Incompatible Arrows, I: Martin Amis

By Sean Carroll | March 31, 2008 10:35 am

Reverse chronology — narrating a story, or parts of one, backwards in time — is a venerable technique in literature, going back at least as far as Virgil’s Aeneid. Much more interesting is a story with incompatible arrows of time: some characters live “backwards” while others experience life normally.

Probably the most famous contemporary example is Martin Amis’s chilling novel, Time’s Arrow.

Eating is unattractive too… Various items get gulped into my mouth, and after skillful massage with tongue and teeth I transfer them to the plate for additional sculpture with knife and fork and spoon. That bit’s quite therapeutic at least, unless you’re having soup or something, which can be a real sentence. Next you face the laborious business of cooling, of reassembly, of storage, before the return of these foodstuffs to the Superette, where, admittedly, I am promptly and generously reimbursed for my pains. Then you tool down the aisles, with trolley or basket, returning each can and packet to its rightful place.

The narrator of Time’s Arrow is a disembodied consciousness who lives inside another person, Odilo Unverdorben. The host lives life in the ordinary sense, forward in time, but the homunculus narrator experiences everything backwards – his first memory is Unverdorben’s death (although, for expository purposes, he comes into existence as a full, speaking intellect). He has no control over Unverdorben’s actions, nor access to his memories, but passively travels through life in reverse order. At first Unverdorben (going under the name of “Tod Friendly”) appears to us as a doctor, which seems like a morbid occupation – patients shuffle into the emergency room, where the doctors suck medicines out of their bodies and rip off their bandages, sending them out into the night bleeding and screaming. But near the end of the book, we learn that Unverdorben was an assistant at Auschwitz, where he created life where none had been before – turning chemicals and electricity and corpses into living persons. Only now, thinks the narrator, does the world finally make sense.

  • Richard E.

    My favorite example is Billy Pilgrim (Slaughterhouse Five), who lives his life going forwards, but out of order: “Billy is spastic in time, has no control over where he is going next and the trips aren’t necessarily fun. He is in a constant state of stage fight, he says, because he never knows what part of his life he is going to have to act in next.”

  • John Merryman

    Time does go in both directions.
    While physical reality goes from past events to future ones, the information of these events goes the other way. First it is future potential, then past circumstance. If time is a fundamental dimension, then physical reality proceeds along it, from past events to future ones, but if time is a consequence of motion, then physical reality is simply energy in space and the events, once created, are replaced by the next and recede into the past. It isn’t presentism because time as a point would be meaningless as a measure of motion. The only absolute time would be like absolute temperature; the complete absence of it. Of course most motion is at the speed of light, but we cannot process it in real time, so our minds create flashes of perception, like frames of film. Thus to us, time does seem like a series of instants. So the physical brain moves forward in time, but the mind is a record of the events receding into the past.

    Consider a thermal medium, say a pot of hot water, with lots of water molecules moving about. To construct a timekeeping device out of this we would measure the motion of one of these points of reference against the medium it is moving through. The point is the hand and the medium is the face of the clock. Obviously all the other points are hands of their own clocks, but are medium/face for all other clocks. The motion of any point/hand is balanced by the reaction of the medium/face of the clock. So to the hand of the clock, the face goes counterclockwise. At any one moment, the positions of all these points constitute an event, so while any and all of them go from past events to future ones, the medium against which any point is being judged is the overall context, which once created, is displaced by the next, as all these individual points move around, so the events go from future potential to past circumstance. The illusion of direction is created because the reference point moves through the series of circumstances, though these events go the other way. There are innumerable points of reference describing their own narrative, so every potential clock constitutes its own measure of time. Whether the earth rotating and creating days, or a cesium atom going through transitions, or strings and vibrations, conserved energy goes toward the future, as the information defining it recedes into the past.

  • John R Ramsden

    There’s also a very gross recent (2002) French film called Irreversible.
    [ ]

    Thought I’d mention it for completeness, given the theme of this discussion, but can’t think of any other reason it deserves publicity.

