Of Antagonía' s four volumes, the longest, Recuento, is divided into nine chapters of greatly varying length. It has already been noted that the text is tripartite in terms of its major narrative divisions which are related to temporal and developmental stages in the life of the protagonist. There is a continuance of structure between Recuento and Los verdes in that the division of material which predominates in Los verdes, sections separated by spacing and beginning with a capitalized word or phrase, is begun in the final pages of Recuento when the third person narrative changes over to the first person account of Los verdes. Raúl basically comes to terms with the external world in his exploration process in Recuento. The first person voice of Los verdes has the task of exploring more fully the subconscious realms of the personal and collective psyche.

Los verdes has six chapters, correlated in the text to the six days that it took God to create the world and Raúl' s six days in Rosas as he begins serious work on his book: "Un trabajo no muy distinto, a fin de cuentas, del que supone la obra en cuestión, seis días entre todo, un tiempo tradicionalmente apropiado para dar por acabada una o b r a" (II 110). The chapters are sub-divided into sections focusing on a theme, a character, a plot situation, an interpolated story, or the author' s metafictional or autobiographical speculations and com­ments. This format will be repeated, with variations, in parts of La cólera and in Teoría.

The number of sections in each chapter varies: Chapter I has four; chapter n, six; chapter III, nine; chapter IV, twelve; chapter V, four; and chapter VI, though not divided by sections as in the other chapters, contains thirty-six paragraphs.1 In aH, counting the final chapter as one section, there are thirty-six sections, a number which is repeated in the thirty-six paragraphs of the final chapter. From this brief review, it can be seen that the predominant numbers in the structure are multiples of three and the number four.

La cólera, like Recuento and Teoría, is tripartite; it has three distinct sections consisting of three chapters each. Echoing the nine chapters is the fact that the name, Matilde Moret, if reduced to a single number, also yields the number 9.2

Teoria is composed of three, first person narrations. The diary of Carlos-hijo is presented in the first two chapters, the first of which is divided in nine sections headed by dates, beginning with Sept. 9 (9 + 9=18=1+ 8=9) and ending with Sept. 27 (9+ 2+7=18=1+ 8=9). The second chapter also contains nine entries, dated froID October 20 (10+ 20=30=3) to November 7 (11 + 7=18=1+ 8=9). The total number of sections (eighteen) is repeated by many of the dates whose constituent numbers also add up to 18 (which can be reduced to the single digit "9" as seen aboye).

Ricardo Echave' s four chapters consist of the transcription of his recorded notes. Chapter III has two sections; chapter IV, four; chapter V, two; and chapter VI, one, for a total of nine sections. The final six chapters of Teoría relate the verbal testament of el Viejo. These are divided into six sections in chapter VII, seven in chapter VIII, nine in chapter IX, twelve in chapter X, seventeen in chapter XI, and two in chapter XII, for a total of 53 sections (5 + 3=8). The death of the old man concludes the novel and the cycle it represents.

There are a total of 36 chapters and 81 sub-divisions in Antagonía. Please note that both 36 and 81 are multiples of nine. The textual divisions into multiples of three is one of its most salient characteristics, with a constant reiteration of the number 9. The number of chapters and sections, the repetition of multiples of three, and the fact that four volumes make up the one novel aH carry a symbolic significance that is intimately related to the thematic structures in the text.

One thematic thread running throughout Antagonía is the author' s return to certain basic ideas proposed by presocratic philosophers. The ideas of the followers of Pythagorean thought provide one interpretation of the significance of numbers as they relate to the nature of life and the cosmos. According to G.S. Kirk, J.E. Raven, and M. Scholfield, authors of the book, The Presocratic Philosophers: A Critical History with a Selection of Texts, Pythagoras "is the archetype of the philosopher considered as the sage who teaches men the meaning of life and death" (213). In this respect, a parallel can be drawn between him and the character of the old man in Teoría, a great admirer of Pythagoras, who attempts to impart his own ideas about the nature of know ledge to his successors through his narrative legacy.
 

Basing their arguments in references made by Plato concerning Pythagoras and his followers, the authors of The Presocratic Philosophers note that there are two "faces" of Pythagoreanism, one corresponding to the religious/ethical and the other to the philosophi­caVscientific aspects of knowledge. Neither Pythagoras' nor his followers' works have been handed down to us; in fact, it is thought that they purposely may not have written down their ideas (221). It is perhaps for this reason that Pythagoras has acquired an almost mystical and mythical quality; rus ideas has be en left open to interpretation throughout history without the limitation of a written source in which those interpretations had to be based.

Numerical symbolic systems have a long history even though numbers, counting systems, and their symbolic relationships differ significantly from one culture to another (Cirlot 231-231). In westem civilization the notion that numbers carry within them symbolic meanings appears to have its foundation in Pythagorean thought dating back more than twenty-five centuries. For the Pythagorean thinkers, the systems of order in the universe were inherent in and revealed through the relationships of numbers.

