Science Fiction Studies

#66 = Volume 22, Part 2 = July 1995

George Slusser and Danièle Chatelain

Spacetime Geometries: Time Travel and the Modern Geometrical Narrative

We wish to consider the synchronous appearance of two very similar narrative forms—time travel and the geometrical narrative—in unconnected venues— science fiction on one hand, “experimental” modernist fiction on the other— and to examine the implications of this synchronicity. As we will see, both forms, in their respective currents, are considered radical. Radical in the manner in which, even in the general context of reaction against traditional realist fiction, each seems to reduce narrative to the sparse outlines of a logical game.                

Time travel is accepted, by consensus, as sf. Yet writers as diverse as Stanislaw Lem and Larry Niven take pleasure in rejecting it, even in the act of writing it. Lem calls time travel “an intellectual game, fantasy making which alters in a logical or pseudo-logical manner current scientific hypotheses.”1 To Niven, it “violates too many of the laws of physics and's a form of fantasy superbly suited to the games of logic.”2 Both, of course, are merely paying lip service to the accepted view that sf must respect the tenets and methods of science, and that the logic of science is empirical, not “intellectual” in nature. Dr Robert L. Forward seems to deliver the coup de grace: “Anything that produces logical paradoxes is not science. Time machines produce logical paradoxes. Therefore, if time machines exist, they must use magic, not science.”3 When we think however of all the time travel stories written (and still being written) by sf writers, we realize this is just so much rhetoric, one that exonerates writers from thinking (out loud at least) about the possible relationships between logical and physical paradoxes.                

In the mainstream modernist tradition, as well, there is a strong subcurrent that subjects the empirical stuff of narrative to logical or “geometrical” forms, be it the elegant balance of the equation, or perfection of the circle or loop. The current is, first of all, part of an international modernist movement. Early in the century, Kafka dislocates narrative by recounting irrational or absurd situations in hyper-logical, in some cases geometrical language.4 Paul Valéry calls for the reduction of such “realist” devices as plot and character to bare equations, a play of pure relationships. Slightly later Borges, in his narrative paradoxes, combines absurdity with geometry to turn story into a particular kind of game played with reader and reality. The current blossoms however in the French New Novel and anti-theater of the 1950s, in writers like Robbe-Grillet, Butor, Ionesco, achieving theoretical formulation in Jean Ricardou's books on the “nouveau roman.” By a curious synchronicity, we can trace an analogous development in the case of time travel, as it evolved within the hermetic matrix of American pulp sf. We find, mostly in the didactic parts of pulp stories in the late 1920s-1930s, endless fascination with time games and paradoxes. Ingenious forms are devised in the 1940s and 1950s to “tell the paradox.” Finally, interest in such geometrical ingenuity seems to fade in the 1960s (Damon Knight writing in 1962 concedes as of then the difficulty of inventing new twists on the old paradox).5 Sf's “exhaustion” with time travel, then, seems co-temporaneous with the passing from modernist to “post-modernist,” the latter's abandonment of purely formalist concerns.                

These similarities are intriguing. They make a minor point: that no ghetto is an island, and sf is not to be excluded from the deep currents of change in narrative forms in this century. They suggest, however, a larger issue: namely, that this “geometrizing” of narrative answers, it seems, to a general need to complicate the space-time relationship insofar as it provides the frame for human actions. The complicating factor is logic, translated here as the means, both in the sense of play and experiment, of shaping human experience into forms that, when contrasted to the old sense of a linear life-line, are paradoxical in nature, “beyond what is thought.”               

The differences, however, are more interesting yet. Comparison of time travel with the modernist geometrical narrative brings to light a relation not readily apparent in the “games” of the latter: that of human logic to material spacetime. In both forms, time is said to be subject to logical manipulation. But these forms have, each of them, quite different cultural contexts. What does it mean for the modernist to “manipulate” time? More importantly, what can this mean in terms of the resolutely empirical or “physical” imperative that traditionally governs sf? To answer these questions is to offer significant insight into the nature and extent of so-called “experimentation” with spacetime categories in modern narrative.                

Our analysis centers on two parallel stories, both published in 1941, and both “classics,” one of modernist geometrical narrative, the other of time travel: Jorge Luis Borges's “Death and the Compass,” and Robert Heinlein's “By His Bootstraps.” The stories are similar in converting traditional narrative categories—the relation of “plot” and “character” to a chronologically determined event—into a set of logical relationships, whose sole “meaning” lies in the clever working out of a conundrum or paradox. Yet, when examined against their respective cultural backgrounds, we see two very different senses of temporal paradox here. These, in turn, translate quite opposite views of the relation of mind to material reality. The result of Borges's game with time is a rejection of fabula, or material history, and the substitution of a mental, thus quasi-metaphysical, itinerary for the causal “chain” of events that limits human action. Heinlein's use of logical or geometrical figures in narrating his time paradox, however, has an opposite purpose. The “game” here is less a means of rejecting fabula, than of engaging a new, and physical, sense of its nature.  Forward speaks as scientist and sf writer when, in the end, he admits that temporal paradox is a function both of logic and the material world: “Two of the most respected...theories of physics, the Einstein Theory of Special Relativity and the Einstein Theory of General Relativity, allow time to be manipulated.” Heinlein's story, however logical, unlike Borges at, the same time resembles a physical experiment: “travel” is literal; the protagonist steps bodily through a “time gate” and must experience his spacetime curves in the flesh. In a sense, the paradox here is less in the geometry than in the fact that Heinlein is able to narrate such Einsteinian manipulations successfully within the Newtonian limits of conventional narrative, where space is separate from time, and sequency and simultaneity incompatible: one person cannot be in two places at once.

1. Modernism's “Geometrical” Narrative. Modernists rejected traditional categories of narrative because these were no longer felt to correspond to modern ways of seeing and representing the world. Nathalie Sarraute defines what is meant by “traditional” in her refusal to “tell a story where one watches characters act and live” [raconter une histoire où l'on voit agir et vivre des personnages].6 But once story is freed of the “tyranny” of motive and causality, of chronology and historical event, what provides its structure and order? A pervasive means of getting rid of this 19th century “sense of life” is to subject human sentiments to the rigor of a logical proposition, and human actions to the elegant regularity of numerical series or geometrical figures. Narrative now obeys no higher law than a formal structure that, because it exists only in and for itself, is stripped of deterministic or fatalistic connotations. To “plot” a story then, in accordance with logical or geometrical propositions, is little more than a game, where fictionality is reduced to the proposition or  riddle, and things like climax and denouement become examples of inversion of proportionality, or tracings of perfect yet arbitrary forms like the circle or spiral.                

The most radical spokesman for this view, in France, is Jean Ricardou. His 1972 manifesto, Le nouveau roman, traces the idea back to Paul Valéry's famous reduction of narrative to a “mathematical” proposition:

Je vis une ligne et deux points sur cette ligne. Qui dira comment ce A et ce B sont devenus Hortense et Henri? Moins hasard, eux?—Une loi existait entre ses deux points. Une loi toute mathématique. L'un aimait l'autre—quand il en était près—et l'autre aimait l'un quand elle en était loin. Aimer—naturellement, je ne sais pas ce que c'est et n'approfondirai pas.” [“I posit a line, and two points on that line. Who can tell me how this point A and point B came to be called Hortense and Henri? Are they there by chance? No. A law exists that links these two points to each other. But it is a wholly mathematical law. One was in love with the other —when he was near the one he loved—and the other was in love with the one when that one [she] was far away. All I know is this inverse proportionality. What “to love” is, naturally I don't know what it is and don't want to go any deeper in the matter.”]7

The “New Novelists” were not to implement this theory until (at the very earliest) the late 1940s; indeed Ricardou's analysis begins with the first published novels of Robbe-Grillet and Butor. Yet, in a way somewhat like the sf “workshop,” these ideas were in ferment long before. First of all, as Pierre Astier tells us (and the dates in Ricardou's “bibliographie” confirm), the New Novelists were conceiving and writing long before they saw print.8 Moreover, the older writers in this group, like Nathalie Sarraute, were well aware of efforts of earlier writers in this direction. The first essay in her collection, L'Ere du soupçon, “De Dostoievski à Kafka,” first published in 1947, rediscovers the fictional games and parables of the latter.9 Finally, simultaneous with the ongoing theoretical pronouncements of Valéry, were those of the surrealists. Their direction is more ambiguous. In the Manifeste du surréalisme, the realist novel is rejected in terms that remind us of Valéry's reduction of plot and character to A + B = C. At the same time, as Maurice Nadeau tells us, the surrealists steadfastly reject a fiction of pure logic.10 Nevertheless, we see all this didactic activity (for and against) leading to fictional works, in Borges and in Ricardou's writers, in which human experience is subjected to geometrical forms.                

