The Fourth Dimension of the Non-Euclidean Mind; Time in Brothers Karamazov or Why Ivan Karamazov's Devil Does not Carry a Watch
Liza Knapp, University of California, Los Angeles
In the detailed description of the devil who appears to Ivan Karamazov, Dostoevsky tells us that "he was no longer young, il frisait la cinquantaine," that his jacket was "of a fashion at least three years old that had been discarded by smart and well-to-do people for the last two years," that his trousers were "too tight for present fashion," and that his hat was "out of keeping with the season." (p. 602; XV:70)(1) While these sartorial details may have been intended to convey a general sense of the devil's
poshlost', they serve a more specific function as well.(2) The fact that his clothes are out of date and out of season implies that Ivan Karamazov's devil is temporally disoriented. But even more revealing in terms of the devil's curious relationship to time, is the fact that he does not carry a watch: we are told that "on the middle finger of his right hand he wore a massive gold ring with a cheap opal stone" and that he had "a tortoise shell lorgnette on a black ribbon," and: "he had no watch." (p. 603; XV:71.) Why does Dostoevsky bother to tell us that the devil does not carry a watch and, more importantly, what does this detail reveal about the devil's "creator," Ivan Karamazov, and his own relationship to time?
A clue as to why the devil carries no watch lies in his
travels. Traveling is ordinarily associated with an extreme dependence on time,
and, in fact, the devil, like earthbound mortals, frets about not arriving at
his destinations on time. He even complains to Ivan of how he caught cold in the
process of rushing from some place in outer space down to Petersburg where he
was expected at a diplomatic soirée. He caught cold,
he says, in spite of the fact that his trip "took only an instant, but you know,
a ray of light from the sun takes fully eight minutes, and fancy in an evening
suit and open waistcoat." (p. 607; XV:75). Quick as it is, such travel has its
If the devil does not carry a watch, it is not because he is oblivious of time or indifferent to it; rather it is because of the fact that the astronomical nature of the distances he travels and the speed at which he travels (a speed which, as his remarks imply, approaches or even exceeds that of light) make chronometry, at least as it is known on earth, useless. (3) In Ivan Karamazov's devil's watchlessness there are intimations of modern notions of time, specifically of the notion that absolute time does not exist, that time is relative and depends on spatial coordinates which provide a frame of reference. (4) These concepts, indirectly hinted at by Ivan's devil, became scientific dogma in the early 20th century upon Albert Einstein's formulation of the theory of relativity.
This theory challenged the common tendency to see time as an absolute, as a continuum independent of space. As Einstein himself put it, because of the theory of relativity, "time is robbed of its independence",(5) or, in the words of Hermann Minkowski (which Einstein was fond of quoting) because of relativity, "space in itself and time in itself sink to mere shadow and only a kind of union of the two retains independent existence."(6) Thanks to Einstein's discoveries, we in the twentieth century have at least been conditioned to accept the relativity of time (whether we actually do or not).
