So now we know the difference between empirical and logical possibility. If something is logically impossible it’s called—as Leonardo said—a logical contradiction. Another example of a logical contradiction would be: 2 + 2 = 5. And yet another example, so many people believe, is time travel.
Time Loops and Paradoxes
Time travel does seem to lead to logical contradictions. In the story “The Invisible Enemy” (1977) Leela is immune to the virus that threatens everybody else in the story. She contributes her anti-bodies, which in turn save the human race. However, it’s from a later stage in the human race’s development that she inherits her immunity (the story is happening in her past). So, Leela is both the cause and the effect of the antibodies: she wouldn’t be there if it weren’t for the anti-bodies, but at the same time, the anti-bodies wouldn’t be there (at the time of her conception) if it weren’t for her.
It’s a paradoxical loop where the anti-bodies don’t seem to have come from anywhere and this is impossible according to our understanding of causation. There’s a similar idea in an Anthony Burgess story, The Muse, in which a character travels back in time and furnishes Shakespeare with all his plays so that Shakespeare simply copies them out. This would mean that nobody actually created Shakespeare’s plays. “Blink” is another example of this in Doctor Who.
Think about it: who wrote his lines on the DVD Easter egg? The Doctor simply reads them from the document he’s been given by Sally Sparrow, and they’re only on the document because Larry Nightingale copied them from the DVD. Again, nobody actually created them.
One of the basic laws of logic is the law of non-contradiction. It states that something can’t both be true and false at the same time. In the story “The Edge of Destruction” (1964), the Doctor and his companions find themselves at the very beginnings of the universe itself, so it’s safe to say that all the non-Gallifreyan characters, Barbara and Ian, are at a point in time before they were born and it would therefore both be true that they had been born and that they had not been born and this does seem to contravene the law of non-contradiction. Philosophers would say: it cannot be the case that it’s true that both ‘p and not p’.
The Doctor (who obviously knows that time travel is possible because he’s spent his entire life time-traveling and that would make it contradictory for him to say that it isn’t possible) might point out here that the above example is just a contradiction of statements. So, you may be contradicting yourself to say these two things but that doesn’t mean they can’t be true. There’s a famous example that bares this out.
The ancient Greek philosopher Zeno of Elea (490 B.C.E.) concocted what the Oxford philosopher Gilbert Ryle has claimed is the quintessential philosophical problem. And what makes it interesting to us is that it’s a logical problem that leads to a contradiction that seems to entail that something couldn’t be true that our experience tells us must be. The problem is called Achilles and the Tortoise. Achilles, the great Greek sprinter, is to race a tortoise. Knowing that the tortoise will be much slower, he gives the tortoise a head start. Now according to mathematics, whatever distance has been covered by Achilles as he races to catch up with the tortoise, there’s a corresponding smaller distance covered by the tortoise. The problem is that the tortoise always moves away by some degree from Achilles however much closer he is to the tortoise. So it seems that logic tells us that Achilles can never overtake the tortoise, but we all know that reality tells us he can.
Just in case you are asking yourself, how does logic tell us that? It’s not clear to me. Then let me try to explain in other words. If you have two objects at some distance apart and then you try to move them closer, geometry tells us that the distance between them can always be halved ad infinitum. But this means that the two objects could never actually reach each other, though quite clearly they can. Is there any way around these contradictions?
The Paradox Machine
The Master, in “The Sound of Drums” (2007) introduces a plot that is potentially paradoxical: the Toclafane—the future descendants of human beings—are brought back in time to destroy their human ancestors, without whom they couldn’t exist. Aware that this is paradoxical, the Master converts the TARDIS into a paradox machine and its purpose is to resolve any paradoxical problems and thereby allow events to occur that would otherwise be cancelled out by a paradox. So, in our attempt to circumvent the paradoxes of time travel, we’re invoking our own paradox machine.
An Australian philosopher, David Lewis (1941-2001), tackled these problems in his article “The Paradoxes of Time Travel.” He believed that there are ways in which time travel stories can be seen as consistent, avoiding paradoxes. Lewis’s implication is that time travel is, at least, logically coherent—that is to say ‘possible’.
The TARDIS Inside and Out
David Lewis suggests that we can overcome the paradox mentioned earlier, with reference to the story “The Edge of Destruction,” where it’s both true and false that Barbara and Ian have been born, by thinking of time in two senses: external and personal time.
External time is the time line that the time traveler is traveling through either backwards or forwards through time, and personal time is the time line of the time traveler themselves that must always be moving forward. So, the Universe’s history (outside the TARDIS) is the external time through which the Doctor moves around, the direction of which is at his discretion, but inside the TARDIS is his personal time that’s always moving forward.
We’ve drawn a distinction between two kinds of time: external time and personal time. Returning to Barbara and Ian’s case in the “Edge of Destruction,” it’s true in her personal time that she has been born and it’s false in external time that she has been born. By drawing a distinction, we’ve avoided contravening the law of non-contradiction.
