Lessons for

Interdisciplinary Working from Medieval Science

Tom McLeish (Physics, Durham University)

and

Giles Gasper (History, Durham University)

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Whenever we start talking about the ‘Ordered Universe’ project, people’s eyebrows and the corners of their mouths go up in equal measure. It operates with an approach that is both deliciously subversive and essential for the elucidation of its subject matter: the thought-world of the European 13th Century. The ramifications of the project on the legacy that period has for the way we think today, and on how we can work creatively between and among disciplines from the humanities and sciences, moving from respectful conversation to intense collaboration, are radical and illuminating. In this Project Short we summarise some of the lessons from the project and the way they have played out in the journey that took us from mutual interest in a treatise from c. 1225 on the metaphysics of light, to new editions, new translations and new science published in leading scientific journals. All of this was stimulated from the ideas of a medieval scholar, one of the most dazzling minds of his generation.

Working together, creates an environment in which the insights of scientists enrich humanities understanding of medieval thought. At the same time this environment enables modern scientists to engage with scientific thinking from previous centuries resulting in new work in their own domains. Together, we bring the medieval texts to life in all of their dimensions, emphasising the longer narrative to the place of science in human culture, and the mutual importance of the past and the present.

The Challenge; the Interdisciplinary Mix in the Solution

How do we understand a treatise on colour written in about 1225? Robert Grosseteste, Master to the Oxford Franciscans and later (from 1235) Bishop of Lincoln, wrote a series of thirteen treatises on natural philosophy and phenomena from about 1200 to 1230, covering

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light, the celestial spheres, comets, the generation of sound, lines and angles, the phenomenon of colour, and many more. The latter, an exquisite jewel of no more than 400 words of Latin, has an especial charm. Its concentration of ideas, mathematically-ordered grammar, taut prose and oblique references to Arabic transmission of Aristotle, have puzzled scholars since its last edition by the German scholar Baur in 1912. It might not contain equations, but the logic of the treatise is clearly mathematical – a listing of the qualities of colour leads to a subtle counting argument, a move from discrete to continuous gradations of colour and an intriguing reference to things one could prove per experimentum [through experiment or experience].

De colore (on colour) is written in Latin (so we need Latinists). It exists in eleven manuscripts scattered about European libraries and of uncertain provenance (so we need palaeographers). It draws on early medieval Arabic philosophy and mounts an implied critique of Aristotle (so we need historians of philosophy and Arabists). It refers to the human perception of colour in detail (so we need colour vision psychologists). It invokes combinatorial calculus – once you know what you are reading (so we need mathematical physicists).

That represents only the bare minimum of interdisciplinary mix. Later we discovered that the colour theory could only be completely understood when compared to Grosseteste’s related treatise on the rainbow (De iride). To address that turned out to require additionally a detailed knowledge of meteorology (so an atmospheric scientist), physical optics (more than one experimental physicist/engineer), and atmospheric absorption of sunlight (that needed an astronomer).

That amounts to a considerable collection of disciplinary. All are required to elucidate Grosseteste’s extraordinary textual legacy. The complex nature of his scientific texts, their taut linguistic expression, and their computational virtuosity present intellectual challenges which can only be addressed with an interdisciplinary approach. The stereotypical view of the Middle Ages as a period of scientific stagnation, a dogmatic straightjacket, at best a recapitulation of antiquity could not be more further from the truth.

Interdisciplinary Working Practice

The principal working method that really delivered effective results turned out to be remarkably simple. We all sit down for three days together and read the text. That’s it. Our palaeographer and Latinist will have prepared, in consultation with other medievalists within the team, a draft edition from the various manuscripts (with a list of Latin variants should we need them) together with a preliminary translation. Then, line by line, we read through. Everyone has both Latin and English in front of them. The scientists are not spared the details of the text, languages and historical context, nor the humanities scholars the discussions on the geometrical or combinatorial logic implied by the text.

Translation becomes a highly interdisciplinary and non-linear practice itself. This is necessary to deal with a Catch-22. On the one hand it is not possible to translate the text properly

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without knowing its mathematical and physical meaning; on the other it is hard to identify the mathematical and physical meaning without some sort of translation. This conundrum is resolved by iteration. A first pass of the literal translation often reveals sections where the meaning is far from clear, but in mutual struggling with the text a plausible rendering among the alternatives eventually surfaces. In the case of descriptions of natural phenomena, physical processes or geometrical patterns, the mathematical logic of Grosseteste’s discussion is often central to teasing out the meaning of the text. The essential ingredient in our working practice is to engage together. There is never a clear boundary between a philological, philosophical or contextual discussion and mathematical reasoning or discussion of wave optics. Scientists need to feel free to question accepted translations and to suggest new ones. Humanities scholars need to know that they are welcome to challenge the kinematic interpretations or optical references and speculation advanced by the scientists. So no one has the luxury of ‘time out’.

