 I'd now like to welcome to the stage Professor Jeffrey Hamburger, the Kuno Franke Professor of German Arts and Culture at Harvard University. Tonight, his lecture is entitled, Poetry, Play, Persuasion, the Diagrammatic Imagination in Medieval Art and Thought. Jeffrey. Well, first of all, thank you all for coming, for having found the stamina to come to the third in this series of three lectures. I'd also like to take this opportunity to thank everyone here at the British Library for their hospitality and for all of the logistics that have gone into making this lecture series possible. Poetry and play, these are probably the last words that come to mind when most of us think about diagrams. Persuasion, perhaps, but not fancy and freedom. As we have seen, diagrams are serious stuff. And at times, perhaps, even a little bit dull, what might want to ask does the discipline of the diagram have to do with the freedom from conventions that we associate with poetic license? As I hope to show you, a great deal, and not only in the rather literal-minded way documented by this detailed diagram, which descending from the top, labeled pest or foot, the measure of poetic meter, breaks down the various types of poetry according to the classification provided by Donatus, the mid-fourth century grammarian, who was the tutor to Jerome, the patron saint of philologists. Another diagram, the so-called Wheel of Virgil, seen here in a German manuscript of John of Garlandia's Parisina Poetrya, systematizes style and subject matter according to a three-fold division codified after the works of the Augustan poet, the lowest style according to the Buchalix, the middle style according to the Georgics, and the highest or sublime style according to the Aeneid. Diagrams constitute an accompaniment to poetry and other literary works, not just poetic treatises. Consider, for example, this manuscript, an English miscellany of the 14th century comprised of several parts that perhaps belong to Robert Ivory, a Carmelite of London, who fiercely opposed John Wycliffe, the Oxford professor and translator of the Bible, whose followers are known as the lullards. In addition to Ivo, an 11th century bishop of Schott, which treat matters liturgical, canonical, and dogmatic, it also contains the Anglo-Norman Romand Rue by the poet Wase, a verse epic devoted to the history of the Dukes of Normandy. And another work on the complaint of nature by the 12th century poet, Alanus de Insilis, a homophobic work of neoplatonic Christian naturalism that provided an important source for the Romand de la Rose. Within the Wase, a genealogical diagram devoted to the kings of England follows a format reminiscent of Peter of Poitiers' compendium of biblical history. Texts remain subservient to the dictates of the diagram. The same section devotes a page to a diagram of the Heptarchy, the seven kingdoms of Anglo-Saxon England, East Anglia, Essex, Kent, Mercia, Northumbria, Sussex, and Wessex. A circular diagram of the Heptarchy had some 13th century roll chronicles, leaping animals inhabiting the interstices set the whole into motion. Detailed in the Wase are the counties and in the last column, the bishoprics, which in the textual version account for the crossed lines as some bishoprics span several counties. On the preceding page, a similar systematic diagram tabulates the provinces of Asia, Africa, and Europe. The diagram translates a TO map into systematic form, underscoring the close kinship between maps and diagrams in the Middle Ages. How does play come into any of this? With this diagram of a Beck-Gammon board, which is incorporated into the account of the Norman kings that follows another cartographic component of the work, a tabulation at the top of the page of the itinerary linking London to Avignon. A Latin treatise describes eight variants of the game, of which the first designated the ludus anglicorum or the game of the English is the longest. The text uses the diagram, specifically the letters designating the various compartments or houses, as they are called, to explain the rules. Hard on the heels of the treatise on Beck-Gammon comes another on chess in Anglo-Norman verse. It, too, is accompanied by diagrams. Like chess, Beck-Gammon was considered a royal pastime. In this 15th century Alsatian manuscript, a copy of Conrad von Amenhausen's chessbook, a translation of a Latin work by Jacobus de Chessellis, different activities exemplify different ranks and classes of society as does the game of chess itself with the king at its head. The connection between games and diagrams goes deeper, however. Diagrams play a critical role in modern game theory, in which they are used both to describe and model game structure, including the distribution of and interactions among agents. In the words of a recent introduction to the subject, quote, although game usually implies fun and leisure, game theory is a serious branch of mathematics. Games like blackjack, poker, and chess are obvious examples, but there are many other situations that can be formulated as games. Whenever rational people must make decisions within a framework of strict and known rules and where each player gets a payoff based on the decisions of all the players, we have a game, unquote. The author continues, examples include auctions, negotiations between countries and military tactics. Not by chance is Ulysses Sean playing chess in his tent during the Trojan War. In this, the largest compendium of Christine de Pizan's writing commissioned by Queen Isabel of Bavaria and produced under Christine's supervision. It is not only that games lend themselves to being diagrammed. By likening diagrams to games, we remind ourselves that they are puzzles to be manipulated in the mind according to certain sets of rules. Games involving sets of pieces whose interactions are governed by rules effectively resemble diagrams in motion. A temporal as well as a spatial element is at play. At stake is not just the matrix of pieces that presents itself at any given moment, but also what has happened and what might happen next. As in a diagram process the process by which a given configuration is generated and that by which it is read or acted upon performs a constitutive