Mathematics, administrative and economic activities in ancient worlds

Weitere Verfasser: Chemla, Karine , [HerausgeberIn]
Michel, Cécile , [HerausgeberIn]
Ort/Verlag/Jahr: Cham : Springer International Publishing AG, 2020.
Umfang/Format: 1 online resource (560 pages)
Schriftenreihe: Why the sciences of the ancient world matter v. 5
Schlagworte:
Electronic books.
Parallelausgabe: Michel, Cécile, Mathematics, Administrative and Economic Activities in Ancient Worlds (Print version:) | ISSN: 9783030483883
Online Zugang: Available online
Inhaltsangabe:
  • Intro
  • Contents
  • 1 Mathematics, Administrative and Economic Activities in Ancient Worlds: An Introduction
  • Abstract
  • 1.1 The Project of the Book
  • 1.2 The Sources for the Book, the Numerical Data They Contain and Mathematical Practices
  • 1.2.1 A Documentation Yielded Through Excavations: Cuneiform Texts of Practice
  • 1.2.2 Cuneiform Scholarly Texts and Their Relation with Texts of Practice
  • 1.2.3 Articulating Handed Down Sources and Excavated Documents: The Case of Chinese Texts
  • 1.2.4 Working Mainly with Handed Down Sources: The Documentation in Sanskrit
  • 1.2.5 For the Sake of Comparison: Some Late Medieval Manuscripts
  • 1.3 Types of Tasks, Types of Actors and Contexts
  • 1.3.1 State Administrations
  • 1.3.2 The Diversity of Contexts and Their Relationship with Each Other
  • 1.4 Mathematical Writings, Regulations, Laws and Norms
  • 1.4.1 The Language of Numerical Values
  • 1.4.2 The Language of Technical Terms, of Operations and of the Shape of Quantities
  • 1.4.3 A Clear-Cut Case Showing the Links Between Legal and Mathematical Texts
  • 1.5 Quantifying Spatial Extension, Quantifying Work
  • 1.5.1 The Use of Mathematics in Carrying Out Quantification
  • 1.5.2 How and Why Were Different Measurement Units for Volumes Used Conjointly?
  • 1.6 Quantifying Land and Surfaces
  • 1.6.1 How Approximations Shed Light on Practices of Computation
  • 1.6.2 Shedding Light on the Diversity of Mathematical Practices
  • 1.7 Prices, Rates, Loans and Interest
  • 1.7.1 Using Values of Different Mathematical Nature and Using Them Differently
  • 1.7.2 Identifying Different Cultures of Computation Through the Way Quantities Are Handled
  • 1.7.3 Identifying Different Cultures of Computation Through Ways of Organizing Knowledge
  • References
  • Part I Mathematical Writings, Regulations, Laws and Norms.
  • 2 A Comparative Study of Prices and Wages in Royal Inscriptions, Administrative Texts and Mathematical Texts in the Old Babylonian Kingdom of Larsa
  • Abstract
  • 2.1 Introduction
  • 2.1.1 The Quantities and Numerical Values Analyzed
  • 2.1.2 Larsa, as a Case Study
  • 2.1.3 Textual Sources for Prices and Wages
  • 2.2 Prices and Wages in Old Babylonian Larsa Texts
  • 2.2.1 Prices and Wages in the Inscriptions of the Kings of Larsa
  • 2.2.2 Wages in the Hammurabi Code
  • 2.2.3 Wages in Mathematical Texts Presumably from the Larsa Area
  • 2.2.4 Prices and Wages in Larsa Administrative Tablets
  • 2.3 Comparison of the Data Given in the Different Text Types
  • 2.3.1 Equivalences of Commodities
  • 2.3.2 Wages
  • 2.4 Conclusion
  • References
  • 3 Computation in the Arthaśāstra
  • Abstract
  • 3.1 Introduction
  • 3.1.1 The Arthaśāstra and Classical Statecraft
  • 3.1.2 Computation and the Early Classical State
  • 3.2 Assigning Value
  • 3.2.1 Measuring
  • 3.2.2 Counting (gaṇita)
  • 3.2.3 Appraisal (tarka)
  • 3.3 Operations and Procedures
  • 3.3.1 Increase
  • 3.3.2 Decrease
  • 3.4 Some Computational Practices in State Administration
  • 3.4.1 Inspecting Changes in Volume (2.15.24-37)
  • 3.4.2 Determining Fines for Erroneous Weights and Measures (4.2.3-12)
  • 3.4.3 Calculating Interest for Coinage Fees (2.12.25-26)
  • 3.4.4 Excavating and Constructing Defenses (2.3.4-33)
  • 3.4.5 An Overview of Computation and the State
  • 3.5 Thinking of Computation in the Arthaśāstra
  • 3.5.1 gaṇita)
  • 3.5.2 sam + khyā
  • 3.5.3 anumāna
  • 3.5.4 tarka
  • 3.5.5 Other Terms
  • 3.6 The Arthaśāstra and Cultures of Computation in Classical India
  • References
  • Primary Sources
  • Secondary Sources
  • 4 Official Salaries and State Taxes as Seen in Qin-Han Manuscripts, with a Focus on Mathematical Texts
  • Abstract
  • 4.1 Sources and Historical Scope.