Ricardou's book is a fascinating compendium of graphs and diagrams, showing the regular (and predictable) figures that  replace plot and character. The choice of texts is selective (are all French new novels so radically reducible?), but the geometric  structures of the works analyzed very real. Focusing on Robbe-Grillet's first novel Les gommes (1953), Ricardou plots the trajectory of its narrative as a spiral which graphs precisely 36 hours in the life of an “inverted Oedipus.” Robbe-Grillet (he argues) consciously inverts the riddle of the Sphinx (“aveugle le matin, inceste à midi, parricide le soir”). Wallas the detective investigates the murder of a certain Professor Dupont that took place at 18:30 hours. Wallas does not know that the murder was faked, nor that Dupont is possibly his father. It is his investigation that leads him, in exactly 24 hours, both to meet (and covet) a possible mother, and to commit a murder that really kills Dupont, at precisely 18:30 hours the next day, the very moment when his watch, which stopped 24 hours earlier, starts to tell time again. Sophocles' protagonist discovers, with tragic consequences, that he is the “evildoer” he set out to find, a man caught in a fatal web of events. Robbe-Grillet's protagonist catches up only in the end with his mythical crime, yet remains unaware that he has committed it. Robbe-Grillet's intention, clearly, is to replace the structure of human drama with geometrical and numerical relationships that seem self-generating. Bruce Morrissette describes Robbe-Grillet's plan for an earlier (unrealized) narrative, to be constructed around “108 elements (or narremes?) corresponding to the 108 scales on the body of the serpent Ouroboros.”11 Indeed, a like fascination with arbitrary relationships —puzzles, anagrams, numerological oddities—marks Robbe-Grillet's use of “objective correlatives,” here between the Oedipus story and the modern murder of Dupont. Morrissette signals, as example, an inscription under a randomly encountered statue: “`Le Char de l'Etat—V. Daulis, sculpteur,' an anagram for Laius, father of Oedipus, killed in his chariot.”                

Ricardou meticulously plots the fearful symmetry of other contemporary fictions. Michel Butor's La Modification is described thus: “Un proverbe retourné, `loin des yeux, près du coeur,' peut résumer cette relation inversement proportionnelle qui lie proximité spatiale et proximité sentimentale.” (52) For the same novel he produces a graph that traces the slight variations in a regular pattern of episodes, variations of five identifiable time moments, designated in their periodic recurrence by the letters A,B,C,D,E. The design for Claude Ollier's novel, La mise en scène (1959) is a circle, “un espace symmétrique” that the protagonist traces “selon le sens giratoire de droite.” Ollier uses the same geometrical language to describe his later “sf” novel La Vie sur Epsilon (1972): “[ce roman] repasse par les points qui définissent les coordonnées de La mise en scène. Mais le système a été mis sur orbite, c'est dans un autre espace qu'il accomplit maintenant ses révolutions.”12 Ricardou's readings are perhaps reductionist, but they make clear that there was a real penchant for such narrative geometry in French modernist fiction of the 1950s, which continued in writers like Ollier, and metamorphosed into diagrammatic verbal charades in Ricardou's own fiction, such as La Prise de Constantinople (1965). This fascination went beyond this “new” prose fiction in the 1950s: witness Ionesco's play La Cantatrice chauve, the “anti-play” first performed in 1950. “Characters” here are ciphers: a Mr and Mrs Smith and Mr and Mrs Martin. It was purported that dialogue was randomly lifted from the “Méthode Assimil d'Anglais,” a popular language-instruction method, as is the “Englishness” of the setting, which exists in a totally confused spacetime (“La pendule frappe dix-sept coups anglais.” Mme Smith: “Tiens, il est neuf heures”). Yet all is bound by an inexorable logic of the loop: the play begins with Mr and Mrs Smith sitting in their English parlor about to begin a “soirée anglaise”; it ends with Mr and Mrs Martin sitting in exactly the same situation, about to recommence the same evening. There has been an inversion of names, but roles are the same—and the anti-play promises to be neverending, with meaningless action looping forever around this meaningless yet inexorable exchange of “positions.” Ionesco's next play, La Leçon (performed 1951), offers a variation on this figure. The “intrigue” of the play is a structure diagrammed in a long set of stage directions that preface the action. These tell us we are about to witness an encounter between teacher and pupil that is an exact inverse proportion. And lo, the pupil arrives, a self-assured girl who faces a shy and confused teacher. Gradually her assurance turns to cringing passivity, while in directly inverse fashion the teacher becomes increasingly cruel and domineering. In the end the teacher kills the pupil. But there is no end, for the doorbell rings, and a new aggressive pupil stands facing a once-again timid professor. Circular, yes, for it is the same actress and actor playing these “new” characters. But as the play was staged under Ionesco's direction, the maid, hearing the doorbell announcing the new pupil, picks up the notebook of the one before, and tosses it in a pile of such notebooks in a corner. We are promised endless repetition of this scene. But is it the same scene, for though the notebooks are all identical, there is a different one each time, which at the very least implies a series of identical scenes? The play inscribes a structure much like that of a Moebius band.

2. Synchronicity: The Time Travel Story. The development of the time travel story, as analogous game structure, follows a path that, if separate, is quite parallel. Time travel develops in an almost self-contained milieu, in the sf pulp magazine “ghetto” that is, in the 1920s and 1930s, totally impervious to the work of a Valéry. Yet we witness, in this milieu, a same fascination with the figures and geometries of spacetime, again irrespective of any concern with psychological “realism.”  Hugo Gernsback officially introduced the “scientifiction” reader to The Time Machine in May, 1927. Yet the arcana of temporal paradox was discussed in popular science magazines, such as Gernsback's Science and Invention, on many occasions much earlier. And from the inception of Amazing Stories, we note continuous interest, both in editorial comments and letters, and in stories, in time travel. There was a spate of such stories that, throughout the decade of the 1930s, marked the transition from Amazing to Campbell's Astounding Science Fiction, the venue in which Heinlein's “By His Bootstraps” appeared in October 1941. A surprising appearance, because a look at the stories that preceded it gives no hint of the technical or “geometrical” sophistication that this narrative, by telling rather than merely describing the time paradox, achieves.                

Many stories that deal with spatiotemporal distortions appear in the pulps during the 1920s and 1930s. We identified 40 or so such stories in a quick search. R.D. Mullen, in a personal communication, found twice as many.13 Most are full of ingenious speculation on time travel; in all cases, however, theory is presented didactically. Time travel remains a pretext for, or vehicle that activates, conventional romance or adventure narratives. Never is it the structure of the narrative itself.               

As example, let us look at the first story on Mullen's list: G. Peyton Wertenbaker's “The Man from the Atom.”14 We see this story as something like a relativistic variation of Swiftian proportionality.15 Mullen calls it a “clock effect” story, and adds this comment: “If atoms are solar systems within a universe which is part of the atomic structure of a larger universe, and if our solar system is an atom in a larger universe, then time must move infinitely faster here than there.”16 In this story however, the fascinating speculations serve primarily to fuel a conventional romance plot. Time travel (which should detail the “effects” of clock-effect on the people involved) becomes simply a means of bouncing around the Einsteinian universe trying to get back to the girl you love. Kirby has an oddly Newtonian desire to go home, “to take the size God intended I should have,” forgetting of course that, for him, size is not independent of time. Shrinking returns him (as in the Twins' Paradox) to a time frame where, relative to his “large” world, millions of years have passed. All is not lost however, for he finds a planet of humanoid beings— attractive and, of course, highly advanced—and falls in love with Vinda. These people know “Einstein's theory of the curvature of [space]time.” Time is cyclical, and his hosts help him calculate a size-time “trajectory” that will take him home, at least to the corresponding world on the next cycle, which bears the designation 1848 rather than the original 1943. But as these cycles prove progressive, he meets here an advanced version of Professor Martyn, the man who first sent him on his size-time quest. The story ends with Martyn  having fine-calibrated to the point that he promises to return Kirby to Vinda—the same Vinda.17  Up to this point, the narrative, with its past tense, reads like the tale of a dream (“I never hoped—never dreamed, when I wrote the tale you have read, that I should ever see Earth again”). It ends with pure wish and speculation. The possibility of finding another version of himself in this nearly-same world, and perhaps fighting a duel for the hand of Vinda, will complicate this future quest. Once again, the subject, what structures the narrative, is not the spacetime geometry in and for itself, but the imperatives of love and adventure. Narrative is located either in a retrospective past, or in a speculative future. We will have to wait until Heinlein before the sequency-simultaneity paradox becomes an actual, existential situation for a character.

3. Time Travel as Logical Game: Wells and Heinlein. We have an analogy, in terms of gestation, between the geometrical narratives of time travel and those of mainstream modernist fiction. In both cases, a theoretical or didactic “underground” prepares the way to formal experiment. But the question of passage from shadow to act remains. It seems indeed that no sf story previous to Heinlein's “Bootstraps” displays the narrative rigor of its spacetime figures. Plausibly, an idea in some didactic passage in a text, or editorial comment, could have sparked the story.18 There is, however, a possible narrative model for Heinlein's particular spacetime geometry, and it is found in a far more obvious place—Wells's Time Machine.               

Heinlein was a man of little theory. He did have this to say, however, about his other geometrical time travel story, “All You Zombies—”:

Mark Twain invented the time travel story, six years later H.G. Wells perfected it and revealed its paradoxes. Between them they left little for latecomers to do. But they are still fun to write.19

All the elements are here: time travel is a game (“fun to write”), and one based on paradoxes or logical structures. But what does it mean to say these paradoxes were “revealed” by Wells? Suffice it to say that, in light of the sophisticated speculations we have seen in the (post-Einsteinian) sf pulps, Wells does little more than suggest the paradoxes of time travel. Paradoxes exist in TM as tantalizing contradictions. But this is precisely the point: it can be argued that Wells's “errors” have provoked numerous rewritings of the seminal text, first and foremost of which is Heinlein's “By His Bootstraps.” For if Wells “missed” important aspects of the new temporality, he did suggest the one paradox that was to generate the time travel story in the form that concerns us here—that which combines spacetime curves with logical games. This is the sequency-simultaneity paradox.                