role. The manipulation of the parts whether the pieces of the game or the components of the diagram rather than some process performed on the object in fact constitutes the object. Just as the operations of a machine form part and parcel of what it is. Indeed, in the age of computers the operations performed by machines are as in a diagram as much mental as they are physical. The comparison of diagrams to a board game is neither idle nor a historical. Treatises on games for example the chess board on the left had a place as in this manuscript in miscellaneous on mathematics. As in the present so too in the middle ages diagrams were linked to games that were intended to be edifying as well as entertaining. Sir Thomas Moore banished dice from his Utopia in favor of Rhythmo Machia a monastic game diagramed on the right in the same manuscript which inculcated the principles of Boethian mathematics. Players sought to position their pieces which stood as tokens for numbers to construct harmonious ratios. Nicholas of Cusa invented a bowling game which he allegorizes in his treatise De Ludo Globi on the game of the sphere here in a 16th century edition. Cusa characterizes his game as a speculazione figuratio, not an actual sport but rather an object of meditation and philosophical conjecture. Played on a circular field with nine concentric circles corresponding to the nine orders of angels the game requires a ball scooped out on one side which causes it to spiral inward towards the center whereas the ball and its vicissitudes represent the path of the soul the center standing for the 10th element or Pythagorean decad that comprises all the other numbers represents Christ who is the circle whose circumference is everywhere and whose center is nowhere. Whoever reaches 33 points corresponding to the number of years Christ lived on earth is the winner. Sounds like a lot of fun, doesn't it? The Constantinian poet, Optatian one of whose gridded poems you see here in a Carolingian copy invited its comparison to the grid of a game board stating of his works in this curious and complicated genre. I, Publilius Optantianus Porphyrios have played these things. The Latin verb is ludo. This example embeds verses forming the name of Jesus and the Cairo monogram a nomen sacrum or sacred sign for the same within the fabric of a larger poem written in long lines. Optation's ingenuity constitutes more than a virtuosic tour de force. It presents the reader and no less the viewer with the puzzle to be teased out. Such works are not diagrams per se but they share with diagrams geometrical and numerological structure not to mention the ratios embedded in meter that serves not simply as a frame but also as a matrix for the making of meaning. Form and content are indissoluble from one another. Which admired throughout the Middle Ages Optation's picture poems spawned numerous imitations. Constantine's vision of the cross stands behind this picture poem and diagram appended to an early 13th century theological miscellany from St. Albans. The cross constituted the Christian diagram par excellence. It recurs in a 12th century gospel lectionary likely from the monastery of Mozart in southern France inscribed Rex, looks, Rex, looks, pox, and which one am I forgetting? Rex, looks, pox, and lex. King, light, peace, and law, which converge on the pregnant letter X at the center, itself an emblem of chiastic form. In a letter to Cigarius, the bishop of Otin, Venancias Fortunatus, the sixth century bishop of Poitiers, characterizes the accompanying picture poem as a gift proffered in exchange for a prisoner held captive by the bishop. Fortunatus invokes Horace's Ars Poetica to justify his combination of a poem and a picture. What then, what should my modesty offer as a gift as I was hesitating to decide in my inertia the words of Pandaric Horace came to mind? Painters and poets have always enjoyed equal sanction to dare anything. In pondering the verse, I wondered if each artist intermingles what he wants, why should not their two practices be intermingled, even if not by an artist, so that a single web be set up simultaneously a poem and a painting, unquote. Comparing the prisoner whose freedom he seeks with humankind freed by Christ's sacrifice, the poet makes himself a prisoner by limiting his license in the form of a grid of 33 letters, again corresponding to the 33 years of Christ's life. Quote, I wove a poem of just that number of verses and letters. Consequently, what was I to do or where was I to go, deterred as I was immediately by the difficulty of the task, or rather in difficulties because inhibited by the constraints of meter and the restraint on the number of letters? He then adds, I began to be bound by a task undertaken for a man to be freed, and with the reversal of roles I enchained myself as I sought to remove the captive's ties, unquote. The letter further characterizes both the pictorial form of the poem, a cross made up of two intersecting diagonals set within a square, and the color red in which the intakes are written, the whole constituting in the poet's words a loom of letters, a metaphor that puns on the double meaning of textus as both text and textile, and which the poet allegorizes by comparing its texture to that of the priestly garments described in the Old Testament. In this version, the entire poem takes on the appearance of a temple crowned by the cross, hung with the alpha and omega. The picture poems in praise of the cross by the Carolingian polymath, Rabbanus Maurus, seen here in a late 12th century copy from the Premon Stratensi and monastery of Einstein, offer the most celebrated example of such poetic pyrotechnics. This poem represents the 12 apostles as branches of a golden cross. Just how difficult it was for scribes and artists to coordinate in the production of such picture poems can be seen from two other pages in the manuscript. The first, a botch, removed to the back of the book, and the second, a more successful attempt. In the first instance, the artist gave Christ too tapered a waist, leaving insufficient space for the letters that had to coincide with it exactly. Textual and figural corpus had to be won. Far less familiar is a late medieval