Abstract
Four thousand years ago scribal schools flourished in Mesopotamia and neighboring regions. In these schools young scribes were educated to develop mastery of cuneiform writing on clay tablets, and to learn literature and mathematics. These ancient schools left a huge amount of archaeological and epigraphic evidence. In this chapter, I examine some of this evidence to analyze the material produced or used for teaching, and I attempt to identify and investigate authors, users, function, and status of different types of mathematical writings produced. Although the situation observed is far removed in time, the analysis is likely to provide insights into phenomena such as the change of knowledge medium, from memorisation to writing; standardisation processes, notably in the field of writing and metrology; the emergence of a set of ideological references specifically linked to a scholarly milieu. The cuneiform school texts allow researchers to study teaching and learning processes over a very long term, thus integrating more than any other contribution in this volume the time factor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The historian of education very rarely has the chance to have access to students’ work (drafts, notebooks, exams), which had no value in the eyes of its authors, and was generally destroyed.
- 2.
Veldhuis (1997). We don’t know how old the students were at the beginning of their scribal education. They were old enough to be able to manipulate clay and “calame” (the cane the scribes used to impress signs on wet clay), but still in the charge of their parents. Moreover, the age of the students could have changed according to the place and the period.
- 3.
Old Babylonian tablets from Nippur and now kept in Istanbul and Jena are published in Proust (2007, 2008a). Photos and informations are available on line at http://cdli.ucla.edu/ (Cuneiform Digital Library Initiative website), by entering Museum number or CDLI number (both information are provided here). Parts of the Philadelphia tablets are published in Robson (2001). Veldhuis’ Ph.D. thesis contains a study of lexical tablets from Nippur, and a detailed reconstruction of Nippur curriculum (Veldhuis, 1997).
- 4.
We know six Edubba texts. The Electronic Text Corpus of Sumerian Literature (ETCSL, http://etcsl.orinst.ox.ac.uk/) provides the following list: Edubba A or “Schooldays” (Kramer, 1949); Edubba B or “A scribe and his perverse son” (Sjöberg, 1973); Edubba C or “The advice of a supervisor to a younger scribe” (Vanstiphout, 1996, 1997); Edubba D or “Scribal activities” (Civil, 1985) – see below; Edubba E or “Instructions of the ummia”; Edubba R or “Regulations of the Edubba”. A French translation of “Edubba A” by Pascal Attinger, with philological notes, can be found at: http://www.arch.unibe.ch/content/e8254/e8548/e8549/index_ger.html?preview=preview%26lang=ger%26manage_lang=ger
- 5.
See also Civil (1985, pp. 71–72).
- 6.
In order to erase signs impressed in wet clay, scribes simply rub them lightly with their finger. Tablets bear often fingerprints and erased signs covered by others.
- 7.
The term “metrological” refers to the measure systems (see the following page).
- 8.
Metrological systems (systems used for noting measures of capacity, weight, volume, surface, and length), were described in “metrological lists”. Metrological tables provided a correspondence between measures and abstract numbers, that is, numbers written in sexagesimals place value notation. SPVN was used in mathematical texts. This notation used 59 digits (1–59), made of two kinds of signs: ones (vertical wedges
) and tens (oblique wedges 
), repeated as many times as necessary. For example, 12 is noted 
. The numbers are made of sequences of digits following a positional principle in base 60: each sign noted in a given place represents 60 times the same sign noted in the previous place (on its right). SVPN does not specify the magnitude of the numbers. For example, the numbers 1, or 60, or 1/60 are noted in the same way (a vertical wedge 
). Initial and final zeros are unnecessary, and indeed, they are not attested in any known cuneiform text. However, the absence of notation for median zero was a weakness of the system, which was corrected in later periods: in the mathematical and astronomical texts from the last centuries before our era, scribes used signs indicating the absence of a power of 60 in the positional numbers. In the transcriptions, digits are noted in the modern decimal system, and separated by dots. For example the numbers 44.26.40 which appears in Table 9.1 is a transcription of the cuneiform number 
. For more details on place value notation, see Proust (2008b). - 9.