In most ways, Wells's narrative retains the conventional structure of the voyage to a far (or imaginary) place and return. However contemporaries read Wells, the Traveler's return would be most problematic for the sf reader. He moves at a relative velocity much greater than that of the initial spacetime frame. In his travels around the continuum he measures approximately seven days by the clock in his frame. We of course know, given this, that he would not return to find a comfortable dinner and friends waiting for him. All would be dead and gone. Wells seems to be using, as model, time lines flowing parallel to each other but at different rates. The Traveler leaves his friends one week, lives seven days of his (hence their) time in the future, and returns to join their company for next week's supper. You get off the train, and catch it at the next stop. This would be fine, except that Wells complicates matters by having his traveler leave, not a week previously, but the very morning of the day he returns. If Wells ignores the twins' paradox, his making problematic the narrator's own time line, our sense of his “now” and “then,” reintroduces a relativity of sorts, but this time located at a cusp of logical contradiction: the possibility of being in two places at once.                  

To avoid being such is, in a sense, the mainspring of all time paradox tales. What Wells brought future readers, when he problematized the point of re-entry, was a dynamic for generating narratives. Time travel, at this nexus, is a confluence of physics and geometry, or rather of two contending spacetime geometries. On one hand there remains a yearning for the perfect Euclidian circle, in the need of the traveler to go home, to return to the point of origin. On the other hand, in terms of relativistic spacetime curves, the exact point in the old system proves not to be so in the new, and there is no going home once the voyage is undertaken. Robert Silverberg, in another Wellsian rewrite, Up the Line, makes a rule for time travel: you can travel anywhere in the future, but there is no way at all to get into your future or into your past.20 Einstein agrees:

The most striking [thing] is that all of the past and all of the future, for each individual, meet and forever meet, at one single point, now. Furthermore, the now of each individual is specifically located, and will never be found in any other place, than here (wherever the observer is at).21

Time travel, in its most basic sense, plays with the sanctity of sequency within the traveler's own spatiotemporal continuum. Again, Silverberg describes its basic condition: “A time traveler in transit is a drifting bubble of now-time ripped loose from the matrix of the continuum, immune to the transformations of the paradox” (38). But the word “immunity” points to another paradox; for the time traveler's freedom to move (as with Rousseau's statement that everywhere we are free and everywhere in chains) occurs only if he reintegrates the continuum at the exact instant of departure. Immunity means a reprieve from sequency, whose sway is inflexible. For if re-entry is at some other instant, however slight the difference, simultaneity occurs. The results can be disastrous. This is the “grandfather paradox,” which warns of the possibility of a wayward traveler mistakenly killing his own grandfather, thus erasing himself from his time line.22              

The Grandfather Paradox involves wide “misses” in re-entering the continuum. Many time travel stories however—those that strike us as “geometrical” —cultivate the close miss. Here a minute discrepancy in re-entry “twins” the traveler, creating time “doubles.” It seems that Wells is the first to suggest the difficulty of a traveler re-integrating the original temporal continuum. This occurs in the curious Mrs Watchett episode. As the Traveler departs, moving relative to the original frame of his laboratory, he sees his housekeeper Mrs Watchett enter: “I suppose it took her a minute or so to traverse the place, but to me she seemed to shoot across the room like a rocket” (§3:28). Returning, he experiences the following: “I passed again across the minute when she traversed the laboratory. But now here every motion appeared to be the exact inversion of her previous ones” (§12:143). If the Traveler, in his new circumstances, finds clocks imprecise, Mrs Watchett seems a watch most precise, a fixed Newtonian point that the Traveler can leave and, by exactly retracing his movements, absolutely rejoin.               

Yet if we read the Traveler's account carefully, exact re-entry does not take place. He is aware of a disparity in spatial location between point of departure and point of return, and measures it: “That gives you the exact distance from my little lawn to the pedestal of the White Sphinx, into which the Morlocks had carried my machine” (§12:143). The exact geometry of Mrs Watchett's inversion, however, should allow no disparity, calculable or otherwise. But if we read Wells's clocks, disparity is there. Reading the biological “clock” of beard and torn clothes, we assume the newly-arrived Traveler has been gone a week since the last dinner. But his story gives new information. He did not leave a week ago. Because the machine needed repairs, he only departed this Thursday morning: “It was at ten o'clock today that the first of all Time Machines began its career” (§3:27). At ten o'clock, he lightly touched the level of his machine, then looked up to notice the clock now read “nearly half-past three.” It was then that he noticed Mrs Watchett, who had just entered the room, shoot by. Not only can we not explain the beard. But if he exactly inverts the trajectory, he must meet Mrs Watchett near three-thirty, then “come to rest” at ten, exactly at the moment he started. Yet here is his account of arrival:

For a time my brain went stagnant. Presently I got up and came through the passage here limping.... I found the date was indeed today, and looking at the timepiece, saw the hour was almost eight o'clock. (§12:144)

Even if this were a textual oversight, it is one with enormous consequences for later time travel stories. This “presently”  can encompass several hours of stupor, a tired man after a long voyage.  Or Wells may be pointing out a disparity in the time of arrival itself, where a same self re-enters a same continuum, but at slightly different instants of that continuum. In the latter case, we have time “doubles.” By simply imagining their existence, we open a Pandora's box of paradoxical imbroglios. We can play the game with Wells's text. Traveler 1, returning exactly at three, would be the “younger,” having lost no biological time in coming back to the precise moment, in his continuum, of departure. But the traveler the narrator follows, Traveler 2, shortly coming to his senses upon arriving, sees it is eight o'clock, and goes at once to the dining room, where indeed dinner is occurring. As both are now in the same frame of reference, Traveler 1 will have to live five hours before he can enter that dining room. Is he not then both younger and older than his double?

4. The Logical Game as Time Travel: The Nouveau roman. Wells of course, by giving voice to the eight o'clock Traveler, consigns the ten o'clock version to limbo. But later writers will actualize both. Indeed, they must do so, for they have new Einsteinian rules for playing time traveler. For if there is no way to get into one's own future, there is no way of getting into one's past either, no way of attaching the “now” bubble of the time machine to the “then” from which it departed. Martin Gardner tells us that for Special Relativity: “There is no absolute time throughout the universe by which absolute simultaneity can be measured. Absolute a meaningless concept.” Gardner goes on to qualify: “Of course, if two events occur simultaneously at the same spot, it can be said absolutely that they are simultaneous. When two airplanes collide in midair, there is no frame of reference from which the smashing of both planes will not be simultaneous.”23              

Substituting temporally displaced events for airplanes, John Wyndham calls such collisions “chronoclasms.” Wyndham's story “Chronoclasm,” however, is not about disaster. Rather, it is a game played with paradox, where time “doubles” trace timelines that skirt but always avoid catastrophic disruption of the continuum.24 Wyndham has reconfigured a story “line” to form a spacetime curve that passes (and promises by the nature of its configuration to pass forever) between “now” and “then,” allowing persons from different temporalities to meet without making any causal or “historical” contact. The figure they inscribe bears resemblance to the Moebius band. George Gamow traces an itinerary on this band using a walking donkey:

By walking around the surface of Moebius, our “left-profile” donkey has turned into one with a “right profile.” And, mind you, this has happened in spite of the fact that the donkey has remained on the surface all the time and hasn't been taken up and turned around in space.25

Time travelers, of necessity, move on this same “surface.” The instant they leave the continuum they step onto it, and must remain on it if they are to avoid potential disaster (as happened to Bradbury's traveler as he stepped from his time band to crush the fatal butterfly). Indeed, staying on this surface, curving without end around the “now” moment, is the only way to sustain order and continuity once the initial step is taken. In Wyndham's case, the new order is that of tautology: here a letter is sent to the future to guarantee that a traveler will come from that future to be the “cause” that this letter will be sent “in the first place.” In the case where right—and left—profile figures are of the same person, the play is with oneself, a form of solipsism.                

All kinds of variations on this loop proliferate in sf, each demanding the highest degree of ingenuity. In terms of time doubles meeting each other, they can have a wide age span at the moment of Gamow's “turn,” as in Chris Marker's La Jetée (1962). The film begins on an airport platform with a boy watching a man being shot and die. The boy grows up and follows a loop that “ends” with him on the same platform, now as the man being shot, perceiving the boy he “was” watching him die. Or the “biological” gap can be hours, minutes, even seconds. An example is Silverberg's Up the Line (1969), in which a time guide, having lost a tourist, slips in and out of the continuum at very close intervals, and thus generates a series of minimally different time doubles. The difference however proves sufficient to allow each to become conscious of a “self.” What ensues is a struggle for identity that ceases only when we learn that the “first person” narrative we have been reading in fact belongs to one of the secondary temporal manifestations. Certainly, important issues are raised in such fictions: matters of identity and self, of free will and determinism, that are worked out in a variety of ways ranging from the tragic (in La Jetée) to the philosophical or purely speculative. In all cases however, what strikes the most is the re-configuration of things once thought bound inexorably by causality and linearity. We admire the ways in which the old invariables, plot and character, are made to conform to new spacetime geometries. In the end, we yield to the game. It is the game Heinlein played, with consummate skill, in “By His Bootstraps.”               