J.E. Cirlot, in his Dictionary of Symbols, states that numbers do not just indicate quantity, "but idea-forces, each with a particular character of it own" (230). Annemarie Schirnmel, in The Mystery of Numbers, reiterates this concept:

With the continuing quest for measures of life and for an all-embracing harmony, even Plato, otherwise somewhat critical of the Pythagoreans, accepted that the numbers contained certain keys for solving the mysteries of nature. Pythagorean and Platonic ideas were carried over in Neo­platonism and the gnostic systems and gave rise to a number mysticism that can briefly be surnmarized as follows: 1) Numbers influence the character of things that are ordered by them. 2) Thus, the number becomes a mediator between the Divine and the created world. 3) It follows that if one performs operations with numbers, these operations also work upon the things connected with the numbers used. (16)

One aspect of numbers which particularly interested the Pythagoreans was the dual nature of the universe as revealed through the difference between odd and even numbers (Schirnmel 13). In general, the even numbers express the infinite, the unlimited, the manifold, the moving, darkness, evil, and the feminine principIe; the odd numbers are related to the limited, the resting, light and goodness, and the positive, active, male principIe (Schirnmel 13). Schimmel notes that there is a numerical prejudice in westem civilization expressed in the form of a marked predilection for odd as opposed to even numbers. Ritual acts, prayers, incantations, and even magical acts are usually repeated an odd number of times, often in groups of 3 or 7 (14).

Another Pythagorean idea was the existence of "perfect" numbers whose components, "when added up, produce the number itself. The first of these is 6 (l + 2 + 3); the next one is 28 (l + 2 + 4 + 7 + 14) (Schirnmel 14). For the Pythagoreans, the most perfect number was 10 since it was the sum of the first four integers (1 + 2 + 3 + 4) and so symbolized multiplicity returning to unity (Schirnmel 15). This concept gives us a cIue as to why Goytisolo might have chosen to write a novel made up of four thoroughly interrelated parts. In the following section a brief description of the symbolic nature of numbers will be coupled with a few examples of how that symbolism is played out in the structures and themes of Antagonía.

The number 1 represents the concept of potential and commencement. More than unity, it indicates the beginning of diversity, of the relations of the parts within the whole. While linked to the concept of individuality, ir is also symbolic of essence and pure energy. It is supremely spiritual with no trace of materiality. The word "antagonía," when reduced to a single number, yields the sum of "1," making it a doubly fitting title, both for its etymological significance and its symbolism of the integration and potential from which everything flows. Goytisolo anudes to the power emanating from this number in Chapter IX of Recuento:

De ahí la diversidad de nombres del Creador, la ambiguedad de sus orígenes, sus confusos lazos de parentesco, Júpiter, Jehová, Ormuz, Elhoim, Saturno, Arimán, El. Es decir, el que no tiene nombre, el innombrable. Aquel que es uno mismo y su contrario. (1.570)

The author will circle back to this theme in Teoría del conocimiento when it is made clear that el Viejo must understand that he has created his own adversary in the person of el Moro before he can find peace and face his death as a kind of transcendence which indicates the end of one cyele of existence and the beginning of another.

The number 2 embodies the concepts of "echo, reflection, conflict and counterpoise or contradiction" (Cirlot 232). It also expresses the forward progression of time, nature in opposition to the creator, the moan as opposed to the sun, the ominous, the shadow, and dualismo Two is related to matter, difference, and essence. Whether represented by such images as yin and yang, male and female, heaven and earth, good and evil, day and night, or the polarity of life after the creation (the division of the one), it has long stood as a foundation for attempts to understand reality. In the west, it provided a basis for Manicheism whieh posited that aH good things were spiritual and aH evil ones were material. This eoncept is reflected in the early Christian thinkers such as St. Augustine and his insistence on the need to fight the desires of the body in order to purify the soul. Sehirnmel points out that this negative view predominates in "mystically oriented religions," but in the "prophetie" religions, a positive value is seen in the "tension between the one and the many, between creature and creator, for their goal is not so much the final unification of the erea­ture with the divine One ( ... ), but rather the creative dialogue, the awareness of the relation between I and Thou in prayer" (51). The possibility of union is never forgotten and is often symbolized by the sexual act.

Antagonía's structure, particularly in Recuento, demonstrates a marked focus on the concept of duality following in the tradition of mystically oriented religions. Raul wages a war in Recuento to free himself from the antagonistic, supposedly irreconcilable forces he inherits from the society, education, politics, and religion into which he is born. The proponents of one point of view see those of other persuasions as being evil or totally wrong. Through his writing Raúl pits those concepts against each other-Cataluña vs. Castille, commu­nism vs. Franco, etc.-and within the framework of the narrative he is creating, he destroys the myth of either/or, opening up the possibility that the life force emanates from the creative tension flowing between male AND female, good AND evil, etc. This conceptual shift allows him to focus on the vitality and necessity of the never-eeasing ebb and flow which is the very force of life.

Everything is a matter of perspective; what is important is that the opposing of such ideas creates a powerful energy. To have an enemy is often to find the strength to fight that enemy. Raúl searches for a way to create the same energy found in opposition without having to limit himself to accepting only one point of view to the exclusion of all others. When he finds the way to do so, he experiences the sensation of tapping into the power of creation. At that moment, the symbolism inherent in language regains its strength and he is able to en ter into a living, dynamic relationship with the reality it represents.

This change is noted beginning in Los verdes in which the oppositions are focused around the cyclical nature of such relation­ships as dominance and weakness, the sexes (where the hermaphrodite is expressed as the ideal), the passage of time, and creation and destruction. When the antagonist in any given situation disappears for whatever reason, the opponent die s as well, unable to find a purpose in life once the creative tension of the conflict no longer exists. This conceptualization of the nature of existence is basic to Goytisolo' s theory of knowledge.