Current digital databases permit a simultaneous representation of both composite text and real texts written in available sources. The advantages of digital media over paper to represent the lexical lists in all their dimensions have been noted by Veldhuis in his study of school texts of Veldhuis (1997, Ch. 5). He exploited these advantages in the development of his online database (DCCLT, http://cdl.museum.upenn.edu/dcclt/).
- 10.
One of the rare exceptions is a mathematical prism now kept in the Louvre (AO 8865, CDLI No P254391), of unknown provenance. It is a large prism carefully written and crossed by an axial hole, probably to be easily usable. This prism is a precious object which looks very different from the drafts of students. This prism could indicate that the “composite text” was not always entirely memorized by professional scribes, who needed to consult a reference text.
- 11.
This conclusion is largely based on discussions with Anne-Marie Chartier, at a workshop on education in Mesopotamia (Paris, 15/03/2006).
- 12.
- 13.
These states were ruled by two king dynasties in two periods separated by one century: the Akkad dynasty, 2300–2200 (Sargon and successors), and the Ur III dynasty, 2100–2000 (Ur-Nammu, Shulgi and successors).
- 14.
See Ist Ni 374, CDLI no. P257557.
- 15.
A regular number in a given base (here in base 60) is a number whose reciprocal can be written with a finite number of digits. These numbers are products of divisors of the base, therefore, in base 60, their decomposition into prime factors does not include factors other than 2, 3 or 5. The ancient Mesopotamian mathematicians certainly knew all the one-place regular numbers (given in standard tables), and probably all two-places regular numbers, as well as a large stock of larger regular numbers (three or more digits). Their algorithms, including the division which was performed by means of multiplication by reciprocal, were mainly based on regular numbers.
- 16.
In translation, the exclamation point after 40 means that indeed the scribe should have written 40 on his tablet, but in fact wrote something else (in this case, he wrote 41 instead of 40).
- 17.
For this reason, Friberg gave the name “trailing part algorithm” to this method (Friberg, 2000, pp. 103–105).
) and tens (oblique wedges 
), repeated as many times as necessary. For example, 12 is noted 
. The numbers are made of sequences of digits following a positional principle in base 60: each sign noted in a given place represents 60 times the same sign noted in the previous place (on its right). SVPN does not specify the magnitude of the numbers. For example, the numbers 1, or 60, or 1/60 are noted in the same way (a vertical wedge 
). Initial and final zeros are unnecessary, and indeed, they are not attested in any known cuneiform text. However, the absence of notation for median zero was a weakness of the system, which was corrected in later periods: in the mathematical and astronomical texts from the last centuries before our era, scribes used signs indicating the absence of a power of 60 in the positional numbers. In the transcriptions, digits are noted in the modern decimal system, and separated by dots. For example the numbers 44.26.40 which appears in Table 
. For more details on place value notation, see Proust (References
Bernard, A., & Proust, C. (2008). La question des rapports entre savoir et enseignement dans l’antiquité. In L. Viennot (Ed.), Didactique, épistémologie et histoire des sciences. Penser l’enseignement (pp. 281–302). Paris: PUF, Collection Science, histoire et société (dir. D. Lecourt).
Cavigneaux, A. (1989). L’écriture et la réflexion linguistique en Mésopotamie. In S. Auroux (Ed.), Histoire des idées linguistiques (1): La naissance des métalangages en Orient et en Occident. Liège, Bruxelles: Pierre Mardaga.
Charpin, D. (2008). Lire et écrire à Babylone. Paris: PUF.
Civil, M. (1985). Sur les “livres d'écoliers” à l'époque paléo-babylonienne. In J.-M. Durand & J.-R. Kupper (Eds.), Miscellanea Babylonica, Mélanges offerts à M. Birot (pp. 67–78).Paris: ERC.
Friberg, J. (2000), Mathematics at Ur in the Old Babylonian period. Revue d’Assyriologie, 94, 98–188.