collection, the book on the distinctions of meter by James Nicholas of Denmark, commissioned by Marie de Saint-Paul, Duchess of Pembroke, best known as the founder of Pembroke College in Cambridge. The occasion for the commission was the death of her husband, Imère de Valence, Duke of Pembroke, who had passed away in 1324. All the poems deal with death. One of the poems takes Optation's concept of picture poetry as play. Literally, it is modeled on the board game known as Merrill's or Nine Men's Morris in German Mühle. The poem, the 27th in the series, consists of four strokes. The first three constituted successively by the verses making up the three squares, one set inside the other, identified as the outermost median and smallest squares that mark the paths along which the game pieces can move. The fourth and final stroke by the words, all beginning with the letter M, as a small illuminated initial, that join the three squares to one another. In these poems, as in other Carmina figurata, words constitute the structure of the diagram and lend themselves to combinator readings. In this instance, given the subject matter, less playful than mournful. James lends the 23rd poem, a diagrammatic structure based on a familiar model, the ubiquitous square of opposition, a logic diagram. In the center, at the point at which the diagonals representing the contraries converge, stands an illuminated initial M for Moore's death. A reproach against death's destructive power, the poem, like the square, requires combing its components, combining its components according to the logical patterns, contrarity, some contradiction, sub-alternation and contradiction that the square maps out. Thus, the top horizontal, read from left to right along the line of contrarity, reads, death makes the dark night and the world replete with anxiety. That along the lower horizontal, the line of sub-contrarity, the first several of which only fully makes sense when combined with others, a robber inflicts wounds, the noose of death shows itself to me. Those along the vertical lines of sub-alternation read, death inflicts suffering, he fabricates deceit like a thief and crying with anxiety, I decay, I see the end coming. And those along the diagonals of contradiction read, death doubles tears, the other visibly confuses death and a robber robs you of wealth, death seizes you forcefully with anxiety. As James explained in the commentary, other combinations are possible. The verses can always be read in a backwards manner, this is James himself speaking, or in a direct manner progressing from side to side from one corner to another, the contrary, sub-contrary, sub-alternates and contradictions of the opposite corners and in other diverse ways, and thus when ascends to 32 verses or more. The logic of the patterns plotted by the poem matched the inevitability of death that the poem laments in interlocking repetitive verses. What happens when we bring the habits of mind and of viewing dictated by such diagrams to other works of art? A single object, the Alton Tower's tryptic, named after its former home, the seat of the Earl's of Shrewsbury, demonstrates the intersection of faith and the visual rhetoric, sometimes referred to as visual exegesis, of diagrammatic demonstration. It does so in terms of typology. Typology is as old as Christianity itself. Words attributed to Christ in the gospels make use of the method. In 12th century enamels, however, typological method as a system of representation reaches its apogee. Its systematization does not simply press pairings of Old Testament type and New Testament antitype into a geometrical framework. As in a stained glass window, the diagrammatic framing elements themselves are constitutive of meaning. In addition to bearing inscriptions that identify, clarify, and through the use of verse, amplify the images, they impose logical relationships among them. Thus the crucifixion within the trapezoid at the center surrounded by the symbols of the four evangelists directs the viewer along its vertical axis towards the two additional New Testament scenes, above the three marries at the tomb, and below Christ's descent into hell. The resurrection might have made more sense in this spot, but by virtue of its placement below the cross, as if underground, the descent obeys a certain visual logic, all the more so in that it is flanked by personifications of earth and sea. Nested between two supplementary trees, the cross arm of the cross defines the other direction in which this diagrammatic constellation of images must be read. It points to the subsidiary scenes on the wings, all drawn from the Old Testament, to the left the sacrifice of Isaac, and to the right Moses and the brazen serpent, both conventional types. Like the scenes they supplement, those on the wings also occupy two circles framing a central trapezoid, none of which however, in keeping with their status as prophecies, is complete. At the upper left Jonah emerges from the mouth of the whale, and at the upper right the bones of Elisha bring a dead man back to life. Both scenes anticipate the resurrection signified by the absence of Christ's body from the tomb at the center. At the lower left God, not Christ, is indicated by the absence of a cross halo, fishes for Leviathan, a soteriological allegory based on Job. No less unusual is the coupling of the descent with the scene at the lower right, Samson carrying away the doors of Gaza. Just as the trees to either side of the cross elaborate the vivifying power of Christ's sacrifice, thereby lending all the triptych's vegetal ornament a quickening charge, so too the verse inscriptions broadcast a strong soteriological message. For example, the verse accompanying the crucifixion itself reads, Christ dies on the cross and repays the debts of the first created man, and that adjacent to the scene of the brazen serpent, those whom the serpent bites the image of the serpent restores. In combination with the relics presumably once contained within the triptych, such proclamations lend the images an operative apotropaic power. The resemblance of the triptych's central configuration to representations of Christ in majesty underscores its underlying message. Within historical