Systems of Weight in the Bronze Age Aegean, Part 1:

An Introduction to the Archaeological and Epigraphical Evidence


Karl M. Petruso, University of Texas at Arlington


      One of the areas of research that has occupied me over the past 25 years is a rather arcane one: historical metrology, the study of measurement systems of past cultures. As practiced by scholars over more than a century, historical metrology has often been technical in the extreme, and very esoteric. It need not be so, as I shall try to demonstrate below in the context of a project that occupied me in the writing of my doctoral dissertation in Greece, and subsequently doing research in Cyrpus. Such research has much to tell us about early cultures that might not be immediately obvious.
      What follows is an essay on some of the more interesting case studies in ancient metrology that have occupied me on and off since the mid-1970s. The reader who desires a closer look at this material and a more scholarly presentation with references is referred particularly to my book, Keos, Vol. VIII. Ayia Irini: The Balance Weights(Mainz am Rhein: Philipp von Zabern, 1992), and its bibliography, which cites my more specialized articles. A later study which employs the quantitative approach I have relied on in presentation of the material below is the doctoral dissertation of Cemal M. Pulak, Analysis of the Weight Assemblages from the Late Bronze Age Shipwrecks at Uluburun and Cape Gelidonya, Turkey(Dept. of Anthropology, Texas A&M University, 1996), which is a throrough examination of two large groups of balance weights from the mid-14th and late 13th centuries BC.

      Historical metrology had its formal origins in the mid-19th century. The German scholar Friedrich Hultsch collected the evidence in Greek and Roman testimonia for the names of units of length, area, weight, and volume, and published exhaustive works on the units and their uses in the classical world. He had only passing interest in the archaeological data, however. This would not be expressed for another generation, when Sir William Flinders Petrie became intrigued by the thousands of recognizable metrical artifacts he himself had excavated in Palestine and Egypt in the late 19th and early 20th centuries. Petrie published a very useful monograph in 1926 entitled Ancient Weights and Measures. Based upon his statistical analysis of marked metrical artifacts--linear rules, graduated pots, and, above all, stone and metal balance weights--Petrie put historical metrology on an empirical footing for the first time, relying on the archaeological data for determining the absolute values of the standards in antiquity and the mathematical structures that governed their use.
      There have been some odd contributions to this endeavor as well, largely, I think, a product of the seduction of numbers. A book appeared in 1955 entitled Historical Metrology. The author, British civil engineer A.E. Berriman, contended that all metrical systems throughout history and throughout the world, are related. This was a hyperdiffusionistic thesis, and I have never understood why the book achieved the prominence it did. The implicit assumption in this and similar, more recent works (e.g., Lyle Borst's Megalithic Software, a book that appeared in the 1970s) was that contiguity implies continuity. I would argue that we must be very cautious in invoking this possibility.
      When I began my attempts to decode the system of weight used in the Bronze Age Aegean, I did so rather intuitively. I sought to answer two fundamental questions: The best way to do this, I reasoned, was to search for patterns. The fieldwork for the dissertation research consisted of traveling about Greece and the Aegean Islands for two years, identifying Bronze Age balance weights from archaeological sites and weighing them on my own laboratory balance.
      In the course of spending hundreds of hours hunkered down over a pocket calculator, I came to the conclusion that there is some advantage in approaching this subject with a certain amount of ingenuousness and naïvete. I read some years ago a biography of the architect and visionary R. Buckminster Fuller. He wrote that he had had very poor eyesight as a child, and did not get eyeglasses until he was 10 or 11 years old. He thus was unable to see details, and was forced to deal only with broad visual patterns. And he began to think in broad patterns as well: he saw forests, not trees, and was led to propose innovative, nonlinear and comprehensive solutions to large problems, rather than piecemeal and discrete solutions to parts of problems. This was an incidental comment in his biography, but it has stuck with me. What was for Fuller a highly productive but involuntary stimulus--the inability to cope with detail--became for me a voluntary handicap. I maintain that we must be concerned at one level with large patterns, and not minutiae. We must put on glasses that make the data somewhat fuzzy, and squint as we look at them. As it happens, ancient--and especially prehistoric--metrology happens to lend itself very nicely to self-imposed naïvete.
      Patterns are fascinating, and seductive. We have a natural tendency to want to isolate them. This is what we do at a fundamental level of scientific observation. But where patterns do not exist, we have an urge to impose them anyway. For the historical metrologist, this can present dangers. We must be aware constantly of this urge, and must ask ourselves periodically whether we are discovering patterns, or merely inventing them, in order to make the chaos of existence comprehensible and ultimately meaningful. To put it another way: Are mathematical patterns revealed to historical metrologists, or are they imposed by them?
      With these questions in mind, let us make one final aside, about the relative reliability of archaeological data, with respect to their potential to inform on the standard units of an ancient system of measurment and the mathematical structure on which the system is based.
      Tthe table below presents two lists of archaeological sources for deriving ancient systems of measurement.