Einstein's contribution to physics is known for its radical genius. Still, as he himself often pointed out, he drew on other people's discoveries and experience as he formulated his ideas. As regards the sources of his inspiration, he proved to be an eclectic. In fact, he is reported by Alexander Moszkowski, to have remarked that he learned "more from Dostoevsky than from any scientific thinker, more even than from Gauss."(7) (Karl Gauss was, along with Lobachevsky, Riemann and others, a pioneer in the field of non-Euclidean geometry, which provided the foundation for Einstein's theory of relativity.) Einstein failed to clarify the precise nature of what he may have learned from Dostoevsky.(8) Consequently, the field has been left open to speculation, by scientists as well as students of Dostoevsky, about what, in fact, Einstein may have had in mind in making such a statement. The Einstein-Dostoevsky "connection" has been discussed in Russian publications of recent decades, in the general context of discussions on the relationship of science and literature, as well as in the more specific context of whether or not Dostoevsky ' s poetics can be considered "rational."(9)
One point of view on the subject of what Einstein may have learned from Dostoevsky has been provided by Boris Kuznetsov, a chairman of the International Einstein Society.(10) He bases his argument on a very elegant analogy drawn between what he sees as the essence of Dostoevsky's literary oeuvre, a search for a cosmic harmony that would not ignore the fates and suffering of individuals,(11) and the essence of Einstein's scientific oeuvre which he sees as an attempt to discover a macroscopic harmony that would not ignore microscopic processes. ('12) Kuznetsov finds particularly strong evidence of this outlook of Einstein's in his abiding resistance to discoveries in quantum mechanics which imply that microscopic processes are of a random, indeterminate, chancy nature. Kuznetsov cites Einstein's famous statement that "God does not play dice [with the universe]." More specifically, Kuznetsov sees in Einstein's dogged insistence that God does not play dice even with the fate of microscopic particles an analogy to Ivan Karamazov's rejection of any harmony built on the suffering of a child, for this would imply that God "plays dice" with the fates of certain small individuals.(13)
As may be gathered from this brief summary of his argument, Kuznetsov was less interested in Dostoevsky1s physics than in Einstein's humanism. He contends that Einstein's humanistic approach to science "stems in part from the gallery of suffering characters that Dostoevsky introduced to world culture."(14) In keeping with this viewpoint, he looked to
ethics rather than to physics, for an answer to the enigma posed by the Einstein's remarks that he learned more than Dostoevsky than from any scientific thinker. He writes:
We must find what may be called the "invariant of the transformation from Einstein to Dostoevsky." It cannot be found in his physics for this would result in extremely superficial and formal analogies. The invariant is necessarily psychological, an inner dissatisfaction with the accepted scheme of cosmic and moral harmony.(15)
Indeed, he rejects the notion that Einstein might actually have gotten scientific inspiration from Dostoevsky.
And yet analogies may be drawn between the physics of Dostoevsky and those of Einstein.(16) In pointing out the affinities between Dostoevsky's understanding of the physics of the universe and that of Einstein, I do not intend to speculate on what, if anything, Einstein may have learned from Dostoevsky. Rather, this affinity will be explored in an attempt to crack another riddle, that of the mysterious relationship of Ivan Karamazov to time.
A key issue associated with Ivan Karamazov (if not with the novel as a whole) is his returning his entrance ticket to heaven and his inability to accept God's universe and its harmony.(17) In conversation with Alyosha, Ivan attributes this failure to certain limitations of his mind, specifically to the fact that he has a "pitiful, earthly, Euclidean understanding." Ivan possesses a "three-dimensional" mind whereas divine harmony seems to operate in some fourth dimension:
There have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely the whole of existence, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidean earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions, (p. 216; XIV:214)
Ivan justifies his failure to transcend the limitations of his earthbound mind on the grounds that mystical, otherworldly concerns are out of his ken. Rejection of the fourth dimension, he implies, is the only possible response for a sane, reasonable man who values earthly experience.
Einstein, in his own attempts to spread the news about the existence of the fourth dimension, shows an understanding of the layman's impulse to reject the fourth dimension as some-
thing smacking of mysticism. He writes:
The non-mathematician is seized by a mysterious shuddering when he hears of "four-dimensional things," by a feeling not unlike that awakened by thoughts of the occult.(18)
(Perhaps Ivan Karamazov's bewilderment about the fourth dimension contributed, in some subliminal way, to Einstein's awareness that the concept of the fourth dimension can prove to be an obstacle, barring the spectical layman from grasping those other concepts which depend on comprehension of the fourth dimension.)
Whether Dostoevsky himself was "seized with mysterious shuddering" upon first hearing about the existence of a fourth dimension is not known. (Perhaps Ivan's response reflects some of Dostoevsky's own
initial scepticism.) He is assumed to have become acquainted with Lobachevsky's non-Euclidean (four-dimensional) geometry in the course of his studies at the Academy of Military Engineers, and he is believed to have renewed and expanded his acquaintance with new geometry at the time of writing
Brothers Karamazov.(19) In the work of 19th century geometricians, this fourth dimension was not claimed to have "real existence in our physical space," but rather was regarded as "an ideal creation of the human mind." In the early 20th century, the work of Einstein and Minkowski firmly identified
time as this fourth dimension, thus making it more real. This insight on their part was not, however, brand-new because the 18th century mathematicians D'Alembert and Lagrange had identified time as the fourth dimension. (21) For various reasons, it took over a century for this notion to become widely known and accepted.