time the crucifixion looks back to Old Testament types, but it also points to Christ in eternity outside of time. The six medallions divided into two groups of three, charity sun and moon at the top, sea, earth, and justice at the bottom, root the overall scheme based on cosmological diagrams in an ordered whole in which theology and cosmology are grafted together. Whereas the first trio forms an extension of the crucifixion in which images of sun and moon refer to the eclipse that according to the gospels took place at the moment of Christ's death, the placement of justice opposite charity at the bottom of the image effectively summarizes the triptych's opposition of the old and new law. Like typology diagrams are fundamentally relational in character. In lieu of linear or continuous narrative of a kind brought to perfection in antiquity, typological art lent itself to demonstrative, didactic, and diagrammatic modes of image making. The triptych's geometry speaks through the relationships established in conjunction with its narrative imagery. In a manner typical of much medieval art, the triptych conjoins two modes of image making. One abstract, the other figural. The one completes the other according to an incarnational logic. Just as the word became flesh, so too Old Testament prophecies prefigured their New Testament realizations. This fleshing out constitutes the foundation of figuration in Western art. Within this framework to read the geometry of the triptych simply as a means of laying out previously established pairings would be to underestimate its formative role, not only in clarifying relationships but also in generating meaning. Far from an underlying element, the geometry manifests itself on the surface and controls the way in which the parts are read. The interlocking forms, which like interlaced pass above and below one another in regular alternation, rearrange episodes of linear narrative into repetitive patterns that lend themselves to being read in typological terms. The circles and squares spread across its surface, linked like the parts of a chain, knit the disparate scenes from salvation history into a single matrix. When open, the two wings of the triptych where they joined together would match the geometry of the center. When closed however, the object would have looked like nothing so much as the form traditionally given to the tablets received by Moses on Mount Sinai, the literal embodiment of the old law. Only when opened is the old law broken, revealing the truth of the Christian dispensation at the center. Typology effectively turned sacred history and even natural history along with it into a colossal diagram. Its contents were codified in later medieval works such as the Bibliopauperum, the so-called Bible of the Poor, a misnomer, I should add, and the Speculum Humanae Savationis, the Mirror of Man's Salvation, both of which originated in the 13th century and which came to serve as iconographic handbooks for works in multiple media. In this Bibliopauperum, probably but not necessarily unfinished in so far as uncolored line drawing, the didactic medium par excellence characterized all but the most luxurious copies of these handbooks, types from the Old Testament are conjoined with others from natural history. The elephant who carries a tower into battle and the beaver who builds his house with branches, both appropriated from the natural histories of Thomas of Cantempré and Pliny before him, represent borrowings from a far larger but also much, much rarer compendium of typological lore, the Concordancia Caritatis seen here on your right, written by Abbott Ulrich of Lillienfeld in Austria during the first half of the 14th century. According to Ulrich's sources, the elephant, the chased animal, is often killed in battle and hence is comparable to Christ. The beaver in turn is often hunted and killed within the house that he has built. The speculum employs a different indeed variable layout but the underlying principles remain the same. This rare early English copy deploys types from natural history, the pelican piercing its breast to feed its young and once again the elephant but in conjunction with the crucifixion rather than the carrying of the cross. In all such works, diagrammatic modes of representation initiate as well as instruct. Not only was figural imagery incorporated into diagrams, diagrammatic matrices became an integral part of figuration. The linking of abstraction and figuration was also deeply rooted in Christian theology. Just as according to the doctrine of the incarnation, Christ possessed two natures, one divine, one fully human, so too medieval religious imagery integrated abstraction and naturalism. Paradigmatic of this process are the illustrations to the specular virgenum, the mirror of virgins attributed to Conrad of Hirsau, a benedicting reformer of the early 12th century and intended as a handbook for the pastoral care of nuns. The British Library's copy, the earliest extant, comes from the Cistercian monastery at Eberbach in the Rhineland. The illustrations, whether the complimentary trees of virtues and vices or the diagrammatic representation of the parable of the sowers, do not simply supplement the text, they complement the discursive discussion to which they add a diagrammatic dimension. Even though the text refers to the images, it does not explain them. They both illuminate the text and have their own independent existence. Moreover, the diagrammatic components do not simply follow one another in paratactic fashion like so many illustrations to an argument. Rather, as with the tree of Jesse on your left and the Tower of Wisdom on your right, they create internal typologies that compound meaning by virtue of shared forms and structures that allow for multiple paths and points of entry. In short, they speak of visual language that betokens an understanding of the power of the visual in terms of its immediacy and its explanatory power. Few works of medieval art testify more eloquently to the consummate fusion of complex geometric armatures with a dynamic yet abstract figural style than the frontispiece to the book of Job in the Flareff Bible, illuminated at the Premonstratensian monastery in