Wednesday, June 5, 2019

Sir Gawain ad Quadratum





On Monday I awoke to a beautiful spring day, and with intellectual prospects to match it.  My project for the next little bit is the polishing of an essay about “Sir Gawain and the Green Knight,” a wonderful poem by the only medieval English poet who can be regarded as Chaucer’s peer both in his manner and his matter.  Unfortunately the works of the anonymous “Gawain-Poet” are even less known to general readers than the poetry of Chaucer.  The Gawain-Poet wrote in the old alliterative style and in a difficult Midlands dialect replete with unfamiliar words, many of Scandinavian origin, that found no permanent home in Modern English.  Even so, many people know the outlines of the mind-boggling story: a beheading contest initiated by a ferocious green knight who appears on horseback (horse also green) in King Arthur’s dining room.  Needless to say beneath the exciting surface story lurks a complex moral allegory.  Sir Gawain, who rather rashly puts himself forward as the champion of the Round Table, undergoes a series of related tests, though critics can agree neither on what the tests test, exactly, or on what grades to assign Gawain for his efforts.

The Gawain-Poet was a learned theologian, with a sub-specialty in architectural mathematics.  All of his poems are “numerological” in structure, a feature of especial importance in his conception of this great romance.  If there is a single key number it is five.  The poem is composed of 101 stanzas, each ending in a five-line "tail", and  with a total line count of 2530.  The stanzas vary in length, but they average jut over 25 lines each.  The interior of Gawain's shield bears a private devotional image of the Virgin.  Its exterior is decorated with a pentangle, or five-pointed star, the moral meaning of which is developed by the poet at some length.  One thing the poet is covertly conveying is that he has constructed his poem ad quadratum—an architectural term I shall explain in a moment.

The once-magnificent medieval cathedral of Trondheim (Niardos) in Norway was by the middle of the nineteenth century in very bad shape.  The Norwegian government decided, out of national historical rather than religious piety to restore it, and in this regard they sponsored an architectural competition to come up with a plan.  It was in this context that a quasi-mystical architectural scholar, Fredrik Lund (1863-1943), undertook through archival study and on-site investigation to attempt to discover the precise original plan of the building.*  Though still regarded as kooky by many sober architectural historians, his book is full of golden nuggets strewn among the pyrites.  Ancient Latin architectural manuscripts speak of building ad quadratum.  The verb quadro meant to square or give regular shape to, and a quadrum was a square or other regular rectangular solid, in masonry a precisely squared stone.  But Lund deduced that by the technical phrase ad quadratum the master masons meant construction according to certain precise geometrical principles of proportion deriving from ancient Pythagorean mathematicians and visually evident in surviving examples of the sacred architecture of both the Greeks and the Romans.  It included prominent exploitation of the “line of beauty” or “golden ratio” mathematically achieved in an irrational number (now known as phi, 1.16803) by the procedure of division of a line in mean and extreme ratio.  Concrete manifestations of phi exist throughout created nature, and are closely related to the spatial representations of the famous numerical “series” identified by the thirteenth-century Italian mathematician, Leonardo Fibonacci: the “Fibonacci numbers”.

            Though the literary applications of architectural harmonies are necessarily limited, obviously artistic use of the golden ratio is found in many places in ancient, medieval and especially Renaissance European poetry.  It is an artistic commonplace.  But I think the Gawain-Poet took matters a step further, recognizing in the pentangle a “natural” and universal emblem of artistic harmony and, by extension, moral order itself.  “The temple was supposed to be the material image of the mystery of existence” writes Lund.  “Its proportioning was therefore established according to an irrational measure, in an ascending, harmonic, geometrical progression, from the unit to the totality as this progression appears in the pentagram, which was the symbol of the harmonious system of the Cosmos, the masterpiece of the universe”.   The master builders knew, as the Gawain-Poet knew, that the geometric construction of the pentangle within a regular pentagon would unleash cascades of ascending visual harmonies corresponding to the mathematical laws within which they are based.  According to Lund’s theory, the architects’ ascending harmonic, geometrical progressions in stone were structural in both concrete and ideal expression.

            In the Christian era, Scriptural exegesis joined with Pythagorean number theory to form a single stout cord of meaning.  The poet tells us that the pentangle was devised by Solomon, builder of the biblical Temple, as a “token of truth”.  The poetic connection between stone-masonry and the philosophical quest would eventually become widespread in the secular world through the Free Masons of the Enlightenment.  Such theories were “esoteric” not because they involved magic or the supernatural, but because they dealt with an inner knowledge of Nature possessed only by a learned few.  Every Christian could claim the protection of the Virgin, whose image adorns the inner face of Gawain’s shield.  The pentangle is inscribed on its outer side, its public side so to speak, and like Gawain the reader must come to know its deeper meaning by trial and error.

            Few of us when invited to examine the delicate loveliness of a nautilus shell, are likely to think, “O, sure, 1.16803 and all that.”  A normal response is the enjoyment of thrilling beauty.  In like manner only the leaden hand of an intrusive literary analysis could encourage a reader to a mathematical first response to Gawain.  What the reader sees is a beautifully crafted, brilliantly plotted, structurally precise, suspenseful and action-packed story.  As its “meaning” is debated by the romance’s characters themselves, the reader surely has no obligation to have a single fixed opinion.  But whether in the nautilus shell or in the construction of the poem, there is a there there.  According to Shelley, poets were the “unacknowledged legislators of the world.”  But the medieval poet could rightly hope to surpass even that grandiose claim.  The medieval poet could claim to participate,  in howsoever small measure, in the artistic activity of the divine Creator of all things visible and invisible.

* Fredrik Macody Lund, Ad Quadratum: A Study of the Geometrical Bases of Classical & Medieval Religious Architecture  (London: Batsford, 1921)