Thus a time traveler’s personal time can bend back on itself in such a way that two different stages of personal time can even occupy the same point in external time. To see how this is possible, Lewis compares it to a train track that curves around, eventually intersecting itself. The point that is five miles down the line might be at the same location as the point ten miles down the line. But this intersection of points does not require positing an additional spatial dimension. Likewise, a stage of a time traveler’s personal time can intersect with an earlier or later stage without requiring us to posit an additional time dimension. This occasionally happens to the Doctor when he meets other regenerations of himself. Lewis’s distinction between personal and external time allows us to see how this is possible.
Another important consequence of four-dimensional time travel is the possibility of reversed causation. According to Lewis, travel into the past necessarily involves instances in which effects precede their causes. Normally, causes precede their effects—so much so that some philosophers claim that this is part of the very meaning of word cause, and reversed causation can be ruled out because of the meanings of words. But if time travel is possible there can be instances in which the effect actually precedes the cause. And this is very important for understanding the Doctor’s philosophy of time. Lewis asks us to imagine a time traveler who gets punched in the eye just before traveling into the past. The effect of a black eye might happen years or even eons before he was punched. Notice that the distinction between personal time and external time explains this unusual phenomenon. In terms of personal time the black eye occurred after the punch, just as it usually would. But from an external, objective point of view, that is, viewing all of space-time as a whole, the black eye exists before the punch.
Consider another example, a thirsty time traveler about to travel into the past. As the time machine is activated, he drinks an Old Speckled Hen. From the standpoint of personal time nothing unusual has occurred. The traveler was thirsty and then satisfied his thirst by drinking an excellent English ale. But the standpoint of external time yields a bizarre and borderline paradoxical result. The traveler’s thirst becomes satisfied before, possibly eons before, he ever became thirsty.
I think that reversed causation is precisely what the Doctor has in mind when he explains that time isn’t what people normally think it is. Non-time-travelers assume time is a straight progression from cause to effect because they don’t need to distinguish between personal and external time. From the subjective and linear point of view of personal time, their assumption is essentially correct. There is a straightforward progression from cause to effect. But from the non-linear and non-subjective point of view of external time, strange phenomena such as reversed causation, are entirely possible. In other words, the Doctor’s big ball of wibbly-wobbly, timey-wimey stuff is Lewis’s four dimensional manifold of events.
Let’s Do the Time Warp Again!
An important consequence of reversed causation is that if it’s possible, then completely closed causal chains also become possible. A closed causal chain is sequence of causes and effects in which the normal chain of events loops back on itself in such a way that the chain, as a whole, is the cause of itself. Imagine meeting a future version of yourself, whose TARDIS suddenly materializes in your room. After telling you how much fun time travel is, the traveler gives you instructions on how to build or grow your own TARDIS. You follow the instructions and then, after years of work, travel back in time to deliver them to yourself. Where does the information contained in the instructions originally come from? According to Lewis there’s simply no answer. The apparent uncaused, spontaneous existence of the information is very strange, but it’s logically possible, and showing this, after all, is Lewis’s only goal. Lewis thinks we shouldn’t be surprised that a world in which time travel occurs is very strange.
Sure enough, “Blink,” and by extension the Doctor’s explanation of time, hinges on a closed causal chain. The Doctor is sent back in time without his time machine, a time traveler’s worst nightmare. The only way for him to retrieve the TARDIS is to communicate with a woman named Sally Sparrow in 2007 and persuade her to send it back to him. What makes this communication possible is a closed causal chain.29
Though trapped in 1969, the Doctor communicates with Sally by sending her a DVD Easter egg. As Sally watches the video, the Doctor is able to communicate with her because he already has a complete transcript of the conversation, which he reads from an autocue (teleprompter). During the conversation Larry Nightingale adds what Sally says to his transcript of the Easter egg. Then, in the future, Sally herself gives the Doctor the now completed transcript before he becomes trapped in the past, enabling him to undertake the creation of the Easter egg, starting the chain again. The normal chain of causes and effects here loops back on itself forming a closed system, and the Doctor cleverly exploits this feature of space-time to communicate with Sally Sparrow. Once again, Lewis’s four-dimensionalism provides a model by which we can clearly see how this is possible.
However, the theory of four-dimensional time travel does have significant philosophical problems, the most famous of which is the dreaded Grandfather Paradox. Sometimes called the Bilking Argument, the paradox goes like this: if a closed causal chain was possible, then it should also be possible to interrupt such a chain of events, thereby disrupting or bilking the loop. The classic example involves a foolish time traveler who travels into the past and kills his own grandfather before his grandfather can procreate. If he can kill his grandfather, and it certainly seems possible for one person to kill another, then his grandfather would never procreate and as a result he would never exist to travel back in time and kill his grandfather in the first place. It seems that the time traveler both can and can’t kill his grandfather. Traditionally, philosophers have thought that such a contradiction shows that time travel is impossible.