   IMMEDIATE EVIDENCE      DERIVATIVE EVIDENCE   
Balance weights
Weighed items
Linear rules
Architecture
Graduated vessels
Standardized pots

'Immediate evidence' is the name I give to those artifacts that can provide unequivocal information as to the standards and structures of the systems they represent. These artifacts are relatively rare (they are listed in order of the likelihood of their preservation archaeologically and hence the likelihood that we will be able to recover the systems they represented). In the second column I have labeled, under 'Derivative evidence,' those indirect sources for our decoding of metrical systems. These items--such artifacts as coins and ingots; architecture; and pots of standardized size and capacity--are listed in order of their reliability as sources of evidence, from most to least reliable. Both mass and length are measured on a linear scale; capacity is more slippery in its potential indications since it is usually established in terms of spans of length and/or mass. One thing that must be kept in mind in dealing with such artifacts is that we do not know, a priori,whether or not they were, in antiquity, metrically configured--that is, whether they were manufactured according to some standard, as opposed to having been manufactured without regard to any metrical standard. A coin, a building, or a pot might or might not be metrically configured; it is our first task to determine whether it was or was not. For this reason, I take as the most important lines of evidence as to ancient metrology the metrical artifacts themselves, that is, the items in the first column. Of these, balance weights are the artifacts by far best represented in the archaeological record. Hence, they are the most accessible and reliable witnesses for our investigation into early cultural metrics.
      Let us now turn to two case studies. They will be presented in order of difficulty--first, a best-case scenario, and second, a worst-case scenario. We shall start with the Minoan Bronze Age, in the Aegean, where we are fortunate enough to have two lines of evidence that converge to enable us to produce a particularly complete picture of weight metrology. The artifacts dealt with here date to the Middle and Late Aegean Bronze Ages, from roughly 1700 to 1200 BC, and were excavated at approximately two dozen sites in Crete (e.g., the palaces of Knossos, Mallia, and Zakros) the Cycladic Islands (primarily Keos and Santorini), and mainland Greece (notably Vapheio and Mycenae). While the island of Crete and the Greek mainland developed material cultures that were distinct from each other in many ways, and the natives spoke different languages, they were in frequent economic contact both with each other and with the other polities in the eastern Mediterranean in the second millennium BC. This was a period often characterized by scholars as international in spirit; there was likely a fair amount of pressure in this cosmopolitan region to adopt or adapt successful technological and commercial processes and customs. The evidence of the tablets which will be detailed below comes largely from the thirteenth century, but it is clear that methods of accounting had been standardized long before then.
      The first line of evidence that bears upon our investigation is the masses of the Minoan balance weights (those that are well-enough preserved to make us confident that they are at or close to their originally-intended masses), and more particularly, the ratios that relate them to one another. Nearly 200 identifiable Aegean balance weights (mostly simple disks of lead or stone) are catalogued and tabulated in my book (cited above). Happily, many of these disks bear markings which can be read as numbers. These markings have helped to confirm the attribution of standards, fractions and multiples that can be derived on mathematical grounds alone. Click here to view a table summarizing the most important marked weights and their interpretation.
      In short, the strictly metrological analysis of the weights and the ratios by which they are related indicates unequivocally that the main designated unit was in the vicinity of 61 gm. Dozens of marked and unmarked examples answering to multiples of 2, 4, 6, 8, 12, 16, and 24 times this mass; and fractions of 1/4, 1/3, 1/2, 2/3, and 3/2 are known, many of which are also marked. A duodecimal "flavor" is apparent in the way these weights related to one another in the area under consideration.
      But the line of evidence that has both complemented and confirmed the analysis of the masses and ratios that relate them comes from readable contemporary texts in the form of clay tablets written in the script known as Linear B, which renders an early form of Greek. Even before Linear B was deciphered in the 1950s, Dr. Emmett L. Bennett of the University of Wisconsin was able to derive the principles of accounting with which most of the tablets were concerned. He determined the relative values of measures of weight and capacity (volume) in the texts--the Mycenaean versions of pounds and gallons, as it were--and their multiples and fractions. With a large corpus of identifiable balance weights that had been weighed to a uniform standard of accuracy, I was now able to look for correspondences between the artifacts and the accounts. An obvious first question to be asked was whether we might at last be able to identify in the balance weights the denominations mentioned in the tablets.
      The Linear B symbols used for measures of weight (indicated by their conventional Latin letters) are tabulated below. The names of the denominations (based on the later Greek talantonand mnaare conveniences only; we do not know what the Bronze Age Greeks called these denominations. For a fuller treatment of the evidence for weights and measures in the Linear B tablets, the reader is referred to Michael Ventris and John Chadwick, Documents in Mycenaean Greek,second revised edition (Cambridge: Cambridge University Press, 1973, pp. 53-60; and John Chadwick, The Mycenaean World(Cambridge: Cambridge University Press, 1976), pp. 102-108.

