Counter Culture: Towards a History of Greek Numeracy

Netz, Reviel

doi:10.1177/007327530204000303

Cited by 59 publications

(11 citation statements)

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“…These findings have profound implications, not only for the interpretation of the use of clay objects and accordingly the nature of Neolithic village societies; the assumed function of Neolithic clay object as ‘tokens’ has directly impacted on the wider understanding of humankind in a broader sense: our cognitive abilities, the evolution of the ability to understand and convey abstract numbers, the ability to perform counting tasks, the use of inanimate objects as symbolic information storage devices. The understanding of all such developments is incorrectly based on the apparent sudden, and universal, appearance of clay ‘tokens’ acting as mnemonic recording devices in the early Neolithic period (Malafouris 2010, 8; 2013, 106–11, 111–15; Netz 2002; Overmann et al 2011, 143; Schmandt-Besserat 1992a; 1996, 7, 100, 102; 1996, 6–7). There is no evidence for a Neolithic, Near East-wide, universal accounting system.…”

Section: Discussionmentioning

confidence: 99%

“…In ancient Greece, for example, identical counters were used in conjunction with a flat board marked with lines. The resultant squares were labelled with set numerical values, allowing the ‘counters’ to be placed as required (Netz 2002). Within this system, complex calculations could be performed, yet the ‘counters’ themselves retained no numerical value nor symbolic meaning once removed from the board.…”

Section: Subject Overviewmentioning

confidence: 99%

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Reconsidering ‘Tokens’: The Neolithic Origins of Accounting or Multifunctional, Utilitarian Tools?

Bennison-Chapman¹

2018

CAJ

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The origin of record keeping is a key question in the development of social complexity and specialized economies, representing the first step towards the emergence of written communication. Yet the precursors of the world's earliest writing and its initial stages of development remain little understood. Small, geometric clay objects ('tokens') appear in the tenth millennium cal. BC, the start of the Neolithic in West Asia, prevailing into the first millennium. It is largely assumed that from their inception clay objects played a crucial role in record keeping, directly evolving into the world's earliest known writing. Utilizing new and previously unpublished Neolithic data comprising almost individually studied 3000 objects, accompanied by information from 56 further Neolithic sites, this article investigates the meaning of Neolithic 'tokens'. Analysis proves the basis of their predominant interpretation to be incorrect; clay objects appear earlier than previously recognized and are not a necessary component of Neolithic agro-pastoral villages. 'Tokens' were multi-functional artefacts; even within a single site clay objects performed multiple roles. Though likely used in simple counting activities, this was not limited to the accounting of agricultural produce. Nor was counting the sole function of clay objects in the Neolithic. Clay objects were not created to administer agricultural produce and there is no evidence to suggest that in the Neolithic they formed part of a unified symbolic system. ). Though concerns were raised at the time of publication (such as Pollock 1999, 166; Zimansky 1993), Schmandt-Besserat's work remains mainstream, despite evidence to support her claims, especially the reasons for the initial appearance and use of 'tokens' in the Neolithic period being far from secure.This article investigates evidence for the predominant interpretation of the earliest 'tokens', those from the Neolithic period. To date no convincing evidence supporting Denise Schmandt-Besserat's interpretation of the function of pre-historic 'tokens' has been published. This paper utilizes new and previously unpublished Neolithic data comprising almost 3000 individually published objects, in addition to data from a total of 79 sites (Table 1). Importantly, the research specifically incorporates information regarding the immediate and wider context of clay objects in the Neolithic. Analysis proves that, far from being the unequivocal precursors of cuneiform script and part of Schmandt-Besserat's proposed symbolic administrative 'token' system, clay objects were basic, multi-functional tools with a range of meanings, functions and uses.The abundance of clay objects found across an expansive temporal and geographic zone (Fig. 2), spanning the entire West Asian region across many millennia, implies an important role for these artefacts, a role which may relate to one of the many economic, cultural, symbolic and lifestyle changes seen at the start of the Neolithic, the period in which they initially occur. 'Tokens' are char...

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Section: Discussionmentioning

confidence: 99%

Section: Subject Overviewmentioning

confidence: 99%

Reconsidering ‘Tokens’: The Neolithic Origins of Accounting or Multifunctional, Utilitarian Tools?