In case you’re bothered about issues such as autonomy, agency, and intentionality, other versions of the paradox have been developed that don’t involve abnormal temporal suicide. Some examples take human intentionality out altogether by focusing instead on inanimate objects such as rockets or even time-traveling positrons. But for our purposes let’s just imagine a world in which the Doctor refuses to accept the transcript from Sally Sparrow. If this happened it would bilk the chain, the Doctor wouldn’t be able to make the video, Larry wouldn’t be able to complete the transcript and Sally would then have no transcript to deliver.
This is more than merely an obstacle standing in the way of the Doctor’s plans of escaping 1969. The mere possibility of bilking a closed causal chain threatens to generate a logical contradiction that would make time travel impossible. Lewis attempts to solve the problem by claiming that the paradox rests on an equivocation of the word can and thus leads to no real contradiction. He explains the equivocation using a linguistic analogy:An ape can’t speak a human language—say, Finnish—but I can. Facts about the anatomy and operation of the ape’s larynx and nervous system are not compossible [able to exist or happen together] with his speaking Finnish. The corresponding facts about my larynx and nervous system are compossible with my speaking Finnish. But don’t take me along to Helsinki as your interpreter: I can’t speak Finnish. (p. 77)
Lewis both can and can’t speak Finnish, yet there’s no paradox or contradiction involved because the word can is being used in two different ways. Likewise, a time-traveler both can and can’t murder his grandfather, and the Doctor both can and can’t refuse to accept the transcript, yet there is no contradiction and the paradox is solved.
But this also reveals a kind of fatalism that four-dimensional time travel seems to entail. Strictly speaking, from the point of view of external time, it’s not possible for a time traveler to travel to the past and murder his grandfather. Likewise, it’s not possible for the Doctor to refuse to take the transcript. The fact is, at least on Lewis’s view, that the Doctor received the transcript and that’s that. No a
mount of time traveling can ever change it. The sense in which he can refuse to accept the transcript is analogous to the sense in which Lewis can speak Finnish. So, if Lewis is correct then closed causal chains do not entail logical contradictions and time travel is logically possible. But mere logical possibility is cold comfort for someone wanting to explain that closed causal chains aren’t just possible but actually exist. And it’s particularly nippy when you’re explaining this to someone stranded in a 1969 shop job. Here the similarity between the views of the Doctor and Lewis start to break down. According to Lewis:The paradoxes of time travel are oddities, not impossibilities. They prove only this much, which few would have doubted: that a possible world where time travel took place would be a most strange world, different in fundamental ways from the world we think is ours. (p. 67)
Lewis doesn’t believe that time travel occurs in the actual world, but the Doctor certainly does. The views of the Doctor and Lewis aren’t identical, but they’re very similar. And this similarity allows us to use Lewis’s four-dimensionalism as a model to elaborate and elucidate the Doctor’s view. But we shouldn’t expect a perfect fit between them.
Another difference between the views of Lewis and the Doctor may be the possibility of additional temporal dimensions. As I have shown, Lewis’s view doesn’t include multiple temporal dimensions or the threat of their creation. But these both seem to be possibilities for the Doctor. When “Blink” is seen in context with other adventures such as “Father’s Day” (2005) and “The City of Death” (1979), the fabric of space-time seems more fragile, and the threat of bilking seems to be a real and dangerous possibility. But the Doctor is still basically a four-dimensionalist, and at least under normal circumstances multiple temporal dimensions don’t exist. No bilking occurs in “Blink,” and the closed causal chain involved is completely unbroken and consistent within a single temporal dimension.
Diagnosis
By briefly considering the views of two additional philosophers we can see precisely where the Doctor’s philosophy of time fits into the contemporary scholarship. Paul Horwich has completed a careful investigation of multiple examples of closed causal chains and defends them against several objections. In his article “Closed Causal Chains,” Horwich agrees with Lewis that such causal chains can’t be ruled out. He sums up his view in the following way:Theories that countenance what are naturally termed ‘closed causal chains’ cannot be dismissed on a priori [based on reason alone] grounds, and cannot invariably be ruled out by the a posteriori [based on experience] bilking argument. The latter argument shows that closed causal chains imply uncaused correlations. But the import of this result is not uniform. In some cases the proper conclusion is that such a phenomenon is incompatible with what we know. In others we may infer that closed causal chains do not and will not occur—but we cannot conclude that a spacetime structure permitting them is not actual. And in a third class of cases the bilking argument has minimal force; for the uncaused correlations to which it draws our attention are not improbable. The overall moral is that the bilking argument, even in its strongest form, should not be regarded as a general argument against backward causation and closed causal chains. Its significance can be assessed only with respect to specific hypotheses. (“Closed Causal Chains,” p. 267)
Horwich agrees with Lewis that closed causal chains are logically possible. Also, like Lewis, he thinks the existence of closed causal chains might entail strange coincidences and uncaused correlations. For example, each and every time the time traveler tries to murder his grandfather something always goes wrong. This happens no matter how many times he tries. Such coincidences are very strange but aren’t impossible. They are, however, highly improbable. Horwich and Lewis agree that while reversed causation and closed causal chains are possible, they don’t occur in the actual world.
