Stemma of Boethius

A new tabulation of online Boethius manuscripts which contain his famous stemma, or arbor porphyriana, has just appeared on my website. (Here.) I have not done serious work on Boethius for more than three years, so I spent a couple of days looking again at the sources.

I find it remarkable that so many of these documents can now be seen remotely via the internet: there are no fewer than eight manuscripts accessible, and three of them duplicate the stemma, so we have a total of eleven early medieval drawings to study.

A task remains for any eager reader. I have not heard that the Greek text of Porphyry, or the translations to Latin, Syriac and Arabic (list by Roger Pearse), contain such a diagram. One is reluctant to trust the critical editions, since text scholars generally leave out diagrams. If anyone would care to comb online versions of these, it would be good to have a clear yes-or-no answer about this.


Our Secret Reasoning Device

A book published a couple of months ago by the German cognitive scientist Markus Knauff contains some remarkable new evidence and discussion about the seat of human reasoning. Summing up a couple of decades of experiments, he argues that a brain structure which can demonstrably be shown to analyse and reason is the so-called dorsal pathway.

This is the "where" stream which handles our awareness of space, our actions and, as a recent review article by Borst and others argues, our expectations. (All references below.) There has been some criticism in another review article by Schenk and others of the claims that this pathway is entirely distinct from the ventral or "what" pathway, but the dichotomy does seem to be holding up well.

In Space to Reason: A Spatial Theory of Human Thought, Knauff emphasizes that this dorsal pathway is not a self-aware channel, so it is easy to overlook its operations. It shows up in brain imaging, but we cannot examine it by introspection.
... people certainly have no clue about the mechanisms that work on a symbolic spatial array, and they are certainly not aware of a complexity measure that results in certain preferences. (190) [and quoting Goodale & Westwood:] ... the processing of spatial information in the dorsal stream is impenetrable to our conscious awareness. (191)
Knauff does not mention diagrams in his book at all. Most of his experiments involve reasoning about very simple problems such as:
The blue Porsche is parked to the left of the red Ferrari.
The red Ferrari is parked to the left of the green Beetle.
Is the blue Porsche parked to the left or to the right of the green Beetle? (2)

However he proposes that these yield valid data about problems such as:
If the teacher is in love, then he likes pizza.
The teacher is in love.
Does it follow that the teacher likes pizza? (95)
The cars problem is not difficult but it requires effortful thinking, whereas the if problem is instantly understandable. You will probably have guessed at the conclusion before you were conscious of reading the last line, which is said by some authors to be a characteristic of dorsal cognition.

Now there are two competing established accounts of what is going on: one is that we might pretend to see a real teacher whom we know and because we are so smart at understanding from sight, and teasing meaning from sight. we can deduce from visual indications that he is biting a slice of pizza that he must therefore be in love, just as we deduce from a distended belly that a woman is pregnant.

The rival account - propositional reasoning - maintains that we have a kind of machine language inside our brains, a computational logic. It does not use a language like English, but perhaps a language like JavaScript, and it tells us from the if what the only logical conclusion is.

Knauff argues for a third option: if I interpret this correctly, we have a black-box process in which we use the dorsal channel to simulate the problem as if we were perceiving something real. A mental model is constructed where the teacher, his state of romantic excitement and the pizza are encoded as spatial entities. Putting them in the only possible logical order allows us to grasp the conclusion.

The heart of his argument is that evidence shows the ventral stream need not be involved. One of the salient points about the spatial-thinking model is that the mental representation excludes all unnecessary information. The shape or colour of the cars or the exact distance between them does not need to be encoded, nor does the shape of the teacher's face or the flavour of the pizza.

As I have said, Knauff does not mention diagrams, let alone the Great Stemma or the Compendium of Petrus Pictaviensis. But the sense of excitement his book generates in the diagram researcher comes from the fact that the sparse, austere mental models he envisages as the bearers of human reasoning resemble the simpler sort of diagrams that are drawn on paper or on displays.

Reviel Netz suggests in The Archimedes Codex and his various articles that the Greek mathematician did not use diagrams to merely illustrate ideas that he had been thinking through in some propositional fashion. Archimedes was doing mathematics by manipulating spatial representations in his head. Since he was thinking about space, not propositions, the diagrams were the closest external representation to his raw thoughts. As far as I can guess, Netz's ideas are partly rooted in the ideas about external representations generated by externalists in philosophy of mind debates over the past 20 years.

Stemmata and diagrammatic chronicles are not direct reasoning tools in quite the way that geometrical drawings are. Geometry can yield mathematical proofs without numbers or words, whereas chronicles are not there to reason with, but usually serve to re-express histories or genealogies that have already been set down in textual form.

Their purpose is communication. I have always maintained that they are a form of direct author-to-reader communication which eschews the need to convert their content into language. An author massages his ideas into the most lucid spatial arrangement he can come up with, puts them on paper, and the reader's spatial reasoning abilities are sufficient to decode what is meant with a minimum of textual input.