By taking this scientific notion, established after Dostoevsky's time but hinted at before it, making it conceivable that he was familiar with it, and applying it to Ivan Karamazov's case one comes to the hypothesis that Ivan was unable to accept the harmony of God's universe because he was unable to understand the mystery of time - time being the "fourth dimension" from which his three-dimensional, Euclidean mind barred him. Since, in a sense, this hypothesis reduces Ivan's existential dilemma (and a major issue of the novel) to the level of a conundrum, the answer to which is time, it, naturally, prompts one to ask whether intrinsic grounds exist for assuming the "dimension" Ivan is missing to be time. Aside from the devil's temporal disorientation, as exemplified by unseasonal clothes and lack of a watch, does anything suggest that a grasp of time is what Ivan lacks?
Dostoevsky's works, in general, have been noted for their particular treatment of time, to wit, for the "allergy toward epic time" and the apparent desire "to destroy time" that they manifest.(22) This attempted neglect of time has been further characterized by Jacques Catteau when he writes that Dostoevsky "sees and thinks about the world primarily in space rather than in time."(23) In this sense, Ivan Karamazov's personal response to time reflects Dostoevsky's general artis-
tic one. Clearly discomfited by time, Ivan demonstrates what may be seen as a spatiotemporal synesthesia whereby he perceives time only in terms of space. In his intellectual struggle to master time, Ivan is joined by the devil, who is himself temporally disoriented, at least from an earthly frame of reference.(24) Together, they engage in the exegesis of a legend originally composed by Ivan. (25) It is related by the devil:
"This legend is about paradise. There was, they say, here on earth a thinker and philosopher. He rejected everything, law, conscience, faith, and above all the future life. He died; he expected to go straight to darkness and death and instead he found a future life before him. He was astounded and indignant. 'This contradicts my principles!' he said. And he was punished for that... that is, you must excuse me, I am just repeating what I heard myself, it's only a legend...he was sentenced to walk a quadrillion kilometers in the dark (we've adopted the metric system, you know) and when he was finished that quadrillion, the gates to heaven would be opened to him and he'll be forgiven [...] Well, this man, who was condemned to the quadrillion kilometers, stood still, looked round and lay down across the road. 'I won't go, I refuse on principle!' Take the soul of an enlightened Russian atheist and mix it with the soul of the prophet Jonah, who sulked for three days and nights in the belly of the whale, and you get the character of that thinker who lay across the road." [...] "Well, is he lying there now?" [asked Ivan.] "That's the point, that he isn't. He lay there almost a thousand years and then he got up and went on." "What an ass!" cried Ivan, laughing nervously and still seeming to be pondering something intently. "Does it make any difference whether he lies there forever or walks the quadrillion kilometers? It would take a billion years to walk it?" "Much more than that, I haven't got a pencil and paper or I could work it out. But he got there long ago and that's where the story begins." (pp. 610-611; XV:78-9)
This legend deals with time and, more specifically, with the human mind's difficulty in comprehending temporal concepts, especially that of eternity (a unit of time of considerable interest to Dostoevsky). This general difficulty results in a tendency to rely on a body's motion in space to assess time. In this manner, time is domesticated. Traditionally time has been measured in terms of the motion of a body through space, whether the motion of the sun, the earth, or cesium atoms. However, in the 19th century, scientists began not simply to
measure time in terms of motion through space but also to define it in these terms, thus abandoning the concept of absolute time. In particular, Lobachevsky defined time in terms of the relative movement of material bodies: "The continuation of the motion of one body, taken as being known for comparison with another, is called time."(26) Through such a material, relative definition of time, Lobachevsky, according to the current Soviet interpretation of his work, transcends both the "methaphysical" limitations of Newton's definition of time as an absolute