modern day Belgium, around 1170. Why Job, you might ask? Because the book of Job falls approximately halfway through a complete Bible in two volumes. The monks of Flareff, however, seized this opportunity to create a programmatic image. We readily recognize the page on the right as a depiction of, at the top, the transfiguration, the moment at which Christ first revealed his divinity to the apostles, and below the last supper. The subject matter of the page on the left is more difficult to discern. The diagrammatic armature, however, alone suffices to inform us that this is a didactic image predicated on elaborate exegesis. Hard though it may be to believe, the story depicted here, that of Job and his children, is the same that you see here in the Burry Bible, illuminated by Master Hugo on commission from Herve, the sacrist for his brother Talbot prior of Burry St. Edmund's Abbey, around 1135 to 38. Whereas the narrative image in the Burry Bible adopts the grandiose rhetoric and scale of monumental wall painting and mosaics, its continental counterpart speaks in the language of the diagram. As allegorized in the image, the story of Job identifies first his 10 children with the seven gifts of the Holy Spirit and the three cardinal virtues, and second his feast with Pentecost, the moment at which those gifts are transmitted to the apostles. The gifts further manifest themselves in the seven works of mercy depicted at the bottom of the page. The inscription that embraces the entire opening, which draws on Job, reads, this image, namely that on the left, is given as a model of good behavior. This image, referring to the one on your right, teaches the depths of divine mysteries. This verbal exemplar, in addition to explicating the juxtaposition of Job's travails as an example of the vita activa and the transfiguration as an example of the vita contemplativa, exemplifies the mixed life to which the patrons and producers of the manuscript, the premonstitensian monks of the Abbey of Floref, aspired. Another premonstitensian Bible held at the British Library, illuminated in the 1170s, comes from the same library as the Rabanus Maris I showed you previously, that at Einstein. Its text and many of its initials were copied directly, if rather freely, from the Floref Bible, indicating that within their order, the monks must have practiced a form of interlibrary loan. The Bible's chief glory is made up of the pages that preface the four Gospels in which text and image can hardly be distinguished from one another. Framing the Bible's second volume, however, is a set of diagrams that was added on blank pages at the front and the back. More than just an efficient use of available space, the diagrams present a curriculum in natural philosophy that complemented scripture. At the front, we find a hand for calendrical calculations, similar to those found in treatises on the computers. At the back, we find, at the upper left, a schematic diagram of the branches of philosophy. Below it, a Mapa Mundi. Then, at upper right, the Mundus Homo Annus diagram, derived from Isidore of Seville, and a diagram of the path of the sun through the signs of the zodiac. Then below them, complementing the world map opposite, a diagram of the climate zones and the courses of the planets. Overleaf follow diagrams of both lunar and solar eclipses, another climate zone diagram incorporating the winds, and lastly, a smaller diagram charting the paths of Mercury and Venus around the sun. The facing page presents the monstrous races described by Pliny, thought to inhabit the farthest reaches of the earth. In keeping with scriptural exegesis of the 12th century, which placed ever greater emphasis on the literal sense, and with it the importance of God's creation as an ordered image of the divine, the diagrams convert the Bible into a schoolbook for a curriculum that comprehends history, nature, and the liturgy. In this same spirit of literal and historical exegesis, scholars endowed their Bible commentaries with diagrams that reconstruct biblical structures. As in this diagram of Noah's art at the front of the Bible of Robert de Bello, written at Canterbury between around 1240 and 1253, which carefully collates four different reconstructions based on at the top scripture in the middle, Augustine and Josephus, then at the bottom, that it says of many others who remain unnamed. The drawings, which likely represent an addition, draw on a manuscript of Petrus Comestor's Historia Scholastica, such as this example in Cambridge. In the Psalter, the diagrams complement the depiction of the Ark in the Bible's elaborate initial for Genesis. In their relative simplicity, an application of a critical comparative method, such diagrams stand at a considerable remove from the exegetical edifices fashioned by Hugh of St. Victor only a century earlier. In similar fashion, in his commentary on Ezekiel, seen here in an English copy of the late 12th century, the Parisian theologian Richard of St. Victor sought to reconstruct not only the plan, but also the elevation of the temple in Jerusalem. Richard resorted to geometry. In this instance, the ratios of the sides of a right triangle to construe measurements not provided by Ezekiel's vision. Driven by his emphasis on the literal rather than the allegorical sense of the text, Richard drew in part on comparable diagrams in Rashi's commentary on the Pentateuch, seen here in a German copy dated 1341. And here's a manuscript I was just looking at a few hours ago up in the reading room. Diagrammatic didacticism permeates vernacular works of the later Middle Ages, among whose purposes was the popularization of scholastic learning. Unopening this 13th century copy of the encyclopedic Book of Treasure composed in 1260 by Brunetto Latini, Dante's revered teacher, whom the poet nonetheless placed among the sodomites in the seventh circle of hell, a reader would have been confronted by this two-page spread, no less ambitious than that prefacing Job in the Floref Bible. The verso tabulates and correlates the arts and sciences, including the black arts of nigrimancy, inspired by the devil. You'll see that at the upper right corner of the left-hand page. And on the right, yes, excuse me, the