  • Andy

    On a less cerebral note: The Red Dwarf book uses a similar device in which the characters’ time runs backwards. It seems to me that there are some unfotunate paradoxes in the plot/concept – it helps if you try not to think about them too much. Nevertheless, it’s a good comedy.

  • Andy

    Messed up the link, sorry


  • jackd

    The character of Merlin in T.H. White’s The Once and Future King is also living backward, but White doesn’t press it – it’s kind of a conceit he uses whenever he wants to.

    There’s also a character named Rachel in Dan Simmons’ Hyperion who is caught in a “time tide” (named but never described) which causes her to age backward. In the setting of the novel she is an infant. Her father’s retelling of their story is heartbreaking.

  • cinyc


  • B

    To add a piece of irrelevant information: ‘unverdorben’ means ‘ingenuous’.

  • Ben

    The narrator of Sean O’Faolain’s novel “And Again?” relives his life in reverse from death to birth. I’ve been a little surprised that nobody ever mentions this novel (from 1979) when reviewing Amis’s “Time’s Arrow” since they seem quite clearly related, though O’Faolain’s is closer to autobiography and there is no Amis-Holocaust-shock value component.

  • No. 9

    ?wolp eht evigrof mrow tuc eht seoD .dnatsredu ot detimil ot tsuj si dnim rouY !cinyc ,hO

  • Steve

    By the Way, Imagine you could trace a trajectory in space
    who could counteract all the movements to which we are
    subjected, so we could stand still motionless in a point
    in the universe. What would happen to our time?.
    Is it not very similar to be flying at c where time gets
    Some one to answer?

  • Jason Grossman

    Surely someone’s going to mention Greg Egan’s masterful story “The Hundred Light-Year Diary” (from his book Axiomatic)?

  • Matt

    I had an idea once, of what if we all experience “now”, our consciousness at this moment, at entirely different points. So, from my perspective, the rest of you are robots, locked in place, while someone else’s “now” is yesterday for me. Anyway, pointless idea, just kind of interesting to consider.

  • Neil B.

    I’m sure arrows of time going in different directions are incompatible. Consider again the weird thought experiment I posed before in the “Arrow of Time FAQ”:

    Suppose I could intervene in a time-reversed world W’. I could deflect a bullet that (to me) had popped out of a tree it “hit”, and then – instead of reentering the gun barrel, it would smack into maybe some other tree that it shouldn’t be “coming out of” from the point of view of W’. That would be weird, and it would ruin the whole “past” of W’. Well, we think our own past has already happened, so what if (if time flow really is relative) some Being did that to us, how could it possibly alter our past? Food for thought. I figure, worlds either can’t be intervened in from the outside, or time flow is absolute.

  • Lawrence B. Crowell

    My posts are not showing up here for some reason. So this is a bit of a test and I will make it short. The basic dynamical equations are time reversal invariant, such as Newton’s second law of motion. Yet for a large number of particles or states we have to approximate things and use statistics. The H-theorem of statistical mechanics is used and we then compute thermodynamic variables such as temperature, pressure and entropy. These are time irreversible. Yet, as statistical mechanics is based on a Bayesian system it then appears that thermodynamics and time irreversibility is a subjective aspect of nature. Mind you it is stiff and perpetual motion machines are still outlawed, but it is probably due to our observer perspective which we model with coarse graining.

    Lawrence B. Crowell

  • Freiddie

    It’s hard to think how energy flows, now that entropy *decreases*.

  • Bad

    The chilling thoughts in Time’s Arrow are not just the backward narrative, but the realization that as far as we know, we could well have multiple “experiencing” beings in one brain/mind, all unaware and isolated from each other, but perhaps all experiencing different aspects of reality (for instance, our lower brain could have its own primitive consciousness separate from what we consider “us”). A backwards consciousness is just one of many many possibilities.

  • Eugene

    Aww Spoilers!

  • Mattie

    Trolls experience time in reverse, too.

  • ObsessiveMathsFreak

    If this thread ends up in NODNOL, I hope Kryton is around to translate the papers.

