Three-Month Workshop Cultures of Computation and Quantification – 2013

The 3-month Workshop Cultures of Computation and Quantification will take place in January – March 2013. It consists of a series of one-day seminars each dedicated to a specific topic. Most seminars take place on Fridays (two will take place on Wednesdays and one on Tuesday) starting at 9:30 and ending about 17:30. They all take place in the Bâtiment Condorcet; maps and directions can be found here.


The first phase of the SAW project will be concluded by a three-month workshop devoted to a description of different cultures of computation and quantification that have been identified in China, the Indian subcontinent and Mesopotamia, mostly in relation to administrative and economic activities. The sessions will be devoted to the reading and discussion of sources.

Information about the texts read for the sessions can be obtained by writing to Karine Chemla (, Agathe Keller ( or Christine Proust (, depending on whether they deal with China, the Indian subcontinent or Mesopotamia.


Friday 11 January 2013 – Room 483A-Malevitch
Cultures of computation: elementary operations and fractions, session prepared by Agathe Keller, Alessandra Petrocchi, and Catherine Singh

In this session we examine how sources in the Indian subcontinent evoke elementary operations: what vocabulary was used for them, what rules were given to carry them out, on what quantities they were to be executed and how their execution can be reconstructed. The texts examined will be from commentaries on the Brahmasphuṭasiddhānta (628), the Gaṇitasārasaṃgraha (ca. 850) and the Gaṇitatilaka (11th century). Emphasis will be on what characterizes each commentator’s practice of computation, making it unique compared to others.

Friday 18 January 2013 – Room 646A-Mondrian
Mathematical texts and regulations texts in early imperial China
, session prepared by Peng Hao

In the last decades, several mathematical manuscripts from early imperial China were excavated from tombs or bought on the antiquities market. In the same sets of bamboo slips, regulation texts were regularly found. The session aims at examining more closely the kinds of relationship that can be established between the two types of documents as well as the ways in which these relationships can be interpreted.

Wednesday 23 January 2013 – Room 646A-Mondrian
Quantifying and computing before, during and after the invention of Sexagesimal Place Value Notation in Mesopotamia, session prepared by Christine Proust and Xiaoli Ouyang, with participation of Noemi Borrelli, Camille Lecompte, and Robert Middeke-Conlin

The goal of this session is to examine the circumstances in which the sexagesimal place value notation (SPVN) appeared and developed in Mesopotamia. First, we shall analyze quantification and calculation practices in field texts from Pre-Sargonic and Sargonic periods (about 2600-2100), that is, documents written before the earliest evidence of the SPVN found in written sources. Second, we shall examine the marginal numbers noted in Ur III administrative texts (2100-2000) and the calculation practices they may reflect. Third, we shall compare some of the 3rd millennium calculation practices with Old-Babylonian methods taught in scribal schools, where SPVN was widely used.

Tuesday 29 January 2013 – Room 646A-Mondrian
Computation with volumes units, capacities units and weight units in 7th century China, prepared by Zhu Yiwen, and  Wang Mang’s bronze vessel for the system of capacity units of measurement, prepared by Michael Loewe

7th century commentaries on classical books contain evidence of a culture of computation with measured quantities, to which no mathematical document known at the present day bears witness. Part of the session, led by Zhu Yiwen, will be devoted to inquiring in detail into this culture. One of the topics in relation to which these computations were carried out is the commentary on standard measuring vessels for capacity measuring units. Among these vessels, an artefact stands out: the official vessel embodying the system of measuring units for capacities designed by Liu Xin, under Wang Mang’s interreign. Michael Loewe will read documents related to the shaping of the instrument and its meaning.

Friday 1 February 2013 –  Room 646A-Mondrian
Quantifying with bricks, volume units, capacity units and weight units in Mesopotamia, session prepared by Cécile Michel and Robert Middeke-Conlin, with participation of Damien Agut , Xavier Faivre, Grégoire Nicolet, Christine Proust, and Martin Sauvage

The session concerns quantifying using weight, capacity and volume units in educational and professional environments, as well as official standards. It will start with presentation of standards and lexical traditions concerning quantities in a more general sense and then will focus on brick quantifications and use.