black arts of nigrimancy, inspired by the devil, along with other manual skills, such as alchemy, husbandry, weaving, and carpentry. The page on the right crams into a single folio, two trees, one of the virtues, the other of the vices, with all their various ramifications. Beneath the tree of virtues, souls are gathered into a three-fold bosom of Abraham, an image of the Trinity, whereas at the right, malfactors end up in the mouth of the demonic dragon. Given its close attention to the natural world diagrams, some derived from Goswin Demetzi's Limage du Monde, a popularization of scholastic science, constitute a frequent accoutrement of Brunetto's text, as in an early 14th century copy from Picardy, in which the marvels of nature spill over from the miniatures to the margins. Literature overlapped with the historical, not only in accounts tracing the descent of kings, but also that of the gods, of which Giovanni Boccaccio's on the genealogy of the gods of the Gentiles, written after 1360, provides the most famous example. Boccaccio's account is also famously confusing, a welter of relationships that the diagrams in this Venetian copy only partially help to untangle. The celebrated humanist, however, was not the first to attempt such a genealogy. Witness the work of Paolo de Perugia, who from 1324 until his death in 1343 worked at the court of Robert of Anjou in Naples. Drawing primarily on the avid, he compiled several mythographic works, whose existence, if not whose content, was known to Boccaccio. A manuscript of Neapolitan origin from around 1374 gives the gods family descent in visual, not textual form, in an extended diagram modeled primarily on the family trees found in genealogical scrolls, the form in which these diagrams most likely were first presented. Diagrams play no less integral role in the brevieri of love of Matfrey Amangot, a jurist from Bezier in southern France who died in 1322. His encyclopedic Asatan poem of more than 35,000 lines offers a summa on the unity of love, erotic as well as divine, and offers a fascinating fusion of poetry, piety, and natural history that provides the laity a pathway to the divine. In addition to scholastic authorities, Matfrey names 65 troubadours whose works are placed at par with those of Latin authors. An elaborate program of 273 illustrations combining narrative and diagrammatic imagery structures the work. The pictorial program owes an evident debt to scholastic diagrams such as the trees that structure the works of his contemporary, the Catalan poet and philosopher Raymond Lull. In Erma Gunko's manual, a full-page image of a top-down tree does double duty as title page and table of context, effectively offering a flow diagram of the argument. Front and center stands a crowned female figure labeled Donna de Lab, the Lady of the Tree. A further inscription in her nimbus identifies her as a personification of all-encompassing love. The dove of the Holy Spirit that hovers above her head indicates that she is divinely inspired. In her hand, she holds a disk that speaks of the love of the sun, a motif that manifests her kinship with the Virgin Mary. Medallions descending from her womb split into three branches, of which that in the center is rooted in a bust of Christ from which radiate 12 characteristics of charity. Flanking the structure to either side are Christ at the left who displays his wounds as he turns away from the devil, and at the right, personification of the church, holding a chalice who shuns blindfolded synagogue. The central trunk further divides into two branches, that on the right, the tree of knowledge, of good and evil, representing the laws of nature, that on the left, the tree of life, the laws of man, a distinction rooted in Justinian. Whereas the laws of man bear fruit in the form of 14 Christian virtues, the laws of nature culminate in the equivalent number of courtly virtues. On each side, whoops, I'm sorry. On each side, personified vices with swords and giant axes seek to lop off branches of the trees. Other diagrams of which I can show only a sampling depict the nine choirs of angels, the universe as a clock-like mechanism whose axis two angels turn, the 12 signs of the zodiac, the sun's course, an eclipse of the sun, a rather drastic simplification of the scientific diagrams with similar subject matter in scholastic manuscripts, the phases of the moon compared here with the same subject in a contemporary scientific miscellany, the spheres of the elements and the planets, an image that, as you can see here, he lifted from Gossouin de Metz, also the winds, the planets that govern the days of the week, the seasons, and the six ages of the world. Remarkably, of 12 extant manuscripts, the British Library owns no fewer than three. Although they vary in style, their program of illustration remains remarkably consistent. The text references the images, which both constitute an integral part of the work's didactic apparatus and assume their reader's diagrammatic literacy. Nonetheless, as Sarah Kay has observed, text and image offer differing interpretations of love's ramifications, undercutting, or at least complicating, the work's overall message of love's unity. Montfrey's work exploits the full poetic potential of the diagram, not simply as outline or illustration, but as a method for moving the minds and hearts of his readers. His work points to the late 13th century as a period of transition, when a profusion of pastoral literature in various vernaculars produced in the wake of the Fourth Lateran Council of 1215 brought the diffusion of diagrammatic didacticism, previously the province of scholars, to a wider lay public. Like the ramifications of a tree, however, his work also points to a divergence in the history of the diagram. The influence, the influx and impact of Aristotelian science at the universities, supported by translations from the Arabic, in particular from Al-Kindi and Al-Hazim, led to a newfound sophistication in diagrammatic demonstration that is nowhere more evident than in the work of the Franciscan Roger Bacon, celebrated as the Dr. Mirabilis, but also as a magician, a designation that he would have rejected. Bacon championed the empirical study of