The nearest that Knauff comes to this is when he suggests that there is a kind of diagrammatic substrate to reasoning, and compares this to subway or underground-rail diagrams:

I used the metaphor of a subway map to show that a qualitative representation does not display the shares and sizes of the stations or metrical distances between the stations but only represents the data that preserve spatial relations between stations and lines, for example, that one line connects with another. ... a visual image is completely different from a subway map. It is more like a topographical map ... that captures distances, streets, buildings, landform information, and so on. In contrast, spatial layout models are like schematic subway maps... (192)
His findings and his interpretation have some interesting implications for diagram studies. If the  mental model in our heads is somewhat like a diagram, it ought to be possible to devise diagrams that can inspire such mental models with a minimum of translation.

Since the precise distances between the elements, and their sizes, do not encode any information, both of the following work equally well.

The left diagram is a 6th-century classification system drawn by Cassiodorus, while the right one comes from the 5th-century Great Stemma. I have translated the text from Latin to English. Whether the circles are large, small or non-existent, or whether the text is inside them or out, does not matter. Spatial reasoning merely needs apartness.

Overall orientation does not encode information, so all of the following directions of ramification are functionally equivalent.

Spatial reasoning is also likely to be highly tolerant of defective alignment, so that curved or crooked pathways in a diagram do not make them ineffective.

If this is correct, node-link diagrams which use a spatial encoding to express hierarchical relationships are likely to be a powerful means to manipulate a complex type of data while directly engaging with human intelligence. Working pragmatically and without any scientific evidence from cognitive research, the Late Antique inventors of node-link diagrams established an effective means of simplifying information without losing its essential structure.

Borst, Grégoire, William L. Thompson, and Stephen M. Kosslyn. ‘Understanding the Dorsal and Ventral Systems of the Human Cerebral Cortex: Beyond Dichotomies.’ American Psychologist 66, no. 7 (2011): 624–632. doi:10.1037/a0024038.

Goodale, Melvyn A., and David A. Westwood. ‘An Evolving View of Duplex Vision: Separate but Interacting Cortical Pathways for Perception and Action’. Current Opinion in Neurobiology 14, no. 2 (April 2004): 203–211. doi:10.1016/j.conb.2004.03.002.

Knauff, Markus. Space to Reason: A Spatial Theory of Human Thought. MIT Press, 2013.

Netz, Reviel, and William Noel. The Archimedes Codex. Revealing the Secrets of the World’s Greatest Palimpsest. London. Orion, 2007.

Schenk, Thomas, and Robert D. McIntosh. ‘Do We Have Independent Visual Streams for Perception and Action?’ Cognitive Neuroscience 1, no. 1 (26 February 2010): 52–62. doi:10.1080/17588920903388950.



Some years ago, the French cultural historian Christiane Klapisch-Zuber examined the Great Stemma. Because she was in Paris, the nearest manuscript at hand was a late recension, from Gascony, which is held by the French National Library or BNF. In colour and effect, the sumptuous polychrome diagram in the Saint-Sever Beatus is a beautiful thing, but in organization it is curiously incoherent.

Among its great oddities is a fishnet pattern among the descendants of Noah that largely obliterates the careful encoding of their relationships which was characteristic of the original model. That led Christiane Klapisch-Zuber, who is the greatest scholar to have surveyed the full history of such diagrams, to dismiss the whole class of Spanish Bible diagrams as an affront to the principles of ‘graphical semiology’. She argued in her 2000 book that no coherent biblical genealogical diagram had existed before a medieval work, the Compendium, was devised by Peter of Poitiers.

Her point of view was taken up and amplified soon after by Beate Kellner, who is now deputy principal of Munich's  Ludwig Maximilians University (LMU), in her Habilitationsschrift, which was published in 2004. Kellner also focussed this part of her research solely on the Saint-Sever manuscript in Paris.

She seemed to be even more troubled by the way the diagram strung out siblings like beads on a string instead of exhibiting them in hierarchical fashion as we do in "family trees", and spotted another oddity of the Saint-Sever manuscript, its curious folding together of the descendants of Leah:
Here the organization of the panels avoids a coherent reading order as we would conceive it, from the top to bottom or from the bottom to top ... The genealogy below Jacob and Leah begins with their son Reuben ... His brothers Simeon, Levi, Issachar and Zebulun follow in a series of roundels which is open to interpretation as a genealogical line of descent since the line is graphically vertical, although in fact it links persons of a single generation. The sons of Zebulun are similarly connected by lines to one another in the vertical, and with their father, in such a way that the arrangement is effectively an ascending one. (JBP translation, hover for German original)
The sketch below shows the situation referred to, with the remainder of the environs omitted, and it must be agreed that the Saint-Sever artist took a very free attitude to his Vorlage when he arrayed Reuben's sons to both the left and right and ran Zebulon's sons up the page instead of downwards:

Now this is not the place to consider whether Kellner's overall characterization of medieval genealogy is correct or not. But the Saint-Sever treatment of the Great Stemma is so original and so untypical of its diagrammatic tradition (list of manuscripts here) that it can hardly be taken as representative of very much other than the artistic sensibility of Stephanus Garsia Placidus, the monk who seems to have been its creative director and principal artist. Yolanta Zaluska has pointed out odd inconsistencies in the diagram which suggest that something went wrong with the project and that someone other than the original director completed the diagram.

