Number

Throughout the middle ages, number was understood to be the basis of matter. We get some sense of the implications of this principle in Westminster’s spectacular Cosmati pavement. The riddle-like inscription embedded in the floor renders the age of the primum mobile (i.e., the first or outermost sphere of the heavens) in terms of the combined lifespans of the creatures within its ambit. To find the number, readers must add the age of a hedge to that of a dog, a horse, a man, and so on, to whale and even to world! Number’s power is on show: as quantity, nature’s variety becomes commensurate, comparable and tractable; its divine origin apparent.

According to the Bible, Creation was the act of a mathematically minded God who made all things by ‘measure, number and weight’ (Ws 11:21). This well-worn passage from Scripture was read alongside Plato’s Timaeus, a dialogue on the cosmos that underpinned much medieval and early modern science. According to these sources and the pavement, numeric qualities inhere in all bodies—whether plant or animal, natural or manmade, living or inanimate—and constitute immutable truths. Humans were thought to be specially equipped to detect such truths. Plato maintained that the ‘supreme good’ of vision was the ability ‘to denumerate’ (dinumerare in the Latin translation), meaning to discern number, count or calculate (47a). For the influential Saint Augustine, mathematical and artistic form was enmeshed. He wrote, ‘Artisans have numbers in their craft which they apply to their works . . . whatever delights you in a body and entices your bodily senses is full of number’ (De libero arbitrio 2.16.42). Here, the frisson of aesthetic pleasure arises from number’s sensation, its denumeration.

This project examines the extent to which shared belief in number’s elemental status inflected how people perceived and interacted with the material world. I am working on a book tentatively titled Numeracy and Visuality in the Central Middle Ages, that reconstructs numeric study circa 1000, and traces its effects on representation in Europe, especially in religious art and architecture. The latter offer a fresh view of medieval mathematics, emphasizing number as an agent of faith, beauty and play.

Publications
‘The Geometry of Jesus, c. 1000’ [expected completion 2024]

Number and Visuality in the Central Middle Ages [expected completion 2025]

‘Grid Space in Boethius’s On Arithmetic’, in Jeffrey Hamburger, David Roxburgh and Linda Safran (eds.), Diagram Paradigm: Byzantium, the Islamic World, and the Latin West (Washington, DC: Dumbarton Oaks Publications, 2022).

‘Romanesque Abstraction and the “Unconditionally Two-Dimensional Surface”’, in Elina Gertsman (ed.), Abstraction in Medieval Art: Beyond the Ornament (Amsterdam: Amsterdam University Press, 2021).

‘Imaging and Imagining Solidity’, in Beatrice Kitzinger and Joshua O’Driscoll (eds.), After the Carolingians: Re-Defining Manuscript Illumination in the 10th and 11th Centuries (Boston: De Gruyter, 2019), 86–117.

‘Picturing as Practice: Placing a Square above a Square in the Central Middle Ages’, in Anthony Grafton and Glenn Most (eds.), Canonical Texts and Scholarly Practices: A Global Comparative Approach (Cambridge: Cambridge University Press, 2016), 200–23.

‘Picturing Number in the Central Middle Ages’ (PhD, University of Michigan, Fall 2015).

Presentations
‘The Medieval Meander: Depicting Depth and the Corporeity of Paint’
Image, Ornament, Matter: An International Symposium on Their Limits and Intersections in the History of Art, University of Florida, 12–13 April 2019

‘The Grammar of Time’
The Monastic Experience of Time, Durham University, 18–19 April 2019

‘Medieval Corporeity’
Thinking Materially, Medieval Research Seminar, Cambridge University, 11 October 2018

‘Diagrams and Dinumeratio in Medieval Europe’
The Diagram Paradigm: Byzantium, the Latin West, and the Islamic World, Dumbarton Oaks, 20–21 April 2018

‘Romanesque Abstraction and the “Unconditionally Two-Dimensional Surface”’
Fifth Annual Symposium on Medieval and Renaissance Studies, Saint Louis University, 19–21 June 2017

‘Gospel Books as Geometric Argument, c. 1000’Mittelalterliche Bildgeometrie, Technische Universität and Staatlichen Kunstsammlungen Dresden, 23–25 November 2016

‘“Between Angels and Humans”: Engraving in the Central Middle Ages’
International Congress on Medieval Studies, Western Michigan University, 12–15 May 2016

‘Christ × Christ × Christ’
History of Science Society Annual Meeting, 19–22 November 2015

‘Numeracy and Representation around the Year 1000’
Medieval Art History after the Interdisciplinary Turn, University of Notre Dame, 28–29 March 2014

‘Mathematics in the Margins’
Commentary Cultures: Technologies of Medieval Reading, Zukunftsphilologie, Freie Universitaet Berlin, 16–17 May 2013

‘Figura, Forma, Pictura: A Study in Terms’
Maps and Diagrams in Medieval Art, Index of Christian Art, Princeton University, 15–16 March 2013

Symposia, Workshops & Conference Sessions
Circular Thinking: The Drawing Compass as a Premodern Tool of Creation in Europe (co-organiser with Sarah Griffin)
The Warburg Institute, School of Advanced Study, University of London, 10–11 June 2021

‘The Elements and Elementality in Art of the Premodern World’ (co-chair with Michelle McCoy)
College Art Association, 21–24 February 2018

Time Bound: A Workshop on Computus in Medieval Books (co-organiser with Danielle Joyner)
University of Rochester, 15 November 2019
Southern Methodist University, 10 November 2017

The Materiality of Scientific Knowledge (discussant & co-organizer with Dahlia Porter, et al.)
Kislak Center, University of Pennsylvania, 30 September–1 October 2016