The number 3 represents the solution of conflict and duality, the attraction of opposites, "the harmonic product of the action of unity upon duality" (Cirlot 232). It is associated with the ideas of heaven and the Trinity and the growth of unity within itself since the number provides the energy to create connections between opposites. The 3 also symbolizes the manifestation of action out of passivity, and inner, spiritual or vertical structure, as opposed to the external, earthly structure represented by the number four (Cirlot 336). The impor­tance of the number 3 to the ways in which the perception of reality is framed can be seen in the human perception of time in terms of past, present, and future, and the three dimensions of the spatial world. These aspects are integral to the structure of language and narrative; for example, the average sentence is divided into subject, verb and object, and stories generally have a beginning, a middle, and an end.

Schimmel points out that:

( ... ) from time irnmemorial, thinkers have tried to explain the unfolding of the One into multiplicity with special reference to the three. Lao-tzu says: "The Tao produces unity, unity produces duality, duality produces trinity, and the triad produces all things." The Pythagoreans likewise postulated that the unqualified unity was divided into 2 opposing powers to create the world and then into tri-unity to produce life. For Dante the three, as he saw it incorporated in the Trinity, revealed the principIe of love, that is, the synthetic power. (60)

Triads are omnipresent in human thought in the fields of religion, psychology, philosophy, and even in superstitions such as "three times is the charm," and "good things come in threes." In Christianity, there are many references to the number 3: there were three wise men; Christ arose on the third day; Jonah was in the belly of the whale for three days; etc.

One way to approach the possible significance of the number 3 in Antagonía is to consider the nature of the third part, La cólera, within the whole. An interesting aspect of this text is its distinct change of narrative voice and point of view. As we have seen, Raúl' s review of his outer life from an observer' s viewpoint in the first part of Antagonía, Recuento, yields its opposite, a journey through his inner world, in the second part, Los verdes. La cólera can then be considered as a connection of opposites, in this case the inner and the outer perspectives, in a text which simultaneously views its narrator from both the inside (Matilde' s view of herself), and the outside (the author and reader's view of her). Matilde's unreliability as a narrator in La cólera subverts her authority and creates a direct dialogue between Goytisolo and the reader about her. In this way, the author is able to establish a flow from Recuento to Los verdes to La cólera which in itself constitutes a cycle. These perspectives and others then are incorporated into the fourth part, Teoría, which, I would argue, while closing the cycle represented by Raúl' s life and the writing of that text, simultaneously begins a new cycle in which the reader will continue to build on what s/he has learned from the text mixed with his/her own life experience and whose end we cannot foresee. In this way, the novel spirals out from the world created within Antagonía to the reality beyond rather than closing it in upon itself in an insulated circularity.

In summary, the relationship between the numbers 1, 2, and 3 is expressed during the fantastic voyage of the characters of Los verdes, significantly placed in Chapter VI of that volume:

Aspectos contrapuestos y compensatorios, simetrías invertidas que desde su dicotomía esencial, el hombre proyecta sobre el mundo. De ahí el Uno, la única forma de concebir a Dios, como unidad, ya que el Uno es la más perfecta representación de lo que ni tan siquiera tiene partes puesto que no existe; y de ahí también el Caos, el todo que precede a lo que no existe, algo hecho añicos desde siempre, el espejo de lo que no se recuerda. Y de ahí, finalmente, que el número dos sea en realidad el primer número, respecto al cual el número uno no es más que la expresión ilusoria y virtual de una de las dos mitades que lo componen, resultando ser, en consecuencia, el número tres el segundo número de la serie natural a la vez que síntesis de los que le preceden, de lo real y de lo especulativo, de lo que existe y de lo que no existe. Ya que, como el dos, su antecedente, así la persona, la relación antagónica entre las partes de luz y de sombra que la forman. (II 104)

This citation gives explicit clues to many of the structural and thematic touchstones in the novel. The energy begins within each individual, the microcosm, and continues like the ripples of a stone dropped in the water throughout each successive level of existence until it includes the whole of the macrocosm: "Y fijar este instante, esa duración, supone un desarrollo centrífugo, círculos que se dilatan sucesivos, que se amplían como las ondas que se agrandan en torno a donde la piedra se hundió en el estanque o como una metáfora dentro de una metáfora supone un relato" (I 577). In this way, the novel as a form of expression is comprised of the same forces as all other forms of life and thus is able to embody and express them fully.

