The Numerical Rhizome

Padma Devkota

    After I once scored a hundred marks in a math test in class three, my mathematical ability has constantly declined to the extent that, like many other people today, I rely heavily on the calculator for easy additions and subtractions. I certainly made an early discovery that numbers beyond hundred do not exist for some people. Some early and later civilizations did not find it necessary to count beyond ten or twenty and were therefore not able conceive the words for million or thousand or even five hundred until well after the barter system was replaced by functional bank notes. Others such as the Greek civilization were able to build the four-sided Great Pyramids at Giza that were as tall as 481 feet and had a large base that covered 755 sq. ft. Pythagoras (580?-500 B.C.), the Greek mathematician, assigned mystical properties to numbers. He was a philosopher of immortality and a believer in the reincarnation of the human soul.

    Numerical relation may not be everyone's meat. However, for the Greeks and Hebrews, and also for the Egyptians, Druids, and Hindus, it was real venison. They delighted in number symbolism to the extent that numbers were charged with mystical and magical powers, which were the privilege of the high priests and the shamans. Unlike me who find numbers generally boring, these mystics and magicians found the mysteries of life and death encoded in numbers that spoke directly to their heart in a very spiritual way. Thus, numerology, the study of the influence of numbers on human life, developed as a special branch of knowledge. China, the Hindu's chart of life, exemplifies how the date and time of birth can generate astrological calculations that claim the power to forecast all the major events of human life. Numbers have penetrated rites, ceremonies, astrology, occultism, spiritualism and many other practices of numerous societies. I even dare to presume that numbers spread around the world because of the significance that they accumulated in terms of their mystical and magical properties. Zero, for instance, was not part of the Greek or the Roman numbers. The Arabs learned it from the Hindus and taught it to the others.

    And this is really what literature has drawn from mathematics: the mystery and the magic of numbers applied to social and religious ways of living and thinking. Numbers have gained special symbolical meanings in various cultures. Zero is a circle that represents Nought or Void. It is like a mythic serpent that bites its own tail. Creation begins from zero and dissolution ends in zero. One is the Absolute, the unmatched, the unique. Two recalls the creative dualism of the Samkhya and that of the dualistic Vedanta. All reproductive coupling is a function of two. Three is the trinity in religion: the Father, the Son and the Holy Ghost or the Brahma, Vishnu and Maheshwor of the symbolic letter Om. Where the West sees only four basic elements that compose all life, the East sees five. In this way, each number attaches itself to some fundamental concept of life and the world. Thus, the numerical rhizome sprouts quantitative values in mathematics but mystical values in religion and symbolical values in literature.

    Let me provide a few examples of what I mean from the poetry of Laxmi Prasad Devkota. In "To a Dark Clouded Night," he calls night a "dissolver of the light of day" and sees in it the "visible outline of vast, vast Nought." It's almost as if the nocturnal sky were a round and empty circle, a zero in quantitative terms. This Nought, also called Void, billows and dashes against the individual human consciousness, symbolized by each of the innumerable nocturnal stars. The poet's consciousness is startled by the presence of this Void and chokes with fear of extinction. This is the fear of death and of losing one's identity in the levelling zero. Yet, at the fag end of his life, the poet was capable of reconciling with the onslaught of this Void. He wrote: "Like Void, I dissolve into the Void."

    Devkota had opted for mathematics too at the Intermediate of Science level. That is probably why he even included the algebraic formula a²+b² = c² in an earlier version of the poem titled "The Lunatic." Later, he edited this portion of the text probably because it sounded more pedantic than poetic. The text he left behind reads as follows:

        Clever and eloquent you are!

        Your formulas are ever running correct.

        But in my calculations one minus one is always one.

No mathematician will agree with such calculations because quantitative values do not function in this way. In this poem, one is symbolic of the Absolute from which nothing can be subtracted. The lunatic persona operates with the sixth sense, which is the heart. And the heart is capable of reading symbols in natural objects:

To you a rose is but a rose,

It embodies Helen and Padmini for me.