Bennison-Chapman¹

2018

CAJ

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“…The relationship began in classical Greece. Netz (2002) discusses how money, as a counter, stimulated the development of numeracy and how numeracy impacted political decision making. Seaford (2004) makes a more extensive argument that the widespread use of money by the Greeks enabled them to abstract from the concrete to the imaginary and promoted individualism while a communal attitude to money ensured that society remained cohesive.…”

Section: Context and Fundamental Ideasmentioning

confidence: 99%

The influence of financial practice in developing mathematical probability

Johnson

2020

Synthese

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The purpose of this paper is to discuss the role of financial practice in the development of mathematics as applied in human judgement. The basis of the paper is in historical research from the 1990s that argues that the monetisation of western commerce, which abstracted value into quantified price, was synthesised with scholastic analysis resulting in a "mathematical mechanistic world picture" that led to the widespread use of mathematics in science from the seventeenth century. An aspect of this process was the quantification of chance that led to the development of mathematical probability, the branch of mathematics most relevant to judgement and the focus of this paper. Ideas from this historical research are related to the fundamental theorem of asset pricing (FTAP), the foundational theory of contemporary financial mathematics. The paper observes that vestiges of medieval scholastic attitudes to financial ethics can be discerned in the FTAP, offering a novel interpretation of the mathematical theorem. The paper then considers the Dutch book argument (DBA), the most popular justification for subjective probability. The paper's main contribution is in describing the significance of financial practice in validating the DBA and the paper explains how the FTAP addresses some criticisms of how the DBA represents beliefs. The conclusions emphasise the distinction between pure and practical reasoning and that this should be mirrored in a distinction between the mathematics of physica and practica. This point is important as mathematics is becoming more widespread in modelling, and directing, social systems.

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“…Az 1960-as évektől kezdve számtalan, átnézésre érdemes tanulmány jelent meg az olvasástudás kiterjedéséről és jelentőségéről (például Stone 1964és 1969, Goody és Watt 1963, Goody 1968. Ahogy a szövegben is megjegyeztem, az 1980-as években a tudományos kutatások meglehetősen más irányt vettek, viszont fontos új tanulmányok jelentek meg, főként ennek az időszaknak a kezdetén (Például Harris 1989, Clanchy 1993, Netz 2011) 3 Például Bodde 1991, Crosby 1994, Netz 2002, Chrisomalis 2004, Olson és Torrance 2009, Chrisomalis 20104 Street 1984és 1987, Chartier 1989Thomas 1992 cserélhetik azokat, melyek az elmúlt néhány százezer év alatt alakultak ki. Ez azonban még nem történt meg, ám az információtechnológia történeti pontszámainak kiszámításakor ezeket a bonyolult, egymást átfedő mintákat is fel kellett ismernünk.…”

Section: Ian Morris: Az Információtechnológia Civilizációs Pályája: Munclassified

Az információtechnológia civilizációs pályája: mérés és osztályozás

Morris¹

2018

InfTárs

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Ian Morris a társadalmi fejlődés (social development) fogalmával az emberi közösségek képességét fejezi ki „dolgok elintézésére” a világban. Az így értelmezett társadalmi fejlettség mérhető és összehasonlító állapotokat jelent, térben és időben. Morris 4 tényező (az energiafelhasználás, a társadalmi szerveződés, az információtechnológia és a hadviselő kapacitás) kvantifikálásával megszerkesztett indexét kifejtő könyvéből az információtechnológiára vonatkozó, a többihez hasonlóan a Kelet és a Nyugat összehasonlítására épülő fejezetet fordítottuk le. Úttörő okfejtései és becslései remek kiindulópontok, hogy újraértékeljük és alaposan végiggondoljuk az információtechnológia helyét és „küldetését” a beavatkozásképesség, a cselekvési hatékonyság szempontjából. A tanulmányt Z. Karvalics László bevezetésével közöljük. --- The civilization path of information technology: measurement and classification Ian Morris defines social development as “social groups’ abilities to master their physical and intellectual environments and get things done in the world”. From this approach, “social development is - in principle - something we can measure and compare through time and space”. The Social Development Index of Morris is based on the quantifiable attributes of four pillars: energy capture, social organization, information technology, war-making capacity, comparing the numbers of the West and the East. We have translated and published the information technology chapter of his book with Laszlo Z. Karvalics’ introduction to support the re-evaluation of the role and mission of information technology throughout the ages from a special point of view: to facilitate the ability to act effectively.

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Counter Culture: Towards a History of Greek Numeracy

Cited by 59 publications

References 15 publications

Reconsidering ‘Tokens’: The Neolithic Origins of Accounting or Multifunctional, Utilitarian Tools?

Reconsidering ‘Tokens’: The Neolithic Origins of Accounting or Multifunctional, Utilitarian Tools?

The influence of financial practice in developing mathematical probability

Az információtechnológia civilizációs pályája: mérés és osztályozás

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