Friday 8 February 2013 – Room 646A-Mondrian
The construction of fortifications in Classical South Asia, session prepared by Mark McClish

This session will concentrate on the third chapter of the second book (or 21st topic) of the Arthaśāstra, a manual on statecraft (ca 100 BCE- 100 CE). We will read portions of the text dealing with the construction of fortifications that imply that computations and measures were carried out.  The question of the relation of such computations with what is known from mathematical texts will be raised.

Friday 15 February 2013 – Room 646A-Mondrian
Features of quantities and computation in ancient China (Place-value number system; abstract numbers and their relation to questions of units, unit prizes, and equivalences)
, prepared by Karine Chemla; plus, if needed, a continuation of the 29 January session, prepared by Zhu Yiwen

The session will focus on division and related operations. Its aim is to assess whether a series of clues related to this operation in various documents from ancient China discussing computations can help us identify various cultures of computation in ancient China. In particular, we will address the issue of whether we can capture hints of an emergence of a place-value decimal system.  We will also examine the management of operands having measuring units and the part devoted to abstract numbers. Lastly, we shall analyze the part played by the problem of computing unit prizes and its articulation to other types of problems.

Friday 22 February 2013 – Room 646A-Mondrian
Mathematical texts and legal texts in Mesopotamia, session prepared by Carlos Gonçalves and Christine Proust, with the participation of Cécile Michel, Grégoire Nicolet, and Sophie Démare-Lafont

This session deals with the relation between regulation of prices, wages and rents in school and legal contexts. In order to do that, we will compare the data in law collections, royal inscriptions, contract models, lists of coefficients and mathematical texts. We will also search for possible specific characteristics of the north, by comparing, the laws of Eshnunna, on the one hand, to the laws of Hammurabi; and, on the other hand, to the mathematical tablets from the Diyala region.

Friday 1 March 2013 – Room 646A-Mondrian
About measuring units in different kinds of Prakrit and Sanskrit sources
, session prepared by Alessandra Petrocchi and Catherine Singh

Lists of technical terms for different kinds of measuring units and their corresponding values are usually given in the first chapter of Sanskrit mathematical texts, in a way which seems to leave very little room for debate.

In this session, however, we will aim at showing that behind this apparent simplicity, many questions can be raised and discussed. The sources examined will concern the Gaṇitasārasaṃgraha (ca. 850) and two more texts of the jaina tradition (Tiloyapannatti and Anuyogadvara, 5th – 7th CE),  the political text Arthaśāstra (4th BCE-3rd CE) with its commentary Cāṇakyaṭīkā ( sometimes before 10th ?) and the
mathematical texts Līlāvatī ( 12 th) with its commentary Kriyākramakarī (16th CE).

Friday 8 March 2013 – Room 646A-Mondrian
Equivalences and conversions in Mesopotamia
, session prepared by Cécile Michel and Robert Middeke-Conlin

This session concerns equivalences and conversions as well as tax and interest rates in both mathematical and economical texts, taking in consideration different regional practices.

Friday 15 March 2013 – Room 646A-Mondrian
Loans and interest in Sanskrit and legal mathematical texts, session prepared by Takanori Kusuba and S. R. Sarma

This session will examine rules concerning loans and interests in a series of mathematical texts ranging from the Āryabhaṭīya (499) to the Gaṇitakaumudī (ca first half of the XIVth century). Echoes with prescriptions on loans to be found in different law treatises (dharma-śāstra) will be evoked as well.

Wednesday 20 March 2013 – Room 646A-Mondrian
The management of grains: value, equivalences, measuring units, as well as mathematical objects and concepts,
session prepared by Karine Chemla and Ma Biao

Part of a Qin regulation text devoted to the management of grains is quoted in the Book of mathematical procedures, a manuscript found in a tomb sealed ca 186 BCE. The session is devoted to how the context of the quotation allows us to interpret the fragment. It also aims to determine how mathematical documents can help us cast light on the management of grains in early imperial China. The various manuscripts and texts handed down bear witness to the transformation of mathematical tools used in that context between the 3rd century BCE and the 1st century CE. We shall address the question of determining how the management of grain may have provided a context for the promotion of new mathematical ideas. In particular, the different ways in which equivalences were approached and their relation to other mathematical issues will be examined.

The worskop will conclude with the conference Cultures of computation and quantification in the ancient world, which will take place on the 25th-29th of March 2013 in Paris.