Systems of Weight in the Bronze Age Aegean, Part 2:

An Introduction to the Archaeological and Epigraphical Evidence

Karl M. Petruso, University of Texas at Arlington

     The case considered above was, as previously noted, a best-case scenario. Following is a set of data that has occupied me more recently, namely the Bronze Age balance weights from the island of Cyprus. The balance weights from this island are not nearly so accommodating as were their contemporary counterparts from the Aegean. Now Cyprus is interesting to us in many ways. Its pivotal geographical position alone suggests that we should expect to see evidence of an ability to trade with other cultures and polities of the ancient eastern Mediterranean. Balance weights are, among other things, tools of trade. They facilitate the common evaluation of goods and commodities in different places. Indeed, the ceramic record, as well as finds of exotic materials in Late Bronze Age Cyprus, and of Cypriot materials in mainland archaeological sites in the Near East and Egypt, speak of vigorous contacts with foreign lands, and this is unremarkable. However, when we look to Cypriot balance weights for quantitative information about such foreign contacts, we are faced with two formidable difficulties:
      We are, in short, doubly handicapped: We are given no external clues to assist us in determining either the absolute masses or the structures of the system or systems in use in the island.
      Recently there have appeared several scholarly reports on caches of well-preserved balance weights excavated from Late Bronze Age contexts at several Cypriot sites. In the absence of markings on these items, the archaeologists who have studied them have very subjectively attributed them to one or another system known to have been in use in the ancient eastern Mediterranean. An unmarked stone weighing, for example, 93 grams, might conveniently be labeled 10 Egyptian qedets of 9.3 grams, simply on the basis of its mass. This is, of course, a possibility, but it is only one of many. What is needed is a more objective method of assigning particular balance weights to particular systems. The fundamental issue is this: If we have neither markings nor epigraphical information to guide us, we must conceive of the problem as a strictly mathematical one, demanding a strictly mathematical solution.
      One way to approach this material is to search for simple ratios relating specimens; and for clusters of specimens at particular masses, as proved useful with the Minoan material. Unfortunately the Cypriot weights ar not as easy to decode as were their Minoan counterparts. When we recall the geographical position of Cyprus, particularly its proximity to the Syrian and Anatolian coasts, we have reason to expect the metrical picture to have been clouded by the presence of more than one system. The Aegean weights, by contrast, seemed to be sui generis,and there is very little evidence for foreign systems in the Aegean. In the corpus of balance weights excavated in Cyprus, on the other hand, we should not be surprised in the least to see represented Egyptian, Anatolian, Syrian, and Palestinian, as well as perhaps indigenous Cypriot systems. How, then, do we deal with such a confusing picture, without falling into the trap of arbitrarily assigning specimens to one system or another on the basis of their masses alone?
      As it turns out, there isan objective means of determining the most likely attributions for data suspected of having been metrically configured. It is the result of research into the so-called "megalithic yard," on the basis of which many scholars believe Stonehenge and other megalithic monuments of the British Isles were designed. In 1974, D.G. Kendall, a statistician at the University of Cambridge, defined and tested the following trigonometric function.

phi(t) = (SQR (2/N)) * sum, from N=1 to j, of ((cos(2*pi*Xj*t))),

phi(t) is an error term, measured in radians, either positive or negative in sign;
N is the number of observations in the population analyzed;
Xj is an individual measurement;
t is the reciprocal of a tested quantum; and
(SQR (2/N)) is a scaling factor, permitting comparison of populations of different size.

In a typical non-quantally configured population, phi(t) will approximate to zero, and will be negative or low positive in sign. In a quantally configured population, it will be relatively high in value, and positive in sign.