existing independently of the (relative) motion of bodies in space whereby men, more or less accurately, measure time, and the "subjective" limitations of Kant's definition of time.(27) In discussing time in
Critique of Pure Reason, Kant had referred to time as being "nothing but the form of our internal intuition."(28) In
The Devils, when Kirilov, in conversation with Stavrogin, declares time
to be "not a thing but an idea," Kantian notions of time are hinted at. (29) In
Brothers Karamazov, when Ivan and his devil toy with material definitions of time in terms of motion through space, they hint at other more scientific definitions of time which were gaining popularity in Dostoevsky's Russia.(30)
Within Ivan's legend, these constant translations back and forth between units of time and units of space (a quadrillion miles' walk being greater than or equal to a billion years, etc.) reveal the material, earthly nature of the protagonist's mind, as well as of that of Ivan himself. Such a mind, unable to perceive time itself, much less eternity, strives to make it physically real by translating it into the motion of a body through space. (Having it be the motion of one's own body perhaps constitutes a compromise between the materialism of Lobachevsky, who defines time strictly in terms of motion, and the subjectivism of Kant, who defines time as something internally perceived.)(31)
The man in the legend initially refuses to believe in eternity because he cannot conceptualize it. The material, earthly nature of his mind causes him to reject eternity and thereby provokes divine wrath. And as fitting punishment for this crime (of having a material mind that makes eternity inconceivable) , he is condemned to a material or spatial
imitation of eternity: a quadrillion-kilometer walk. As in Dante's Inferno (to which Ivan himself makes reference in another context [XIV:224]), the punishment to a certain degree perpetuates the sin itself. But the long walk actually is purgatorial. From a human frame of reference, a quadrillion-kilometer walk may be taken for an eternal punishment; however, the man eventually arrives in paradise to find that there is no less time to praise the Lord than there was when he began. In the process, he learns that true eternity cannot be translated into space and comprehended simply in relative terms of motion. The devil describes the man's arrival into paradise and his enlightenment as to the nature of eternity as follows:
A tol'ko chto emu otvorili v rai, i on vstupil, to, ne probyv eshche dvukh sekund - i eto po chasam po chasam (khotia chasy ego, po-moemu, davno dolzhny byli by razlozhit'sia na sostavnye elementy v karmane dorogoi), -ne probyv dvukh sekund, voskliknul, chto
za eti dve sekundy ne tol'ko kvadrillion, no kvadrillion kvadrillionov proiti mozhno, da eshche vozvysiv v kvadrillionnuiu stepen'! (XV:79)
This passage has been quoted in Russian because of a
possible ambiguity as to the meaning of the man's statement that "za eti dve sekundy ne tol'ko kvadrillion no kvadrillion kvadrillionov proiti mozhno." The prepositional phrase "za eti dve sekundy" is ambiguous. Is he saying that "for the sake
of those two seconds" one can walk quadrillions of kilometers or is he saying that "in the course of those two seconds" it is possible to walk quadrillions of kilometers?(32) This latter interpretation may be considered more provocative since it contains possible intimations as to the relativity of time and space. Either way, the implication is certainly that seconds in paradise are of a totally different order than seconds on earth, whether because they are "worth the walk" or because they, seconds though they are, encompass what
- from an earthly point of reference - would be tantamount to eternity.
In many of his works, Dostoevsky explores this notion that certain moments can contain a lifetime's worth, if not a billion years' worth, of experience. Several of his characters experience and comment on this phenomenon. In depicting time in this way, Dostoevsky probably was influenced by his own personal experience of epilepsy. Yet he also may have drawn on literary depictions of this phenomenon.(33) The
Koran provides the locus classicus in the passage where Mohammed tells of having been awakened by Gabriel and been taken by horse from Meccah to Jerusalem and from there to heaven then back to Meccah - in an instant of time - that is,
before all of the water had flown from the pitcher which Gabriel had knocked down when he entered Mohammed's room. The wealth or quantity of experience packed into one moment of time is here described in terms of great distances being covered in space. Space is used to evaluate and assess time.