nature, especially optics, albeit always within a Christian metaphysical framework. Diagrams litter this, the earliest extant copy of several of his works, written at some point during the last quarter of the 13th century, most likely at Oxford, where Bacon taught when he wasn't in Paris. The diagrams demonstrative function makes them integral to the text. Looking at this manuscript, one inevitably thinks of another great student of the subject, Leonardo da Vinci, whose Arundel codex includes optical diagrams. The resemblance, however, is rather deceptive. Despite Bacon's appeals to experience, what his diagrams ultimately represent are geometrical thought experiments. Historians of pictorial perspective seeking to explain its initial formulations in the late 13th century have appealed to Bacon, who declares, quote, since therefore ingeniously constructed works like Noah's Ark and the Temple of Solomon and of Ezekiel and Esdras, and other things of this kind, almost without number, are placed in scripture, it is not possible for the literal sense to be known unless man has these works depicted for his sense, ad sensum, but more so when they are pictured in their physical forms, unquote. What Bacon appeals to hover is not perspectival pictures, but rather exegetical diagrams of the kind we have seen and see here again, whether in the Polychronicon of Randolph Higdon, a universal chronicle originally completed in 1340, or here, in a late example, dating to the first half of the 16th century, a biblical and genealogical chronicle that runs from Adam and Eve to Edward VI, where it is juxtaposed with the familiar figure of a TO map. Although now populated with pictures in their basic diagrammatic structure, nothing has changed. Of such diagrams, Bacon states, quote, and thus have the sacred writers and sages of old employed pictures and various figures that the literal truth might be evident to the eye and as a consequence, the spiritual truth too. Montfrey's diagrams invoke the authority associated with this mode of visual presentation, but applied in different ways towards different ends, whereas Bacon's diagrams are stripped of any and all figural elements, Montfrey operates with the diagram as metaphor. He offers us leaps of the imagination, whereas Bacon draws lines of thought. To end on a lighter note, many of you no doubt remember Roald Dahl's square suites that look round. Here from a manuscript of the French prose Brut, named after Brutus, the legendary founder of Britain, is a diagram of the Arthurian round table that looks square. The poetry of the diagram, it seems, can sometimes prove rather prosaic. I hope, however, to have convinced you that in our own networked world, in which it seems not only all knowledge, but even our own selves can only be understood in diagrammatic terms. Medieval diagrams, no matter how remote some of them might seem from our own experience, can still speak to us in terms of both poetry and persuasion. Thank you. Thank you very much. I think there's time for a few questions if any of you have some. I have a question from the live streaming audience. My question is stated twice differently. How did diagrams play into the life of non-elites? Is the mental work and the instrumental role of diagrams in the sacred as true for the common population? And were any of these diagrams monumentalized into the public sphere? Good questions. I must confess that diagrams, by their very nature, are largely directed at a literate audience and an educated audience. And that shouldn't come as a surprise given that the overwhelming majority of them are found in manuscripts. And most of those in Latin. What I tried to show in this last lecture, however, is that especially over the course of the 13th century, much of this scholastic learning is translated, literally translated into the vernacular in the context of the pastoral mission of the church is defined after the Lateran Council in 1215. And that is part and parcel of that pastoral movement. Diagrams begin to manifest themselves in vernacular contexts. One of the most famous examples is here in the British Library, the Arundel Salter. I showed an image from it in an earlier lecture. That is a manuscript that was made, admittedly for an aristocratic recipient, hardly a commoner, but it is an exemplary of quite a number of examples in which we find ambitious diagrams, also artistically extremely accomplished diagrams, being disseminated to a lay audience. So if not penetrating all the way down to the popular, we do begin to see what I characterized as a shift in the history of the medieval diagram. And in some way, Matfrey Emangot's work, of which I showed you quite a number of images, I fear they might have gotten out of sync as I was going through them, no more than a foretaste of this firework of a poem, really encyclopedic in its ambitions. But the diagrams in his work would have been very frustrating to a scholastic who really understood their workings. But he's using them more as rhetorical artifacts to entrance and persuade his audience, as well as to lend his own arguments a certain authority. So that's one part of the answer. Whether such diagrams find their way into the monumental sphere, they do. And we have written accounts from the Middle Ages that suggest that diagrammatic images were found in monumental contexts. The most controversial example is probably the Ark of Noah associated with Hugh of St. Victor. And some scholars have tried ingeniously to reconstruct it. I count myself amongst those who think that it is more of a rhetorical device and that it was never actually generated as an image. There are too many internal contradictions for it to have easily worked as an image. It's more of a mental map to a whole universe of learning. But there are examples that we know of that were laid out on a very large scale. A famous example is the Bonaventure and Tree of Life based on a treatise of the Franciscan theologian of the 13th century Bonaventure, of which there are numerous monumental examples, both north and south of the Alps, as well as large scale panel paintings. And so these works often, if not always, hung in a public setting. One has to assume that there was some kind of