    Another instance of the failure of quantitative calculation is found in "We Are Seven" by William Wordsworth who tells of how a young female child fails to understand that the death of her brothers and sisters has resulted in a quantitative decrease of the members of the family. She insists that they are seven children although some of them are already in the grave.

    Other poets too have made use of the magical, mystical, or symbolical use of numbers. In "Kubla Khan," which is a dream fragment, S.T. Coleridge has a vision of an Abyssinian maid who is playing on her dulcimer. He says that if only he could revive within himself the girl's "symphony and song," he would be so ecstatic with the artist's inspiration that he would, with the help of music,

              build that dome in air,

That sunny dome! those caves of ice!

And all who heard should see them there,

And all should cry, Beware! Beware!

His flashing eyes, his floating hair!

Weave a circle round him thrice,

And close your eyes with holy dread,

For he on honey-dew hath fed,

And drunk the milk of Paradise.

Divine inspiration has rendered him into something like an ancient magician or a holy sage with unearthly powers. This is why common men are asked to weave carefully a magic circle thrice around him.

    Any discussion of literary symbolism of numbers would be incomplete without a brief discussion of William Butler Yeats. In his book titled A Vision (1926), Yeats develops his theories on human personality, on history, culture and civilization. He bases the symbolic system on the lunar calendar and counts the twenty-eight phases of the moon, which form a complete cycle or circle. There is a bright half and a dark half of this circle. The individual soul begins its journey out of primal darkness in a state of natural innocence. It grows intellectually. The fourteenth phase corresponds to the full moon. This phase symbolizes the victory of wisdom over brute power. This is also the height of the individual's personality, which imposes itself upon the external reality. After this, the external reality begins to regain its primacy until, in the twenty-sixth phase, the soul loses its distinguishing personality. In the twenty-seventh phase, the soul stops longing for the lost personality, and in the twenty-eighth phase, the soul is like the mythic Fool who wanders aimlessly into dangerous places. This forms a complete cycle.

    Cultures and civilizations too undergo a complete cycle. In a 1924 sonnet titled "Leda and the Swan," W. B. Yeats dramatizes the historical point where the Babylonian Heroic Age was replaced by the Classical civilization, which in turn was later replaced by western Christian civilization. Zeus, in the form of a swan descends to the earth to violate the chastity of Leda, wife of Tyndareus. Out of this rape are born two twins: Helen and Pollux and Clytemnestra and Castor. Hellen, married to Menalaus, eloped with Paris. Troy fought a very long war to bring her back. Similarly, Clytemnestra murdered her husband Agamemnon, a hero of the Trojan War. Recalling this story, Yeats asks whether human beings are ever aware of the consequences of their own actions, for such awareness would be prophetic.

    And, such changes in civilization occur every two thousand years, according to the calculations of the poet. So, against the background of the First World War and many other civil wars, Yeats sees the dark forces of the pre-Christian age return as Anti-Christ in "The Second Coming." His own death in 1939, the year in which the Second World War begun, is symbolic in terms of this prophecy, which also promises the rebirth of Christ in the year 4000. We are today, according to Yeats, in the dark phase of the Christian era.

    Prophets, poets, sages, highpriests, magicians, and mystics (and I might add mathematicians too) all have something in common. The poet, however, often displays a greater love for natural beauty than the mystic who gazes at the unseen or the highpriest for whom beauty can lie only in moral conduct. Some poets, it is true, are prophets too. Their prophecies may or may not make use of mathematics. They may not be able to say like scientists, "Give me a place to stand in space to use my lever. I will move the earth to the spot you desire." They will say, "What's in a name? / A rose by any other name will smell as sweet." This is common sense expressed in the best possible way in a language that cannot be rewritten to excel what it already is. And common sense is the best logic I have come across thus far. Logic and mathematics are intimately interwoven into each other's fabric.

    However, poets have other functions to fulfill besides that of prophecy alone. They are artists, too, with a sense of proportion, of harmony, of symmetry. Mathematics mothers symmetry. Aestheticians have calculated ratios of physical beauty: the ratio of the length of the nose to the height of the forehead; the ratio of the length of the metacarpus to the length of the fingers; the ratio of the length of the thigh to the length of the leg. There is always some mathematical ratio between parts wherever there is symmetry. Poets and artists do not need to walk around with rulers and verniers. They walk around with an innate sense of proportion and harmony that most people are born with.