LINEAR B
SYMBOL
DENOMINATIONMASS (gm.)FRACTION OF
TALENT1
FRACTION OF
PRECEDING
DENOMINATION
( L )
Talent

29000        

1 / 1
--
( M )
Double Mina

967        

1 / 30
1 / 30
--
Mina

483        

1 / 60
1 / 2
( N )
Half Mina

242        

1 / 120
1 / 2
( P )
1 / 24 Mina

20.2    

1 / 1440
1 /12
( Q )
1 / 144 Mina?2

3.36  

1 / 8640
1 / 6

1 The fractions in this column are very complex and unwieldy; surely palace stewards and scribes reckoned denominations in terms of their relationship to the next larger or smaller denomination (shown in the fifth column).
2 This denomination, and hence its calculated mass, is rarely attested and is conjectural.

      It is noteworthy that the all of the ratios of the major units predicted in the table above by Bennett are attested in the masses of many specimens in the corpus of Minoan balance weights (including, curiously enough, a stone disk from Crete which weighs 3.6 gm. and whose markings, I have argued, can be read "1/6"). Puzzlingly, however, there is no identifiable Linear B symbol for a denomination of about 61 gm. in the tablets, although such a mass is quite comfortable as 1/8 of the mina. I am as yet unable to offer a compelling explanation for this discrepancy; the possibility exists, however, that it is not a discrepancy at all. The palace accounting system was an official one whose primary function was to tally goods and raw materials in the palace storehouses for the tracking purposes in the Bronze Age system of economic redistribution. It is possible that the unit of about 61 gm. had its own common everyday uses in the economy whose use is now lost to us. Many examples can be cited of this phenomenon in metrical systems old and recent, for instance, measuring the height of a horse in hands, or counting by the dozen.


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