  • John R Ramsden

    There have been times after being woken by the abrupt onset of some sound, such as an alarm, when I’ve had a clear recollection of an interrupted dream in which the same sound occured as the natural culmination of what seemed a logical progression of events.

    Now I don’t believe in premonitions, and my body clock isn’t accurate to anticipate the morning alarm to the nearest second. So it seems the most likely explanation is that the alarm has triggered a fast sequence of “reverse inferences”, subsequently recalled in the opposite order as a meaningful plot.

    I wouldn’t be surprised if most dreams actually run in reverse, in so far as they unwind previous wakful experiences or occur in response to external stimuli (or internal for that matter, such as from the brain stem).

  • The Almighty Bob

    Mattie: they visualise time in reverse, not experience it.

  • Reginald Selkirk

    Eating is unattractive too

    The unattractiveness of eating in that context pales in comparison to that of bowel movements.

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  • Adam P

    Okay, so I know it’s gross to think about but the bowel movement made me wonder. How is physics affected by time in reverse? Relative to the people that experience the reversed time they would certainly find a different set of theories that attempt to explain the world around them right?

  • Reginald Selkirk

    Relative to the people that experience the reversed time they would certainly find a different set of theories that attempt to explain the world around them right?

    Not necessarily. They might rejoice in and worship the mystery, and persecute anyone who tried to make sense of it. Some things are polarity-neutral.

  • Ross Presser

    One more example, not so masterful: Bearing An Hourglass by Piers Anthony. Contains at least one extended scene where the hero’s arrow is opposed to everyone else’s &emdash; although he fudges a bit, making people who interact with the narrator have their arrow’s “partially” reversed. (He has a conversation with a woman, whose sentences are backwards but progress forward in paragraphs; she eats backwards but speaks forward (sound travels from her mouth to the hero’s ear), etc.

  • jeff

    …Just to elaborate a little on my last post: I once had a memorable experience that I’m sure many others have also had. I was anesthetized for several hours while my wisdom teeth were removed. The amazing thing was that those hours went by instantaneously for me. I was asked to count backwards from 100, and when I got to 97 the doctor said, “We’re done!” It was disorienting and hard to believe. A completely dreamless sleep. A sharp temporal discontinuity
    – like a robot being turned off and on again.

    When I recall that experience, I wonder if death might be like that – the ultimate temporal discontinuity. When you are dead, any finite amount of time will pass instantaneously. Twenty billion years or eight hundred googleplex years, it doesn’t matter. As far as we know, consciousness ends permanently at death, effectively erasing time and pulling the plug on the universe. As long as it’s finite, the universe will be over and gone as if it had never existed. A brief dream, and a dream without a dreamer has no chance of being remembered. On the other hand, if time extends infinitely into the future…

  • jeff

    (Sorry! That last post should have been in incompatible arrows II)

  • Shanth

    There’s also the character Janus Poluektovich in the Strugatsky brothers’ Monday begins on Saturday, who goes through time in a piecewise continuous fashion, living each day normally, and then jumping to the previous day at midnight. It’s a delightful book overall.

  • Randy

    I’m surprised nobody has mentioned the movie “Memento” yet, probably the most well-known recent example. It’s developed a large fan base.

    There also was a Seinfeld episode that took place in recent order. The plot involved a trip that the characters took to India for a wedding.

  • Rat Poison

    Surely we can take a relativistic position and say that for any given event there is a future which can be signalled and a past from which signals may be received? The “arrowhead” of the arrow of time associated with such an event just points towards the future for our mental convenience.

    Observation is concerned with the past; anything that can receive a signal is a potential observer, and anything that receives such a signal is an actual observer. This applies to classical events as well as quantum ones.

    Signalling is concerned with the future; anything that may generate a signal is a potential actor, anything that generates a signal is an actual actor. Again, this applies to classical events as well as quantum ones.

    For our own convenience we connect actual actors to appropriate actual observers with unidirectional arrows, and call those connections causal relationships. We consider potential interactions similarly – connecting actual or potential actors to potential observers with unidirectional arrows.

