William F. Klein

title.none: Condren, The Numerical Universe of the Gawaine-Pearl Poet (William F. Klein)

identifier.other: baj9928.0402.025 04.02.25

identifier.issn: 1096-746X

description.statementofresponsibility: William F. Klein, Kenyon College,

publisher.none: .

date.issued: 2004

identifier.citation: Condren, Edward I. The Numerical Universe of the Gawaine-Pearl Poet: Beyond Phi. Gainesville: University Press of Florida, 2002. Pp. x, 205. $55.00 0-8130-2554-0. ISBN: .

type.none: Review

relation.ispartof: The Medieval Review

The Medieval Review 04.02.25

Condren, Edward I. The Numerical Universe of the Gawaine-Pearl Poet: Beyond Phi. Gainesville: University Press of Florida, 2002. Pp. x, 205. $55.00 0-8130-2554-0. ISBN: .

Reviewed by:

William F. Klein
Kenyon College

In 1985, Condren tells us, he had the experience of holding in his hand British Museum Manuscript, Cotton Nero A.x. That moment determined the direction of his study of the "Gawain Poet" for the next seventeen years. The result is this book.

He doesn't indicate what prompted his sense of excitement or how that turned into the investigation that produced this book. Perhaps it was something quite simple and obvious, like the fact that both Pearl and SGGKare composed of 101 stanzas. This has been noted often enough before, but there is something special about Condren's imagination, something perhaps unusual for Medieval Studies where "authorship" and real mathematics are rare visitors. Condren noticed that 101 is number 25 in the sequence of prime numbers. And this in turn led to observations with a genuine claim to be being really "numerical."

Of course, Marie Borroff, considering the "affinities" of SGGK and Pearl, notes "Finally, Sir Gawain resembles Pearl in that each is composed with a numerical design" (Sir Gawain and The Green Knight, Patience, and Pearl: Verse Translations, Norton, 1999, 12). She indicates that her sense of this numerical design has also been recognized by Kent Hieatt, who noticed that the "five fives" of Gawain's pentangle recurs as a pointer to the overall numerical design. "The echo of line one [referring to the "siege and assault of Troy"] occurs in line 2525, which is followed by the concluding five lines of the bob and wheel." And we find at the bottom of the page a note that really seems to belong in the body. "It is a curious fact that in Sir Gawain as in Pearl, the total number of stanzas is 101." The connection is not just numerical. It goes to the core of meaning in the two poems. The "bliss" of the bob and wheel is the vision of heavenly bliss that is Pearl.

Condren's book is a thoroughly worked out exploration of the connections of which "bliss" is one important instance. I am not suggesting that Borroff's observations had any influence on Condren. Condren had much earlier embarked upon his resourcefully sustained study of the numerical design and its relation to the meaning, not just of these poems, but the entire manuscript. But let Condren say it in his own words.

This book alleges nothing to upset current critical opinions. It contradicts none of the excellent studies that have appeared over several decades; indeed it draws upon many of them. Nor does it offer for this quintessentially medieval collection a reading incompatible with the beliefs and traditions of its day. Nevertheless, the chapters that follow propose a thesis that reaches beyond anything that has yet been suggested for this subject: Cotton Nero A.x is not an anthology of four unrelated poems. It is a single, tightly constructed artifact with four movements, each of them connected to the others by precise links that represent and attempt to resolve the central problem facing humanity. It reconciles the measured, corporeal, earthly world of every human being' daily concerns and the limitless, incorporeal, divine world to which all humanity is summoned. (2)

Condren does review some of the aspects of the poems that Borroff and others have noted. His excitement at what his study has brought him to see is hardly more enthusiastic than Borroff's sense of the art of the poems. Of Pearlshe says:

One of the most striking and significant aspects of the poem is its conformity to an all-encompassing and highly elaborated design. Elements of this design are found elsewhere, but the intricacy of their combination in Pearlis unmatched in English poetry before or since....Circularity or roundness is a symbol not only of eternity but of perfection. Another visible symbol of perfection is symmetry, exemplified most notable in Pearlin the shape of the celestial Jerusalem. (120)

I cite Borroff not to diminish the value of Condren's book. It is true that the most important aspects of thematic meaning, at least of Pearl and SGGK are readily apparent, but the amazing complexity and intricacy of the numerical design is not at all readily apparent. To appreciate that fully requires a careful reading of Condren's book with a copy of a good scholarly edition at hand (for example, Andrew Malcolm and Ronald Waldron, The Poems of the Pearl Manuscript, Exeter, l987.) The intimacy of perception that this kind of reading produces is clearly manifest in the language of both Condren and Borroff. The kind of reading required approaches the kind of prayerful reading that in the twelfth century came to be called lectio divina.