But don't modernist writers play a like game in their parallel universe? Structures here are not just the Euclidean spaces drawn by Ricardou; they are temporal figures as well. Real analogies can be drawn between the modernist protagonist and the time traveler, in the way they apprehend time, indeed in the way time apprehends them, bending their life lines in strange new figures. For the time traveler, disengagement from Newtonian time creates new rules, beyond chronology and causality, for human thought and action. Return to any absolute time of origins and ends is now impossible. And yet, by the same token, the traveler is now free to play upon the wish and need for such a return, to create arabesques that flirt with a reentry point that has now become “forbidden” if not impossible. The traveler is between worlds in Matthew Arnold's sense, one dead, the other powerless to be born.26               

This is precisely the situation of the modernist “hero.” He/she must, being “modern,” reject the classical sense of time. This rejection of chronology however creates a new tyranny, in the form of a yearning or desire to return to a temporal fixity now known to be impossible in terms of the new rules adopted. The only way to reconcile new rules (and new narrative figurations) with this desire for old time, is to subsume both in a fictional game. Under this new dispensation, classical time is recoverable only to the extent that it becomes an object of play.                

Robbe-Grillet calls for the abandonment—in his fictional and film narratives—of the “temps des horloges” for the now moment of what he calls “temps humain,” or “l'expérience vécue.” This latter, free of the tyranny of “history,” forms an unprecedented zone of play, where narrative follows the arabesques of invention rather than the dictates of causality. Robbe-Grillet however, in “deconstructing” the binary, only generates more ghostly twins, where the free “now” moment is made to yearn for what has become its irretrievable “then” on the fixed line of history.27 For instance, he calls his film L'Année dernière à Marienbad, despite the fact he tells us there was no last year, neither past nor future, only a series of now moments, those apprehended in the hour and a half it takes to view the film?28 Like the tracking camera that wanders back and forth through the corridors of this film's present, all linear time lines (ours and the protagonists') loop through this “now.” The loops however are charged with memories and a desire for an elsewhen, for a time and place when this floating world was perhaps connected to some real “story” of love and death.                

In like manner, Les gommes effects a closed spacetime curve that inscribes a “now” zone of free play lifted from the precise sequence of events which (in terms of genre) is that of the mystery novel, or (in terms of myth) of the Oedipus story. Inverting the causal pattern of the mystery narrative, Robbe-Grillet gives us punishment and crime rather that the opposite, tracing a path where a murderer full of cultural memory of a “past” crime still moves toward its commission in the “future.” All sense of motive and causality are erased. Instead we have a game, played along a curve of non-time (the missing 24 hours of a stopped watch), in a plenum inscribed by this single yet eternal turn of a day. Here is a “now” realm, where the elements of a mystery—“clues” or investigation—lose all sense of direction and are manipulated at will. This day is lost, but it is only one turn of the circle; the watch will start again, and we realize that the commission of the crime was not stopped, merely deferred. In this circular game, what is ever deferred must endlessly occur as well. Robbe-Grillet however was not the first modernist to develop such a realm of play, curving on itself in hopes of forever forestalling the reappearance of linear time. We must go back to Borges's “Death and the Compass,” published a few months later than Heinlein's story, in May 1942.29

5. Borges's “Death and the Compass.” Borges's story is a striking example of a similar “histoire comme conséquence.” Again, in place of the absolute chronology mandated by the mystery story, he substitutes a sweep of the compass that brings “lives” and “actions” around to close in on a now moment that is at once a rendezvous with time (death) and perpetual displacement from time's finality. Borges tells of the highly literate detective Lönnrot, whose name, significantly, is the same as that of the poet-philologist who pieced together, indeed fabricated after-the-fact, an “early” Finnish national epic The Kalevala.30 Borges's Lönnrot, beset by a series of seemingly random murders in the maze of modern Buenos Aires, likewise sets out to impose geometrical order, through a swing of the compass which inscribes past and future in a closed now-space of signs and their manipulation:

The three points were, in fact, equidistant. There was symmetry in time (December third, January third, February third); now there was symmetry of space as well. All at once he felt he was on the verge of solving the riddle. A pair of dividers and a compass completed his sudden intuition. He smiled, pronounced the word Tetragrammaton...and called the Inspector on the phone. (72)

Traditional narrative here becomes puzzle or game: actions and “agencies” yield to cabbalistic signs, numerological patterns that figure the order underlying seemingly chaotic things or events. There is the concordance of word game—the Tetragrammaton or four consonants in the Hebrew name for God— and geometrical figure: the rhomboid inscribed in Lönnrot's compass, whose fourth point, like the final phoneme in the unspeakable name of God, is the fatal “place” where the detective, following his own elegant logic, discovers the culminating murder to be his own—again occurring at the “now” moment that enfolds and contains all past and future possibilities.31 Lönnrot realizes that he and the murderer are one, and that the “lives” of killed and killer are inextricably tangled into a single strand. The latter's name is Red Scharlach, and as Borges puts it in his “commentary”: “The end syllable of Lönnrot means red in German, and Red Scharlach is also translatable, in German, as Red Scarlet” (269). The detective is not “an unbelievable fool walking into his own death trap” (an explanation that still respects motive and causality) but “in a symbolic way a man committing suicide.” As a logic of signs equates plot with character, enfolding them into a single solipsistic act, so the lines of two distinct “destinies” converge at a same point. Scharlach speaks here for both parties:

All roads lead to Rome. At night, my fever fed on that metaphor. I felt the world was a maze from which escape was impossible since all roads, though they seemed to be leading north or south, were really leading to Rome, which at the same time was the square cell where my brother lay dying and also this villa, Triste-le-Roy. (76)

A process is at work here that systematically reduces conflict and opposition to something comparable to mathematical equations. All places in the geography of this story—whatever their direction or emotional charge—are equatable to “Rome,” just as actors are less psychological doubles than simply (to use Wyndham's expression from  a time travel story) “opposite numbers,” counters on opposite sides of an equal sign. The story concludes with an elegant balance that suspends all finality, even that of Borges's word “suicide.” Even if Scharlach and Lönnrot are one, we expect death, the ending of Lönnrot's lifeline, to reassert sequency. It should be “death or the compass,” yet the title of the story belies this. And though one double “shoots” the other, neither admits an end: they speak of a “next incarnation,” of the “next time I kill you.” In paradoxical manner, a sequence of events, time's arrow that is both irreversible and irreversibly kills, has been bent to the compass's endless curve. Arrow and curve fuse as both doubles concur in the existence of a maze (the confounding of cause and effect implied in a “next time” for death) that is “a single straight line”—the line of the Zeno paradox, where all bullets fired like this one will have their time lines halved and halved again in unending manner, so that the bullet that always hits the mark in the world of Robbe-Grillet's clock time, now at the same time never hits it. In most astute manner, Borges enfolds past (the firing) and future (the hitting) in an ever-perpetuated in-between moment, the moment of half-life that exists after any halving of distance.32

6. Heinlein's “By His Bootstraps.” Heinlein, in “By His Bootstraps,” appears to play a  comparable, quite modernist, game with characters and events caught in the maze of a paradox.33 We have, in the relation of Heinlein's protagonist Bob Wilson to the older man “Diktor” he rivals and finally replaces, something comparable to Robbe-Grillet's later play with Oedipal myth and complex. The French writer would applaud the way in which the patriarch Dik(ta)tor is in fact “dictated” into existence by Bob's act of writing a dissertation about the inverted causalities of time travel. As in both Robbe-Grillet and Borges, Heinlein's protagonist is led to pursue a space-time mystery. Here a “time gate” opens, an initial event happens which forces Bob to explore the connection of this random occurrence with the familiar world of his room. Like Lönnrot, Bob is an active intellect. And like him, he would subject an apparently chaotic series of encounters to logical analysis, only to discover that he himself is moving to the patterns of a relentless geometry, where sequency and simultaneity fuse, and he finally learns that he and Diktor are one and the same—caught in a Borges-like maze where there is, at one and the same time, a next time, and no time at all.                

Heinlein's “game” is highly sophisticated; indeed, the extreme complexity of its re-figuring of conventional narrative requires a detailed tracing. The story opens as Bob Wilson, a graduate student writing a Ph.D  dissertation on mathematical metaphysics, reaches a passage on the material unfeasibility of time travel. At this neat crux, a hole appears in the wall of his room that proves to be a Time Gate. Through this hole first one, then a second individual appears. The first wants Bob to go through the Gate, the second seeks to prevent this. A fight ensues between the two, and Bob, trying to intervene, is inadvertently knocked through the Gate. He awakes in another spacetime, peopled by effete humans (shades of Wells's Eloi) and ruled by an older man who calls himself Diktor. Diktor tells Bob how the Time Gate works, and promises him a “great future” if he goes back into his spacetime to get a list of things Diktor needs to secure control over the world Bob has fallen into.                

