It is sometimes said that in interdisciplinary conversation, “iron sharpens iron”. When those trained in different intellectual pursuits meet for serious discussion, the result is often a sharpening of insight with respect to their own particular field, as well as a clearer perception of another. I was asked as a professional theologian to engage with the material in these chapters (and to take part in the symposium that led to them) with an eye to the Templeton Foundation's enquiry into ‘the roots of spirituality’ – the origins of religious belief and practice. The following is offered in the hope that, just as I gained an enormous amount from being plunged into the world of archaeology, those at work in that world might find it useful to consider their findings from the perspective of someone at work in the world of religion and ‘spirituality’.

It is far beyond the scope of a single chapter even to outline the various connections between religion and the material in these fascinating contributions. What I attempt here is something much more modest: to highlight some of the basic issues implied in any enquiry into the ‘religious’ or ‘spiritual’ dimensions of human behaviour, not least when the attempt is made to trace the links between archaeological data and religious activity. Especially illuminating in this respect, I am going to suggest, is the concept of ‘worldview’.

Remaining initially in the Indus Valley, Section III focuses on relationships between measurement, architecture, cosmology and belief systems. Some of the key finds of the earliest excavations at the Indus Valley city of Mohenjo-Daro consisted of weight and linear measurement systems. Drawing upon his own and others' recent work at the site, Michael Jansen outlines the nature of these systems and their relations to architectural structure. These can be considered in terms of their orientation, the dimensions of their constituent rooms, and the dimensions of the bricks from which they were constructed. The bricks maintain a consistent ratio of dimensions and were made in standardised moulds, with the average size being derived from the width of the hand. There appear also to be two different orientation systems, one of which orientates to the cardinal points, although these two systems may actually be related and orientated towards different elements or periods of the same celestial system. Indeed, the ‘great ring stones’ found at the site have been identified as ‘calendar stones’, not only part of a calendrical system but also serving the function of astronomical observation instruments associated with the cosmology of the region. Jansen highlights the need for cross-site comparisons within the Indus Valley if we are to understand better the significance of the measurement and orientation systems in use at Mohenjo-Daro.

Half a world away, Saburo Sugiyama elaborates on the use of standardised measure in the creation of the architecture of the Mesoamerican city of Teotihuacan, Mexico.

Introduction

The origins of certain types of weights and measures in South Asia can be traced back to the earliest cities of the Indus civilization. This chapter presents an overview of the types of artefacts that inform us about ancient Harappan measurement systems, in order to gain insight into their concepts of order and cosmology. The main focus is on recent discoveries at the site of Harappa, Pakistan, where detailed measurements have been made of a wide range of artefacts in an attempt to understand better the standardization and regional variation of Indus measurement systems.

The Indus civilization or Harappan culture refers to the first urban society that emerged in the greater Indus valley of Pakistan and northwestern India, between 2600 and 1900 BCE (Figure 9.1). After its discovery in the 1920s, in the course of excavations at the sites of Harappa and Mohenjo-daro (now in Pakistan), the Indus civilization was widely thought to have been one of the most highly organized urban societies in the third millennium BCE. This perception was based in part on general impressions about the layout of city streets, and the similarities of brick and weight sizes throughout the greater Indus valley. The north-south and east-west layout of the architecture and city streets, along with the relatively uniform proportions of baked bricks, was thought to reflect concepts of order, cosmology and standardization imposed by the rulers of the Indus cities.

In this chapter I investigate the possibility that the Aztecs constructed their ritual precinct at Tenochtitlan along the dimensions of sacred time. Saburo Sugiyama makes this point for Teotihuacan (1993; 2005; this volume), and I have made similar claims for even earlier centers (Clark 2001; 2004a, b). These proposals for Mesoamerican centers have relied on analyses of archaeological data to infer ancient units of measure and their numerical modularities. I reverse the procedure here and start with verified Aztec units of measurement and deploy them to propose numerical values for the dimensions of palaces, temples, and plazas. Discussion is organized in three parts. I first summarize the Aztec system of linear measurements. Next follows my evaluation of the dimensions of two palaces known from early historic records. Finally, I analyze the most current information for the ceremonial precinct of Tenochtitlan (now downtown Mexico City) in light of different native units of measure. These two applications of native measures to public architecture support the premise that the Aztecs, as did earlier Mesoamericans, built their sacred center to accord with the dimensions of sacred time.