      This expression is a powerful tool: It enables the historical metrologist to test a group of observations--spans of length or masses of balance weights--with a view to determining the "quantum," or value (if any), on which they were standardized. A high positive value returned for phi(t) will be a relative measure of the goodness-of-fit for a tested quantum. Kendall took thousands of measurements on Stonehenge and other megalithic monuments, and determined with a high degree of probability--and in the process put the venerable megaltihic yard controversy to rest--that there was indeed a megalithic yard in Britain, and that it was about 166 centimeters long. This just happens to be about 5 feet 5 inches, and thus leads us to wonder whether the megalithic yard was pegged to the height of an adult male in prehistoric Britain, but we cannot be distracted by that particular observation here. The first scholar to apply this function to Aegean material was Dr. John Cherry of the University of Michigan in the journal Antiquity(vol. 57, 1983, pp. 52-56). He carried out a superb analogous study of Minoan palatial architecture with a view to determining the span on which the Bronze Age palaces might have been laid out (the so-called "Minoan foot"), and the project met with good success.
      Since length and mass are both measured on a linear scale, Kendall's statistic can be of use to us in disentangling the picture of Cypriot weight metrology as well. We are, however, immediately at an advantage over the megalithic yard situation. In the case of megalithic architecture, we did not know originally whether all these monuments, or any specific ones, had indeed been quantally configured. In terms of the categories I set up above, the monuments were derivative sources of data. In the case of the Cypriot balance weights, however, we know that they must have been quantally configured to some system, because their shapes and materials were so well known (sphendonoids and dome-tops, which were canonical shapes for balance weights in the ancient Near East and Egypt as early as the 4th millennium BC). Our task is thus to distinguish one system from another, and to determine--objectively and quantitatively--how many distinct systems were represented in the island.
      The necessary calculations, as you might guess, are tedious, and are best done on a computer. I long ago wrote a program in BASIC which does this, and have more recently configured it to work (albeit somewhat more cumbersomely) in a Microsoft Excel spreadsheet. Below is an example of a quantal run which tested the 176 well-preserved balance weights from the Aegean for peak phi(t) values in 5-gm. ranges from 5 to 70 gm.

   Q RANGE (gm.)      BEST Q (gm.)      phi(t) PEAK    
5.0 - 9.9
10.0 - 14.9
+ 1.103
15.0 - 19.9
+ 2.343
20.0 - 24.9
+ 1.037
25.0 - 29.9
+ 1.981
30.0 - 34.9
+ 1.823
35.0 - 39.9
+ 0.708
40.0 - 44.9
- 0.312
45.0 - 49.9
+ 0.340
50.0 - 54.9
- 1.024
55.0 - 59.9
+ 0.679
60.0 - 64.9
+ 0.682
65.0 - 69.9
- 0.490
70.0 - 74.9
- 0.994

Analysis: It will be recalled that the highest positive values returned for phi(t) are the most likely candidates for quanta on which the entire population was based. In the table above, the highest Q values for phi(t) were returned at periods of approximately 7.5 gm., with noteworthy clusters at around 30 and 60 gm. (significant values shown in boldface). The quantal analysis was of course performed without regard to the evidence from the markings on the weights. Although the peaks at our proposed unit of ca. 61 gm. are relatively low, they are positive and quite high when compared to their adjacent neighbors, and we may be confident that the quantal analysis confirms the evidence from the marks.
      Let us now turn to similar material from the eastern Mediterranean. The fact that deposits of balance weights from many Late Bronze Age sites in Cyprus and adjacent lands have been published has made it possible to do a comparative study that will allow us to put Cyprus into the larger metrological picture.
      The following table shows the quanta most in evidence at four sites in Cyprus (Enkomi, Ayia Irini, Kalavassos and Athienou) as well as at Zincirli (Anatolia), Ugarit (on the Syrian coast), Cape Gelidonya (late 13th century shipwreck off the south coast of Anatolia), and Uluburun (mid-14th century shipwreck, also off the south coast of Anatolia). It is by no means an exhaustive account of the systems in use in the island, but I am confident that it is representative of the major systems in use. All are known at other Cypriot sites with smaller total numbers of balance weights. At the bottom of this table are listed--very provisionally--the suggested attributions of ranges of particular masses.

SITE   Q Peak      2nd Peak      3rd Peak   
Ayia Irini
9.3 - 9.4
7.1 - 7.3
* The quantal peaks cited for Gelidonya and Uluburun were determined by Cemal Pulak in his recent comprehensive study of the balance weights from these two shipwrecks (see his dissertation, cited above, pp. 151 and 254-255.

