The General Theory of Relativity is the best theory of gravity we have; it’s also a theory anyone who wants to comprehend the Doctor should appreciate.

  In his book The Science of Doctor Who, science writer Paul Parsons very helpfully explains that the General Theory of Relativity has the potential to explain how the TARDIS could be bigger on the inside than the outside and how travelers (like the Doctor) could carve non-standard paths through space and time (which, in the General Theory of Relativity, are not actually two things but one multi-dimensional thing—‘spacetime’). On a more mundane level, the General Theory of Relativity can explain some astronomical observations a lot more straightforwardly than the Newtonian theory of gravity. It’s almost certain that the General Theory of Relativity isn’t the last word on gravity. At the moment, physicists are trying to construct a theory of gravity which sits comfortably alongside certain other bits of physics; so-called ‘quantum gravity’. However, it’s clear that the Newtonian theory is a thing of the past, so Field hasn’t succeeded in translating a current scientific theory into mathematics-free language.

  This doesn’t mean that Field hasn’t achieved anything. He definitely has given us some idea of the kind of thing somebody might do to a scientific theory in order to get rid of the mathematics in it. It’s just that he hasn’t done it with a current scientific theory. He hasn’t done any real Carrionite physics, so we’re a long way away from showing that stage #2 of the indispensability argument for platonism is false.

  Not So Much Timey-Wimey, as Teeny-Weeny Stuff

  What’s that I hear you asking? Has anyone discussed whether we could do away with mathematics in real, up-to-date, physical theories? Molto Bene! That’s exactly the right question to ask. Because unless we have a good reason to believe that #2—the claim that we can’t do science without numbers—isn’t true, the possibility of Carrionite physics looks to be on shaky ground. It gets worse for the Carrionites: philosophers have argued that #2 seems pretty solid, because one of our most fundamental physical theories, Quantum Mechanics, is as full of mathematics as the Abzorbaloff is full of people.

  Quantum Mechanics, in rough terms, is a part of physics which helps us understand the behavior of very small things. It could well be a lot more than that: some physicists, and some philosophers who are interested in physics, think that it applies to ordinary everyday objects as well. For all we know, Quantum Mechanics might explain how some of the weirder things which have happened to the Doctor are possible. But at the very least, it predicts how things like photons, electrons and quarks behave. And Quantum Mechanics is full to the brim with mathematics: full to the brim, that is, with incredibly complicated mathematics. The prospects of doing away with this mathematics, while keeping a physical theory that’s powerful enough to explain and predict the things which Quantum Mechanics does, strikes a lot of people as not very good; maybe even impossible.

  But some people, following the Doctor’s lead, like impossible. Mark Balaguer claims to have done for a very important bit of mathematics in Quantum Mechanics what Field did for the mathematics in the General Theory of Relativity. In his book Platonism and Anti-Platonism in Mathematics, he turns on the use of things called ‘Hilbert Spaces’, which I won’t attempt to explain, but which are a development of the idea of vectors, which may be familiar from school. Like a Dalek blasting away at the amassed ranks of Cybermen, Balaguer eliminates this mathematics from scientific theory. Now that’s a bit of Carrionite physics to be proud of. The only problem is that some people don’t think Balaguer has done what he claims.

  There are two basic worries about Balaguer’s work which cast doubt on whether his attempt at Carrionite physics is everything it claims to be. The first is that it rules out some interpretations of Quantum Mechanics. In one sense, Quantum Mechanics is nothing more than a formal theory which tells us how certain things behave. Now, if the Doctor has taught us anything it’s that things sometimes behave very strangely, and Quantum Mechanics is with him on this. In order to explain how the world can be such that things behave as Quantum Mechanics describes, people have suggested a variety of interpretations of Quantum Mechanics. On one interpretation, there are things out there (‘hidden variables’) which explain the oddity. On another interpretation, parallel worlds do the job. And there are other interpretations, most of them equally weird and wonderful.

  The odd thing about Balaguer’s mathematics-free version of Quantum Mechanics is that it rules out some of these interpretations. Not only does this mean that Balaguer’s new Quantum Mechanics is unlikely to appeal to people who support one of these interpretations, it means that Balaguer’s Quantum Mechanics is significantly different from normal Quantum Mechanics. We think that the TARDIS is good at translating because it lets people hear in one language what is said in another. There’s no loss of meaning. It should be a bit like that with ‘translating’ a scientific theory into a mathematics-free version. Obviously the mathematics-free version won’t ‘mean’ exactly the same thing as the standard version, because it’ll avoid making reference to numbers. But we’d expect the mathematics-free theory to say the same kind of thing about the physical universe, to have similar advantages and have a comparable openness to interpretation. But it appears that this isn’t true of Balaguer’s Quantum Mechanics.