    Poets and artists of the Medieval Age were more attuned to the requirements of proportion, symmetry, and harmony than people are today. The divine, the natural, and the human coexisted in their world in a mutually beneficial harmony. Balance and order were the keys to survival. Cosmic vibrations reverberated in microcosms. People lived in a harmonious age dominated by a natural hierarchy in a nexus of ascending order from inanimate to vegetative to animal to human to angelic to divine. God resided in the apex of the triangle, the base of which was the inanimate world. The clock-like mechanical efficiency of the world was both a matter of great appreciation and a proof of infallible intelligence that must envision the minutest details of a very complex universe. The harmony of the clock-like universe pervaded ethics, morals, science, religion, politics and all other aspects of medieval life. Poetry was not untouched.

    Classical poetry gave much emphasis to both internal and external forms and structures. The poet's desire for precision, accuracy, and a strict observation of rules of composition spoke of how mathematical proportions pervaded both art and nature of the Medieval and Classical Ages. This pervasion of mathematical proportions expressed itself in many ways in literature: in the linearity of the oral story-telling tradition; in the rise towards the climax, the crisis in the apex, and the descent of the anticlimax towards the denouement in Shakespearean and other dramatic works that were artistically woven into the five-act structure; in the sonnet form with its fourteen lines divided either into an octave and a sestet (8+6) or three quatrains and a couplet (4+4+4+2), or two quatrains and two tercets (4+4+3+3), and so on. Even the length of poetic lines in each stanza had to be proportionate for the sake of visual aesthetics, which disproportionate lengths would destroy. Poetic lines were measured in terms of the number of meter they contained. Each meter had a foot, which was either two or three stressed and unstressed syllables. Equal number of feet provided a sense of balance and harmony, which was enhanced by end rhymes.

    The adherence to and practice of strict classical requirements of poetic compositions were to shatter only with the dawn of a modern sensibility that stirred with the eighteenth century Romantic revolt against Classical literary practices. The age of literary modernism, however, does not coincide with the age of mathematical or philosophical modernism. It was another mathematician, René Descartes (1596-1650), also known as the Father of Modern Philosophy, who decided to rebuild the western philosophic foundation from scratch by simply doubting the validity of existing knowledge. His law of probability, combined with other intellectual forces that contributed to inductive logic, is in keeping with the philosophic skepticism for which the Roman Inquisition tried Galileo. Descartes too believed in the heliocentric hypothesis propounded by Galileo, but had to cower down before the supremacy of the Bible. He did not shout out his observation that matter throughout the universe was essentially the same type.

    The only thing that really went wrong in the development of knowledge was a rift that grew between the humanities and the sciences. Disciplinary practices grew into specializations that lacked the necessary tolerance towards other disciplines. Scientists looked down upon the humanists even as scholars in the humanities regarded the scientists' cold and impersonal calculations with some contempt. C. P. Snow makes a special case of this in his essay on these two cultures. I prefer to cite examples from Book Three of Jonathan Swift's Gulliver's Travels to show how scientists and mathematicians have been satirized in literature. Gulliver is dining with the King of Laputa. This is how he describes the food:

We had two Courses, of three Dishes each. In the first Course, there was a Shoulder of Mutton, cut into an Aequilateral Triangle; a Piece of Beef into a Rhomboides; and a Pudding into a Cycloid. The second Course was two Ducks, trussed up into the Form of Fiddles; Sausages and Puddings resembling Flutes and Haut-boys, and a Breast of Veal in the Shape of a Harp. The Servants cut our Bread into Cones, Cylinders, Parallelograms, and with several other Mathematical Figures.

    And this is how he describes the scientists' appreciation of female beauty:

Their Ideas are perpetually conversant in Lines and Figures. If they would, for Example, praise the Beauty of a Woman, or any other Animal, they describe it by Rhombs, Circles, Parallelograms, Ellipses, and other Geometrical Terms; or else by Words of Art drawn from Musick, needleses here to repeat.