In “Silence in the Library” (2008) the Doctor meets a character, Professor River Song, who claims to have met his future self. This is quite a momentous event in the Doctor Who series as there are only rare references to his personal time line and almost none to his future incarnations. Another of these rare examples is “Battlefield” (1989) where the seventh incarnation of the Doctor is left a note from a future incarnation in the world of King Arthur where the inhabitants know him as ‘Merlin’.
Does Lewis’s idea make sense? The first question we might ask is: Can we split time into two simply by thinking about it? David Lewis may be guilty of what philosophers call an ad hoc move (literally: for this purpose). This is where you introduce notions simply to get out of a sticky situation or to support something you “like the idea of,” rather than because you think it’s true. One may object to Lewis’s idea by saying that time is a single concept and that logic wouldn’t allow for it to be split into two arbitrarily (if it can be split into two, then why not into three or four?). And we may ask the further question: exactly what reasons does Lewis give for upholding two kinds of time, other than to make sense of time travel for science-fiction geeks like me?
The Paradox of the Time Meddler
In the First Doctor’s serial “The Aztecs” (1964), he repeats the refrain, “But you can’t re-write history! Not one line!” David Lewis would agree and suggests that a consistent time-travel story must have one extra feature as well as this one in order to avoid paradoxes, and that is: the events the time traveler brings about must themselves be the very events that made history as we know it. An example of this in Doctor Who occurs in the story “The Visitation” (1982) in which the events of the story—which includes an alien plot in London of 1666—bring about the Great Fire of London (this fact being disclosed at the story’s end where the camera pans to the street name where the fire has started: ‘Pudding Lane’). This isn’t to be thought of in a fatalistic sense (that the Great Fire of London must happen anyway and whatever events occur will inevitably lead to the realizing of this event), but in the sense that the events of the story are the events that did in fact bring about history as we know it
, and always have been. This avoids the problem of having to introduce strange and inexplicable forces that nurture the events as we know them because they simply are the events that made history. Another example like this is in “The Chase” (1965) in which it’s revealed that the Daleks are responsible for the disappearance of the crew on board the ship that turns out to be the Mary Celeste.
Accepting Lewis’s idea, there follows a problem for the stories in that it excludes those where it’s explicit that causal events are different from history but that the consequent events of history still occur. And it might seem that any interference from a time traveler is likely to cause things to be different in the future if we consider the complexity of causal circumstances. A Whoian example of this kind of problematic story is “The Time Meddler” (1965), which has a mischievous Time Lord character who tries to influence the Battle of Hastings in 1066, unsuccessfully. The crucial point here is that a person deliberately interferes with the facts of history as we know them, but the correct events still occur though the causal chain has been altered.
There’s a very interesting exchange between the Doctor and his companions in “The Reign of Terror” (1964) that considers some of these problems though they all seem to be equally in the dark about it. “Events will happen, just as they are written,” declares the Doctor in his peremptory way that is characteristic of the First Doctor incarnation. “Supposing we’d written Napoleon a letter telling him, you know, some of the things that were going to happen to him,” muses Ian. “It wouldn’t have made any difference, Ian,” replies Susan. “He’d have forgotten it, or lost it, or thought it was written by a maniac.” Barbara then adds: “I suppose if we’d tried to kill him with a gun the bullet would have missed him?” To which the Doctor says, rather vaguely, “Well, it’s hardly fair to speculate, is it?”
The problem of changing history is also hinted at in “The Shakespeare Code” (2007) where Martha is concerned that their being in the past could have devastating consequences, as she notices, “It’s like in the films. You step on a butterfly; you change the future of the human race.” The Doctor simply replies, “Tell you what, then: don’t step on any butterflies. What have butterflies ever done to you?” This being a reference to a Ray Bradbury short story, A Sound of Thunder, in which a character steps on a butterfly in the prehistoric past only to find that this has caused the world in his present to be altered unrecognizably. And this in turn is a reference to chaos theory, which is famous for the idea that a butterfly flapping its wings on one side of the world causes a storm on the other, highlighting the incredible complexity of causal chains.
Another classic paradox of time travel—that Lewis talks about—is also briefly mentioned in “The Shakespeare Code.” Continuing the previous conversation Martha says, “What if ... I don’t know . . . what if I kill my Grandfather?” “Are you planning to?” quips the Doctor facetiously. Martha says, “No,” and the Doctor replies, “Well then,” conveniently avoiding exploring some of the less palatable consequences of time travel. But Martha has hit upon an important problem with time travel: if you kill your own grandfather then you’ve eliminated an essential cause of your own existence. The paradox should be clear.
It would seem to be an unfortunate consequence of time travel stories that allow for even the smallest interference of historic events that they’d inevitably bring about significant changes to future history. But once the time travel story is conceived as the very events that brought about history as we know it then we seem to be left with none of these sorts of problems: history isn’t changed by the meddling time traveler, merely instantiated.