Perhaps the view that best resembles the Doctor’s in the contemporary scholarship is that of Jenann Ismael. Ismael has completed the most detailed analysis of closed causal chains to date, a feat with which the Doctor himself would be impressed. Not only does she agree that the bilking argument doesn’t create a contradiction and closed causal chains are possible, she also thinks that the existence of time travel, including reversed causation and closed causal chains, is probable. She doesn’t even think, as Lewis and Horwich do, that closed causal chains create problematic coincidences. Ismael would be the least surprised of the three, were she to communicate with the Doctor using a causal chain similar to Sally Sparrow’s.
Ismael claims that while it’s true, for example, that something would always prevent the would-be parricidal assassin from succeeding no matter how many times he tried, it involves no strange coincidences, anomalies, or mysterious forces. Such multiple failures only appear strange because we’re focusing on a class of events that already rules success out. Consider, for example, a class consisting of the number of days that I failed to finish grading the midterm exams of my Metaphysics course last semester. When we look at any member of this class there’s always some cause that prevents me from grading the exams on that particular day, but there’s no mysterious force or strange coincidence involved. Each failure to finish grading is produced by perfectly ordinary causal laws. I just focused on a class in which grading the exams was ruled out from the start. Likewise, according to Ismael, failure to kill the grandfather is built into the description of the cases Lewis and Horwich are considering, so no actual anomalies or strange coincidences occur. Thus, closed causal chains aren’t only logically possible but also, given some interpretations of general relativity, physically probable (Ismael, pp. 306-08). The Doctor, of course, would be sympathetic with these claims. The biggest difference between the views of Ismael and the Doctor is that, according to the Doctor, closed causal loops aren’t just probable, they actually exist.
Prognosis
David Lewis provides a four-dimensional model which can be used to expound the Doctor’s brief statements concerning the nature of time. According to the Doctor, the universe is a big four-dimensional ball of wibbly-wobbly space-time. People assume that time is a linear progression of causes and effects because they’re looking at the world only from the point of view of their own personal time. But from the non-linear point of view of external time strange things, such as reversed causation and closed causal chains, can and do occur. These strange features of the universe allow the Doctor to know surprising things, such as what Sally Sparrow will say, long before the event occurs.
The Doctor’s view fits nicely alongside other contemporary views of time travel. This is significant because it means that if the Doctor’s philosophy of time is correct then several contemporary philosophers are on the right track and we now live in the exciting period of history in which the nature of time, at long last, begins to be understood. Like the Doctor, Lewis and Horwich think reversed causation and closed causal chains are possible. Like the Doctor, Ismael thinks that reversed causation and closed causal chains aren’t only possible but also probable. The Doctor takes the next step and proposes that they aren’t only probable but also actual. If the Doctor’s philosophy of time is correct then we live in a very strange world. But as Doctor Who fans, we shouldn’t be surprised.
8
Logically, What Would a Cyberman Do?
GREG LITTMANN
I’m a logician by trade, and if there’s one thing Doctor Who fans know about logicians, it’s that we’re allied with the Cybermen. It is, after all, the Brotherhood of Logicians, presumably our future professional association, who try to take over the Earth by bringing the Cybermen back to life in “The Tomb of the Cybermen” (1967).
As of 2010, none of the professional organizations I belong to are hatching any plots—at least, none that I’m aware of. Yet at some time in the future, according to “Tomb,” it’ll be the logicians who betray the Earth. Why are we doing it? Our leader and top agent, Eric Kleig, explains to Patrick Troughton’s Doctor: “Logic, my dear professor. Logic and power. On Earth, the
Brotherhood of Logicians is the greatest mass-intelligence ever assembled. But that’s not enough by itself. We need power—power to put our ability into action.” Are Kleig and the Brotherhood of Logicians really being logical? The Cyberman Controller thinks so and approves our proposal, telling Kleig, “You are a logician. Our race is also logical. You will be the leader of the new race.”
Logic leads to worse things than that in Doctor Who. The Cybermen are said to be logical creatures—and look how they behave. They’ve become a race of emotionless soldiers devoted to conquering the universe, destroying other species or forcing them to become Cybermen too. Their schemes involving Earth alone include draining Earth of all power in “The Tenth Planet” (1966), sabotaging Earth’s weather in “The Moonbase” (1967), annihilating Earth’s population with a bomb in “Earthshock” (1982), crashing Halley’s comet into us in “Attack of the Cybermen” (1985) and, of course, simply invading to turn us all into Cybermen in “The Invasion” (1968), “Silver Nemesis” (1988), “Rise of the Cybermen” (2006), “The Age of Steel” (2006), “Army of Ghosts” (2006), and “Doomsday” (2006).
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