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Library Catalog No. MWE1980

“The Geometry of the Mind.” Architectural Association Quarterly 12.4 (1980): 32–55.

by Michael W. Evans

e-Copyright © 2007–2016 < http://she-philosopher.com/library.html >



First Issued:  5 June 2007
Reissued:  21 August 2012
Revised (substantive):  n/a

Part I: Editor’s Introduction to Evans’ lecture on medieval information design

decorative initial I (e-copyright 2014) HAVE made Michael Evans’ masterful study of medieval diagrams and the world view which they portray available in HTML format as part of she-philosopher.com’s growing collection of materials on early-modern information design and visual rhetoric (see the Subject Index at the site’s top-level GALLERY page for a list of relevant links). Evans’ essay is full of fascinating insights about geometrical design as a reflection of human thinking and imagination, and deserves to be much better known than it is.

Evans’ “The Geometry of the Mind” was first delivered as a public lecture before the London-based Architectural Association in 1980, and subsequently revised by the author for publication in vol. 12, no. 4 of the AAQuarterly: a specially themed issue titled “Description: Invention: Reality.” As noted by Ranulph Glanville, who organized the Architectural Association lecture series in 1980 and served as editorial consultant for issue no. 4, Michael Evans’ journal contribution is “exactly argued.” The result is a fairly long piece, rich with scholarly detail (90 footnotes and 28 illustrations), having been designed for a print format that does not convert easily to HTML. I have had to restructure it slightly for Web publication, and have divided it into 2 digital parts (this Library digital edition and a companion Gallery exhibit). She-philosopher.com’s HTML transcript includes everything in the printed original of “The Geometry of the Mind” except Evans’ closing “References to the figures” (collated separately on pages 53–55 of the original printed piece). These References will be found in the companion GALLERY exhibit featuring all 28 illustrations from “The Geometry of the Mind,” at larger sizes and higher resolutions. I regret this somewhat awkward styling, but the 2-part restructuring allows me to formally catalog, group, and reproduce Evans’ collection of medieval diagrams for separate, detailed study.

Evans opens with the assertion

... that not only do these inscribed geometrical figures merit study in their own right, as examples of medieval design, but also that they provide a valuable commentary on the way medieval thinkers approached some of the problems most important to them, furnishing an insight into thought-processes in the Middle Ages.

(Evans, 32)

Next, we learn that

Medieval exegesis was particularly suited to, and to some extent influenced by, diagrammatic exposition; so too was medieval logic, because its most characteristic innovations were formalistic rather than epistemological. By the end of the Middle Ages, a thinker like Heimericus de Campo could express his entire philosophical system in a single figure, though these late examples tend to be arcane rather than elucidatory. But during the period to be considered here (mainly the twelfth to fourteenth centuries) geometrical exposition was used in a way that was not only more concise, but also more explicit, than a prose account. It also achieved the status of an abstract art form.

(Evans, 32)

We also learn that a rhetorical use of visual aids — which Evans classifies as typographic, stemmatic, geometric, and emblematic — was, in fact, “more widespread” in medieval MSS. than is usually recognized.

The Middle Ages was well aware of the value of the visual aid. In book illustration, in particular, pictures could perform a didactic rôle, elucidating and amplifying the text. The layout of word and image was calculated so that the one complemented the other, and the picture was keyed to the argument with a phrase like “as the following figure makes clear” (cf figure 23). Even in the absence of pictures, the text was set out in such a way as to enhance the reader’s understanding of its content. A different size of initial was used to begin book, chapter and verse in the Bible; different grades of script were used to distinguish between text, commentary and nominal gloss. A similar concern for the visual effect of the page is seen in the use of ornamental forms to turn potentially dull, tabulated material (calendars and concordances) into grand decorative designs: worthy frontispieces to books of hours or gospels; but still basically functional tables and indices, clearly set out.