The text provides another way to visualize this concepto Goytisolo utilizes symmetrical structures within the four volumes to create an effect similar to that of facing mirrors. At the same time, he often inverts those same structures so ihat they reflect each another from a very different perspective, as if they form a type of parallel, other­side-of-the-mirror, universe. The juxtaposition of the two visions, at times complementary and at times contradictory, creates a system of alternating counterpointed stasis and dynamic movement in the text. To go back to the quote from Los verdes, another way of saying this is that antagonic tension flows from the illusory "one," the source of all that exists, and that the tension manifests itself in the interplay of the parts generated from the chaos that precedes even the illusion of harmony often seen in the concept of unity or the "one." Over the course of time, forces and elements meld, not in a harmonious whole, but in a synthesis of the ever-present tensions constituting the life force as they strive toward a balance. For humankind even to begin to comprehend this process, the significance inherent in such dualities as light and shadow, the seen and the unseen, the real and the speculative, all that exists as opposed to that which doesn't (yet), is essential to an understanding of the process. The numbers 1, 2, and 3 symbolically represent this process. Four is the number of the earth and the earthly, of "the human situation, of the external, natural limits of the 'minimum' awareness of totality, and finally, of rational organization" (Cirlot 232). Schim­mel states that four "is inseparably connected with the first known order in the world (the four phases of the moon, the four seasons, the four directions), and thus points to the change from nature to civiliza­tion by arranging a confusing multiplicity of manifestations into fixed forms" (86). The number was used extensively in the Mayan religion in a mandala type representation of the four directions. Similarly, the Christian cross connects the four cardinal points.

As the fourth part of Antagonía, Teoría del conocimiento focuses on these themes. The preoccupations of each of Teoría's narrators reflect a concern with identity and with the natural limits of the "minimum awareness of totality," in terms of the limits of conscious­ness, of what we can know about the unconscious, and the frontier of death. Specifically, Ricardo draws parallels between the times and themes of his life and the four paints on the compass in Chapter VI. In his narrative, the old man underscores the importance of a reconnection between mankind and his "earthly" environment. Early in his testament, he refers specifically to the philosophy of Pythagoras: "Los únicos pensadores que merecen tal nombre son los presocráticos y, en especial, Pitágoras; ellos aún olfateaban los rastros de una sabiduría desaparecida, los restos del naufragio" (II 529). Presocratic thinkers had in cornmon that they considered Nature as a totality. Pythagoras taught a "doctrine of the transmigration of souls and the consequent kinship of all living things" (Flew 274). In addition, it appears that he discovered:

( ... ) presumably by measuring the appropriate lengths of string on a monochord, that the chief musical intervals are expressible in simple numerical ratios between the first four integers. This apparently modest finding was the cue for the crucial Pythagorean insight, that the secret of understanding Nature lies somehow in mathematics. If numbers alone are sufficient to explain the "consonances," might not everything else be likewise expressible as a number or proportion? And, furthermore, given the importance here of the first four integers, and given that their sum can be represented in a remarkable equilateral triangle of ten dots, perhaps the number ten, the decad, somehow "embraces the whole nature of number". (Flew 274)

The Pythagorean thought which focused on the "consonances" or connectivities between the first four numbers and their manifesta­tian in music are reflected in the old man' s fascinatian with Mozart and Casals, and in the significance of the four parts of Antagonía making up the "oue" novel, whose very title, as we have seen, embodies the number and power of "one." As will be seen later in the discussion of the Ideal City, the number four has further implications for the meaning of Antagonía as a whole. The fact that Teoría is the fourth book of Antagonía also makes it fitting that it be the "creation" of an organized world bom from the chaos of Raúl' s creative experience.

Another close connection can be demonstrated between the four parts of Antagonía and the four elements. Recuento, as the referential base of the novel, is most closely tied to the concept of earth and tangible reality. Los verdes de mayo hasta el mar includes many references to water and its symbolic significance as the life-giving element and the subconscious. La cólera de Aquiles, with its explosive narrator/protagonist and references to Achilles, is connected to the idea of fire, while Teoría del conocimiento, with its ideas, theories, and mysteries, represents air.

There are five different first person narrators in Antagonía, a fact which greatly affects the structure and multiplication of perspectives of the text. The number five is also prominent in the visual image of the Ideal City in Los verdes and Teoría. Five symbolizes the quintes­sence acting upon matter and it is sometimes represented as a square together with its central point or as the human figure as represented by the four limbs plus the head which controls them (Cirlot 233). The quintessence, or "quinta essentia" was revered by medieval alchemists as the real element of life that activated the body. Five is the number representative of human love, being the combination of the feminine number 2 and the masculine 3, and has often been associated with Venus or Eros (Schimmel 106-7). All in all, it intro­duces the human element into the order of the cosmos.

Five is represented by a variety of shapes and images such as the pentagram, the mandala with its four directions tied to the center, and the human hand (with its reference to the five senses). Schimmel speaks of the talismanic effect that the "Hand of Fatima" sculpture over the door to the Hall of Justice in the Alhambra (in Granada) has in supposedly averting the evil eye. Furthermore, this image when written in Arabic script "is reminiscent of the invocation Ya Allah," in Spanish, Ojalá ("God willing") (116). The instability inherent in the number 5 gives it a dynamic, unsettling quality which can work for good or for evil; but generally it speaks to the rebelliousness of man within the order of the cosmos. Certainly, all of Goytisolo's narrators are malcontents of one sort or another whose rebelliousness and instability spur their need to write in order to understand themselves.

Six, as we have seen, is a fundamental number in the structure of Antagonía. It deals with matters of ambivalence and equilibrium and of trial and effort. In addition: "( ... ) it corresponds to the six Directions of Space (two for each dimension) and to the cessation of movement (since the Creation was finished at the end of six days). It summarizes all the plane figures of geometry (point, line, and triangle), and since the cube is composed of 6 squares, it is the ideal form for any closed structure" (Schimmel 122). When 6 is embodied in the hexagram (two superimposed triangles, one pointing up and the other down), it represents the macrocosm (Schimmel 124). In lndian culture, this image is symbolic of the creation and destruction of the material world. It can also be interpreted "in terms of polarities between spirit and matter, God and chaos, transcendent and immanent, which again represents the created world and even more, the male (upward) and female (downward) aspects of life" (Schimmel 126).