Going back, Bob lands in his old room, behind a person who is typing. When another person comes through the gate, he realizes he is reexperiencing the same scene, but from a different point of view, that of the first person to enter the room the time before, the one who sought to persuade him to enter the Gate. When the third person appears, the same fight takes place, and as before, an unwitting punch knocks the thesis writer through the gate. The scene is the same, but Bob (whom the third-person narrator continues to follow) has taken the spacetime position of another of the actors. And, because memory like narration is continuous, he realizes the thesis writer occupies the position he was in “the first time around.” Because narrative is sequential, the Bob we start with is the one we follow, both creating the sequence: Bob 1 and Bob 2, and apprehending it as “younger” and “older” versions of a same self. But do the words “younger” and “older” have any meaning here? How can there be a before and after, a past and present, when past and present occur in a same frame, when “present” self encounters his “past” one, then (in the same spacetime) turns to see the third player as a another, “future” self (“He recognized himself—another carbon copy”)?                

Spacetime twists like a pretzel here. The same imbroglio occurs as Bobs 2 and 3 struggle, and again inadvertently knock Bob 1 through the gate. Bob 3 (the voice from the “future”) tells Bob 2 that Diktor has played them for a dope. But not heeding this, Wilson goes back through the gate to get an explanation from Diktor. Not satisfied by the latter's remarks, he returns to the room, determined “this time” to stop any figure from passing the gate, even though logically this is absurd. For if (from his point of view) all these Bobs are versions of himself, and if he is now situated on the other side of the gate, how can he prevent himself from doing something he has already done? Going back, he finds himself in the position of the third figure, moving in a rondo and yet with each turn pushed progressively up a line of selves: Bob 1, Bob 2, Bob 3....                

Predictably, the other two go back through the time gate, leaving Bob 3 alone in the room. At this point, a new set of events unfolds, tracing a spatiotemporal loop that (at one and the same time) circumscribes, and inscribes itself into, the room and knot of three “selves.” Again alone, Bob sits down to his thesis, only to be interrupted by a call from Genevieve. Frustrated by her (for him “earlier”) calls, he rudely dismisses her. She threatens legal action, but he does not know why. He hangs up, she keeps calling. Hearing footsteps outside, and thinking it is she, he goes back through the gate. He finds himself alone in the control room for the time machine. Here he finds the hat Bob 2 had tossed through, and the list of items Diktor had requested he obtain. Manipulating the controls, he displaces the gate to a place and time, it turns out, slightly before the time frame he has just experienced. He gets the items, and returns to find the gate gone. Later he will learn he has moved it, in fact in the initial act of focusing on the room that precedes moving the gate outside. But now/here (we see these temporal locators becoming useless) his watch reads two-thirty; he realizes the gate is in his room, and will remain till four thirty. Had he been curious about time paradox, he would have waited in the street till four thirty, where he could have greeted himself as he steps forth from the gate. Instead he rushes over to Genevieve's place (”unfinished business”), seduces her, and leaves behind the hat that occasions the calls previously experienced, her rude dismissal, and the return of the hat to its point of “departure.” We imagine her opening the door, finding the room empty, tossing the hat into it. In the narrative, this occurs later than the opening scene, when the hat is in Bob's closet. But if we heed Genevieve's phonecall in that scene, and her claim that she has the hat, the claim generating the series of calls that leads to her dismissal, and return of the hat, then the moment of its return is also earlier than the scene in the room. For how else did it get there?                 

Returning to the empty room, close to the moment of his earlier departure, Bob crosses the gate just before it disappears. He goes back ten years, and sets himself up, with his list of things, as ruler. He reigns, living ten years in biological time, up to the day when a new person tumbles through the gate: Bob 1. Till now, he has followed a single line (however curved) of reasoning. However many “Bobs” he met, these were inconsequential as long as there was Diktor: the older man he first serves, then revolts against, usurping his world. Now, in a moment comparable to the meeting of Lonnröt and Scharlach, the compass comes full swing: Bob suddenly sees he is Diktor; the person he has replaced is himself, just as another self waits, in an endless go-around, to replace him in turn. The “far” points of the spacetime curve meet to fix forever the “now” moment that broke from the continuum when Bob's keys stuck. In meeting, they appear to inscribe the course of his life as the minimal “distance” from one side of the time gate to the other. The “space” here is from Diktor's promise of a great future to Bob's final ironic reiteration: the “great future” is no future at all. Yet what a world separates these two mirroring statements—Bob's entire biological life.                

Heinlein, like Borges, seemingly does not intend his narrative to raise philosophical questions about identity or free will. For as Bob traces his spacetime “knot,” such issues become merely banal tautologies:

“If God created the world, who created God? Who wrote the notebook? Who started the chain? He felt the intellectual desperation of any honest philosopher. He knew that he had about as much chance of understanding such problems as a collie has of understanding how dog food gets into cans.” (113)

In his dissertation, Bob argued for free will, and saw time travel as a way to master destiny. Yet Bob's story plays a geometrical joke on such pretensions. Heinlein's narrator comments: “Everyone makes plans to provide for their future. He was about to provide for his past.” (111) The irony is that, without past or future, he must turn endlessly around the single moment when, just as he finishes typing a phrase telling us duration has no Ding an sich, his keys stick, and (living proof of his own postulate) he achieves his duration by becoming unstuck from the continuum forever.                

Heinlein, it seems, offers a geometrical game similar to Borges. And yet, differences are significant. Borges's narrative is the work of a geometer, while Heinlein's is that of a physicist. If the curve of Borges's compass traces a sequence that closes on death, what it inscribes is an organized space that, in its perfection, at the same time defers death and this excludes time from the closed circle. In terms of histoire and récit, death traditionally belongs to the former, as a moment where time “sticks,” and the individual meets with the absolute and irreversible. But in the perfect, repeating circle of Borges's compass, death is endlessly deferred, present only as a signifier that points, not to time, but to the absence of time.                

It is impossible in the age of relativity that Borges's Euclidian circle is traced naively. It is however a figure made in  reaction to something, and that something may be physical time itself. Surely Borges knows relativity has done away with histoire, in the sense of a fixed, universally valid, event line. Death as a rendezvous with time as “destiny” is nonsense. There are only individual life lines, individual stories and deaths, each unfolding in a continuum composed entirely of “now” moments. In a story, the geometer can bend this life curve around on itself. Yet there can be no perfect circle. This can occur only if one meets one's exact spacetime self. And this is impossible because, in the absence of a general, fixed time line, “now” can never meet “then.” What we have when self meets (as nemesis) its exact double, is the same spacetime event occurring in two spatiotemporal locations at once. The only way to restore simultaneity in this relativistic context then is to meet oneself. What in time travel is chronoclasm is here posited as “death.” Borges's perfect circle, by suggesting yet deferring a “preordained” meeting with death in the guise of one's double, offers a very different solution from Heinlein's to this problem of the new spacetime.                

Both stories deal with a sequency/simultaneity paradox. In terms of the paradox, however, Borges comes down on the side of simultaneity. In contrast Heinlein emphasizes sequency, even though the curve that inscribes Bob Wilson also seems to close on a single destiny, indeed a single spacetime point in that destiny. For when Wilson meets Diktor, he does not meet a double, in the sense of another manifestation of some qualitative “self.” The two are separated by the spacetime of the story, during which Wilson grows into what he will be, once was, and always will be. Wilson may pass through the “same” room and meet “other” Bobs, but from the point of view of the narrative, he does so in each instance once and only once, for each meeting represents a single moment in his time line. If, as Martin Gardner says of Special Relativity, “absolute simultaneity of distant events is a meaningless concept,” Heinlein demonstrates it is  meaningless for the closest of events as well. Bob in the story is engaged, biologically, in living his time line. If logic tells him all the figures he meets are himself, his heart, his existential situation, forces him to reject this identity. If abstract reason tempts him to remain in the street by the time gate and meet his exact self, his drive to be the one and only Bob leads him away. However many “Bobs” there are, the story we read is about this Bob. However many times (an n-number) this same story, logically, must be repeated, for this Bob it can never be repeated.

7. Zeno's Time. The differences between Borges's modernist narrative and Heinlein's time travel story reveal divergent approaches, both to the nature and manner of experimentation with time in fiction, and to the way in which time itself, as central problem of modernity, is apprehended. Borges's story, finally, is an elegant cryptogram, where actors do no more than decipher a higher order behind material appearance. In Heinlein however, human actions are not rearranged by geometrical patterns; actions are that geometry, lines physically lived by the protagonist. Bob Wilson writes that “duration is an attribute of consciousness and not of the plenum. It has no Ding an sich” (50). But this is no theoretical “key” to a logical solipsism, such as Borges gives us in the final lines of his story with the exposition of the Zeno paradox. Bob's keys physically stick as he utters this. The time gate opens, and his entire being is forced to engage a plenum that is raw physical fact.                