Provisional Attributions:
7-2-8.0 grams = Palestinian pym
8.0-8.5 grams = Mesopotamian daric
9.1-9.4 grams = Egyptian qedet
10.0-10.9 grams = Palestinian necef
11.5-11.9 grams = Hittite "shekel"

It is, I would argue, quite unremarkable that such widely-known foreign systems should have been represented in Cyprus, owing to its location. It is even less surprising that several systems should be represented on the two excavated Bronze Age shipwrecks, which were small merchantmen that plied the eastern Mediterranean and needed to be metrically conversant in all the ports where they docked. The existence of the Egyptian qedet is beyond doubt in this region; it is one of the oldest and best-regulated systems known, dating at least from the 3rd millennium BC. We have also strong indications of the Palestinian necef at something over 10 grams (even though its wide tolerance is not as satisfying as that of the qedet); and finally, and most intriguingly, a unit well over 11 grams. it was argued in the 1950s by Heinrich Otten on the basis of epigraphic evidence that there was a Hittite system whose structure was peculiarly vigesimal, that is, based on the number 20 or 40. The Italian scholar Nicola Parise has argued that there was an explicit 4:5 ratio between the Egyptian qedet and the Hittite "shekel"; and our quantal run in this case might well suport this notion. What is particularly interesting, however, is that the sum total of published balance weights from Hittite sites is meager indeed, and the data appear to be equivocal on the existence of a unit of just under 12 grams. It is noteworthy indeed that such a figure should emerge from the quantal evidence.
      From the perspective of the Aegean Sea, the lack of evidence in Cyprus for any representation of a metrical system based on a unit in the vicinity of 61 gm. is striking. The evidence for metrical connections is conspicuous by its absence, and leads one to wonder about the nature of commercial relationships between these two areas. But speculation in this realm is premature, since we know all too little about later Mycenaean system(s) of weight from the artifactual standpoint. It would also be premature at this point to invoke a distinct and different system of weight for Cyprus; all indications at present are that other standards, long in widespread use in the eastern Mediterranean, were adopted in the island during the Bronze Age.
      The common, and crucial, methodological error in historical metrology as it has been practiced in this area of the ancient world is that it has been done subjectively, with attributions often arbitrarily made on the basis of goodness-of-fit. Modesty compels me to note that other scholars have intuitively proposed some of the standards listed above for Cyprus. What I have tried to do here falls less within the realm of discovery than within the realm of clarification and quantification. The statistical function that I have described here will permit ancient metrology in this area of the world to achieve a solid quantitative footing.

      Finally: We might say a word about broader implications of historical metrology in archaeology, on a rather more abstract level. The point was made above that systems of weight are tools of industry and ultimately of trade. But they are much more than that. A metrical artifact--be it a balance weight, a graduated vessel, or a linear rule--is the concrete expression of the purely abstract concept we call a number. As such, these artifacts provide us with a glimpse into the way ancient peoples' minds worked in matters of quantification. Metrical artifacts are extremely valuable for prehistoric archaeology, where we have no written corroborative resources to trust. These objects show how prehistoric people mapped their world, ordered the chaos of their environment, their buildings, their raw materials, their foodstuffs, their medicines, and their finished manufactured goods. Now there are many ways to divide up the chaos of our surroundings. The Bronze Age peoples of the Aegean Islands seemed to have had a distinctly duodecimal turn of mind: the number 12 figures prominently in their metrology, just as the dozen is popular among us today. By contrast, the Egyptians, from the Old Kingdom on, had a very practical decimal orientation to their world--they used hieroglyphic characters for all the powers of ten up to one million. In the Bronze Age Indus Valley, weights were binary in sequence: 1, 2, 4, 8, 16, 32, 64, etc. That was a simple and elegant system indeed. The Babylonians, as is well known, popularized the Sumerian sexagesimal system, based on the number 60. Such a number might strike us as slightly cumbersome, but of course we ourselves work every day with the number 60: Our circle is divided into parts based on the number 60, and the number 60 figures prominently in the way we reckon time. (Its advantage comes in the fact that it is divisibile by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.)
      In the end, all these approaches to quantification have good reason to exist: Each represents a particular solution to a particular problem. If balance weights are the stuff of applied science, then they reflect necessarily a subtle and systematic perception of number--in other words, the foundations of pure science.

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