As a result of the complexities of the texts examined, focussed consideration of particular issues is required from individuals after the collaborative readings. In the several months between collaborative symposia writing, calculation, archival research and other disciplinary activities take place before the same text is revisited. Each text is read through at least twice, and frequently more often. Over the months the outputs begin to crystallise out of the swirling interdisciplinary mix.

Multiplicity and Reciprocity of Outputs – how we Encapsulate and Communicate what we Create

The first conception of the project was to enlist the insights of the scientists to assist in the production of better editions of Grosseteste’s scientific treatises. As noted in the case of the De colore, since the last comprehensive edition over a century ago, more and earlier (generally better) manuscripts have come to light. There has also been significant serious work on the historical, social and intellectual context, Grosseteste’s own reading and influences, and on his later reception. The publication form we have adopted is the traditional ‘Edition, translation and commentary’, but with a difference and with very considerable added value. The commentaries also contain one or more chapters of what we have termed ‘functional analysis’. The name points to their investigation and description of what the treatise does scientifically and how this has been deduced. So, in the

multi-authored book presenting the De colore, The Dimensions of Colouri we describe the three-dimensional combinatorial mathematics embedded in Grosseteste’s tight Latin prose and the various candidate mappings (none entirely successful) from his scheme to modern colour spaces (see the Interdisciplinary Working Case-Study below).

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In pursuing the solutions to Grosseteste’s understanding of natural phenomena other, unusual, publications have emerged. A wonderful and unexpected process of reciprocity arises from each study – at some point the science team realises that there is a calculation, an experiment, a series of observations to collate, stimulated by the interdisciplinary textual work, but that speaks to new or current questions in contemporary science. For example, the work on Grosseteste’s colour-space applied to the rainbow required a detailed calculation of how spectral distributions at different scattering angles, from rain of different drop sizes and illuminated by sunlight at varying elevation, mapped into current psychophysical colour spaces. The result was an entirely new mapping of 3D perceptual colour space that contributes to a current unanswered question in visual colour perception, published in the Journal of the Optical Society of America.ii The uncanny impression that we are, in some sense, collaborating with a 13th Century thinker is hard to throw off when this sort of thing happens time and again.iii

A third, and equally unanticipated, form of output flows from the communication of the project to the wider academic world and wider audiences. The Ordered Universe has captured public imagination and interest, for example as part of the Cheltenham Science Festival. The project website and blogiv has acquired a global and extensive readership. It also provides a forum for reflection on all aspects of the research, from content to methodology, from all participants, from gradate students to those attending public events. Video record of public workshops and lectures, podcasts, our film of the medieval cosmos, and a growing collection of resources for study, are all made publicly available. A wider readership has led to commissions from New Scientist, Nature, Nature Physics and other web and print mediav. Perhaps it is the apparent quirkiness of the project, possibly the mystery and magic of the medieval in the public mind, but surely the element of surprise, almost humour, in the idea of Latinists and optical physicists pouring together over ancient vellum and coming up with the sources of our modern world’s early science, the radical interdisciplinarity of the very idea, also creates its attractiveness.

Rules of Thumb for Interdisciplinary Working

Our experiences of the Ordered Universe project and developing ways of working in collaboration have allowed us to distil some essential practices (see Box 1). To explain a little further:

There are no stupid questions. Established academics tend to develop a terror of appearing uninformed, poorly read or otherwise in the dark. Nothing gives away ignorance with more direct transparency that a public question about something that everyone else surely knows. However, no-one enters a project requiring participation of at least three disciplines with any chance of possessing more than a superficial acquaintance of their practices and subject-matters. Mutually-recommended reading can help to get the team started, but without getting

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Box 1. Interdisciplinary Rules of Thumb

• There are No Stupid Questions • Trespassers will be Welcomed • Remember We are All Students • Focus Matters • Take Time Together • Repeat the Above on Every Occasion

those questions out into the open the vital cross-disciplinary learning will never take place. If you are a project leader, why not make it your goal to ask the ‘most stupid’ question every day? Others will rejoice in the permission.

Trespassers will be welcomed. An orthodox view of interdisciplinary projects has each participant providing expertise from their own background, but not beyond it, carefully policed by the project leaders. While disciplinary perspectives reflect our training, tastes and interests, it is important that they do not impede the intellectual confidence to range into new intellectual spheres. For the Ordered Universe to work, we need the humanities scholars to venture scientific ideas from their fresh perspectives. The scientists must feel welcome to suggest fresh translations of the Latin, informed by the mathematical or geometrical insights they bring to the text. It is the academic trespassing that generates the freshest thinking.

Remember we are all students. A consequence of the vital trespassing is that we all strive to know as much as possible of the territory into which we wander. Here the role of interdisciplinary translation comes to the fore. We will never become experts in each other’s disciplines, but we must learn enough to understand the languages, concepts, and a coarse-grained understanding of our knowledge-worlds. Trespassing in total darkness is fruitless, but more than this, interdisciplinary work keeps reminding us that we never stop being students; it cures us of the illusion that, even in our own fields, we know everything.

