Abstract
An extended model of cultural evolution is brought to bear on the development of practical and theoretical knowledge related to early weighing. We argue that this development can be characterized as an iterative process in which the exploration of the inherent potential of external representations of cognitive structures leads to the establishment of new cognitive structures, whereby this exploration is canalized at each step by historically specific contexts that constrain the actors. We argue that this scheme applies to technological innovation processes as well, and, based on the concrete example of the balance with variable arm length, implications are developed. Thus, the first theoretical writings on mechanics in the western tradition were indeed the result of a reflection on the external representations of weighing techniques. This is contrasted to the case of China. Comparing the historical developments of the two major types of balance with variable arm length—the Bismar and the Roman steelyard—we show how earlier developmental stages function as a scaffold for later techniques and, in particular, how the Roman steelyard required a rather elaborate societal and cognitive infrastructure as the basis for its standardized production. Based on an example drawn from Hero, we indicate how the development of weighing techniques and technical knowledge in turn influenced theoretical knowledge. (An earlier version of this chapter was published in 2016 in eTopoi. Journal for Ancient Studies.)
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Notes
- 1.
See Sommer (2013, Chap. 6).
- 2.
See Geller (2014).
- 3.
See Renn and Damerow (2012).
- 4.
See “Survey 1” in Renn (2012).
- 5.
See Malkin (2011).
- 6.
See Damerow and Renn (2010).
- 7.
- 8.
See Brentjes and Renn (2016).
- 9.
See Damerow (1996).
- 10.
See Laubichler and Renn (2015).
- 11.
See Renn and Damerow (2012).
- 12.
An alteration of both the counteracting force and the length of the arms on which the forces act is conceivable and was in fact realized historically in form of the equal-arm balance with an additional counterpoise. A number of finds suggest that this type of balance, which was fairly common in the Roman imperial period, may be of earlier origin than the steelyard and the bismar types discussed in somewhat more detail in this article. The equal-arm balance with additional counterpoise has not yet received due attention in the literature. For an albeit cursory description, see Corti and Giordani (2001). At the current stage of research, we must assume that the steelyard evolved from this type of balance.
- 13.
The third perceivable variation, a balance in which the distance at which the load acts is altered to achieve equilibrium, was occasionally realized historically but never really established. See Jenemann (1989).
- 14.
See Büttner (2013).
- 15.
The work is presumably pre-Euclidean and may have been initiated during Aristotle’s lifetime. Euclid’s Elements is generally taken to have been compiled shortly after 300 BCE; Aristotle died in 322 BCE. See Renn and McLaughlin in this volume.
- 16.
Vitruvius’ work on mechanics is contained in chapter X of his De Architectura, Vitruvius Pollio (1999). For a recent analysis of the Mechanical Problems, see Chap. 5 in this volume.
- 17.
See Di Pasquale and Parisi Presicce (2013).
- 18.
See Knorr (1982).
- 19.
For the case of China, we will discuss the evidence, some of which is presented here for the first time, in somewhat more detail than this is done for the other societies relevant to this chapter.
- 20.
The Mohist Canon is contained in chapters 40–43 of the Mohist corpus, a compliation of texts that accummulated in the time ca. 500–300 BCE. Mohism owes its name to its legendary founder Mo Di. The Later Mohist texts, to which the Mohist Canon belong, stand out among sources from ancient China for their logical sophistication and topical breadth, see Graham (1989).
- 21.
- 22.
See the discussion in Renn and Schemmel (2006).
- 23.
For a recent discussion, including many references to the literature, see Potts (2012).
- 24.
See Qiu et al. (2001, 33).
- 25.
See, e.g., Qiu (1992, 286–300).
- 26.
See, e.g., items 58 and 59 in Qiu (1992, 34–35).
- 27.
Guo (1993, 29), arrives at a similar conclusion.
- 28.
Steelyards contemporarily produced in China do have standardized moving weights.
- 29.
At least one of the invoked paintings does not hold up to closer scrutiny: The weighing instrument depicted in the painting on the northern wall of cave 254 in Dunhuang, a picture dated to the Southern and Northern Dynasties and often referred to as the earliest depiction of a steelyard in China (Guo (1993, 31); see also Renn and Schemmel (2000, 22)) is in fact an equal-arm balance, as is appropriate in the context of the Buddhist story represented in the drawing, in which a bird is balanced with a person’s flesh.
- 30.
- 31.
This is the ‘Explanation’ (shuo 說) of Canon B 25b in Graham’s numbering (Graham 1978). The translation presented here was prepared in cooperation with William Boltz. It is part of a more comprehensive project on the scientific sections in the Mohist Canon, which is currently being prepared for publication by Boltz and Schemmel.
- 32.