(Evans, 34)

Indeed, diagrammatic exposition (logical demonstration using graphic means) flourished during the Middle Ages, and Evans gives a nice account of why this was (see, e.g., his section 2.4). Most surprising to modern readers raised on novelist C. P. Snow’s “Two Cultures” argument will be yet another discovery of the many ways in which writings in the sciences and the humanities interpenetrate throughout history, especially the medieval “arrogation of scientific diagrams to religious ends” — “a recognition of the irrefutable logic and exactitude of technical illustrations, and an attempt to confer the same qualities on theological propositions.” (Evans, 47)

Some of the most important iconographical themes were depicted in geometrical terms: the conventional representation of the cosmos is a series of concentric circles; that of God shows him in a circular aureole, or one made-up of circular elements; as creator, God wields a geometer’s compasses. He could be defined geometrically as an infinite sphere, its centre everywhere, the circumference nowhere.

(Evans, 33)

For many of us, the famous “dissociation of sensibility” (and in its updated version: “dissociation of feminine sensibility”) we attribute to the rise of modern science is given visual form in the scientific diagram, which we tend to think of as mechanical and abstract. But Evans reminds us that this is a thoroughly modern mindset. Those of us who contest any occurrence of “dissociation” in the 17th century will point to the obvious relevance of theological issues in the framing of the new scientific worldview, whereby the scientist was recast as a “Christian Virtuoso” whose investigations into the laws of nature were a religious exercise. But this scientific ethos was not new with the 17th century. It was a legacy of the Middle Ages — a habit of thinking and being passed on in large part through visual culture.

While some of us today may regard the diagram as lifeless and utilitarian, medieval scribes explored a full range of diagrammatic symbolism, even using geometric drawings to illustrate “ecstatic religious experiences, vatic or revelatory.” (Evans 47) Thus, Opicinus de Canistris (1296–c.1350) “utilised recent developments in navigational charts to record his mystical revelations in cartographic form.” (Evans 47) (According to Ranulph Glanville, who reproduces the map in question as Figure 6 in his essay “Mapping Realities,” Opicinus’ map models “a sort of Gestalt switch, in which the outlines of various countries are seen, not as the countries themselves, but as something else”: “the medieval map of Opicinus de Canistris ... which is surprisingly ‘accurate’, shows the Mediterranean, with Europe and Africa copulating. Quite what the intent of this comment is, is not clear!” [Glanville, 21])

There was, notes Evans, a

practical reason why the diagrammatic forms should be so compatible with visions, dependent on one of the graphic peculiarities of the inscribed schema. This was its ability to express, explicitly, several levels of meaning simultaneously: a quality that renders it virtually unique in visual art. Except in very specific instances, a pictorial representation signifies only one thing. The idea that images embody several levels of meaning is one of the myths of modern iconographic studies, unsupported by any evidence. A diagram, however, can do so: the same schema can accommodate a number of concepts, each identified by an inscription. Thus, the same figure that sets out the Elements and the world can be used at the same time to show Man and his Humours and the Year and its Seasons.

(Evans, 47)

This passage raises several interesting questions about how we understand diagrammatic versus pictorial representation, and about allegorical versus literal forms of visual expression. It would appear that our own modern debates over the literalist interpretation of religious communications — visual and verbal — have at least a 700-year history. Evans’ Figure 22, for instance, is an example of the scientific diagram used as an allusive, non-literal image of the Trinity and the Vision of Ezekiel:

The text facing the miniature describes the difficulty of expressing religious ideas literally, and the value of allegorical communication: “he talks best and more beautifully who is silent about God. The sayings of the Prophets are obscure ... we understand these allegorically so that we are redirected to the path of rightness” (Optime et pulchrius loquitur qui de Deo tacet. Obscura sunt prophetarum dicta ... ea allegorice interpretamur ut ad rectitudinis semitam reducamur).

(Evans, 55)

Evans’ collection of medieval geometrical figures includes 5 tree diagrams (Figures 6, 8, 9, 11, and 19), most of which intermingle botanical, religious and human attributes.

Such trees might be regarded as belonging more to the world of allegory than to that of the scientific diagram; but, as will be seen, the two worlds were not discrete, which accounts for the ubiquity and diversity of these designs.