              Shall we look at just one more example? In the passage below, Swift comes down heavily on the scientists' lack of imagination because of their obsession with specialization.

And although they [the Intellectuals of their Workmen] are dextrous enough upon a Piece of Paper, in the Management of the Rule, the Pencil, and the Divider, yet in the common Actions and Behaviour of Life, I have not seen a more clumsy, awkward, and unhandy People, nor so slow and perplexed in their Conceptions upon all other Subjects, except those of Mathematicks and Musick. They are very bad Reasoners, and vehemently given to Opposition, unless when thy happen to be of the right Opinion, which is seldom their Case. Imagination, Fancy, and Invention, they are wholly Strangers to, nor have any Words in their Language by which those Ideas can be expressed; the whole Compass of their Thoughts and Mind, being shut up within the two forementioned Sciences.

I am pretty sure that this is not the case today because interdisciplinary and crossdisciplinary practices abound in the university departments all over the world. The Central Department of English has already adjusted interdisciplinary studies in its curriculum. The TU Academic Council has already accepted the proposed American Interdisciplinary Studies program, which will soon be offered to students.

    Let me conclude with the assurance that there is more to be said in this area. There are other instances of the use of mathematics in literature. Geometric shapes describe structures of literary compositions. Time in its physical, grammatical, philosophical and psychological aspects plays a very important role in the creation of literature. Children's literature too makes use of mathematics. Often children are taught to count with the help of some nursery rhymes such as "One, two, buckle my shoe."

    Rather than go into all these details, I have pointed out only two important facts: first, that the relationship between math and literature is established by the mystical and magical properties of numbers; and, second, that the sense of symmetry, harmony and balance which give rise to aesthetic beauty is basically a matter of mathematical proportion.

 Of Nepalese Clay 4 (October 2002)

Reinventing Jhiltung

- Padma Devkota

    Gopinath Nepal, known to the inhabitants of Jhiltung as Baburam, must have been a very handsome lad once upon a time. His genial and robust face stared at me with incredulity when Ramesh Prasad Nepal, my companion to Jhiltung, told him that our children were wedded to each other. He was delighted and scrutinized my face in the dwindling light of the evening. I was new to him, but he recognized and greeted my companion immediately. We had just arrived on motorbikes with our young escorts to a point from where we now had to descend down a raised, narrow path that zigzagged through the paddy field to the house below.

    Midway upon a southern, sequestered slope of the mountain, Baburam’s house offered us the most unanticipated warmth, comfort and hospitality. Like a living history, Baburam himself walked slowly around his clean front yard with a grey, metal walking stick with a curved handle because he had probably torn a tendon of his knee by falling from the raised path in the terraced fields. In the shed below the front yard, goats, cows and buffaloes chewed on their fodder. A fresh, white lamb frolicked and gamboled near our feet with two others. A calf had newly arrived and the beestings were shared. Rich milk, skimmed milk and home-made ghee were the major attractions of a vegetarian dinner in the large ground-floor kitchen. At the farthest end of the room, flames leapt above the two holes of a mud-stove upon which soot-blackened utensils sat cozily. From the opposite end, a dark, wooden staircase led to the upper story where we would retire for the night. A man sat on a wooden bedstead on one side of the room as we sat cross-legged on wooden boards on the mud floor to devour with gusto the sumptuous dinner while the women kept goading us to try just some more food “even though it may not be that good!” Baburam was the only person who sat with one leg stretched out before him because he could not fold it.

     After the meal was over he told us that we had come to Jhiltung some two or three years too late. “Gore is gone and nobody in this region knew the poet like he did. I was very young at that time and somebody told me later on that he had been asked to follow the poet wherever he went and to make sure that no harm befell him. O, he used to walk all over the place and Gore used to follow him at a distance, trying not to intrude upon his privacy. They had asked Gore to take care of him because they thought he wasn’t mentally stable, perhaps even suicidal. I think they even called the shamans and witch-doctors to treat him. But, O, he was so cheerful all the time. Gore used to say that he had never seen a face that was so radiant, so full of smile, so bright whenever you looked at it. Once, the poet had walked towards the northern slope of the mountain and over a very narrow path from which, if one fell down, one would fall directly into the torrential Trishuli below. Gore told him to be careful and asked him why he wanted to take that risk. He wanted to see the snow-capped mountains along the northern horizon, he had said. And when he was looking at the mountains, was he looking at the mountains? What was he looking at? As he was returning by the same path, at one point Gore instinctively held the poet by the arm for fear that he would fall down. The poet, instead of being angry with Gore, smiled sweetly at him and freed himself.”