Within Antagonía, it is Raúl' s ambivalence that produces his search for equilibrium through his creative impulse and, as we have seen, Antagonía's plot is centered in his personal trials and the crea­tive efforts springing from them. The cycle of creation and destruc­tion, the interrelationship between the macrocosm and the microcosm, and aH the dualities mentioned aboye are critical elements of the thematic structure. This number resonates throughout the text on mul­tiple levels, creating ever-increasing connections between structure and meaning.

The number 7 coincides with the concept of a completed eycle and has particular value because it is based on the union of the trinity, or heaven, and the quatemity, or earth (Cirlot 283). To elaborate on this concept, we tum to Sehimmel: "lndeed, it consists of a temary of creative principIes (active intellect, passive subconscious, and the ordering power of cooperation) together with a quaternity of matter encompassing the 4 elements and the corresponding sensual powers (air=intelligence, fire=will, water=emotion, earth=morals)" (127).

It is the number of consummation as well as the unfolding of unity and is usually considered to be positive, although it has sorne negative connotations; for example, the seven deadly sins. Usually, however, seven is the traditional "lucky" number, embodying the search for truth, for wisdom, and for universality. It is the symbol of reconciliation, but also of pain. One example, taken from Catholicism whose religious rites are fraught with 7s, is that Mary has seven joys and seven sorrows.

Within Antagonía this symbolism can be see in the situation in which Raúl, in his last jail cell (where he begins the notes for his novel), obsessively paces the seven steps which comprise the diagonal length of the cell. In the first cell in which he was incarcerated, it was three, and in the second one, four. He also compulsively rinses his hands seven times after washing and eats seventy spoonfuls at a time (I 454-455). True to the meaning of 7, this is the time period in which he faces his greatest mental anguish as he searches desperately for truth and understanding; yet, through this experience and its consequences, he ultimately finds reconciliation on a spiritual level which then allows him to begin a new cycle in his life.

Eight is the symbol of regeneration, of the balancing of opposing forces. It has been understood as the number of Paradise (the Muslims believe that there are 8 paradises and 7 hells). It is considered to be a second beginning and, in the Jewish faith, is a day of purification (circumcisions take place on the eighth day). In the Christian faith, "the name of Jesus in Greek letters, IHESOYS, yields the numerical value of 888, a multiplication and hence strengthening of the sacred 8" (Schirnmel 158). For Buddhists, it is the eightfold path which leads to cosmic equilibrium. The significance of this number is included in the chapters in Teoría del conocimiento dealing with el Viejo (whose "name" in the novel, when converted in the number system, yields 8). The fifty-three sections (5 + 3 = 8) of his narration focus on the reconciliation in his mind of his life-Iong animosity with el Moro. The realization that he truly is the combination of himself, or who he thinks himself to be, and his other clears the way for a reconciliation of the various aspects of the self and the regenerative death described as the soaring of a bird at the end of the novel.

Nine is the tripling of the temary and therefore "a complete image of the three worlds" (CirIot 234). It relates to the perfection and integration of the realms of the corporal, the intellectual, and the spiritual: "For the Hebrews, it was the symbol of truth, being characterized by the fact that when multiplied it reproduces itself (in mystic addition)" (Cirlot 234). Goytisolo includes an explicit refer­ence to the importance of this number in Antagonía when he men­tions the "singularity" of the number 9 in Los verdes:

Singularidad del 9: el único número cuyos múltiplos, reducidos a una cifra inferior mediante sumas sucesivas de los elementos que los componen, da siempre como resultado el propio número 9. Asi: 9 x 3=27=2 + 7=9. O: 9 x 7=63= 6 + 3=9. O: 9 x 343 = 3087 = 3+ 8 + 7= 18 = 1 + 8 = 9. (II 63)

Given this not so subtle hínt in the text, it should be no surprise that the number 9 is repeated in many of the structural divisions of the novel and also relates to its symbolic structure sínce Raúl' s desire is to connect with all the sources of knowledge available to him.

When Raúl is placed in cell number 243 (2+4+3=9) on the third floor of the sixth gallery (3+6=9) of the jail (I 501), he is loeated in a physical space transfused with the spiritual power exerted by the number 9. That "coincidence" of forces creates a situation favorable to the experience of a spiritual epiphany capable of changing his life and connecting him with the power of creation. Far from being only an interesting number game, the singularity of the number 9 is critical, not only for Antagonia's structural unity, but as a symbol for the novel' s ambitious efforts to make the reader aware of the need for dynamic connections between the realms of the corporeal, the intellectual, and the spiritual so as to make possible a fuller, more meaningful know ledge of life.

Finally, the number 12 also plays an important role in Antagonía because it signifies the coming together of the number 5, the number of humanity, and the number 7, that of the union of heaven and earth. The twelve signs of the zodiac, the twelve apostles, the twelve tribes of Israel, the twelve days of Christmas, the special significance of noon and midnight, the fact that ayear is divided into twelve months in European cultures -all of these indicate the special relation of this number to the concept of unity and the closure of a cycle, both on the earthly and the spiritual levels.