I believe that Condren's study of the manuscript does in fact display a structural design that cannot be other than utterly intentional and that everyone who would like to claim knowledge of the manuscript and the poems should read his book. But the book is "difficult" and the complexity of that design and the intricacy of its details defies summary description. What I will provide here is an explanation of the significance of the central "numerical" figure and its theological implications, a brief explanation of his application of this figure to poems by Horace and Virgil, a briefer explanation of his intricate application of the figure to the Gawain manuscript, and finally a comment on the implications of the book as a whole.

The book is constructed in six chapters:

1. Introduction (pp.1-13)2. Cotton Nero A.x: A numerical Construct (pp.13-48)3. Pearl (pp.49-73)4. Purity(Clannesse) (pp.74-98)5. Patience (pp.116)6. Sir Gawain and the Green Knight) (pp. 117-146)

This series of chapters is followed by a one page "Afterword" with which I will conclude this review. There are also three helpful appendices and a "Glossary of Mathematical Terms for the Non-mathematician" as well as notes, bibliography, and an index.

The "Introduction" provides the very minimum of "theory" necessary to explain his method of reading. Medievalists are certainly not strangers to texts with numerical design, but I do not know of any systematic treatment of its many possible forms and their potential as signifiers. Of course, one cannot escape thinking of Dante in the context of this text, but the metaphorical resonance of Dante's numerical figures is quite different from the kind Condren finds in the manuscript. The one hundred cantos of The Divine Comedy is a sign of the perfection of poem (as noted above by Borroff on Pearl). The design figure of the manuscript is a sign of an "absolute" creative numerical principle inherent in the universe itself. The "infinite" aspect of its creative principle is like that of a geometrical projection, but more mysterious.

I cannot provide an summary account of the intricate perceptions Condren displays in the substance of the book, but I will at least try to provide an account of the nature of the mathematical principle that may make the idea accessible to "non-mathematical" readers. My hope is that this brief account will make the fuller account Condren provides easier to follow.

Thoughts about Augustine's universe have not been far from critical reflections on Pearl but the connection that brings these thoughts into relation to all four poems and Cotton Nero A.x as a designed artifact is a special numerical figure. It is named in the subtitle of the book: "Beyond Phi".

The popular name for this figure, the "Golden Section," is defined in the American Heritage Dictionary as "a ratio, observed especially in the fine arts between two dimensions of a plane figure or two divisions of a line such that the smaller is to the larger as the larger is to the sum of the two." The plane figure referred to here is the "perfect" rectangle, the rectangle created when two squares of the same size are combined. That this has seemed to many an especially pleasing figure is only an impressionistic effect of its real numerical mystery. Reading Condren will make it easy to understand how the last part of the definition works.

The way the plane figure is translated into a linear one is by drawing a line from the lower left corner of the rectangle to the upper right corner. Then when a compass with its foot at the upper right corner makes an arc from the lower right corner to intersect with the diagonal, the diagonal line is divided into sections of unequal lengths that are in the ratio of the "Golden Section." When this line is measured numerically the result is an irrational number that cannot be represented in a fraction composed of whole integers. The discovery of this ratio reveals mystery at the heart of a commonplace figure, in exactly the same way as the relationship between the circumference of a circle and its radius. "Pi" is an "irrational" number in the sense that calculation to determine its value in any particular case can be carried out to an infinite number of decimal places. The most common "working" value ascribed to it is 3.1416. It represents the eternal and absolute value of the ratio between all circumferences and all radii.

The value of "phi" is a number like "pi," but it is even more surprising than the absoluteness of pi. It can be represented reciprocally as .61803 (calculated to five decimal points) or as 1.61803. These numbers are "reciprocal" in the sense that "1" divided by .61803 yields 1.61803 and "1" divided by 1.61803 yields .61803.

To begin to imagine how this works "numerically" rather than "geometrically" it is necessary to translate the figures into numbers. With Condren the numbers will be the numbers of line different parts of the manuscript. I suppose in these days someone fiddling with a calculator working out the ratios of numerical values of two sums would think her battery was getting weak or that some irrational disfunction had bugged her calculator. But the effect would really be hair-raising when she discovered that when the larger number was measured against the sum of the two parts it had the lesser "phi" ratio to the whole. This ratio, therefore, has, as an additional feature, that new figures can be created out of its parts that are proportional recreated figures of itself. Adding the larger figure of two sums standing in "phi" ration will always create a new figure in which it is the lessor part of the whole. In this sense the figure is the repeating pattern of an infinitely repeatable incremental series based upon an irrational number.

For this reason it has been the focus of fascination for mathematicians for centuries.

In his "introduction" Condren first presents as an example of a poetic adaptation of this figure the Ars Poetica of Horace.