Focus Matters: Conversation between our subjects alone does not sustain an interdisciplinary discourse – we also need an object, external to all of our narratives, that draws our mutual gaze and focusses our concentration. For the Ordered Universe project this is the text. It is in front of all of us continually. We may need to take long excursions into 10th century metaphysics, or the physics of secondary rainbows, but the starting point is the text, and it is to the text that we always return. Like a family and visitors around a common meal, interdisciplinary ‘table talk’ needs a material object to begin, and to be sustained. A point of focus for interdisciplinary analysis is also vital in creating a coherent whole from a community engaged in collaboration. In our case the elucidation of Grosseteste’s texts provide an important framework for privileged trespassing.

Take time together: A common mistake in interdisciplinary projects is to hive-off ‘workpackages’ under the responsibility of the various participants, and subject to their own methodologies. Time together is then spent progress-reporting, but not engaging together at the coal-face of the project. To work at the core of the project does, of course, take a great deal of time. Carving out days together for the readings and discussions has been expensive, but it is the generator of the project. Every step needs every voice.

Repeat the above on Every Occasion: This practice is not just for the necessary and welcome new participants each time we address a new treatise. The old hands of the team need reminding

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of the radical commitment to common thinking, to ‘inter-disciplining’ ourselves with teaching and learning, to extending the vital disciplinary hospitality to the welcome trespassers. It is easy to forget this pattern of working because it does not appear in the programme of background music in our universities.

An Open-Ended Story

As this piece is written, the Ordered Universe team has just embarked on a large AHRC-funded project to complete the work on the scientific corpus of Robert Grosseteste. This will take four years. As we follow Grosseteste’s writings we will both deepen and sharpen our responses to his questions and the answers he proffers. A peculiarly satisfying discovery is that, to unlock the creative thinking of a distant century in which the disciplines were studied together by any university master, we need to bring the same collective academic tradition to bear.

The Ordered Universe as featured in ‘The World Machine’ sound and light and show for Durham Lumiere, 2015.

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Interdisciplinary Working Case-Study: A Medieval Mathematical Colour Space

Color est lux incorporata perspicuo. Perspicui uero due sunt differentie: est enim perspicuum aut purum separatum a terrestritate, aut impurum terrestritatis admixtione. Lux autem quadrifarie partitur, quod est, quia aut lux est clara uel obscura, pauca uel multa.

So begins Robert Grosseteste’s compact (400 Latin words) treatise on colour De colore, from c.1220. Translation issues begin in the very first sentence – a perspicuum is a tricky, and difficult to define Aristotelian term. By 1300 it is used to signify a lens (after the widespread development of that technology), but in 1200 was used for any translucent material. After some labour, our translation reads:

Colour is light embodied in a diaphanous medium. Indeed, this medium possesses two different qualities, for it is either pure, without the element of earth, or impure, mixed with the element of earth. Now, light is divided four ways, namely, it is either bright or dim, scarce or copious.

The triply-bipolar language maps onto a three-dimensional space illustrated below in (A) with the equivalent co-ordinates in (B). White is at one pole and black at the other. This logical framework was not evident in the 1912 edition, which following the manuscripts known to its editor, omitted the word obscura from the description of blackness. The logical framework was confirmed after consultation of earlier manuscripts revealed the obscura, which was restored to the new edition.

Lux igitur clara multa in perspicuo puro albedo est; lux pauca [obscura] in perspicuo impuro nigredo est, is translated:

So, bright and copious light in a pure diaphanous medium is whiteness; scarce and dim light in an impure diaphanous medium is blackness.

Any point in the colour space must be identified by three combinatorial qualities or equivalently three independent numerical values.

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Notes i Greti Dinkova-Bruun, Giles E.M. Gasper, Michael Huxtable, Tom C.B. McLeish, Cecilia

Panti and Hannah Smithson, “Dimensions of Colour: Robert Grosseteste's De Colore; Edition,

Translation and Interdisciplinary Analysis, (Toronto: Pontifical Institute of Mediaeval

Studies, 2013). ii Smithson, Hannah E.; Anderson, Philip S.; Dinkova-Bruun, Greti; et al. “Color-coordinate

system from a 13th-century account of rainbows” J. Opt. Soc. Am., 31, A341-A349 (2014). iii Bower, Richard G.; McLeish, Tom C. B.; Tanner, Brian K.; et al. “A medieval multiverse?:

Mathematical modelling of the thirteenth century universe of Robert Grosseteste”, Proc. Roy.

Soc. A, 470, Article Number: 20140025 (2014) iv www.ordered-universe.com v McLeish, Tom C. B.; Bower, Richard G.; Tanner, Brian K.; et al. “A Medieval Multiverse?”

Nature, 507, 161-163 (2014); HE Smithson, GEM Gasper, TCB McLeish, “All the colours of

the rainbow”, Nature Physics, 10, 540-542 (2014).

Images are courtesy of Giles E. M. Gaper and the EAGLE Project, Institute of

Computational Cosmology, Durham University.

For more on the Ordered Universe project please visit our website and blog:

www.ordered-universe.com