In Los verdes there are twelve towers surrounding the Ideal City indicating the desire to bring into harmony the human, the earthly, and the celestial or universal forces. As Bettina Knapp notes in her book, Archetype, Architecture and the Writer, Plato writes of the importance of the dodecahedron, "in which space, light, line, depth, number-fundamental particles, or as we call them, 'Platonic solids '- are involved in arrangements that trigger sensation; for us this implies an emotional or psychological content" (ix). The Ideal City functions on several levels in Antagonía. It is at once representa­tive of the evolving plan of a novel and also symbolizes a kind of idealized temple representing the links between man and the eternal. That link is repeated in the allusions to etemity included by the death of the old man which occurs in December, the month traditionally correlated to the final stage of life since it is the last month of the year and the beginning of a new temporal cycle.

Through the few examples given here I hope to have established sorne of the connections that are operating in Antagonía at its most basic level, that of the number of its divisions into volumes, chapters, and sections, the numerical details related to its plot and characters, and its thematic and symbolic structures. There are many more examples of the connections which number systems yield in terms of meaning, many of which will be referred to throughout this study.

Certainly, Goytisolo is not the first author to employ this type of code; the inclusion of repeated references in Antagonía to Dante alone provides an indication that numerical symbolism must be con­sidered. Nevertheless, the symbolic connectivity of ancient number systems, which once were a determining factor in explanations of the mysterious links between man and the universe, has generally been dismissed as mere superstition within cultures valuing only that which can be proven by experimentation and rational logic. Goytisolo' s use of this structure speaks to the need to reconsider the dynamic between the rational and altemate means of acquiring information about life and the cosmos. Other strategies and elements of the text will echo this theme, as we will see.

The relationship between certain numbers and the geometric figures to which they correspond was outlined in the previous section. In addition to the symbolism of individual numbers, it is also inter­esting to visualize Antagonía's narrative and thematic structures in terms of the geometric figures. For example, Recuento' s nine chapters, given the images and metaphors employed to "frame" the structure, create an mental image of this part of Antagonía as a circle. The nine chapters of La cólera, however, also sub-divided quite clearly by content into three parts, can only be envisioned as a triangle due to the insistence on the love triangles in the text and the relationship established between the author, text, and reader. This fact affects the reader' s perception of the tone and the meaning of each part because it literally changes the connections and flow of energy between the author, the text, and the reader. Circularity concentrates and focuses energy inward as befits Raúl' s search for knowledge, emanating from the center of his own experience; but the triangle is the shape most often associated with active cornmunication; so while it concentrates energy, it directs it outward, creating a different dynamic and signaling a change in the role of the extra-textual author and the reader from one of observation (as in Recuento) to one of active participation.

As José Angel Valente and Julio Ortega noted in early reviews of Recuento, even the individual chapters of the text project a circular effect:

El mito iniciático del héroe se desarrolla en nueve círculos o capítulos de que consta el texto, itinerario caracterizado por: a) Aislamiento (de su familia y normas sociales); b) Iniciación (amistades universitarias, P.c.); c) Retorno (a Rosas, a la nostalgia juvenil y a la creación literaria). (Ortega, "Asedio" 213)

Recuento progresa en círculos concéntricos, en cada uno de los cuales quedan reiteradamente inscritos todos los núcleos argumentales de los círculos precedentes. Los círculos son en su total nueve, como en el Inferno y en el Paradiso de la Commedia. (Valente, Insula 12)

Both writers arrive at their impressions using criteria which are based, in part, on the movement and temporal frameworks of each chapter in relation to the others, and, in part, to the repeated references, particu­lady in Chapter IX, to the nine circles of hell in Dante' s Commedia. While I disagree with Ortega' s conclusion that there is a neat correlation between the content of chapters I-III, IV-VI, and VII-IX and the stages of purgatory, hell, and paradise in the protagonist' s life, it is clear that Goytisolo has capitalized on the spatial imagery borrowed from this well-known source by adapting it to his own purposes.

Many other images repeat the leit motif of circularity in terms of time and motion in Recuento. One example already cited reflects Raúl' s desire to experience and capture the supreme metaphorical moments of life:

( ... ) hay igualmente instantes en la vida del hombre que, por su fuerza metafórica, vienen a ser resumen o compendio de todas sus percepciones conscientes e inconscientes, la concentración, una dentro de otra, de toda experiencia implícita, instante y duración, un tiempo muy superior, en su elasticidad y amplitud, al tiempo cronológico. Y fijar ese instante, esa duración, supone un desarrollo centrífugo, círculos que se dilatan sucesivos, que se amplían como las ondas que se agrandan en torno a donde la piedra se hundió en un estanque ( ... ). (I 577)

Throughout Antagonía, the theme of circularity will be presented through images such as streets arranged in expanding concentric circles in the Ideal City, as well as in more subtle thematic and content repetitions, such as the similarity between Matilde' s opening discourse on beauty in La cólera and that of Carlos-hijo en Teoría, or the reference to Dante's journey as a "periplo" at the end of Recuento, and the "Periplo," the fantastic journey to the underworld, at the end of Los verdes. On one level, the circularity helps to weave together the various elements of the text, creating a high degree of intratextuality as well as intertextuality with other texts, as it "loops back" to pick up, and often amplify and modify, an image so that it creates new associations within different contexts. On another level, it creates an evolving visual image in the reader' s mind which speaks to the transformative nature of reality.