The first 294 lines concern the craft of poetry as it shapes the two forms of literature then current in Rome, verse and drama. The remaining 182 lines, from 294 to the end of the poem in line 476, focus on the poet and especially his interaction with the critic. As George Duckworth(1962) demonstrated forty years ago, the relative sizes of these two sections are not arbitrary, but conform to the unique proportion, known popularly as the Golden Section and called phi by modern mathematicians.... This mathematical proportion underscore perfectly the point Horace makes in the poem as a whole. The craft of poetry is means by which the lesser extreme, poets and critics, achieves the greater extreme, literature (7-8).

Next he analyses the numerical structure of Virgil's Georgics I and displays a more elaborate use of the same Golden figure in numerical relations of the line numbers of the seven distinguishable parts of this text. As you may readily imagine, seeing the design that Condren describes is very much aided by graphics, but the fundamental analysis is still numerical. The key to the design is the value of phi 1.61803 within very narrow tolerances. He concludes his very convincing "demonstration" in this way:

By arranging his lines in such a way, to show both the measurement of the a year and the mathematical proportion shared by all things in the universe, Virgil demonstrates the unity of the four orders--not separate orders, but four different expressions of a single order, the earth, mankind, the heavens, and God. (10)

The final section of his "Introduction" Condren makes a brief case for the reading of numerical relations as a method of achieving an understanding that Plato would call Wisdom.

Chapter 2. "Cotton Nero A.x: A Numerical Construct" is the most elaborate and intricate chapter in the book. What Condren seeks to demonstrate is that the both the figure and its rhetorical function in the poems of Virgil and Horace are repeated in the structural design and the rhetorical effect of the manuscript as a whole. On the face of it I find it impossible to distinguish between my amazement and my sense of being dazzled by the complexity and intricacy of the structures and effects Condren describes.

I am not at all certain that I have followed Condren all the way through his meticulous analysis of the numerical relations of the parts within the parts and their relationship to the whole and its thematic sense, but I do believe the patterns are readily discernible, even "ineluctable," as Stephen Dedalus would have said, and that they demand an analysis of the kind Condren provides. That his analysis is sound I cannot claim or argue. His book will have to make its own way in the world. How does one judge a unique kind of argument arguing for a perception of a clearly imaginable idea represented in a unique, not to say anomalous, form? Without the precedent of Horace and Virgil the construct would seem impossibly complex. At this point we must give Condren the benefit of our doubt.

Before I ask my final question about the implications of his study I would like to give him the liberty of his brief and eloquent "Afterword."

The implications of the highly wrought strategy we have been discussing, in which mathematics serves as a revealing analogue to metaphysical matters, might be stated in various ways depending on the context one wishes to emphasize. To a mathematician the conversion of a measuring system based on fours into a system based on fives requires the magic of an irrational number that leads to infinity if applied repeatedly. To a medieval theologian the New Law expands and enriches the Old Law through the advent of Christ, whose teaching, if continuously applied, in turn translates the New into eternal salvation. To a poet there is little difference, for his epiphany comes in recognizing the parallel between mathematics and theology and in realizing poetry's power to make palpable what otherwise would be ineffable. Pearl and Sir Gawain and the Green Knight have a foot in both the four cornered world and the world that supersedes it. The duodecimal basis of the former, the four fitts of the latter, and the worldly concerns of both suggest the sphere of Purity and Patience. The 5 square prime number of stanzas in both Pearl and Gawain, the fifth Platonic solid suggested by the former, and the latter's pentangular emblem, five-line bob-and-wheel, and power of regeneration imply the abode of the Pearl maiden. Above it all lies the manuscript's astonishing representation of elegant coherence. The profound congruence of the universe with man's theological and moral concerns, and with all that lies on his too-much-loved earth, unfolds before us with subtle simplicity. The disciplines of the quadrivium--arithmetic, music, geometry, and astronomy--have been drawing their lines unwaveringly toward the judgment on which will depend the eternity, not only of the characters described in its lines, but also on every reader humbled by this manuscripts exquisite beauty. (147)

Very early in his "Introduction" Condren makes a brief statement of one of the critical issues about this manuscript to which he hopes his book will contribute. To the old question of whether the manuscript was a miscellany of work by various poets and a scribe that Larry Benson laid to rest for most scholars with his 1965 argument for one poet for our four poems Condren wanted to add his support. "The evidence at the heart of the present study strengthens this conclusion by demonstrating that all the lines of poetry in the manuscript as well as all its decorated initials express the intention of one author, intricately planned and almost perfectly realized."

I can hardly suppress my impression that what has been at the center of Edward Condren's encounter with this manuscript is an experience of communication, of having heard, perhaps for the first time, the inflection of meaning which is what all poets write in the hope of achieving and do so in moments that are unique, anomalous, and utterly "beyond."