George, A. R. (2005). In search of the é.dub.ba.a: The ancient Mesopotamian school in literature and reality. In Y. Sefati, P. Artzi, C. Cohen, B. L. Eichler, & V. A. Hurowitz (Eds.), An experienced scribe who neglects nothing: Ancient Near Eastern studies in honor of Jacob Klein. Bethesda: CDL Press.
Kramer, S. N. (1949). Schooldays: A sumerian composition relating to the education of a scribe. Philadelphia, PA: The University Museum.
Michalowski, P. (1987). Charisma and control: On continuity and change in early Mesopotamian bureaucratic systems. In M. Gibson & R. D. Biggs (Eds.), The organization of power, aspects of bureaucracy in the Near East (Vol. 46). Chicago: The Oriental Institute of the University of Chicago.
Michel, C. (2008). Ecrire et compter chez les marchands assyriens du début du IIe millénaire av. J.-C. In T. Tarhan, A. Tibet, & E. Konyar (Eds.), Mélanges en l’honneur du professeur Muhibbe Darga (pp. 345–364). Istanbul, Turkey: Sadberk Hanim Museum Publications.
Proust, C. (2000). La multiplication babylonienne: la part non écrite du calcul. Revue d’histoire des mathematiques, 6, 1001–1011.
Proust, C. (2007). Tablettes mathématiques de Nippur. Varia Anatolica (vol. XVIII). Istanbul, Turkey: IFEA, De Boccard.
Proust, C. (2008a). Tablettes mathématiques de la collection Hilprecht. Texte und Materialen der Frau Professor Hilprecht Collection (vol. 8). Leipzig, Germany: Harrassowitz.
Proust, C. (2008b). Quantifier et calculer: usages des nombres à Nippur. Revue d’Histoire des Mathématiques, 14, 143–209.
Proust, C. (2011). Interpretation of reverse algorithms in several Mesopotamian texts. In K. Chemla (Ed.), History of mathematical proof in ancient traditions: The other evidence. Cambridge: Cambridge University Press.
Robson, E. (2001). The tablet house: A scribal school in Old Babylonian Nippur. Revue d’assyriologie, 95, 39–66.
Sjöberg, A. W. (1973). Der Vater und sein Missratener Sohn. Journal of Cuneiform Studies, 25, 105–169.
Tanret, M. (2002). Per aspera ad astra. L’apprentissage du cunéiforme à Sippar-Amnanum pendant la période paléo-babylonienne tardive. Mesopotamian History and Environment, Serie III Cuneiform texts (MHET) (Vol. I/2). Ghent, Belgium: Université de Gand.
Thureau-Dangin, F. (1930). Nombres concrets et nombres abstraits dans la numération babylonienne, Revue d’assyriologie, 27, 116–119.
Vanstiphout, H. L. J. (1978). Lipit-Eshtar Praise in the Edubba. Journal of Cuneiform Studies, 30, 33–61.
Vanstiphout, H. L. J. (1979). How did they learn sumerian? Journal of Cuneiform Studies, 31, 118–126.
Vanstiphout, H. L. J. (1996). Remarks on “Supervisor and Scribe” (or Dialogue 4, or Edubba C). NABU, 1.
Vanstiphout, H. L. J. (1997). School dialogues. In W. W. Hallo (Ed.) The context of scripture, I: Canonical compositions from the biblical world (pp. 588–593). Leiden/New-York/Köln: Brill.
Veldhuis, N. (1997). Elementary education at Nippur, the lists of trees and wooden objects. Ph. D. dissertation (Retrieved from http://ls.berkeley.edu/dept/ahma/Faculty/veldhuis.htm), University of Groningen.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Proust, C. (2011). Masters’ Writings and Students’ Writings: School Material in Mesopotamia. In: Gueudet, G., Pepin, B., Trouche, L. (eds) From Text to 'Lived' Resources. Mathematics Teacher Education, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1966-8_9
Download citation
DOI: https://doi.org/10.1007/978-94-007-1966-8_9
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-1965-1
Online ISBN: 978-94-007-1966-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)