  • 4.2 Official Salaries in the Qin-Han Period
  • 4.2.1 Rank and Salary of Government Officers
  • 4.2.2 The Mathematics of the Payroll
  • 4.3 State Tax Collection
  • 4.3.1 Primary Forms of Taxation
  • 4.3.2 The Collection and Management of Field Taxes
  • References
  • Pre-1850s Sources, Excavated and Received
  • Secondary Sources
  • Part II Quantifying Spatial Extension, Quantifying Work
  • 5 Insights into the Administration of Ancient Irrigation Systems in Third Millennium BCE Mesopotamia
  • Abstract
  • 5.1 Introduction
  • 5.1.1 Environmental Background
  • 5.1.2 Socio-political Background
  • 5.1.3 Management of the Agricultural Land in the Province Umma
  • 5.1.4 The Agricultural Administrator of the Various Districts
  • 5.1.5 The Labor System in the Ur III State
  • 5.1.6 Bureaucracy in Ur III Times
  • 5.2 Administrative and Computational Steps in the Organization of Irrigation Works
  • 5.2.1 Initial Inspection of the Condition of Water Control Devices
  • 5.2.2 Surveying Text 3 (YBC 01821)
  • 5.2.3 Surveying Text 4 (Um. 1594)
  • 5.2.4 Assignment of Work Projects
  • 5.2.5 Execution of the Projects
  • 5.2.6 Remuneration of Workmen
  • 5.3 Conclusion
  • References
  • 6 Mathematical Computations in the Management of Public Construction Work in Mesopotamia (End of the Third and Beginning of the Second Millennium BCE)
  • Abstract
  • 6.1 Introduction
  • 6.2 Mathematical Text Data
  • 6.2.1 Labor Norms
  • 6.2.2 Coefficients
  • 6.2.3 Combined Coefficient Problems
  • 6.3 Mathematical Computations in Administrative Texts: Some Examples from the Ur III Period
  • 6.3.1 Evidence of the Use of Labor Norms in Ur III Administrative Texts
  • 6.3.2 A Provisional Estimation Text for the Construction of a Storehouse
  • 6.3.3 Brick Carrier Texts from Garšana
  • 6.4 Conclusion
  • Appendix: Texts
  • References.
  • 7 The Use of Volume in the Measurement of Grain in Early Imperial China
  • Abstract
  • 7.1 Introduction
  • 7.2 The Earliest Extant Mathematical Documents from Early Imperial China
  • 7.3 Quantifying Volumes
  • 7.3.1 The Expression of Amounts of Volume in Early China as Evidenced by Mathematical Documents
  • 7.3.2 Geometry and Computation: How Does One Assess the Volume Occupied by an Amount of Grain?
