Robert William Middeke-Conlin

Robert William Middeke-Conlin

Marie Curie Fellow

I am an historian of mathematics and knowledge who pioneers what may be termed the "philology of numbers". As a master’s student I was trained in Assyriology and philology. At that time, my biggest questions surrounded numbers, more specifically, "why did numbers seem wrong so often in administrative texts?" My query on “going wrong” sparked my interest in mathematics and led me to apply for a pre-doctoral fellowship with the Mathematical Sciences in the Ancient World project in Paris. Since then I have worked as a post-doctoral associate at Yale University and a post-doctoral fellow then associate at the Max-Planck-Institut für Wissenschaftsgeschichte (MPIWG) in Berlin.

Primary fields of research

The term, "philology of numbers" belongs to my primary PhD advisor, Christine Proust. I first became aware of this phrase during a masterclass led by her at the MPIWG. To my mind, the distinction between traditional philology and this numeric philology is cognitive: numbers and language are processed in different centers of the brain. A philology of numbers is different from traditional philology in that it examines how numbers developed over time, how they were produced, understood, and learned within the society that produced them, etcetera: many things traditional philologists examine, but with numbers. This means that the philological tools I learned as a master’s student are useful to the study of numbers. 

Philology of numbers aptly describes my main interest. However, this philology has many components. For this reason, I've branched out to study knowledge itself, more specifically knowledge production, acquisition, and change in the ancient world. At the moment I focus on mathematics and literacy in the Old Babylonian period Southern Mesopotamia (c. 2000-1600 BCE), asking three central questions:

  • How and to what extent did education relay the practical knowledge necessary for a professional career?
  • How was mathematics expressed in education and in professional practice between time and place?
  • How did knowledge transfer between cultures?

The Old Babylonian period is a fruitful place for my research because it is one of the best documented in history in terms of economic/administrative, mathematical, and literary texts as well as educational materials of all types. I research mathematics in particular because it affords as-yet understudied evidence for economic practices, intellectual thought, and technological innovation. Literacy is chosen because it affords an image of knowledge, generally speaking, within a period and place. 

Current research

I have two ongoing projects that explore this philology of numbers. Both projects come from my first and longest lasting research project to date. In this first project I used discrepancies found in both administrative texts and in student practice texts to produce an image of mathematical knowledge as it existed in the Old Babylonian period kingdom of Larsa. At the SPHere lab in Paris and then the MPIWG, I developed a technique to exploit discrepancies found in the administrative texts to elucidate mathematical processes. A discrepancy in a figure encountered in a text is a deviation between what is expected and what is stated. When it is observed in an administrative text, it yields clues about the mathematical operations and procedures that produced the figure. When compared with student practice, both elementary and advanced, it helps us to understand what knowledge was transmitted through education. The results of this project can be seen in my 2020 book, The Making of a Scribe: Errors, Mistakes, and Rounding Numbers in the Old Babylonian Kingdom of Larsa.

This project left me with two unanswered questions: "Can we examine an entire ancient knowledge system?" and "How do these systems change over time?" My primary project here in the Department of Cross-Cultural and Regional Studies explores the first question. I intend to examine as much of a knowledge system as I can. To do this, I seek to produce an image of literacy, that is, prose, documentary, and numeric literacy, between male and female professionals from a specific city, the Old Babylonian city of Nippur. The ability to read and comprehend a text (the prose), understand and manipulate its format (the document), and interpret and calculate with the numerical symbols (the numeracy) that may accompany, compliment, influence, or even constitute the text offers a tripartite image of a society’s knowledge system. The city of Nippur offers a very fruitful place for a study on literacy because it is home to one of the largest groupings of Mesopotamian academic texts, was also the base of several important cultic-administrative text groups, and yielded numerous economic texts from familial archives. This project has already produced a conference, co-organized with Anuj Misra, entitled, Exchange of Knowledge Between Literate Cultures.

Literacy and knowledge change itself marks the focus of my second project, which began years ago at Yale University. There, I was given the opportunity to take high quality images and then draw copies of one hundred texts dealing with what is often called the surveyor’s tradition. This surveyor’s tradition is well documented in the mathematical tradition and in administrative texts, especially in the second millennium BCE. From these texts it’s clear that surveyors were tasked with administering land in the forms of both agricultural output and water works. They had a long lasting, wide reaching, and well documented tradition that lasted from the fourth millennium BCE through the sixth century CE and from Southern Mesopotamia to the lands of Greece and Egypt during the Hellenistic period. Beginning with the Ur III period (2100-2000 BCE) and through the first half of the Old Babylonian period, a “paradigm shift” occurred, with the development of what is often called sexagesimal place value notation by modern researchers. This system afforded an easier method to multiply dissimilar objects or values, such as length by width to produce area. What I will call a “controversy” probably appeared with this development. The scribes and administrators were exploring whether and how to integrate this new development into their knowledge economy. This “controversy” will also be the subject of a book, tentatively titled, The surveyor’s controversy: changing knowledge in the Old Babylonian period.

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