  The second worry is that Balaguer’s new Quantum Mechanics might not be what it says it is. It’s always worth checking whether something is what it claims to be: that looks like Santa walking down the street playing a trombone, but ... Remember that Balaguer claims to have done away with mathematics in his theory, and so to have made progress towards attacking stage #2 of the indispensability argument. There’s doubt about whether he’s really done this. It all gets horribly complicated at this point, but in essence it seems as though Balaguer hasn’t got rid of the mathematics to everyone’s satisfaction.

  But even if B
alaguer has carried off doing a bit of Quantum Mechanics without doing mathematics, the foes of the indispensability argument still have a long way to go. Balaguer focuses on one part of Quantum Mechanics, not even the whole of Quantum Mechanics, let alone the whole of physics. The person who wants to defeat stage #2 of the indispensability argument has a tough job. And it could be a lot tougher than some people realize. A lot of people—not just philosophers—assume that all of science boils down to physics. We might study things like biology, polymer chemistry, or advanced sonic technology, but the things we study when we study these subjects are the way they are because of the kind of thing studied by physics. Donna behaves as she does solely because of what lots of little particles in her body are doing. Krelatine oil has the properties it does, similarly, because of stuff going on at the sub-atomic level.

  The view that everything in science is physics is sometimes called microphysicalism. This is a popular position, but that doesn’t make it true. It’s a popular position that car SatNavs are harmless. If microphysicalism is false, people who want to attack the indispensability argument have an even tougher time of it. Not only do they have to get rid of the mention of mathematics from physics, they have to do it with the other sciences as well. But biology and chemistry contain lots of mathematics. As for the social sciences—can you really imagine economics without mathematics? It’d be easier to imagine a celibate Captain Jack.

  Aww, . . . Poor Monster. Should We Feel Sorry for the Carrionites?

  So far we’ve looked at stage #2 of the indispensability argument, and quite right too, because it’s stage #2 that—in effect—claims there couldn’t be Carrionites. Even so, somebody could attack stage #1 of the argument, which says we ought to believe that everything necessarily mentioned, when giving our best scientific account of the universe, exists. Actually, philosophers normally put things a bit more precisely than this; they say that we should believe in things we need to mention in a particular way (called ‘quantifying over’) in a formal logical language. A few people have actually gone about attacking stage #1 as well. With reckless abandon, however, I’m going to ignore them. If you’re interested, you can read about this—as well as much more that I’ve skimmed over here—in Mark Colyvann’s book The Indispensability of Mathematics.

  The reason that I’m skimming over attacks on stage #1 of the indispensability argument is that there’s a far more interesting question to ask about the argument. Suppose that the argument doesn’t work. Suppose that it really is possible to do science without using mathematics. There really could be Carrionites. The interesting question is this: so what? Even if there were Carrionites, even if we no longer need numbers to do science than modern Daleks need a stair-lift to climb stairs, does that mean that numbers don’t exist? Why should it?

  Here’s an argument that numbers would exist even if we didn’t need them to do mathematics. If there were Carrionites, they’d be missing out on something. Question: what? Answer: mathematics. Even if the Carrionites could understand the entire physical universe, and exercise control over it without using numbers, they’d be deprived of a type of knowledge which humans (and Time Lords) have; knowledge of mathematics. We don’t just know things like: ‘At standard pressure, water boils at 100°C’ and ‘A healthy human heart contains two ventricles and two atria’ (notice, by the way, that numbers naturally creep into even the most simple scientific statements). We also know things like ‘2 + 2 = 4’ and ‘there’s no largest prime number’. When we know things like this, aren’t we knowing about numbers in the same way as chemists know about water, biologists know about hearts and experts in Earthonomics know about Earth (or ought to)? But, if this is right, don’t there have to be numbers for us to know about?

  There might be a lot wrong with this sort of argument, and many philosophers have claimed that there is. But isn’t it worth asking: don’t we think that mathematicians discover true things, that they really know things? Working mathematician Marcus du Sautoy says this about mathematics, “These truths are simply waiting to be unearthed, and no amount of creative thinking will undermine their existence.” Earlier in the same book he also said: Some philosophers might take issue with such a Platonist view of the world—this belief in an absolute and eternal reality beyond human existence—but to my mind that is what makes them philosophers and not mathematicians. (The Music of the Primes, p. 7)

  Harsh words! And, in fairness to the anti-Platonists, there are in fact mathematicians who don’t agree with platonism. But du Sautoy’s words are food for thought.