  • 7.4 Grain and Volume
  • 7.4.1 Volumes of Grain, Unit of Value and Vessels
  • 7.4.2 Vessels and Volumes
  • 7.4.3 The Use of Volume Computations to Assess the Value of Grain
  • 7.4.4 Comparing the Use of Volume and Capacity in the Measurement of Grain
  • 7.5 Conclusion
  • References
  • Part III Quantifying Land and Surfaces
  • 8 The Measurement of Fields During the Pre-sargonic Period
  • Abstract
  • 8.1 Introduction
  • 8.2 General Observations
  • 8.2.1 Evidence of Land Surveying
  • 8.2.2 The Social Framework of Land Surveying
  • 8.2.3 Length and Surface Systems
  • 8.3 Land Surveying and Geometry
  • 8.3.1 Fields Measured as Rectangles
  • 8.3.2 The 'Surveyor's Formula'
  • 8.4 The Use of Rounding and Approximation
  • 8.4.1 Simplification of the Area: Rounding
  • 8.4.2 Larger Approximations
  • 8.4.3 Some Observations on Rounding-Additive Computation with Tables
  • 8.5 The Shape of the Fields-The Sides us2 and saĝ
  • 8.6 Conclusion
  • Appendix 8.A Excursus-Land Survey Texts from the Umma Region
  • Appendix 8.B: Texts Related to Land Surveying from Girsu
  • Appendix 8.C: Fields and Area Calculation. Land Surveying in Lagaš
  • Appendix 8.D: Data Related to the Fields in Girsu
  • Appendix 8.E: Chronology
  • Appendix 8.F: Fields' Shapes
  • References
  • 9 Early-Dynastic Tables from Southern Mesopotamia, or the Multiple Facets of the Quantification of Surfaces
  • Abstract
  • 9.1 Introduction
  • 9.2 On Visual and Textual Aspects of Early Dynastic Tables.
  • 9.2.1 On Layout
  • 9.2.2 On Notations of Measurement Values
  • 9.2.3 On Multiplication
  • 9.3 Early Dynastic Tables
  • 9.4 Tables of Surfaces in a Tabular Format (Texts 1-3)
  • 9.4.1 Text 1 (VAT 12593)
  • 9.4.2 Text 2 (MS 3047)
  • 9.4.3 Text 3 (Feliu 2012)
  • 9.4.4 Computation
  • 9.4.5 Size of the Fields
  • 9.5 Tables of Surfaces as Lists of Clauses (Texts 4 and 5)
  • 9.5.1 Text 4 (A 681)
  • 9.5.2 Computation
  • 9.5.3 Text 5 (CUNES 50-08-001)
  • 9.5.4 Organisation of Text 5
  • 9.5.5 Computation
  • 9.6 Conclusion
  • Appendix 9.A: System G and the Sign GAN2
  • Appendix 9.B: Chronology
  • Appendix 9.C: Transliteration and Translation of Text 5 (CUNES 50-08-001)
  • References
  • Part IV Prices, Rates, Loans and Interests
  • 10 Computation Practices of the Assyrian Merchants During the Nineteenth Century BCE
  • Abstract
  • 10.1 Introduction
  • 10.2 Numbers and Quantities in the Old Assyrian Archives
  • 10.2.1 The Archives of the Assyrian Merchants at Kaneš and Their Context
  • 10.2.2 The Notation of Numbers and Quantities as Illustrated by a List of Weights
  • 10.3 Conversions
  • 10.3.1 Conversions in School Texts
  • 10.3.2 Conversions Operated by Merchants in Their Everyday Activities
  • 10.3.3 Computations Carried Out in Such Letters: A Combination of Conversions and Additions
  • 10.4 Analysis of Conversions
  • 10.4.1 Conversions of Gold into Silver
  • 10.4.2 Conversions of Tin into Silver
  • 10.4.3 General Observations and Clues on Computation Methods
  • 10.5 Conclusion
  • References
  • Primary Sources
  • Secondary Sources
  • 11 Connecting a Disconnect Can Evidence for a Scribal Education Be Found in a Professional Setting During the Old Babylonian Period?
  • Abstract
  • 11.1 Introduction
  • 11.1.1 Methodological Note
  • 11.1.2 Definitions
  • 11.1.3 Equivalency and Value
  • 11.1.4 Measurement Values
  • 11.2 YBC 7473
  • 11.2.1 The Text and Its Context.
  • 11.2.2 Transliteration and Translation.

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