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a general sense of the devil's poshlost', they serve a more specific function as well.(2) The fact that his clothes are out of date and out of season implies that Ivan Karamazov's devil is temporally disoriented.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 inconveniences.

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.

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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

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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-

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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-

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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

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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

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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:

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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

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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

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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 Pensées:

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)

NOTES

1. The page numbers of references to Brothers Karamazov are given in parentheses after citations. The first page number will refer to the English translation, the second, to the Russian text. Editions used are: Fyodor Dostoevsky, The Brothers Karamazov, trans. Constance Garnett (New York: Norton, 1976); and F. M. Dostoevskii, Polnoe sobranie sochinenii (Leningrad: Nauka, 1976), XIV & XV. Slight
   
   

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   changes have occasionally been made in the English translations.
2. The devil later comments on Ivan's pride and romanticism which cause him to be insulted by the devil's poshlost': "You are really angry with me for not having appeared to you in a red glow, with thunder and lightning, with scorched wings, but have shown myself in such a modest form. You are wounded, in the first place, in you aesthetic feelings, and secondly, in your pride. How could such a vulgar [poshlyi] devil visit such a great man as you! Yes, there is that romantic strain in you, that was so derided by Belinsky." (p. 614; XV:81).
3. In discussing the man who walked a quadrillion kilometers and finally arrived in heaven, the devil remarks: "to my thinking his watch must have long dissolved into its elements on the way." (p. 611; XV:79).
4. A lack of absolute time results in the "time dilation" phenomenon whereby identically constructed clocks function differently in moving frames of reference.
5. Albert Einstein, Relativity: The Special and the General Theory, trans. Robert W. Laws (New York: Crown, 1961), p. 56.
6. Quoted in: Albert Einstein, "Time-Space" in Encyclopedia Britannica (London, 1929), 14th edition, XXI:105.
7. A. Moshkovskii, Al'bert Einshtein (Moscow, 1922), p. 162. Einstein's reference to Dostoevsky is mentioned by Fridlender in his notes to Brothers Karamazov: Using the geometric ideas of N. I. Lobachevsky as a springboard, Dostoevsky ingenuously through the mouth of Ivan provides a link to the great discoveries in physics and new ideas in philosophy of the 20th c. It is not by chance that the colleague of A. Einstein and author of a book about him cites the remark of the scientist made in conversation with him: [Einstein's remark about Dostoevsky follows here]." (XV:473)
   Mozkowski's memoir, based on conversations held with Einstein in 1919 and 1920, is available in English translation: Alexander Moszkowski, Conversations with Einstein, trans. Henry L. Brose (New York: Horizon Press, 1970). Einstein's remark about Dostoevsky appears on p. 185.
   I am grateful to Diane Thompson for alerting me of the fact that some who knew Einstein did not consider Moszkowski to be fit to report on Einstein and objected to the publication of his book. She also notes the fact that Einstein's remark about having learned more from Dostoevsky than from Gauss appears only in this one source. Thus, we are left with not proof, other than Moszkowski's report, that Einstein actually said this.
   Although the remark about Gauss and Dostoevsky may
   
   

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   possibly be apocryphal, Einstein's affinity for Dostoevsky, in general, and for Brothers Karamazov, in particular, has been well-documented. For example, C. P. Snow writes: "The Brothers Karamazov - that for him in 1919 was the supreme summit of all literature. It remained so when I talked to him in 1937, and probably until the end of his life." ("Foreword" to Alexander Moszkowski's Conversations with Einstein, p. vii.)
8. Although Moszkowski questioned Einstein about the meaning of his remark, they got sidetracked onto the subject of whether scientific discoveries, if not made by one man, would be made by another or whether they, like artistic creations, depended on the unique genius of individuals.
9. A series of articles on the broader subject appears in: Voprosy literatury, no. 8, 1964. One of them, D. Danin's "Vozmozhnye resheniia" discusses, among other things, Einstein's remark about Dostoevsky. (pp. 88-111).
   Boris Meilakh discusses Dostoevsky and Einstein in: "Polemika o problemakh vzaimosviazei nauki i iskusstva" in Na rubezhe nauki i iskusstva (Leningrad: Nauka, 1971); "Problema 'Upravleniia svoim talantom': Dostoevskii" in Talent pisatelia i protsessy tvorchestva (Leningrad: Sovetskii Pisatel1, 1969).
   See also: Grigorii Pomerants, "'Evklidovskii' i 'neevklidovskii' razum v tvorchestve Dostoevskogo", Kontinent, no. 3, 1975. pp. 109-150. Pomerants suggests that Einstein may have gained inspiration from Dostoevsky's "relativistic" novelistic structure with its "multitude of equally-valid points of reference."
10. Boris Kuznetsov, Einstein and Dostoevsky, trans. Vladimir Talmy, (London: Hutchinson Educational, 1972). This book is a translation of material which appeared in Russian in the sixties. Response to Kuznetsov's conclusions and method may be found in "Protivorechiia Dostoevskogo i printsip dopolnitel'nost" by M. Gus. (Voprosy literatury, no. 3, 1968, pp. 166-180).
11. For example, see Kuznetsov, p. 12: "Whatever one may think of Dostoeyevsky's public views, however erroneous or reactionary his political and social ideas may have been the essence of his art is an appeal addressed to the twentieth century; man needs a social and moral harmony that does not ignore local disharmonies and that refuses to accept the individual sufferings of any man, a harmony that leaves no place for coercion, oppression or contempt for the weak."
12. Kuznetsov, pp. 39-40.
13. Kuznetsov, pp. 41-42.
14. Kuznetsov, p. 108.