(Evans, 36–7)

In note 89, Evans speaks of the occasional “conflating” of “rotae and trees,” and describes Figure 9 as a diagram that looks like a tree, but is really a table: “Although embellished with leaves and a trunk, this is structurally a table rather than a tree, and is to be read downwards.” (Evans, 54) Moreover,

The example of the Lullian ars [Evans’ Figure 14] demonstrates that although wheels and trees were formally different, they could be used as alternatives to set out the same philosophical system. Trees and tables, too, were sometimes used interchangeably: trees exhibited conspicuous lateral correspondences, and tables assumed arboreal growths (figure 10). This was despite the fact that the two forms are not only structurally distinct, but also that they correspond to two different medieval speculative methods: the scholastic distinctio described above, and typological exegesis.

(Evans, 45)

Tree diagrams (such as the Jesse Tree and Tree of Consanguinity, Evans’ Figure 6) are one important graphic legacy of the Middle Ages (and she-philosopher.com will offer several gallery exhibits on historical uses of information trees). But there are others as well, as even a cursory review of Evans’ collection of figures reveals. Medieval “use of rotae in scientific works” (Evans 43) clearly influenced the ongoing design and development of paper instruments and calculating machines (variations on the analogue computer) during the 17th century. Robert Wood’s “emblematical garter” (or “hieroglyphick of the year”), which was “put into a gilt frame” and presented to the Royal Society in 1681, was described by Wood as “very easie and ready for Practice, either by Memory, Pen, or Clock-work.” Wood’s volvelle was soon after published in the Society’s scientific journal for its readers to cut out, paste on boards and/or transfer to other media, and was used for “adjusting the account of time by the moon, soe as not to miss one day in 24000 years,” as Robert Hooke wrote to Henri Justel, then secretary to Louis XIV.

Evans remarks that

These and similar rotae figure extensively in school-books and manuals of learning, and in the Middle Ages would have been as familiar a part of the educated man’s visual experience as the graph is of the modern reader’s.

(Evans, 43)

and this held true for later centuries as well. Thus do we find the 2nd earl of Westmorland, Mildmay Fane (1601–1666), embellishing his privately-printed volume of religious and occasional verse, Otia sacra optima fides (London, 1648), with sacred diagrams during the first half of the 17th century. Not only do “the diagrammatic indications of parallelism and opposition” undergird the graphics and poems in Westmorland’s privately-circulated Otia Sacra, they also carry over into his dramas, such as his De pugna animi of 1650, and into the set designs for his masques and plays. In his illustrated book, Westmorland claims to have coined the verb “to emble” (to emblematize), and indeed, Otia Sacra is full of “embling,” as he phrases it (he also uses the noun, “Emblemer,” to refer to himself and others who integrate the visual and verbal in such manner). And the visual experience of medieval scribal publications is everywhere apparent in Westmorland’s embled Otia Sacra. E.g., the well-known “Heavenly Ladder” or “Scala virtutis” (see Evans’ section 4.2) is here reconceived by Westmorland as the “Scala Sacta,” and he has the familiar medieval motif of “A Pelican feeding her young with blood out of her own Brest” typeset aenigmatically.

Even 17th-century Puritan poetry was heavily influenced by medieval figurae. The various schemes of quaternities (e.g., Evans’ Figure 23) resonate, for instance, in the poems of Anne Bradstreet (1612?–1672), the New England emigré who wrote learnedly about “The Foure Elements,” “Of the foure humours in Mans constitution,” “The Four Ages of Man” (of note, Comenius treats this as one of the Sevens, diagramming Septem Ætates Hominis, “The Seven Ages of Man,” in his Orbis Sensualium Pictus), “The four Seasons of the Yeare,” and “The Foure Monarchies” (i.e., “Assyrian, Persian, Grecian, Roman”) in her The Tenth Muse Lately Sprung up in America (London: Stephen Botwell, 1650).

So, given its undisputed prevalence, is such diagrammatic logic universal?

Historically, the elucidatory diagram originated coevally with the illustrated text, in classical Antiquity. It was, with the depiction of narrative, one of the two earliest forms of textual illustration. Aristotle’s works were almost certainly illustrated with diagrams, and while it is unlikely that the Platonic dialogues were, commentaries on them employed figures extensively. Medieval copies of these commentaries may preserve authentic Antique schemata; available evidence suggests that, compared with representational images, diagrammatic designs are transmitted with remarkably little variation. Most such diagrams are geometrical figures or simple linear stemmata; but when early medieval authors took them over to illustrate their own writings, they were embellished with figurative elements: plants, animals and human beings. These may have a mnemonic function; they may, however, be symbolic, or purely decorative.