Section B 26, see Graham (1978, 390–392). The passage appears to be concerned with an arrangement involving a pulley, or a curtain being pulled over a rod.
- 33.
- 34.
- 35.
On the relation between natural philosophy and technical knowledge in seventeenth-century China, see Cullen (1990).
- 36.
See Laubichler and Renn (2015).
- 37.
In the history of the steelyard, this tendency is nicely illustrated by the apparent loss of the ability to produce fully functional steelyards with two or three fulcra in the Merovingian period. See Werner (1954).
- 38.
The theoretical explanation presented here is informed by a theory of extended evolution as laid out in Laubichler and Renn (2015).
- 39.
As the abundant representations of weighing with equal-arm balances that have been preserved show, the lack of pictorial representations of bismars cannot be explained by the fact that weighing as an everyday technology was not the subject of such representations.
- 40.
- 41.
- 42.
For the earliest evidence of weighing in the Indus valley culture, see Kenoyer (2010).
- 43.
For the concept of design space, in particular in relation to the formation of specific “body plans” or “dominant designs,” see Murmann and Frenken (2006).
- 44.
See Jenemann (1989).
- 45.
A statistical analysis of the deviation of the scales’ marks from their ideal positions in Roman steelyards has shown that the scales of these balances were produced by gauging at regular intervals. The intermediate marks were placed by dividing the distances into an appropriate number of equal parts. As concerns the bismar, a similar gauging routine for the establishment of the scales has been assumed, see Damerow et al. (2002) and Jenemann (1994,) but awaits confirmation by a detailed examination of the objects.
- 46.
Aristophanes’ description, however, is not merely based on a superficial similarity of a trumpet and a bismar, as the instruction to fill the bell with lead corresponding to construction knowledge illustrates.
- 47.
A summary of the discussions of this particular object can be found in Damerow et al. (2002). Jenemann takes the Pompeian bismar as an indication that bismar technology was still in widespread use in the second half of the first century, Jenemann (1994). In view of the simplicity of the construction the argument is not very cogent.
- 48.
Peculiarly, Vitruvius’ description is the only unambiguous reference to a steelyard that can be found in textual sources from antiquity and late antiquity, see Rohmann (2017).
- 49.
The spread of the steelyard over a vast geographical area, and its persistence over time can be characterized as a complex innovation process in which different subtypes of steelyards emerged and replaced each other. This innovation process is being studied in detail by a Topoi junior research group (https://www.topoi.org/project/d-5-5/). The new findings concerning unequal-arm balances presented in this article result from this research agenda.
- 50.
In equal-arm balances, the weight of the instrument itself influences its operation too, although not the equilibrium configuration. For the bismar, the influence of the dead weight of the instrument is handled with the gauging of the scale.
- 51.
Whereas the earliest preserved steelyards all have two fulcra, instances of later types tend to have three. For a typology of steelyards, see Franken (1993). A new catalogue is in preparation and will be published soon. A prototype can be accessed via the webpage of the Topoi junior research group D-5-5 (http://www.topoi.org/project/d-5-5/), accessed August 23, 2017.
- 52.
See Renn and Schemmel (2000).
- 53.
This method was performed by a steelyard-maker in Tongzhou (near Beijing) and described by a steelyard-maker in Changsha, see Renn and Schemmel (2000, 17).
- 54.
This was explained to us by the master steelyard-maker at the workshop at Tongzhou, see Renn and Schemmel (2000, 19).
- 55.
The value of 21.5 for determining the position of the second fulcrum was used both in Tongzhou and in Changsha, see Renn and Schemmel (2000, 18, 32). For the first fulcrum, the number of sections used in Changsha was 7.2.
- 56.
Renn and Schemmel (2000, 18–19). The method was explained to us by a steelyard-maker in Tongzhou. The numbers used at the workshop in Changsha are compatible with the application of the same method.
- 57.
- 58.
See Sommer (2013, Chap. 4).
- 59.
See Wilson (2002). Wilson’s paper is an effective response to the widespread idea that technological innovation and economy were not linked in antiquity. This idea was diffused by M. I. Finley. See, in particular, Finley (1965). For a large study on the relation between technology and economy in antiquity, see Lewis (1997).
- 60.
For the production of steelyards in modern-day China, see Renn and Schemmel (2000).
- 61.
See Hero (1900, 86), authors’ translation.
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Büttner, J., Renn, J., Schemmel, M. (2018). The Early History of Weighing Technology from the Perspective of a Theory of Innovation. In: Feldhay, R., Renn, J., Schemmel, M., Valleriani, M. (eds) Emergence and Expansion of Preclassical Mechanics. Boston Studies in the Philosophy and History of Science, vol 270. Springer, Cham. https://doi.org/10.1007/978-3-319-90345-3_4
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