Aztec linear units and their metric values

Aztec linear measures were calibrated to the human body, and in ways similar to the Spanish system to which it was later correlated. Both the Spanish and the Aztecs emphasized various arm measures, particularly the braza. A braza was two varas long.

The calendar(s) employed by the earliest known Chinese state, the Shang (ca. 1600–1044 BC), have been tentatively reconstructed from the divinatory inscriptions carved on bovine scapulae and tortoise plastrons. The calendar is woven into these inscriptions because they are all dated, and the forms and content of dating evolve over the few centuries in which the inscriptions were made (roughly 1300–1050 BC). These materials show the close interconnection of the measurement of time not only with divinations but with a broader range of ritual practice organized around the ancestral cult. They also present an interesting case in which we can observe the interplay among the calendar as a liturgical schedule, the calendar as a mode of divination, and the calendar as a measure of the cycle of lunations and solar seasons. In this chapter I will briefly sketch what the inscriptions reveal about the origins of the calendar in China and about the enduring impact of those origins on the uses of calendars and time measurement in Chinese civilization.

The earliest method of measuring and recording time in the inscriptions employs the sexagesimal cycle formed by the sequential and synchronized enumeration of a cycle of 10 graphs (later called the ‘celestial trunks’ [tian gan]: jia, yi, bing, ding, wu, ji, geng, xin, ren, gui) and another cycle of 12 graphs (later called the ‘earthly branches’ [di zhi]: zi, chou, yin, mou, chen, si, wu, wei, shen, you, shu, hai).

Introduction

When and how did humans begin to count? Where does arithmetic come from? Are humans innately endowed with arithmetical abilities or is human numerical cognition a strictly cultural achievement? To a large extent the answers to the preceding questions depend upon how precisely we define human numerical cognition and arithmetical abilities.

If by numerical cognition we refer to the property of approximation – that is, the capacity for a basic appreciation of changes in quantity and a simple number sense (oneness, twoness, and threeness) – then several lines of evidence in contemporary cognitive neurosciences clearly support the view that this can be considered to be an evolved, innate biological competence shared by human infants and other animals. For example, a number of studies show that both preverbal infants and animals are able to detect numerocities, discriminating between small sets of objects or sequences of sounds both within, but also beyond, the so-called subitizing range (up to three or four objects) (Antell & Keating 1983; Wynn 1996; Davis & Pérusse 1988; Brannon & Terrace 1998; 2000; 2002; Biro & Matsuzawa 2001) – provided that in the latter case the comparison ratios are large enough (i.e., infants were able to discriminate 8 from 16, but not 8 from 12 items) (Xu & Spelke 2000; Lipton & Spelke 2003). More characteristic might be the finding that infants as young as five months old (Wynn 1992), but also untrained rhesus monkeys, seem to have additive and subtractive expectations when they observe or choose between arrays containing small number of objects.

Introduction

Teotihuacan, an ancient and highly planned city in the Mexican Highland, has been the focus of varied archaeological inquiries. Those related to its genesis, including the causal factors behind the foundation of such a populous city at this particular location, are of concern not only to Mesoamericanists, but also to those who pursue general themes related to state formation, preindustrial urbanism, or the evolution of human cognitive systems. Ideological factors and an innovative system of urban planning were formulated and applied on a grand scale at Teotihuacan, as is suggested by its unique city layout, unprecedented monumental architecture, and consistent spatial orientations. Here I discuss an indigenous measuring system that the Teotihuacanos could have used to create their precise city layout and major constructions. With newly available data I identify a measurement unit used in Teotihuacan. I pre­sent my preliminary interpretations of the ideological principles underlying Teotihuacan's urban arrangement and suggest how the ruling groups of this city conceived their world in time and space and materialized their worldview in city planning. Teotihuacan is a source of exceptionally comprehensive data relevant to better understanding the cognitive structures of ancient Mesoamerican societies, compiled through the extensive excavation and consolidation of the city's major monuments, which are maintained for our benefit by the Mexican National Institute of Anthropology and History (INAH).

The concepts applied in prehistoric societies and early civilisations to quantify the number of things and their length (including speed and distance), volume and weight offer an important and direct understanding of the minds of the ancient people, the organisation of their societies and their contacts with the neighbouring cultures. However, analysing early quantification has never played a major role in archaeology. This is partly a result of the difficult evidence one is facing: the detection of ancient measurement in the archaeological record is surely one of the greatest difficulties to be overcome in the study of early quantification. This also holds true for early weight metrology. Nevertheless, the importance of this topic and its relevance for early societies have been acknowledged by more and more scholars in recent years. More detailed empirical work is needed before the establishment of broad theories and reconstructions becomes possible. For example, there are still many questions about the spread and adoption of the various weighing systems used in the eastern Mediterranean, in the Near and Middle East and in Europe during the Bronze and Iron Ages. It is still a matter of debate as to the earliest date from which weights were known and used in some parts of the world.