The classical arrangement of the sons of Leah in the Great Stemma is in fact severely regular, and it normally embraces all six sons, not five as in the Saint-Sever recension which omits Judah in this position. Here is a schematic of the same group from the Plutei manuscript, which contains pretty well the earliest format we can discover in the diagram's history:
Now it is true that the reading order of grandson 1, grandson 2 and so on is not the order that we in the 21st century could conceive as proper. But it does adhere to a broad logic in the Great Stemma where certain sibling groups which are only supplementary to the broad purpose of the document are always shown in space-saving fashion as vertical series. This is perhaps surprising to our eyes, but it is not chaos.

Following this generalization, Kellner then ventures the hypothesis that the crowded design of the Saint-Sever diagram deliberately establishes a stemmatic tangle, with extensions running every which way, in order to suggest that kinship by its very nature tends to be a network,
... that genealogy is being placed before us as a tapestry of relationships, as a complex structure oriented in multiple directions and not as a unitone line of descent... My hypothesis is that graphics, which are better able to exploit the two-dimensionality of the page, enable this particular form of discourse from the first glance, unlike a purely textual listing of genealogies, which certainly can employ linguistic features to link backwards or forwards and to that extend is capable of catering for genealogical cross-connections, but is ultimately bound by the continuity of script and creates an impression of linearity from the very character of text. (JBP translation, hover for German original)
One already hears an ominous creaking in this structure of ideas, built as it is on evidence that simply does not support it. Rather than building on the august traditions of German text-critical scholarship, on the detailed analysis of the full range of manuscripts, such an interpretation employs the semiotics approach of Jacques Derrida, Roland Barthes and Co. which was popular in the late 20th century, spinning creative meaning and significance around supposed "signs", while paying too little attention to verifiable data about what one might describe as the ecology of culture - the structures of the human mind, the evolution of artefacts and the phenomenal experience of human societies.

Kellner is undoubtedly right in her observation that Saint-Sever often lacks diagrammatic coherency, but her analysis is based solely on a single, rather non-representative manuscript in Paris and a series of creative blunders when an artist outran his own talents in a single scriptorium in Gascony, leaving her vulnerable to a whole herd of counter-evidence from nearly 20 other manuscripts.

Older recensions of the Great Stemma are generally more coherent and rational in the way that they map family relationships to a consistent code using connections, alignments and orientiations.

Developing her point, Kellner correctly intuits that the genealogical diagram belongs in a tradition where the expansive roll was the more natural medium than the cramped codex page, but strays into even more unsupported territory with a suggestion that medieval historians felt a 2D visualization to be inherently freer than text in its choices of content and arrangement:
The notion of genealogy as a network of relationships could be conveyed graphically using relatively simple shapes such as lines, strips and circles on codex pages - or doubtless ideally in scroll format - because arrangements of the genealogical elements in planar space - and this is the key objective - were able to be selected and combined with greater freedom. (JBP translation, hover for German original)
Here I both agree and disagree. Planar space is a far more comfortable medium to organize one's genealogical data and snippets of evidence than linear text. Sketching and diagamming often help us to organize our ideas and evidence better. Medieval diagrams do indeed breathe a certain air of nerdish delight at being able to amass the evidence to show some new view of it.

But diagrammatics are rarely a zone of freedom. Keller perhaps extrapolates from the freedom of art in comparison with the literary discipline prevailing over poetry and prose. But the overwhelming trend throughout the history of graphic charts and displays has been to bind them as tightly as possible to the habits of human spatial perception: without such discipline, diagrams simply fail to communicate.

Diagrammers who ignore "programming" principles are not breathing the air of freedom or expressing a view about the complexity of kinship relations and the intricacy of existence. When they discard a coherent system that has been handed down to them, they end up writing bad code. The Saint-Sever diagram is an experiment, probably by Stephanus himself, that went wrong.

Kellner, Beate. Ursprung und Kontinuität: Studien zum genealogischen Wissen im Mittelalter. W. Fink, 2004. Discusses the Great Stemma pp 50-53.

Klapisch-Zuber, Christiane. L’ombre des ancêtres. Paris: Fayard, 2000.

Zaluska, Yolanta. ‘Les Feuillets Liminaires’. In El Beato de Saint-Sever, Ms. Lat. 8878 de La Bibliothèque Nationale de Paris, edited by Xavier Barral i Altet. Madrid [Spain]: Edílan, 1984.