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15. Kuznetsov, p. 60.
16. Although it may seem odd to refer to a novelist as having his own "physics," Dostoevsky's works reveal his abiding interest in this field, which was linked, in his mind, to metaphysics. Throughout his works, the heroes' understanding of the actual mechanics of the universe plays a determining role in their consciousness.
17. Kuznetsov gives this issue almost inordinate importance when he writes: "The chapter in which Ivan Karamazov 'returns his ticket of admission' is called 'Rebellion'. It is not only the culminating point of the novel but even perhaps the culmination of all Dostoyevsky's work." p. 11.
18. Einstein, Relativity, p. 55.
19. Fridlender, Notes to Brothers Karamazov, XV:551. For more specific information on Dostoevsky's knowledge of non- Euclidean geometry, see: E. I. Kiiko, "Vospriiatie Dostoevskim neevklidovoi geometri", Dostoevskii: Materialy i issledovaniia, ed. G. M. Fridlender (Leningrad: Nauka, 1985), VI:120-128. Kiiko notes that Dostoevsky was responding not to Lobachevsky's geometry but rather to that of Bernhard Riemann, which was popularized in Russia by an article by Herman Helmholtz, published in the Russian journal Znanie in 1876.
20. Florian Cajori, "History of Geometry", in Encyclopedia Britannica (London, 1929), 14th edition, X:180.
21. Ibid.
22. Jacques Catteau, "Vremia i prostranstvo v romanakh Dostoevskogo", in Dostoevskii: Materialy i issledovaniia, G. M. Fridlender, ed (Leningrad: Nauka, 1978), III:52.
23. Ibid. III:42.
24. Jacques Catteau sees Dostoevsky's use of the device of the double as being a result of his predilection for space over time. He suggests that Dostoevsky's "allergy toward epic time" spurred his creation of "an original, experimental literary space, in which the tangled skein of human life unravels in a series of collisions between an individual and his double." (III:52) Catteau's basic point is perhaps further dramatized by the fact that Ivan and his double, the devil, actually discuss the translation of time into space. Both formally and thematically, then, their encounter demonstrates a spatial, rather than temporal, orientation.
25. As E. I. Kiiko notes in "Vospriiatie Dostoevskii neevklidovoi geometrii", entries in Dostoevsky's notebooks reveal that he was pondering non-Euclidean geometry in the summer of 1880, the period in which he wrote the chapter "The Devil: Ivan Fedorovich's Nightmare." In a footnote,
    
    

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    she adds: "It is possible that the problems, touched on in Helmholtz's article, were in some way to be reflected in the legend of the devil about 'the thinker and philosopher' condemned to walk 'a quadrillion kilometers in the dark.'" The term "quadrillion" also appears in the notebook entries in which Dostoevsky explores the philosophical and religious ramifications of non-Euclidean geometry. (Kiiko, p. 125.) The notebook entries she refers to appear in the Polnoe sobranie sochinenii, XXVII: 43.
26. N. I. Lobachevskii, "Dve lektsii po mexanike", in Voprosy filosofii, 1951, no. 6, p. 194. Quoted in: N. A. Litsis, Filosofskoe i nauchnoe znachenie idei N. I. Lobaohevskogo (Riga: Zinatne, 1976), p. 319.
27. Litsis, p. 313.
28. Immanuel Kant, Critique of Pure Reason, trans. F. Max Muller, (Garden City: Anchor, 1966), p. 33.
29. Kirilov explains to Stavrogin that an earthly eternal life will come about and that "there will be time no more." Stavrogin, pragmatically, asks: "Where will it be hidden?", to which Kirilov responds: "It won't be hidden anywhere. Time is not a thing but an idea. It will be extinguished in the mind." (Polnoe sobranie sochinenii, X:188).
30. The human mind has been converting time into space, and vice versa, for thousands of years. If possible sources of Dostoevsky1s inspiration are to be mentioned, then to the works of scientists such as Lobachevsky should be added the Book of Jonah, which, in fact, is alluded to in Ivan's legend (as well as elsewhere in the novel). In this work, the hero's spiritual dilemma is depicted in spatio-temporal terms, such as those used in Einsteinian "Gedanken" experiments: Jonah is told to go and warn the city of Nineveh of God's wrath and the destruction it will suffer unless it repents. Instead of setting off to Nineveh, Jonah flees and ends up spending three days in the body of a whale. Eventually, he sets off for Nineveh, there being at this point forty days left for it to repent. This city is described as being "three days walk wide" (time used to measure space), thus all inhabitants will not hear the news simultaneously and thus they will experience a "relativity" of sorts. Moreover, the arithmetically-minded reader will note that the time Jonah wasted "pouting" in the whale, three days, was the amount of time required to walk from one end of the city to the other.
31. Along these lines, Henri Bergson suggests that man's willingness to accept the measurement of time in terms of motion through space results from man's subjective, but physical, experience of motion. He writes: "II est donc bien vrai que le temps se mesure par l'intermédiaire du mouvement. Mais il faut ajouter que, si cette mesure du temps par le mouvement est possible, c'est surtout
    