The stated purpose of narratives inspired by Valéry is to expose the artifice of elements in “realist” fiction by forcing these to conform to artificial proportionalities. Fictional characters become mere counters, unaware of what is happening to them, unable to act to alter the geometry of “events” that moves them. When the modernists reject “realist” fiction for fictions arranged by the mind, are they not also rejecting what lies behind realism's demand for fidelity to “things as they are”: the tyranny of matter, of people and places subject to the physical continuum of time. Time travel however, as sf, deals primarily with material entities. Temporal paradox in sf (if it is true to its generic imperatives) cannot be a purely mental structure. Geometry must be applied to something, and time lines and curves, as in Heinlein, are re-materialized, not only within, but actually by means of, the traditional structures of fiction. Like Wells's Traveler, Bob Wilson physically travels in time. But where Wells's Traveler remains an external observer, Heinlein places Wilson inside the time curve, making paradox his existential condition. Narrative here demands we suspend theoretical disbelief, and accept Wilson as a real (i.e. physical) protagonist. By doing so, we allow narrative to give paradox a physical locus. Indeed, the stroke of genius here is that no other medium will do. Were the scene in the room presented on the stage, we would have only simultaneity, four look-alikes running in and out, performing interchangeable gestures. But when presented as a story—Bob's story told from his point of view—sequency and simultaneity intertwine. He realizes he is repeating words and actions, yet knows he is not repeating them, for he never ceases to be himself, selfish, seeking the upper hand over all the other “characters.” Wilson's progress, despite the geometry, remains the traditional one of Bildung. Heinlein uses narrative to restore, beyond logical abstractions, an element of human experience that returns the problem of temporal geometry to its roots in the physical processes of causality and irreversibility.                  

Bob is indeed tempted by pure logic but rejects it as the means of dealing with his situation: “Time after time he had fallen into the Cartesian fallacy, mistaking clear reasoning for correct reasoning” (86). If there is a neo-Cartesian “solution” to time as physical continuum, Bob, and by extension Heinlein and time travel itself, clearly reject it. Not so the modernist tradition. In his Etudes sur le temps humain, Georges Poulet discusses Péguy, Valéry and other early figures in our modernist century in light of their tendency to double Bergsonian “durée” with a mentalization of the temporal moment that can be called “Cartesian.” As Poulet observes, Bergson substitutes “à la place du déterminisme des causes et des effets”:

le sentiment que n'importe quel moment peut être vécu comme un moment neuf, et que le temps peut être toujours créé librement à partir du moment présent. [in the place of determinist cause and effect, {there is} the sense that any moment whatsoever can be experienced as a brand new moment, and that time can always be freely created as of this present moment].34

But Poulet also finds, in response to this free flowing continuum, a fixative sense of durée operating in modern “human time.” Freedom, in this case, results from an act of mind that inhabits Bergson's present moment, and in doing so prevents it from becoming part of the sequence that determines “history.” To Péguy, this “liberté” is a function of “la connaissance du présent qui n'est pas encore de l'histoire.” [freedom derives from the knowledge of a present moment which is not yet a part of history] (45). The time traveler's “now,” however much it “floats,” remains part of a greater spacetime continuum. Here however the “now” moment becomes the creation of mind, insofar as mind, becoming aware of itself as mind, separates itself from the continuum. In Cartesian manner, the “temps des horloges” is relegated to an “out there,” to res extensa. The modernist corollary to this is a substitution of mind for material world, where mind becomes the space in which time can be reconfigured. In Heinlein, story remains a physical act, that occurs in physical time. But in the works of Robbe-Grillet, Ionesco and Borges, récit or narrative is, in opposite fashion, informed by this mental or Cartesian time, where the temporal arabesques of telling are substituted for physical time altogether.                

In Borges's story we see, in the culminating evocation of the Zeno paradox, the celebration of an act of mind that lifts action out of physical and into purely mental time. Whatever Borges's inspiration, it is clear that French modernists from as early as Valéry were aware of this same, Cartesian, potential of Eleatic thought. For Valéry, the time arrow was Zeno's arrow: “Zénon! Cruel Zénon! Zénon d'Elée!/M'as tu percé de cette flèche ailée/Que vibre, vole, et qui ne vole pas! [Zeno, cruel Zeno, Zeno of Elea!/Did you pierce me with that winged arrow/That quivers, flies, yet does not fly!]”35  The Zeno Paradoxes act on the physical fact of an irreversible “time arrow,” which in the physical world cannot be deflected or reversed by any logical maneuver. What Zeno does is double material with mental time. On one line an arrow, or bullet, inexorably hits the mark. But when that motion, by an act of mind, in converted to a line and a virtually infinite series of points on that line, the duration of that motion becomes endlessly divisible. Ricardou uses like logic when he inverts the relation between histoire and récit, using mental structures to defer physical events, thus suspending the time line that traditionally controls narrative. The end result of this logic, as mind arrows no longer connect with the physical plenum, is disengagement from history altogether, an ultimate mind game where the act of narration generates its world ex nihilo.36 So pervasive is this process in a certain aspect of modernist French thought that Henri Lefebvre speaks of the “nouvel éléatisme” as fundamental to what he designates “l'idéologie structuraliste.”37

8. “Time that Flows....” Henri Bergson refutes Zeno by evoking common sense:

We will content ourselves with observing that motion, as given to spontaneous perception, is a fact. . .and that the difficulties and contradictions pointed out by the Eleatic school concern far less the living moment itself than a dead and artificial reorganization of movement by the mind.38

To commit to the living moment is to commit to causality and irreversibility. The Eleatics however claim the power to fix and control temporality. Valéry bids time's arrow to stand still. So at the end of Borges's story Scharlach fires the bullet at Lönnrot that must kill him and break the circle, yet will never do so. Scharlach promises Lonnröt a “next time” because he knows that all bullets fired in Zeno's “straight line maze” remain ever in flight and ever suspended. If we did not know before, Borges's story here makes its final swerve, into a realm of metaphor, a Euclidian mind-space of circle and line from which physical time is excluded. With the frozen bullet, characters we thought adversaries are themselves frozen: the circle itself comes to rest, with hieratic, logical antinomies facing each other, counters to whom simultaneity is given by the sign that equates them. Robbe-Grillet sums up how these writers see time:

Il ne s'agit plus ici de temps qui coule. . .C'est la matière elle-même qui est à la fois solide et instable, à la fois présente et rêvée, étrangère à l'homme et sans cesse en train de s'inventer dans l'esprit de l'homme. [Here it is no longer question of time that flows. . .It is matter itself that is at one and the same time solid and instable, present and dreamed into being, alien to man and endlessly inventing itself in the human mind] 39

To deny temporal flow is to deny matter itself. Matter here is placed outside time, frozen in spatial contiguity with the human mind, in order that mind's power of invention can manipulate it at will, subjecting it to ingenious geometries in its narratives.               

But neither traditional fiction nor modern physics does without “le temps qui coule.” Nor does sf's time travel story, which derives force from both. The paradox of time travel, as Heinlein tells it in “By His Bootstraps,” is less a logical game than a physical spacetime model of a different universe altogether, one in which the continuum of moments, as Bob lives them, takes strange, yet apparently possible configurations. In 1949, Kurt Gödel, in a scientific paper, exposed the model of a universe in which “there exist closed timelike world lines in spacetime.”40 Paul Nahin considers Gödel's structures as physical (or science-fictional) possibilities: “These world lines are the possible paths of space travelers, who always move into the local future but who nevertheless eventually arrive back in their own past.” Earlier in this century, scientists were seriously considering like models. Here is Hermann Weyl in 1921:

It is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a time-like direction at every point, to return to the neighborhood of a point which it has already passed through.41

On his world line, of course, Bob is always moving into his local future while arriving over and over in what he comes to recognize as his own past. Heinlein makes clear that this line is both a singular “point of view” and a body-line. And, in the latter as well as former sense, it is never, as it unfolds, more that “in the neighborhood” of its point of closure. As Nahin sees it, unlike Wells's Mrs Watchett or subsequent “closed loop” time travel, Heinlein in this story may be closer to “getting it right”:

With the four-dimensional block-Universe concept, all world lines lie tenseless in spacetime and so the encounter happens just once in spacetime—the older version speaks the same words he heard (even if he has forgotten them) when his older set of memories formed. He has to or else the past would be changed!42

Heinlein's model, thanks to its use of the narrative rather than descriptive medium, may be more complex yet. The line that narrates Bob's adventures does happen “just once,” because his story is told only once. If its curve means it will be told again, endlessly in fact, the curve is a Möbius band, and each telling will be from a slightly different point of view, even if caused by nothing more than Nahin's memory loss. In terms of memory, here is Bob first meeting Diktor:

 “O.K., Diktor, do you want to know my name?” “Your name?” Diktor chuckled. “I know your name. It's Bob Wilson.” “Huh? Oh—I suppose Joe told you.” “Joe? I know no one by that name. “You don't? He seemed to know you.”...“Joe—Oh!” Diktor chuckled.“It had slipped my mind for a moment. He told you to call him Joe, didn't he?” (58)

The fact that, in the spacetime of a curve, the memory needs (and always needs) jogging means that no “repeat” will ever exact. Between the shadow and act of Heinlein's narrative, we experience what Gödel calls the “relativity of simultaneity.” In Heinlein's telling of the sequency/simultaneity paradox, causality holds. The logic of the game, in the end, answers to as yet unrefuted laws of physical human time.                