  Let’s give almost the last word to Elton Pope:When you’re a kid, they tell you it’s all grow up, get a job, get married, get a house, have a kid, and that’s it. No, the truth is the world is so much stranger than that, so much darker, and so much madder. And so much better! (“Love and Monsters,” 2006)

  That’s the thing about the Doctor, he opens doors to a whole new universe. He shows people that there’s just so much out there, waiting to be discovered. The Doctor helps people discover things about themselves, but he also helps them discover things about other stuff. Rose learns about Daleks, for example.

  There’s a lot of stuff to be discovered. Perhaps some of this stuff is mathematical. Perhaps there are numbers. And if there are—whether or not we need them to do science, whether or not Field and Balaguer are correct—then the Carrionites are missing out. Poor things! Although, perhaps it serves them right for doing horrible things to the Doctor, Martha, Shakespeare, and other innocent humans.

  Either way, there’re no easy answers. One of the gripping things about philosophy of mathematics is that, just when you think you’ve got somewhere, there’s a problem with your view. There’s a problem with every view everyone’s ever come up with. So don’t worry if you haven’t found any of the positions I’ve written about very convincing. Another thing the Doctor does is force people to think for themselves. And that’s what you’re going to have to do on the question of whether numbers exist. But as you think, it’s worth being aware that even the Carrionites fell back on numbers in the end. They needed to use Shakespeare because of his command over language, because it was words (and not numbers), which would gain them power over the portal. Yet, in spite of this, the last words of “Love’s Labours Won” were these: The light of Shadmock’s hollow moon doth shine on to a point in space betwixt Dravidian Shores and Linear 5930167.02, and strikes the fulsome grove of Rexel 4; co-radiating crystal activate!

  Numbers, it seems, just won’t go away. Not even for Carrionites.45

  EPISODE 3

  It’s a Different Morality. Get Used to It, or Go Home!

  The Ethics of Doctor Who

  12

  The Ethics of the Last of the Time Lords

  KEVIN S. DECKER

  A frail old man lost in time and space.... He seems not to remember where he has come from; he is suspicious and capable of sudden malignancy.... He remains a mystery. From time to time the other three [time travelers] discover things about him, which turn out to be false or inconclusive.... They think he may be a criminal fleeing from his own time.

  —C.E. WEBBER, notes on creating Doctor Who46

  The man who abhors violence, never carrying a gun. . . . You take ordinary people and fashion them into weapons. Behold your children of time, transformed into murderers....

  —DAVROS (“Journey’s End,” 2008)

  When the whole universe is at stake, how does the Doctor make moral decisions about who’s saved and who must sacrifice? Do his anti-authoritarianism and constant wandering express a sustainable notion of what a flourishing life could be? Is he a hero or a genocidal murderer (or both)?

  From its very beginnings in a fog-shrouded junkyard in Totters’ Lane, the Doctor’s adventures have flouted television conventions: historical serial or fantastic futurism? Fantasy, drama, or horror? Given this ambiguous heritage, it’s perhaps appropriate that the ethical messages the Doctor sends are equally nebulous. Like the police box shell of the TARDI
S, the alien morality that the Doctor represents has unseen dimensions that no one would suspect lay behind his unassuming façade.

  As a Time Lord, the Doctor’s role as the ultimate outsider complicates the situation: Gary Gillatt, a cultural historian of Doctor Who notes, “In many ways, the Doctor is defined by our distance from him ... we are rarely given access to his thought-processes or motivations, which in turn only adds to the character’s enigmatic appeal.” Complex motivations make it difficult to apply traditional ethical theories to judge the Doctor’s conduct. Not only are the Doctor’s intentions both complex and usually private, but also they often relate to unique situations in which conventional rules don’t seem to apply. The Doctor clearly seems to reject the idea that there’s any clear formula for making the right decision every time and expresses this in many ways: in “Warrior’s Gate” (1981) he quips, “One good solid hope is worth a cart-load of certainties.”

  The Doctor’s unique relationship to time also presents obstacles to using ethical theories that emphasize the importance of consequences to whether an action is right or wrong. Assessing our decisions or administering praise and blame in terms of consequences assumes a linear, cause-and-effect notion of how the universe works. But Doctor Who often demonstrates linear cause-and-effect as a convenient fiction—for example, in the cases of the TARDIS jumping a time dimension in “The Space Museum” (1965), or the insight into our timeline provided by alternate universes of “Inferno” (1970), “Rise of the Cybermen” (2006), and the Master’s Paradox Machine in “The Sound of Drums” (2007). The Fourth Doctor expresses the now-classic formulation of this problem in “Genesis of the Daleks” (1975):Listen, if somebody who knew the future pointed out a child to you and told you that the child would grow up totally evil . . . to be a ruthless dictator who would destroy millions of lives. Could you then kill that child?