Turn Left
We shall take a left turn here because some people attempt to avoid this problem of the subtleties of time meddling by appealing to the notion of possible worlds and parallel universes.
In philosophy two very commonly used notions are that of contingency and necessity and they’re used in relation to truth. A contingent truth is one that could have been otherwise, and a necessary truth is one that could not have been otherwise. And in order to flesh this out, philosophers talk about possible worlds.
Possible worlds were introduced to philosophy by the German Enlightenment philosopher Gottfried Leibniz (1646-1716). He asserted that ours is “the best of all possible worlds.” This idea was entertainingly ridiculed by Voltaire (1694-1778) in his satirical story Candide. In the story “Turn Left” (2008), we have a good example of a possible world: one in which Donna didn’t meet the Doctor and as a result, a whole bunch of other things happen to her. The events that occur in the possible world of “Turn Left” are contingent: that is to say they’re events that we have no problem conceiving as being able to happen but are events that didn’t happen in the ‘real world’. It’s perfectly conceivable that Donna turns right at the junction instead of left. Whenever you do something where it’s conceivable that you could have done otherwise, philosophers say that there is a possible world in which you did turn right instead of left.
Philosophers aren’t suggesting that these possible worlds are actual and exist somewhere in a parallel universe but that they’re conceivable. Philosophers would express this by saying that possible worlds are a logical construction and not actual.... All philosophers, that is, except the Doctor and David Lewis.
Actual Actualists
The Doctor and David Lewis are what are known as actualists about possible worlds: they believe that possible worlds actually exist, and one way of conceiving of this—certainly for the purposes of exploring the possibility of time travel—is that every time a contingent event occurs, such as making a decision to turn right instead of left, possible worlds are created where the contingent events that you didn’t instantiate are instantiated. It’s as if time-streams split to realize all the different contingencies that are possible. This is dealt with in the series when explaining how the different incarnations of the Doctor meet in the multiple-Doctor stories such as “The Three Doctors” (1973).
Strictly speaking, there is an important distinction between possible worlds and parallel universes as possible worlds are logical and parallel universes are actual. This distinction is blurred, however, when we introduce possible world-actualists, such as Lewis.
Alternative Time
There’s a fascinating discussion between the Doctor and Sarah in “Pyramids of Mars” (1975) where they’re discussing whether or not they need to stop the evil Sutekh from his attempt to destroy the world in 1911. Aware that she’s from 1980 Sarah says, “But he [Sutekh] didn’t, did he? I mean we know the world didn’t end in 1911.” Using the TARDIS, the Doctor shows her the future as it would be if they don’t stop him and it’s like the distant future visited by the time traveler in H.G. Wells’s The Time Machine: “A desolate planet circling a dead sun,” as the Doctor says. He then makes an explicit reference to alternative futures that seems to imply the existence of parallel universes in the Doctor Who universe: “Every point in time has its alternative, Sarah. You’ve looked into alternative time.”
The Doctor is an actualist because he has traveled into possible worlds and therefore has personal experience of their existence, notably in “Inferno” (1970), “Rise of the Cybermen” (2006), and, of course, “Turn Left.” This is therefore more of a scientific hypothesis than a philosophical one, and this brings me to the scientific entity of parallel universes, which have been hypothesized because of some unusual behavior in sub-atomic particles that can apparently only be explained by the existence of parallel universes. (It’s important to understand that this isn’t proof of parallel universes but is only a hypothesis). David Lewis is an actualist for purely philosophical reasons that I shall not go into. Suffice it to say that he’s unique among philosophers for holding this view. And the Doctor loves a maverick. As Doctor Who fans, we’re also actualists about possible worlds for no other reason than it’s fun and it allows many of the Doctor Who stories to make sense. But what has it got to do with our paradox machine?
Well, if there are parallel universes then this may get us out of the problem of time loops and the problems of time meddling, because if changes to the events of history inevitably create changes to our present then the changed events and the unchanged could conceivably co-exist, albeit in parallel universes. So, whenever a time traveler goes back in time and turns right instead of left, the subsequent chain of events spin off into an alternative parallel universe and thereby avoid paradoxes (and allow for the possibility of more spin-off series—because there aren’t enough already).
We Wouldn’t Be Here Without Time Travel
According to the story “City of Death” (1979), not only is time travel possible for human beings (and not just Time Lords and Ladies), but it turns out that time travel is essential for the existence of the human race. It’s an explosion caused by the villain of the story, Scaroth (the last of the Jagaroth), that contributes the essential radiation that brings about life in our solar system, and although a possible paradox looms in the story—with Scaroth encouraging and using human-made time travel to try to avert the explosion which would thereby eliminate the causal factor that enables him to do this—it’s avoided by the thwarting of Scaroth’s plans by Duggan punching him (a disconcertingly prosaic explanation for life on Earth) and so is a consistent time travel story according to Lewis’s conditions.
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