And if causality holds, so does irreversibility. By ignoring  the fact of a beginning, the Eleatics create a structure that endlessly defers its ending. Bob can reject such circular arguments because the very existence of his world-line, and the necessity of living it, prove it has begun. His problem, instead, is one of ends. For if he cannot tell, in this chicken and egg loop, which came first and where it all began, he knows it has begun. In his, as in all continuums, where there is motion, there is energy. And where there is energy, there is entropy. Just as Silverberg's time traveler could get into the future but never his own future, so Bob can reach the past, but never his own past: his physical life line is irreversible, and moving inexorably toward an end. Yet the physical Dhalgrenfact of the loop, that bends time and lets him into this general past, at the same time offers the means of recycling energy, thus of preserving itself. Thus the onus falls on Bob, not to reach his “great future,” but to physically engineer his world line so as to “insure” what he thinks is “his past.” The irony is not so much that he has no future, as that he must prevent that future, for with it comes a leakage of energy that will bring him and time machine alike to a standstill. He would “paradoctor” his paradox to insure there will always be a Diktor to write the notebook in the first place, and thus avoid even the minimum duration that exists in anything but exact repetition. But the common sense, not the logic, of the story tells us otherwise. For the reader follows this Bob. And asks: what will happen to this particular notebook, to this Diktor? Indeed, what will happen to all subsequent Diktors, whose disappearance as throwaway selves tip the entropy equation back toward directional time? A band of Wilsons curve around a single temporal point. But at the same time there is nothing that can reverse the course of this and each successive single conscious life. Bob-become-Diktor will train his successor to insure the loop. But each Bob will train only one successor. Just as each notebook in itself must wither, so each Diktor grows old and dies, off the map, beyond the story, and thoroughly in accord with our sense of mortal life. Paradox here, what Bob calls “the perpetual motion fur farm,” is no logical game, but physical process itself, the thermodynamic laws that subsume sequency/simultaneity as the duality of conservation of energy and entropy. A clever Bob can insure that his loop will perpetually turn on itself. He cannot stop it from winding down. For the way of the process is unidirectional, from beginning to end, birth to death. If energy is conserved, something uniquely material is lost.                

Despite real similarities with modernism, the time travel story must ultimately, in relation to the former's eleatic freedom, serve as Dr. Johnson's stone—a material testing-place for its figures and systems. If time travel is a game, it is closer to the experimental game physicists play. A.S. Eddington describes the method of physical investigation in gambling terms:

If we continue shuffling a pack of cards we are bound sometime to bring them in their standard order—but not if the conditions are that every morning one more card is added to the pack.43

Nature adds the cards, and we play them. This is the way of physics, and of the time travel story. A fundamentally open-ended form, time travel has not passed with any modernist vogue, nor succumbed to postmodernist temptations for closure.44 It has continued, in the 1970s and 1980s, to create narrative situations that test ever stranger timescapes. Heinlein's spacetime curve constitutes an experiment, in the realm of fiction, with new possibilities of temporal disjuncture. It is an experiment where the “floating instant of now time” is also a human life, for whom  the paradox of sequency/simultaneity, now played with physical cards in an ever expanding deck, is literally a game of death. The time travel story, far from being logical fantasy, emerges from its comparison with the modernist game as perhaps the hardest form of sf. If modernist fiction aspires to pure geometrical spaces and relationships, time travel's ceaseless need to subject such forms to the test of material reality, by re-locating them in the physical continuum of spacetime, may make it the most truly experimental literary form we have.

