Abstract
The purpose of this chapter is to explore how numerical discrepancies in texts can be exploited in order to explain how the numbers and measurement values in a text were produced. Four questions are introduced to explore the mathematics involved in the construction of each economic text: Is there any discrepancy in the text? If there is, what is its nature? Can this discrepancy or a similar discrepancy be found in other texts? Can this discrepancy be linked to a mathematical practice ? Finally, what can this discrepancy tell us about the text’s construction? To examine the strength of these questions, this chapter considers several economic texts, concentrating on one economic text in particular, YBC 04224 , in order to show that an abacus existed in the Old Babylonian period to carry out basic addition with the metrological systems introduced in Chap. 2. The present chapter highlights the distinction between mistakes and errors proposed in Chap. 1 and goes on to explore mistakes.
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Notes
- 1.
As is seen with this text and the study of it, first by Thureau-Dangin (1922: plates 55–58), then Neugebauer (1935–1937: I 14–22), Bruins (1970) and finally Al-Rawi and Friberg (2016: 43–50), by the Hellenistic period SPVN had developed a null-marker to express magnitude within a number itself, a significant innovation in representing SPVN. Here this null-marker is represented by a ‘0’.
- 2.
Such as 54 instead of the expected 14 and 40 (Proust 2000: 297).
- 3.
Thus, instead of the expected 2:16:41:15, the author wrote ‘2:16:41:0:15’ (ibid.: 298).
- 4.
Such as ‘40:21:42:41:*:9’ for the expected ‘40:21:42:41:0:9’ or ‘1:58:36:15’ instead of the expected ‘1:58:39:8:26:15’ (ibid.: 298).
- 5.
See also Al-Rawi and Friberg (2016: 44–45) where these mistakes are reviewed while discussing AO 06456.
- 6.
See Proust (2000: 302). A similar situation is suggested by Netz (2002) for Greek abaci (as distinct from Roman abaci): simple pebbles worked as counters while counting boards themselves would have been made of wood. Netz (2002: 327) states, ‘Ultimately, indeed, the very notion of the abacus as a clearly defined artifact is misleading. While scratches are useful, the lines can very well be imagined, perhaps referring to whatever irregularity the surface at hand may have. Thus any surface will do. The abacus is not an artifact: it is a state of mind. The western abacus was wherever there were sufficiently flat surfaces—as well as sufficiently many objects that the thumb and fingers could grasp’.
- 7.
The use of diš for gur measure shows a deviation from Ur III texts in which aš is still used in partial-SPVN (cf. Ouyang and Proust, forthcoming).
- 8.
Note that this split does not appear in relation to area in Ashm 1923-340 . However, it must also be noted that only eše, iku, ubu and sar measurement values are added together. bur only appears in totals as the result of addition. There are no upper values to add together. Thus, the author needed only to state the total of lower values without appending these values to the results of an upper value addition.
- 9.
See Chap. 2 for this.
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Middeke-Conlin, R. (2020). Errors, Mistakes and Evidence for a Counting Device. In: The Making of a Scribe. Why the Sciences of the Ancient World Matter, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-35951-5_6
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