(Evans, 35)

I am particularly intrigued by Evans’ claim here about the universality of diagrammatic images (vs. the cultural relativism of representational images). By way of evidence, he points to modifications made over time to the personifications of the liberal arts, which were continually being updated for contemporary sensibilities. Thus, L. H. Heydenreich (in his essay, “Eine illustrierte Martianus Capella-Handschrift”) documents the 15th-century modifications made to pictures of the personified liberal arts as originally conceived for a 12th-century MS. copy of Martianus Capella’s De nuptiis Philologiae et Mercurii (The Marriage of Philology and Mercury), which itself dates from c.410–439 CE, and “incongruously mingles abstractions, gods of various kinds, and ancient worthies, wrestling them all into personification allegory.”

Thus, while a fifteenth-century copy (Venice Marc MS Cl XIV 35) of a twelfth-century MS (Florence Laur MS S Marco 190) of Martianus Capella’s De nuptiis modifies the pictures of the personified artes stylistically and iconographically, the diagrammatic illustrations are preserved unaltered ....

(Evans, 51n24)

Evans’ note to Figure 12 (the Tower of Wisdom), hints at the preservation of these diagrammatic forms across cultures, as well as through time, and he emphasizes the graphic tribute here paid by European scholars to their Arabic sources:

Towers also appear in astronomical figures; here, however, the allusion is not to the house of Wisdom, but to the importance of Arabic sources in the transmission of scientific ideas to Europe. The Arabic word for zodiacal sign, burj, also means “tower” and was translated, and illustrated, as “turris”; Burnett, op cit note 64 below, p. 81.

(Evans, 51n46)

In many ways, the geometrical idiom of medieval scholars translates quite easily, even to our own 21st century. We continue to adapt the medium of geometrical design to our own uses, as with the new “Mammals Family Tree,” a “supertree” described as “the most complete family tree compiled for mammals” (see the Related Links section of the companion Gallery exhibit for a link to this “zoomable, circular dendogram,” with its huge dataset, formatted as a PDF file).

And in this sense, I believe Evans is right. The medieval graphic form carries on, even when the symbolic meaning of its content remains something of a mystery to the uninitiated among us.

Evans’ “The Geometry of the Mind” is organized into 7 sections (perhaps significant, perhaps not), and I give a table of contents below to indicate its range and structure.

§ 1  Scientific diagrams and medieval thought

§ 2.1  Art and geometry
§ 2.2  Geometry
§ 2.3  Art and argument
§ 2.4  Argument

§ 3.1  “Figurae”
§ 3.2  “Divisio scientiae”
§ 3.3  “Arbor scientiae”
§ 3.4  The schematic tree
§ 3.5  “Arbor virtutum”

§ 4.1  Tabulation
§ 4.2  “Scala virtutis”
§ 4.3  “Turris sapientiae”
§ 4.4  Text and image

§ 5.1  “Rotae”
§ 5.2  Astronomy
§ 5.3  “Ars demonstrativa”

§ 6.1  “Enuntiatio” and “interrogatio”
§ 6.2  Square of Opposition
§ 6.3  “Scutum fidei”
§ 6.4  Visions

§ 7.1  The Five Sevens

(Once again: a special thanks to Chet Van Duzer for bringing Evans’ “The Geometry of the Mind” to my attention. I hope he finds just recompense in this HTML transcription.)

Tail-piece from William Cuningham's _The Cosmographical Glasse_ (London, 1559)

NOTE: The digital edition of Evans’ text (in Part II) has not yet been updated. It retains the original format and styling of an earlier reissue of the HTML monograph in September 2009. To learn more about 2012 changes to e-publication formats, visit She-philosopher.com’s “A Note on Site Design” page.

Part II: digital edn. of Library Cat. No. MWE1980 pointer

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