                1. Stanislaw Lem, “The Time Travel Story and Related Matters of SF Structuring,” SFS 1:152, Spring 1974.
                2. Larry Niven, “The Theory and Practice of Time Travel,” Vertex: The Magazine of Science Fiction 1:66, October 1973.
                3. Dr. Robert L. Forward, Future Magic: How Today's Science Fiction Will Become Tomorrow's Reality (New York: Avon Books, 1988), 159. Hoping for the day when time machines will actually be made, not just posited, Forward insists that a radical paradigm shift will have to occur before they can be called “scientific”: “If a present-day scientist were confronted by a real time machine, he would certainly say that the machine had to be run by the rules of magic.”
                4. A fictional germ of the narrative as proposition and logical game is found in certain early sketches and parables of Kafka, specifically the parable of time and distance, “An Imperial Message,” and the time puzzle, “A Common Confusion.” In the latter, we find A going to meet B at H. But where A completes the journey in 10 minutes the first time, the second trip, under identical circumstances, takes 10 hours. Hartmut Binder, in his Kafka-Kommuntar zu sämtlichen Erzählungen (München: Winkler-Verlag, 1975), dates “Eine alltägliche Verwirrung” October 21, 1917, the date given to the piece, then untitled, in Kafka's “sogenannten 3. Oktavheft.” The sketch was first published, posthumously, by Max Brod in 1931, under the title “Ein alltäglicher Heroismus.”
                5. A Century of Science Fiction, ed. Damon Knight (1962; New York: Dell Books, 1963), 77. Knight's remarks however are ambiguous. Commenting on a Keith Laumer story, “Worlds of the Imperium,” (Fantastic, February 1961), Knight says: “Once, a good many years ago, I was rash enough to say in print that I thought the time travel story was played out.” Knight goes on however to qualify this: “I would hate to tell you how many time travel stories I have written since then.” If, in 1961, the form again seems played out, he admits that, with Laumer, a “major new idea” has arisen. More is at work here than ingenious game-playing; the factor fuelling these “revivals” appears to be the restless scientific speculation on the nature of time.
                6. Nathalie Sarraute, L'Ere du soupçon (Paris: Gallimard, 1956), 55.
                7. Jean Ricardou, Le nouveau roman (Paris: Edition du Seuil, 1973). This is Ricardou's third (and perhaps most comprehensive) book on the New Novel [Problèmes du Nouveau Roman, 1967; Pour une théorie du Nouveau Roman, 1971]. Ricardou (52) cites an unspecified edition of Valéry's Cahiers 1:772, If he refers to Volume 1 of the monumental Pléiade edition (ed. Judith Robinson), which appeared in 1973 as well, page 772 is blank. We searched Vols 1 and 2 for this quote (without success), as it is interesting for our argument to know the date of the utterance. But we found many similar “geometrical” schemas of fiction, and some quite early in Valéry's long career. An example is 2:1316: “Trio—A, B, et C—appelons-les: Alceste, Basile, Céphias.” Date is 1913.
                8. Pierre A.G. Astier, La crise du roman français (Paris: Nouvelles Editions Debresse, 1968), 14-15.
                9. One can only imagine the impact of a work like “By His Bootstraps,” and sf time-travel stories in general, on the emerging Nouveau roman.
                10. Maurice Nadeau, Histoire du surréalisme (Paris: Editions du Seuil, 1964). Discussing the Manifeste, Nadeau asks: “Est-ce le sort de la littérature de nous offrir une réaction à peine supérieure au jeu de piquet, et peut-on valablement s'intéresser à la vie de fantoches plus ou moins bien réglés?” (54). Later however, in a look at the surrealists' passion for things oriental, Nadeau (in the spirit of Artaud and others he cites) chides the Western logical mind for destroying imagination and all sense of the marvelous: “Faux ingénieurs, faux savants, faux philosophes, aveugles aux vrais mystères de la vie, du corps, et de l'esprit, parce que momifiés dans les bandelettes de la logique” (72).
                11. Bruce Morrissette, The Novels of Robbe-Grillet (Ithaca NY: Cornell UP, 1975), 38. Robbe-Grillet describes the project for his first novel (subsequently abandoned) in a personal letter to Morrissette.
                12. Claude Ollier, Nouveau roman: hier, aujourd'hui (collection “Pratiques” 10/88 [Union Générale d'Editions, Paris]), 210.
                13. His letter, dated May 16, 1994, offered a detailed list of time-travel-related stories from the pulps running from Wertenbaker to Jack Williamson's “Legion of Time” (May 1938 Astounding). We wish there were space to publish it here.
                14. The story appeared in two parts, in Amazing Stories, April and May 1926.
                15. Kirby's “growing larger” in relation to our Earth produces an effect analogous to Special Relativity, at least in the sense that we equate increase in size with that of mass, and note the slowing of relative clock time. Inversely, to “decrease in size” is to speed up the clock, and Kirby hopes in doing so to reintegrate his “original” size-time frame. It is as if Gulliver, growing far beyond the Brobdignagian, “goes off into ultra-planetary space,” then tries to shrink back to be Gulliver again. 
                16. Letter to GS and DC, May 16, 1994. Mullen cites as influence on Wertenbaker's story a Gernsback editorial, “Worlds within Worlds,” from the May 1922 issue of Science and Invention.
                17. “Man from the Atom,”  Part 2 (May 1926), p. 147: “Martyn has made the calculations. I shall appear to her no more than a few hours after the departure of that person who is following all my adventures. It will, of course, be in the next cycle of time, and there will be changes. But surely my Vinda will be there, and I shall be able to take her in my arms and tell her of all the love I have for her. I cannot believe that it will be another woman.” Faith displaces physics, and love, so we wish, must conquer all, even the cold equations of spacetime geometry.
                18. On this question, see the fascinating “exchange” between R.D. Mullen and Gary Westfahl in Science-Fiction Studies 21:273-283, #64, Nov 1994. Westfahl argues for the primacy of Gernsback's editorial comments and the dialogue these stimulated in letters columns (taking precisely as example our then ongoing research into the origins of “By His Bootstraps”). Mullen places more weight on discussions within the stories themselves. Our sense is that, in the case of geometrical time loops and sequency-simultaneity, both sources are viable. Our reading of “The Man from the Atom” shows how a story like this raises the question of time doubles, only to drop it for the sake of an amorous denouement. And then, of course, there is The Time Machine, which Heinlein in a sense is rewriting.
                19. In Robert P. Mills, The Worlds of Science Fiction, (NY: Paperback Library, 1970), 102. This claims to be an anthology of author's favorite stories. Each author was solicited, and provided comment, thus Heinlein. We are indebted to Gary Westfahl for alerting us to this rare Heinlein comment.
                20. Robert Silverberg, Up the Line (NY: Ballantine Books, 1969), 38.
                21. Gary Zukav, The Dancing Wu-Li Masters: An Overview of the New Physics (NY: William Morrow, 1979), 154. Zukav's book is an excellent (if controversial) exposition of modern physics in its broader cultural context.
                22. The classic 1950s example is Ward Moore, Bring the Jubilee, where the protagonist, by triggering the paradox, not only strands himself in an alien time line, but by actually killing a grandfather (that of his lady friend, the scientist who invented the time machine by which he returns to the past) alters the nature of the continuum itself, causing a bifurcation that “brings” an alternate history). There is a tendency in sf for such “alteration” stories to become disquisitive rather than “tragic.” Take, for example, the recent film “The Grand Tour,” based on C.L. Moore's “Vintage Season.” Here the question debated (by time travellers and the protagonist) is the degree of change tolerated in the past. What, in other words, is the sufficient condition for a chronoclasm?
                23. Martin Gardner, The Relativity Explosion (NY: Vintage, 1976), 45. Gardner is interesting in our context, as he wrote the “Mathematical Games” column for many years in The Scientific American.
                24. John Wyndham (pseud. of John Beynon Harris), “Chronoclasm,” published in The Seeds of Time (London: Michael Joseph, 1956), 11-38. 
                25. George Gamow, One, Two, Three. . .Infinity: Facts and Speculations of Science (New York: Mentor Books, 1955), 69.
                26. To the degree that sf reflects science, the traveler is between paradigms, on one hand Newtonian absolute time, on the other the so-called four-dimensional “Block Universe.” Paul Nahin, in his fascinating and learned book Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction (NY: American Institute of Physics, 1993), traces this specific term for Minkowskian spacetime to Oxford philosopher F.H Bradley, who wrote in his Principles of Logic (1883): “We seem to think that we sit in a boat, and are carried down the stream of time, and that on the bank there are a row of houses with numbers on the doors. And we get out of the boat, and knock at the door of number 19, and, re-entering the boat, suddenly find ourselves opposite number 20, and, having then done the same, we go on to 21. And, all this while, the firm fixed row of the past and future stretches in a block behind us, and before us” (104). To be conscious of the Block Universe is Silverberg's sense of the spacetime self as “drifting bubble of now time.” Nahin makes this clear by quoting Parmenides: “Nor was it ever, nor will it be; for now it is, all at once, a continuous one.” In the old universe, we step out of the boat at number 19, and expect to step back and find ourselves still at number 19; in the new universe, as time travel imagines it, we find ourselves at number 20, but (being emotionally conditioned as Newtonians) want to be back at 19, yet now know we can never go back. The fictional “space” between these two paradigms becomes, for narrator and character alike, a space of play, the generation of spacetime curves that flirt with, yet defy, causality.
                27. It would be interesting to compare time displacement with the shell-game Derrida plays with ontological “presence.” Mind free of chronological fixity in R.G. creates a kind of floating signifier; Derridian “différance” of presence (what else but this Dasein in a spatiotemporal continuum can bestow fixity on an occurrence?) does something like detaching the “now,” generating the famous ratures that simultaneously invite and prevent return to the place-time of origin.
                28. See Robbe-Grillet, Pour un nouveau roman (Paris: Editions de Minuit, 1963), 131: “Toute l'histoire de Marienbad ne se passe ni en deux ans, ni en trois jours, mais exactement en une heure et demie. Et, quand à la fin du film les deux héros se retrouvent pour partir ensemble, c'est comme si la jeune femme admettait qu'il y a eu bel et bien quelque chose entre eux l'année dernière à Marienbad, mais nous comprenons que nous étions justement l'année dernière, durant toute la projection, et que nous étions à Marienbad. Cette histoire d'amour qu'on nous racontait comme une chose passée était en fait en train de se dérouler sous nos yeux, ici et maintenant. Car, bien entendu, il n'y a pas plus d'ailleurs possible que d'autrefois.” The italics are Robbe-Grillet's, and emphasize his sense of the spatiotemporal difficulties of re-locating, once one yields to the “now” (the “ici et maintenant”) of experience, that elsewhere and elsewhen that mark reconnection to the causal realm of history. 
                29. Jorge Luis Borges, “La muerte y la brújula,” first published in Sur, May 1942. English edition is The Aleph and other Stories: 1933-1969 tr. Norman Thomas DiGiovanni (New York: E.P. Dutton, 1970). All citations in the text are to this latter edition.
                30. See Jan de Vries, Heroic Song and Heroic Legend, 143-54, for an account.
                31. At the end of La Jetée in similar fashion the protagonist, now observing from the other side of the loop as it closes on itself, realizes that the murder he saw “in the beginning” was in reality his own murder.
                32. Borges 78: “`In your maze there are three lines too many,' he [Lönnrot] said at last. `I know of a Greek maze that is a single straight line. Along this line so many thinkers have lost their way that a mere detective may very well lose his own way. Scharlach, when in another incarnation you hunt me down, stage (or commit) a murder at A, then a second murder at B, eight miles from A, then a third murder at C, four miles miles from A and B, halfway between the two. Lay in wait for me then at D, two miles from A and C, again halfway between them. Kill me at D, the way you are going to kill me here at Triste-le-Roy.'”
                33. Robert A.Heinlein, “By His Bootstraps,” The Menace from Earth (1959; New York: Baen Books, 1987). Story first appeared, under byline Anson McDonald, in Astounding Science Fiction, October 1941. All citations in the text are to this edition.
                34. Georges Poulet, Etudes sur le temps humain (Paris: Union Générale d'éditions, 1972), 45.
                35. “Le Cimetière marin,” ll. 121-122. In an entry in Cahiers I (Paris: Gallimard/ Pléiade), 1973, p. 316 (dated 1944), Valéry states: “Ainsi 25 ans plus tard, j'ai introduit au “Cimetière marin” la strophe Zénon afin de donner à cette ode le caractère particulier d'être le chant de la méditation d'un `homme de l'esprit,' un possédé de la culture.” There are many comments on Zeno (e.g. “Diviser un temps c'est faire semblant de diviser une ligne.”  554-556).
                36. See Käthe Hamburger, Die Logik der Dichtung, for a radical statement of this view.
                37. Lefebvre, p. 60: “Comme l'ancien, le nouvel éléatisme exorcise le temps.”
                38. Henri Bergson, Matière et mémoire, in Oeuvres (Paris: Presses universitaires de France), 1959. Translation: Matter and Memory (London: Allen & Unwin, 1911), 250.
                39. Alain Robbe-Grillet, Pour un nouveau roman (Paris: Editions de Minuit, 1963), 127.
                40. Cited in Nahin, p. 54. The terms used have, of course, precise definitions in the technical language of physics and mathematics. “Such world lines are called timelike because their projection on the time axis is greater than their projection on the space axis.” “Such world lines, which represent travel at a speed in excess of that of light, are called spacelike because their projection on the space axis is greater than their projection of the time axis.” (307: Tech Note 4). When talking of sf stories however, Nahin tends, as might we, to use these terms with more metaphorical “looseness.”
                41. Weyl, Space, Time, Matter (Dover: New York) 1952, translated from the German text written in 1921, p. 96.
                42. Nahin, 208. Many of these stories considered by Nahin as “errors,” where the maddening cycle of events will go on again and again forever, may be more subtle than he thinks. For example, if we pay attention to narrative point of view in one such circular story of a man apparently “damned” to repeat a cycle of events endlessly, Silverberg's “Mugwump 4,” we notice that, with the initial “wrong number” and picking up of the phone, the narrative point of view is outside the character's mind. With the second picking up of the phone at the end of the story however, even though it is exactly the same gesture and circumstance, we are this time inside the mind of the protagonist, insofar as he now is aware that this is a second time, and that he sees himself doomed to do so endlessly. The story could be another example (much more simplistic than Heinlein) of the left-hand, right-hand figures of the Moebius band.
                43. A.S. Eddington, New Pathways of Science (New York: Macmillan, 1935), 68.
                44. Nahin describes a myriad of time travel stories in the 1970s and 1980s, down to today. Time travel is alive and well, and still, in the high manner of sf, accepting the challenge to make fictional models for increasingly complex physical speculations. The irony is that time travel, so often rejected by sf writers as “improbable,” may in today's marketplace be the sole surviving form of sf in which “hard” scientific concerns are being experimented with.

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