    Again for convenience (“tractability”) we reduce large sets of these unidirectional arrows, using aggregation, probabilistic approximations, and other arrow-hiding techniques. We do this day in and day out in our classical lives, as well as when studying QM. We do this consciously and unconsciously, and we really lack the facilities to *not* do this on a large scale.

    We have little difficulty aggregating mildly disjoint sets of causal relationships, such as those involving different, spatially-separated actual observers. We do this regularly in our own heads – as an example, most of us excel at aggregating lots of little photon-hits-photopsin-just-right events in our retina into a single flash of light. We aggregate ourselves into a single actual observer of a single actual actor, observing a flash of lightning, and usually do not (and probably cannot *completely*) consider each discrete actor-observer relationship that we see first-second-third-or-nth hand, as excited particle releases hot photon, which in turn excites another particle or is scattered, and so on, all the way to the air proximal to our corneas, through our lenses and intraocular media, and into the retinal cell where a protein is deformed. We also don’t consider the actual result of the deformation (we generally assume a signal transduction is the result), and generally have a poor idea of nanoscopic behaviours from there all the way to the visual cortex, and practically no small-scale idea about what happens from that point at all.

    We “see” one event and think of it as one event, although that is a conspiracy involving probabilities of observation by flash-detecting molecules, and how reliable their communication of such observations “into the future” are, which in turn depends on the probabililties of detecting those signals, and generating their own.

    We readily impose our own approximation of causal relationships on observers nearby. We assume that other people nearby see a similar flash, and can make assumptions about the behaviours of non-people observers that reflect, scatter, or absorb signals related to the flash, and assume that everything nearby has a substantially similar relationship to that particular past set of events.

    What happens if we try to break this pattern of thinking?

    We’ve studied QM philosophical problems involving deliberately delaying the connection between actual event and potential observer in the form of cats and puppies, not to mention experiments involving extremely high refractive indices, and day to day experience with long optical fibre runs or communications that detour through a geosynchronous sattelite, meteor burst, or suitably reflective astronomical object (the moon has been done). Astronomers see even longer delays in one-way paths from events, and cosmologists are pretty keen on observations which provide geodesics of dramatically different lengths from closely related events to terrestrial observers.

    These causal relationships are all still unidirectional — same arrowhead, but somewhat different shafts.

    This lets us consider very warped causal relationships, where a signal we generate now is received very quickly by a spatially separated observer along path “A”, whose observation is immediately signalled back along path “B”, which is much much slower. Other tricks for manipulating worldlines lead us into the realm of whether CTCs can exist.

    Correlating actor/observer interactions is useful for a variety of reasons, and a “privileged aggregation” is an attractive coordinate system. Interactions within the CMBR are obviously attractive, and many cosmologists use the idea of other cosmologists who “see” the CMBR in various ways (such as with no dipole anisotropy) as a way of exploring questions involving a variety of correlated observations we make locally. If we figure that there is a universally-available privileged view of the evolution of the CMBR, and use that as a “universal” arrow of time, then we *can* ask questions about observations available to potential observers that would have views of the CMBR with *huge* dipole anisotropies.

    The salient questions to me are:

    * assuming there is some privileged “universally agreeable” time coordinate system
    * assuming that the time coordinate system will *typically* be perceived as monotonic increasing, or mappable to such a perception, for observers we can reason about

    (a) what would be the potential observations available to an entity (human, classical or quantum) with an “extreme” mapping, and (b) can a mapping be “extreme” enough to be considered a reversal?

    Stepping back into a more relativized causality, what kind of interaction could an observer with a receive-from-past/transmits-to-future “direction” which is close to our conventional aggregates have with us?

    If a potential interaction is possible, can we transmit a backwards-moving observer some information we have in turn received “conventionally” from our past? What would that observer learn?

  • Rat Poison

    Stepping back into a more relativized causality, what kind of interaction could an observer with a receive-from-past/transmits-to-future “direction” which is close to our conventional aggregates have with us?


    … “which is NOT close to” or “which is close to the REVERSE of” our conventional aggregates…

    Sometimes the metabolic half-life of caffeine is too short!

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  • Dualist

    Very interesting. Can’t resist to read later parts.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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