In her article in El cosmos de Antagonía, "El cambio, un falso movimiento," Alessandra Riccio concedes the circular nature of Antagonía in its entirety, hut with certain reservations:

¿A qué geometría apelar para definir la trayectoria de Antagonía? ¿Se trata de un círculo, una espiral, una curva parabólica? Porque no hay duda de que comienzo y fin se tocan y que todo el largo y difícil recorrido a que nos ha obligado el autor nos remite ( ... ) al mismo caballo blanco de la primera página de Recuento ( ... ). ¿Un círculo, pues, que se cierra en su misma perfección? ¿O no se trata, más bien, de una espiral que avanza trabajosamente en sus volutas para penetrar más al fondo según indica el lento camino hecho de avances y retrocesos ( ... ) con que, a semejanza de un tigre acercándose en sucesivos giros a su presa, el autor asedia el objeto de su interés hasta conseguir su rendición absoluta. Y, sin embargo, no cabe duda de que el movimiento de Antagonía es también parabólico ( ... ). (22-23)

The temptation toward a circular visualization of the novel, especially given the author' s insistence on such formulations, leads Riccio to very real questions about its nature as a whole which we share here. Is Antagonía best visualized as a circle, complete within itself, or is its structure a more open one? And what connections are there hetween the structure and the content of the novel? Riccio and others speak of the work in terms of circles, spirals, and parabolic curves, mirror images, and labyrinths; however, the image of the circle predominates because of those elements already mentioned as well as others, such as the insistence on self-consciousness, the cycles of nature in Teoría, and those of creation and destruction throughout Antagonía. Goytisolo, when asked about the cyclical nature of the text has responded: "No se trata de un ciclo inacabable, como puede decirse en cambio de otras cosas. Lo que sucede es que la palabra ciclo implica, a la vez que un final, un nuevo comienzo. Pero ese ciclo ya es otro ciclo. Todo ciclo tiene un final" (Ortega, "Entrevista," 146-147). In the lexicon of Luis Goytisolo, then, "cyclical" and "circular" do not correspond to apure repetition which might imply the concepts of futility, perfection, or enclosure. I think this is important to recognize in order to establish the overan tone of the novel. The ending of one cycle and the beginning of another indicates movement, change, and transformation-one cycle yielding the possibilities and potentialities of others which will be inherently different from it and yet connected to it. In that respect, Antagonía, despite its biting satire, extensive use of parody, and the disillusion­ment of its characters, is an optimistic, if not necessarily a happy, novel. It posits the existence of a creative force that derives from, transverses, and transfonns all reality. Within this dynamic of constant creation, human s are uniquely positioned to participate in it in a conscious and proactive manner.

A cyclical conception of time runs counter to the Christian linear progression of time heading toward the endpoint of Judgement Day, a religious concept further emphasized in the nineteenth and early twentieth century in the secular belief in the linear progression of events yielding ever-greater "progress." 1t is, it seems, ironic in and of itself that the secular and the religious force s at work in the nineteenth and twentieth centuries invested so heavily in the sharing of a temporal frame of reference when, ideologically, they pitted themselves against each other in terms of the spirituallmaterial dichotomy.

A cyclical approach to time, in the sense in which it is portrayed in Antagonía, balances respect for nature-as-process with a recognition of the importance of constant change and the potential and risk it implies. The cycles of creation and destruction carry the remnants of the past within them, but they re-order and transform their variables as well as deleting and adding to them within different contexts. All of this information is passed on to human sin innumerable ways, from the mutations of DNA ta the layers of collective memary which inform and shape our personal memories, also constantly transformed by the events and perceptions of each moment we live. The spiraling effect created by Goytisolo's cycles and his imaginative use of numerological symbolism are two strategies of dynamic connectivity that forge a unity within the text while, at the same time, creating the rippling motion Raúl talked about in Recuento, a movement designed to transgress the limits of the fictional space of the novel to affect the reality beyond it. Raúl states his goal far his novel in this way:

Un libro que fuera, no referencia de la realidad sino, como la realidad, objeto de posibles referencias, mundo autónomo sobre el cual, teóricamente, un lector con impulsos creadores, pudiera escribir a su vez una novela o un poema, liberador de temas y de formas, creación de creaciones. (I 576-577)

So the novel is a cycle in and of itself and, like reality, it should be driven by and create force s which will stimulate yet other cycles and other realities. The literary works that accomplish this goal, like those of Dante or Cervantes mentioned in Antagonía, are of the kind that defy the limitations of time by fostering, in whatever moment they are read, new perspectives on life and reality.

Another geometric figure that has a symbolic significance in Antagonía is the triangle. Pythagoras saw the triangle as the '''begin­ning of development' in the cosmic sense because geometrical figures such as the rectangle and 6-pointed stars can be forrned from it" (Schimmel 74). The triangle has been accorded magical powers and used as an amulet throughout history. Especially of significance in Antagonía is the double triangle of hermeticism, signifying "the combination of the microcosmos and the macrocosmos" (Schimmel 74). In the tantric tradition, the triangle was recognized as the primordial symbol for the female. This symbolism is also seen in Greek mythology in which the delta was related to Demeter (Walker 1016). According to Barbara Walker: "(m)ost ancient symbol systems recognized the triangle as a sign of the Goddess's Virgin-Mother-­Crone trinity and at the same time as her genital 'holy place,' symbol of all life" (1016). Later on, the Gnostics appropriated the triangle and aligned it with the masculine creative intellect.