    “Where was he staying then?” I ventured. My mother had told me that one of her elder uncles had treated father with some mantra and sacred ash, and also tied an amulet around his arm to protect him against evil. His health had improved perhaps also because of the fresh air of the hills, the good vegetarian diet and the exercise one gets walking up and down the slopes. Back at home in Kathmandu, his brothers had ridiculed such superstition and torn the amulet out of his arm.

     I was told that Baburam had moved to this new abode from his ancestral home higher up the hill. Again, the reason being he could not walk like he used to and living up there was more difficult. That was several years ago. The deserted house stood with silent dignity amidst the dilapidations of time, showing off its deftly carved wooden door frames and windows to the sugarcane fields below. The boys who had so generously taken us there on their motorbikes over the rough and dangerous mountain road told us they were planning to rent the place for the office of a literary society of Jhiltung, which had been functioning informally for the last two years but was yet to be registered. They had decided upon this place because Mahakavi Devkota had once lived in this house. They too were bent on recapturing the glorious past of a mountain abode sanctified by the brief sojourn there of a beloved national poet. Baburam’s grandson, Achyut, was especially enthusiastic about this project. This was only the second time, I think, that they were commemorating the birth anniversary of Laxmi Prasad Devkota, this time the 105^th, and we were the invited guests. The event took place in the sunny yard of Shree Kamarudevi Higher Secondary School, which showed off its modern architecture in the middle of humbler traditional abodes. And, indeed, this was modern Jhiltung living its influence, trying to establish its worth and planning to project a culturally rich Nepal into the times to come. Probably the literary society of Jhiltung would be called “Kunjini Literary Society.” After all that was a right thing to do because Devkota wrote Kunjani (1945) a long narrative poem about the love affair between Gore and Kunjini who faced a tragic end because the traditional society of the hills was antagonistic to such individual freedom, especially of a woman. In these hills, a girl was still the property of the father legally and ritualistically transferred to the husband without giving her a right to choose. Such practice in these hills did not mean that the same society did not have a long and rich social and traditional culture guided by rich Hindu ethics. Nevertheless, Gore, the poet’s guardian in the Jhiltung hills, and Gore, the principal male character of the long narrative poem, had now merged in an image of love and sacrifice. This was probably the poet’s way of expressing his gratitude to one who followed him everywhere to make sure that no harm befell him. The poet may have appeared mentally unstable to some who did not understand the poetic fire that burned inside him. But he was not. He had studied both the nature and society of Jhiltung sufficiently to write significantly about it during his sojourn with the family of his wife’s maternal uncle.

     Baburam is my maternal grandmother’s nephew. Even though he was one generation higher up, we had met for the first time after I too had developed sufficient wrinkles that spoke of our long and separate past. For him, the poet was a legend. For me, he was a father too. For Baburam, the Jhiltung he was born in had a new name: Dui Pipal, also called Pipalay. For me, the whole region including the low, green paddy fields, the thicker habitation of the Dui Pipal heights and even all the distant blue mountains I could see with my naked eyes was just Jhiltung. Had the clouds on the horizon been transparent, the white peaks beyond, too, would have been Jhiltung. Wherever my father had walked in this region, whatever he had seen near and far, was all Jhiltung for me. I guess I really wanted to see it through his eyes, which was actually quite impossible! His presence there almost seventy-three years ago in 1940 gave the place an aura that continued beckoning to me to look and to look for a Jhiltung from which I have now returned with the satisfaction that I, too, have visited that sacred region of earth. The only thing left for me to do now was to re-read Kunjini again to appreciate how the landscape of the place I had visited had been imaginatively reinvented in the poet’s mind.

 January 7, 2014