In the Bible, this condensation of much experience into a miniscule span of time is associated with the devil (with whom Ivan's visitor has some generic connection). In tempting Christ, the devil "took him up and showed him all the kingdoms of the world in a moment of time..."(34) The notion that in certain short spans of time much territory can be covered may thus evoke both angelic and devilish experience of time. Whatever its associations, its effect is, in a certain sense, to undermine earthly time and, consequently, earthly existence itself, by making normal earthly seconds, and even the minutes, hours, days and years they constitute, appear pitifully insignificant in comparison to what devils or angels can experience in the same unit of time.
Within Brothers Karamazov, Ivan and his devil are not the only ones to discuss the condensation of much experience into a small span of time: it is also discussed by Zosima and his brother Markel'. When the doctors kept assuring the dying Markel that he would live for many days, months and years yet, Markel was not interested in such expanses of time:
"Months and years!" he would exclaim. "Why reckon the days? One day is enough for a man to know all happiness." (p. 268; XIV:262)
Apparently, this startling view of time profoundly affected Zosima, for he incorporates it in his later teaching. In the scene in which he first appears in the novel, he preaches:
There is no need to be troubled about times and seasons, for the mystery of the times and seasons is in the wisdom of God, in His Providence and His love. And what in human reckoning seems still afar off, may by the Divine ordinance be close at hand, on the eve of its appearance. And so be it, so be it! (p. 57; XIV:61)(35)
Zosima's statements seem to promote the general scientific notion of time's relativity. They suggest that perceived from an earthly frame of reference time differs from time from the heavenly frame of reference. That a certain relativity exists in regard to the universe's experience of time is an idea embedded in Russian Orthodox theology. For example, in the following passage, Sergii Bulgakov hints at the relativity of time:
Temporalness [vremennost'] is the universal form of existence, the property of creatureliness [tvarnost'], to which all creation is subject: angels, human beings, the whole world. Notwithstanding this, time can be various, temporality receives expression in concrete, qualitative times: time for angels, one must suppose, is different than for people and for man it is different than for animals.(36)
Zosima appears to be able to accept this mysterious relativity, which, in a sense, constitutes the corollary to his belief that God has transplanted elements and forces from other worlds into this one and thus, in a sense, frustrated human attempts to master the planet in a scientific way. (p. 299; XIV:291.)
For Zosima, then, many aspects of earthly existence cannot be fathomed from an earthly perspective. Thus he leaves this "mystery of the time
and seasons" in God's hands,(37) whereas, goaded by his devil, Ivan tries to crack the puzzle of time, by insisting that it can be translated into material, spatial terms.
In keeping with his conviction that time is a mystery, Zosima's attitude toward time is paradoxical. Just as he counsels a lack of concern about "times and seasons," so too does he counsel that one should surrender to time's flow, to the process of aging, to death and to other effects wrought by time's passage. In this sense, time appears to work in consort with the laws of nature to destroy man and, indeed, when "there will be time no longer," then the laws of nature, as known on earth, will be rendered obsolete. The laws of nature and time are thus inextricably linked. Sergii Bulgakov defines corruptibility (tlennost') as the "destructive force of temporalness" [razrushitel'naia sila vremennosti], arguing that man's goal is to transcend this state. (38) It may seem that in accepting the effects of time as he does, Zosima capitulates to decay and even to the physical determinism implied therein. However, existence for Zosima is not mechanically predetermined and time does not simply serve as a fourth coordinate needed for the enactment of the laws of nature. For Zosima, time can also bring about startling reversals.(39) Although the Second Law of Thermodynamics establishes the notion that
time's direction is one-way and that certain physical processes are irreversible, for Zosima no
spiritual equivalent of this law exists.
Zosima demonstrates that he believes that miracle or the divine will, rather than mechanical determinism, runs the universe. He appears to have "the enlightened eye of the saints" described by Sergii Bulgakov:
Only in exceptional moments does the hand of Providence become noticeably visible in the personal and historical life of humanity, although for the enlightened eye of the saints the world is a continuously-enacted miracle. The conformity to mechanical law ["mekhanicheskaia zakonomernost'"] of the world, the crust of nature ["kora estestva"] conceals divine Providence from us...(40)
Whereas Ivan Karamazov, with his material understanding, concludes that the world operates according to mechanical laws that operate in time, Zosima penetrates this mechanically-operated universe and perceives a universe guided by the hand of providence.