The part of Antagonía that most relies on a structure built on the number 3 and the triangle is La cólera de Aquiles. It is, of course, the third volume of the work, and, structurally, it is divided into three distinct parts, each containing three chapters. The interpolated novel, contained in the second part of the text, mirrors the three part division of the volume as a whole. Ostensibly, the plot of the novel revolves around the love-hate triangle formed by Matilde, Camila, and Roberto, but this triangle is only one of many, such as Matilde, her ex-husband Juan Antonio, and Raúl. That relationship is fictionalized in the inter­polated novel through Lucía, Javier, and Luis. There is also a triangle involving Matilde, her sister Margarita, and Raúl, since both sisters have had affairs with him. All of these relationships may be charac­terized as power struggles growing out of Matilde' s desire to domi­nate and control others.

On another level, Goytisolo establishes a relationship between himself, as the "real" author of the text, and the "real" reader by undermining Matilde' s narrative authority and thus foregrounding his own participation in the novel. At the same time, his implicit inclusion in the narrative creates another triangle between himself, Raúl, and Matilde as authors. Goytisolo achieves a complex interweaving of the various levels of the novel by establishing these parallel structures whose basic point of difference is the altered perspective of their participants as their roles within these triangular mini -dramas shift from participant to spectator and observer to observed.

Another geometric shape suggested in the text by the images used (principally in the Ideal City) and the numbers that are emphasized is that of the squared circle, which, in its graphic form, is a circle placed within a square. The sides of the circle touch those of the square at the mid-point of each of its sides. Antagonía's four parts constitute a cycle within the life of Raúl Ferrer Gaminde as an author, from his birth until he finishes writing his novel. We have already seen that the whole of the work can be visualized as a circle in terms of its content and structure. The fact that there are four parts, however, conjures up the image of a square, especially when the reader takes into account the drawing of the Ideal City in its two versions, one in Los verdes and the other in Teoría. In that drawing, four castles or palaces are placed in the shape of a square at the intersections of the main avenues which are each correlated to a specific color, cardinal point of direction, and season of the year (a complete description of the drawings will be given in the next chapter). The four parts ultimately become the one image, yielding the superimposed figures of the circle and the square.

As Cirlot explains:

'Squaring the circle', like the lapis or the aurum philosohicum, was one of the preoccupations of the alchemists; but whereas the latter two were the symbols of the quest for the eyolutiye goal of the spírit, the former problem concemed the equating of the two great cosmic symbols of heayen (or the circle) and earth (or the square). It is to do, then, with the uníon of two opposites; not juxtaposition as in the coniunctio of the two arms of the cross, for example, but the equation and cancelling out of two components in a higher synthesis. The square was seen to correspond to the four Elements. The aim of 'squaring the circle' (which strictly ought to be 'circling the square'), was to obtain unity in the material world (as well as in the spiritual life) oyer and aboye the differences and obstacles (the static order) of the number four and the four-comered square. (307-308)

This description essentially surnmarizes the overall theme of Antagonía. As we saw in the explanation of the symbolism of the number 2, the process created in the novel affirms the necessity of the existence of aH things AND their other and seeks to erase arbitrary barriers, whether spiritual, social, political, or even literary, which block the energizing flow of the forces that make up reality. Raúl' s primary goal is not to create a work of art, but to leam about life and himself through the process and the insights his art affords him. So, the creative process is a learning experience that provides Raúl with an approach to himself and to the world. The circles, spirals, triangles, squares, and numbers he employs help him to configure that process and communicate it on whatever level the reader is able to engage the text. These structures and the visual images they conjure help the reader to "see" and so simplify in his/her mind the process, but through the symbolism they generate, they also expand meaning beyond the limits of the text.

NOTES

1In the first edition, these words and phrases are printed in all capital letters. In the second edition, the regular rules of capitalization apply. In the third edition, once again the words and phrases are all capitals.

2 For example, Raúl' s full name, if analyzed numerologically, would correspond to the number 6. Following the Pythagorean numerological system, each letter of the alphabet corresponds to a number from one to nine. "A" is represented by 1, "I" is represented by 9, "J" by one, and so on. By adding together the numbers represented by the letters and then adding those numbers together until a single number is obtained, a process called "reduction," one can supposedly understand more about the nature of the personality. Raúl Ferrer Gaminde can be translated into the following number scheme: 9 + 1 + 3 + 3 +7+ 5 + 9 + 9 + 5 + 9 +8 + 1 + 4 + 9 + 5 + 4 + 5 = 96 = 9 + 6 = 15 = 1 + 5 = 6. A "six" personality would have a tendency to be artistic, responsible and caring on the positive side, and doubtful and stubborn on the negative side. The single name "Raúl" corresponds to the number "7," and indicates that the person is analytical, has a need for privacy, is intuitive, reflective and absorbing. All of these tendencies can be ascribed to the oblique portrait that we have of Raúl in the text. 

Aproximations to Luis Goytisolo's Antagonía by Pamela J. DeWeese. Petar Lang, New York, 2000.