The conception and use of measurements are ­inherent within certain prehistoric activities. This chapter ana­lyses the skills and knowledge needed for seafaring in the Neolithic and questions how distance and time may have been conceived and measured in relation to the land and seascape. Our modern notions of measurement dictate the development of science, technology and religion, which in turn guide our comprehension of the world. For example, the question as to who we are has been reduced to what we are and the quest to identify the smallest particles that can currently be measured. That of where we are becomes the study of the universe and the largest conceivable measurements. This in turn connects to concepts of time, the speed of light, the creation of time and of course, the end of it. These lines of thought lead us to cosmology and world-view. Whilst we are still striving to think about these things let alone understand them, how do we begin to investigate how people in prehistory constructed measurement to understand their world?

One place to start is with the physical archaeological correlates for measuring practices: written records and measuring devices, for example, weights or calendars (as discussed in other chapters in this volume). Yet, in earlier prehistoric periods and in contexts where these are not preserved, we can still detect the early incidence and understanding of quantification or measurement through consideration of the knowledge and skills that underpin various activities.

The evidence concerning mensuration and numeration to be gleaned from clay tablets unearthed in and around Mesopotamia has much to say of profound importance for the history of human cognition, if indeed human cognition has a history and we are not merely tracing the results of individual endeavour. We should, for the sake of the perceived relevance of our disciplines, be prepared to state how our research might permit us to say something about ‘becoming human’, and I will, in particular, in the following react to the supposition of the editors of this volume who, when organizing the symposium from which these chapters are derived, wrote that

I will concentrate on the evidence pertaining to the measurement of distances and times in the heavens mainly from Mesopotamian, but also briefly from Greek, Indian, Iranian, and Chinese sources, and the implications thereof for ‘becoming human’. This will be preceded by some comments on the earliest evidence for numeration and measurement in Mesopotamia, matters that concerned the assembled delegates in particular, but first a note of caution must be sounded.

‘Measuring the World and Beyond’ was the official title of the conference that led to this book. In my response to the papers that became the chapters of this book and the discussion, I would like to focus on the phrase ‘and Beyond’ as a point of entry into the broader issue explored by this particular symposium and the project as a whole – the roots of spirituality. The archaeological insights gathered from data analysis around the globe shed new light on the extent to which the construction of modes of measurement in early cultures functioned as a new means of recognizing and engaging with the material world. How is this related to that which we experience as ‘beyond’ the world, ‘beyond’ measurement?

From a philosophical and theological point of view, it is not simply the emergence of the capacity for mensuration that makes early human cultures interesting but also, and even especially, the growing self-awareness among human beings of their lack of capacity in this regard. That is, the human construction of measurement may be a manifestation both of an evolutionary and an adaptive skill for controlling the environment and of an awakening to the recognition of the limits of adaptation mechanisms for manipulating the cosmos. Alongside the discovery of the susceptibility of the world to measurement arose the discovery of the concept of the immeasurable, which invites questions about spirituality and religious awareness.

The volume opens with a section that deals with the conceptualisation of number and measurement, how systems of thought and recording impacted upon the capabilities for measurement activities and numerosity in different parts of the world.

Direct archaeological evidence for measurement activities is the focus of the vast majority of the contributions to this book; however, it begins with a consideration of the extent to which measurement capabilities of various kinds are inherent requirements for other activities for which we have archaeological evidence – activities that do not themselves provide direct evidence of measurement. Amongst prehistoric hunter-gatherer populations there is no unambiguous direct evidence of numeracy of the kinds discussed in the other contributions to this volume, but many of the activities they carried out would have required various kinds of relative and absolute reckoning, including time, distance and division. This first chapter seeks to deconstruct measuring activities into key types, to identify the significant differences and interdependencies between them. It does so in the context of some of the types of reckoning and measurement that would have been required for activities that we know were essential parts of hunter-gatherer life and discusses how these should be conceived. The principal focus of the latter part of this first chapter is the identification of time, cycles and causal relationships, and how these impact on ritual practice and belief systems.