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    parce que nous sommes capables d'accomplir des mouvements nous-mêmes et que ces mouvements ont alors un double aspect: comme sensation musculaire, ils font partie du courant de notre vie consciente, ils durent; comme perception visuelle, ils décrivent une trajectoire, ils se donnent un espace." Durée et simultanéité: A propos de la théorie d'Einstein (Paris: Presses Universitaires, 1968), p. 48.
32. Constance Garnett chose the former - her translation of the passage reads: "Why, the moment the gates of Paradise were open and he walked in, before he had been there two seconds, by the clock, (though to my thinking his watch must have long dissolved into its elements on the way), he cried out that those two seconds were worth walking not a quadrillion kilometers but a quadrillion of quadrillions, raised to the quadrillionth power!" (p. 611).
33. A scientific model for this phenomenon was later provided by Einstein when he developed the notion of "time dilation" in conjunction with the theory of relativity. According to this notion, an observer in one frame of references recording the passage of time in another moving frame of reference will find that time "dilates," that is, appears to move more slowly, with the interval between seconds approaching infinity as the speed of the moving frame approaches the speed of light. See: Gerald Holton, Introduction to Concepts and Theories in Physical Science (Reading: Addison-Wesley, 1973), pp. 516-517.
34. Luke 4:05.
35. Zosima's words echo Acts 1:7: "It is not for you to know the times or the seasons which the Father has put in his own power." (XV:536, notes).
36. Sergii Bulgakov, Svet neverchernii: sozertsaniia i umozreniia (Moscow: Put', 1917), p. 200.
37. The Church's notion that time is a mystery did not keep monasteries from attempting to master and domesticate time. The invention of mechanical clocks took place in monasteries where some artificial means of telling time became necessary since life was dependent on a schedule that did not follow natural time-telling devices (e.g. the sun).
    This link of monastic life to the clock is perhaps reflected in Dostoevsky's novel when the Karamazovs' appointment with Zosima is set for a fixed hour. Fyodor prides himself for having arrived at the monastery on time when he calls punctuality the "royal politesse" ["vezhlivost' korolei"]); Mitya, however, is scandalously late, his excuse being that Smerdiakov lied to him when he asked him what time he was supposed to be there.
38. Bulgakov, pp. 200-201.




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39. For example, Zosima himself had experienced such a change when in his youth he decided to interrupt the duel he was scheduled to fight over a young lady. He quite simply explained to his opponent that he was not going to shoot because: "yesterday I was still a fool but today I know better." ("Vchera eshche glup byl, a segodnia poumnel", p. 278; XIV:271).
40. Bulgakov, Svet nevechernii, p. 208.
41. Meyerhoff sees the human's perception of the "irreversibility of time's movement" as the "most significant aspect of time in human experience, because the prospect of death thus enters, as an integral and ineradicable part, into the life of man." Hans Meyerhoff, Time in Literature (Berkeley. University of California, 1960), pp. 65-6. Meyerhoff also stresses the importance of the Second Law of Thermodynamics to modern perceptions of time.
42. Blaise Pascal, Pensées (Paris: Garnier, 1964), pp. 107-108. No. 135.
43. Since he is aware that eventually "there will be no more time", Zosima recognizes that earthly time, in which change is still possible, is a precious commodity. To illustrate this point, he uses the parable of the rich man who in earthly existence had shown no brotherly love for Lazarus. (Luke 16:19-30). In the eternal life, this man finds that Lazarus is at the bosom of Abraham; he recognizes his past failures but finds that it is too late: "For he sees clearly and even tells himself: 'Now I have knowledge and although I now thirst for love, there would be no martyrdom in my love, nor any sacrifice since earthly life is over and Abraham won't come even with a single drop of living water (that is the gift of earthly life, the previous, active life) to cool the flame of my thirst for spiritual love, with which I, who on earth neglected it, now burn; there is no more life for me and there will be time no more! Although I would be glad to give my life for others, now it's no longer possible, for that life has passed which could be sacrificed in love, and now there's an abyss between that life and this existence.'" (p. 301-302; XIV:293). By means of his interpretation of this parable, Zosima demonstrates that Christ-like love does not have the same effect when "there will be time no more" as it does from the earthly frame of reference. He also shows that repentance is possible only within time.
44. For Einstein's explanation of the "four-dimensional time-space continuum", see his Relativity, p. 56.