The Intangible Weight of Things: Approximate Nominal Weights in Modern Society

Abstract

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The Earliest Balance Weights in the West: Towards an Independent Metrology for Bronze Age Europe

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Figure 2.Quantogram of a perfectly quantal sample: weight values written on the labels of packaged goods in Italian supermarkets. (Ialongo & Vanzetti 2016. )

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“…Positive results occur when ε is close to either 0 or q, i.e. when X is (close to) an integer multiple (Ialongo & Vanzetti 2016. ) of q, where N is the sample size:…”

“…In the Bronze Age of the Near East and the Aegean, the wealth of cross-checked archaeological and textual evidence provides an ideal ground to explore how official, theoretically exact systems were organized and how they were reciprocally connected (Parise 1971; Alberti et al 2006). However, any given physical unit becomes ‘exact’ only as soon as its equivalent value is formally fixed and written down in official accounts: everyday practice was—and still is (Ialongo & Vanzetti 2016)—far from exact, and deviation from the norm was the norm itself (Chambon 2011). Approximate practice determined significant statistical dispersion in samples of balance weights, thus making excessive reliance on supposedly exact units often misleading.…”

“…a sample made entirely of multiples of the same exact number), the CQA will produce peaks of the same height for every single logical fraction or multiple of the unit itself. The example in Figure 2 shows the results for a perfectly quantal set of observations, corresponding to the nominal weights written on the labels of packaged goods in modern supermarkets in Italy (Ialongo & Vanzetti 2016). The Quantogram shows a series of equally high peaks at the values of 1 g, 2 g, 2.5 g, 5 g, 10 g, 12.5 g, 25 g and 50 g: if we did not know that the unit of the Decimal System is ‘1’, we would never be able to figure it out, not even with a perfectly quantal dataset.…”

The origins of money: Calculation of similarity indexes demonstrates the earliest development of commodity money in prehistoric Central Europe

“…Archaeology can provide a unique perspective on the development of money and systems of weighing over space and time, but the discipline has difficulties with the identification of objects that functioned either as commodity money or as (balance) weights. Typical statistical approaches are inadequate for dealing with the approximation that characterizes prehistoric weighing [ 3 , 4 ]. What is needed for archaeology to contribute to the history of metrology and the origins of money are methods for identifying standardization on the basis of perceived similarity.…”