Indeed, Zosima's vision enables him to discover providence at work even in those events that seem to embody nothing more than the triumph of the death-dealing force of nature. His statements about how one ought to surrender to the flow of time both occur when he addresses the issue of a parent's response to the loss of a child. This specific situation epitomizes a crucial facet of man's relationship to time: his realization of the mortality that results from the "irreversibility of time's movement."(41) Zosima focuses on a parent's grief over the death of a child because it serves as the most jarring reminder of human mortality and hence of the tragic effects of time. .Early in the novel, Zosima tells a bereaved mother:
A long while yet you will keep that great mother's grief. But it will eventually turn into quiet joy and your bitter tears will be only tears of tender sorrow that purifies the heart and delivers it from sin. (pp. 41-2; XIV:61)
According to Zosima, time deals cruel blows to man (death), but it also, in passing, brings about other changes which mitigate its cruelty. To illustrate time's mysterious ways, Zosima speaks of Job's loss of his children and how eventually his grief will turn to joy:
And what mysteries are solved and revealed; God
raises Job again, gives him wealth again. Many years pass by, and he has other
children and loves them. [. . .] But how could he love these new ones when those first children are no more, when he has lost them?... But he could, he could. It's the great mystery of human life that old grief gradually passes into quiet tender joy. The mild serenity of age takes the place of the riotous blood of youth, (p. 271; XIV:265)
So what is, for Zosima, the mystery of time? Based on these
passages, it seems to be time's ability gradually to change grief into quiet joy, to reconcile people with loss and injury. The mystery is that of the commonplace, "time is a healer," or that expressed by Pascal in his
Le temps guérit les douleurs et les querelles, parce qu'on change: on n'est plus la même personne.
Ni l'offensant, ni l'offensé, ne sont plus eux-mêmes. C'est comme un peuple qu'on a
irrité, et qu'on reverrait après deux générations. Ce sont encore les Français, mais non les mêmes.(42)
For Zosima, as for Pascal, whatever harmony exists on this earth exists because of the fact that time passes and thereby heals, gradually, but nevertheless miraculously. Harmony exists because time enables people to change and to forgive offenses, even offenses such as the cruel, senseless loss of one's children.(43)
To Ivan Karamazov, such harmony is unfathomable. His test case, on the basis of which he rejects harmony and his ticket to heaven, involves the mother of a little boy whose son has been senselessly murdered (pp. 223-226; XIV:220-224!. Ivan argues that the mother's forgiveness of her son's murderer would mean harmony on earth but he cannot accept such harmony. In
Brothers Karamazov, Dostoevsky juxtaposes Zosima's and Ivan's positions on this same basic issue, a parent's response to loss of a child. Dostoevsky thereby intimates that Ivan cannot accept this harmony (brought about by forgiveness) because he fails to fathom Zosima's "mystery of life," that is, that time gradually works changes in human beings, healing their griefs and offenses and allowing eventual forgiveness. In this fashion, Dostoevsky suggests indirectly that time is the link Ivan is missing. When Ivan says that he cannot accept God's harmony because of his three-dimensional, Euclidean mind, Dostoevsky indirectly seems to hint that the fourth dimension Ivan cannot comprehend, that the fourth dimension barring him from harmony, is none other than time. Ivan Karamazov is barred from accepting some of the mysteries of time and nature (which Zosima is able to embrace) because he holds an earthly frame of reference to be the only valid one. The novel thereby suggests that time is the "fourth dimension," that it provides a fourth coordinate without which events in three-dimensional space cannot be fathomed. In this manner, Dostoevsky's novelistic universe is grounded in physics and, specifically, it depends on a four-dimensional space-time continuum which anticipates Einstein's perception of the physical universe. (44)