mediation, whether from a preacher or from some other guide, kind of art historian of the Middle Ages, who would have used these large scale images as a backdrop for some kind of pastoral instruction. There are numerous other examples that one could cite. There's a church in Bergamo in northern Italy that has fragments of a monumental diagram. It would have been as tall as the walls in this space. Unfortunately, only fragments survive because in the 17th century, the wall was opened up to create a Baroque chapel. But that's another indication that diagrams for the masses existed in spaces used for preaching. Please. I think there's a microphone. If concrete poetry is considered diagrammatic, the Greek poems that appear in print in the form of an egg and an ax and wings, do they have a manuscript precedence that goes through the Middle Ages? Yes, they do. And I'm very glad that you asked that question because there's a direct line linking someone like Rabbanus Morris or Venancias Fortunatus, both to predecessors in antiquities such as Optation Porphyrios and earlier still, for example, in Greek poetry, all the way down through poets like George Herbert in the 17th century in his collection, I think, the Temple, right down to concrete poets of the 60s and 70s into this day, the calligramme of Apollonair are a famous example. I would not go so far as to say that all picture poems are diagrams or even diagrammatic, but there is a vein, there is a tradition of picture poems that have a very strong diagrammatic and numerological element. And so I think there is an overlap between the diagrammatic and the poetic in that respect. And it's interesting in terms of the reception of Rabbanus Morris, for a long time his poems, there are 28 of them in this cycle in his book in Honor of the Holy Cross composed at Fulda in the middle of the 9th century. They were regarded as eccentric oddities. But in fact, his work had a really steady reception throughout the Middle Ages. Their manuscripts from, I believe, every century except perhaps the 14th, right up until its first printing in the early 16th century when German humanists revived it because they saw it as an example of an antique genre. And so the work in its reception and its various transmogrifications becomes a kind of barometer of changing attitudes towards the relationship of text and image. At least that's one way of reading the reception of his work. So yes, there's a very powerful current that runs all the way through from antiquity to the present with only very minor interruptions. The latest manuscript copy of the work as opposed to a printed edition was made for Rudolf II of Prague. It's a magnificent manuscript copied after the presentation copy now in the Vatican. It's also an extremely strange book. It's digitized on the Bibliotheque Nationale's website because it tries to combine a modern, modern by 17th century standards, naturalistic mode of representation with the absolutely flat integration of in-text and text that the work requires. And so it makes you rather giddy when you look at it. But absolutely yes. Sorry for a long answer to your question. Please. This goes back to the first question a little bit. But I was just wondering, because you see quite sort of similar diagrams appearing in manuscripts from different places and but representing sort of the same thing in kind of similar ways, was there a textual communication amongst scholars sort of across the space that was saying this is a good way to represent that? Or were they actually trading in diagrams? Or were they sort of explaining the representations? Well, in the Middle Ages, all learning was transmitted through, or almost all learning was transmitted through the copying of manuscripts. Of course, in the earlier Middle Ages, there was more of a role for the oral transmission of learning. But as I tried to suggest, I think in my first lecture, the diagram is in many respects a site for oral argument. And just as Greek mathematicians might have gathered in the Agora and drawn their diagrams in the sand, so too, I think, when we look at medieval diagrams, we should think of them as having a performative dimension. This is something I touched on in an earlier lecture. So we can read them in some respects as transcriptions of a much more dynamic process of demonstration in the classroom or in other contexts. So certainly these things could have been transmitted orally, but they were transmitted with manuscripts in which they were explained and demonstrated and used, and manuscripts could travel very long distances. But it's not only that the premonstratensian monks of Flaref clearly in modern-day Belgium length their Bible to their brothers in the Rhineland. We know that in England, there was something akin to an interlibrary loan union catalog that I think, if I remember correctly, was created by the Dominicans. I'm looking at David Davray to see if he will nod to confirm. It was one of the mendicant orders that created effectively a union catalog of their works scattered across the various houses across the British Isles so that manuscripts could be borrowed. So there were authoritative texts to which people looked, and there was a corpus of diagrams that circulated very widely. There doesn't have to be another question. I gather there are drinks awaiting us. So let me just say once again, thank you very, very much for your attention. But wait, there's more. Thank you, Mr Davray. It's my pleasure to thank Geoffrey on behalf of the British Library and the Penizzi Council for a wonderful series of lectures on diagrams, medieval art and thought. Geoffrey, thank you on a personal level. You certainly helped bring those diagrams alive for me. And as a former interlibrary loans librarian, to hear that mention twice was doubly wonderful. So thank you. The lectures over this series have been enjoyed by 200 people in the library building and over 1,000 people via the live streaming. And we've been delighted to be able to bring the lectures to a wider audience than before. We now help those of you in the library building can join us at our reception to celebrate this series. And all it remains for me to do now is to thank Geoffrey one more time. Thank you.