Theories and practices of measurement in ancient sciences
New evidence for Late Babylonian metrological practices
The Babylonian units of measurement (length, area, volume, weight, etc), are grouped together in metrological systems. Various metrological lists, tables and problem texts provide evidence for Babylonian computational practices involving measured quantities. In principle, computations were performed in floating sexagesimal place value notation, without any reference to units. The conversion from measurement unit to sexagesimal number was achieved by means of conversion tables, in which a sexagesimal number is assigned to each unit. These practices are well understood for the Old Babylonian period (1800 BC), but not so for the Late Babylonian period. I will present a selection of unpublished Late Babylonian tablets that shed new light on this issue and discuss possible connections to measurement practices in Babylonian astronomy.
Counting the stars and measuring the water – the invention of clocks, hours and a calendar in ancient Egypt
Considering the role of time measurement in the modern world it is hard to imagine a life without a clock. Nevertheless, the development of this practice and its techniques in pre-modern times display a diverse picture. Yet the role Egypt and its religious culture played in this is most often underestimated. Not only the civil calendar, but the division of day and night into 12 hours is to be found there for the first time. As a precondition, this calendar and the 12-hour system provided the primary basis for the invention of clocks. Initially, the observation of the stars and then the development of the first independent time measuring device – the water-clocks – originated in a purely religious context. The necessity of timing prayers and sacrifices at night in order to guarantee a perpetual cosmic circle and thus life itself forced the Egyptians to find practical solutions. These turned out to be groundbreaking. As shown by a water clock from the time of pharaoh Amenhotep III from the temple of Karnak as well as a number of identical specimens from the Early Hellenistic period, this cultural technique found its way from the closed circle of Egyptian priests to prestigious courts in the ancient world. This fundamental step took place initially in Hellenistic Alexandria, when religious necessity was turned into the display of technological knowledge. From this moment on, the ability to measure time played a key role in the display of political and cultural superiority up until modern times. Water-clocks are to be found in the centres of the ancient world, at Alexandria, Athens and Rome. This instrument survived even until the end of antiquity – at least in the eastern Mediterranean in Constantinople and in the Arabic capitals of Spain, North Africa and the Near East. From there, the ability to measure time by the use of a water clock was re-introduced into Western Europe in the medieval period. In this way, this Egyptian instrument has since provided a foundation for the further development.
From shipping routes to the map of the world: time and distances in Ptolemy’s Geography
Seas played a crucial role in the development of Hellenistic and Roman geography. “It is the sea,” wrote Strabo, “more than anything else that defines the contours of the land and gives it its shape, by forming gulfs, deep seas, straits and likewise isthmuses, peninsulas and promontories”. Many ancient geographical works were indeed modelled on periploi; the description of the world followed the coastline from place to place as though guiding the reader on an imagined sea journey. However, the practice of navigation was not only used as a literary trick for scholarly treatises.
The geographical knowledge that arose from shipping routes significantly shaped the mathematical construction of the ancient world map. Although Eratosthenes used astronomical observations and land distances to estimate the earth’s circumference, the corpus of maritime distances elaborated from the Classical period onwards served notably the development of mathematical cartography, though in a less visible way. Ptolemy’s geographical coordinates are less the product of astronomical determination of latitude and longitude than of the re-elaboration of the geographical information taken from shipping routes.
Instruments and methods used by land-surveyors to measure the roads of the Roman Empire could not be applied at sea. Maritime distances were mainly elaborated from time measurement, based on the empirical practice of navigation and on scales of conversion from time to distance. This paper aims to investigate how useful distances for geographers emerged from the shipping routes network and contributed to the construction of Ptolemy’s map. Moreover, I will use the occasion to discuss the approach of Marcian of Heraclea, a geographer active in the fifth or sixth century AD, who read Ptolemy’s maps and used them to reconstitute a set of distances and compose a periplous of the known world.
The invention of latitude: Eudoxus’ measurement of the ‘inclination of the universe’
The first Greek cosmological thinkers imagined a flat earth placed in the centre of the celestial sphere. However, from the sixth century BC, the broadening of Greek horizons through the development of north-south sea routes and the exchanges with other cultures (especially Egypt and Babylon) made clear that the height of the constellations in the sky varies according to the position of the observer. Since the constellations were imagined as fixed on the celestial sphere, this variation in inclination was attributed to the observer, not to the stars themselves: this realisation opened the way to the understanding of the spherical shape of the earth.
How did Greek astronomers quantify the variation in the inclination of the celestial sphere depending on the position of the observer? We are now accustomed to express this value in terms of terrestrial latitude, i.e. as the angular distance between the point of observation and the terrestrial equator. Greek astronomers, having no clue to measure directly the observer’s latitude, attempted to quantify his inclination with respect to the celestial sphere itself. The first attempt in this direction is attributed to Eudoxus of Cnidus (fourth century BC). Eudoxus sought to measure the observer’s inclination with respect to the celestial sphere by defining his position in relation to the path of the sun in the sky. This relation can be expressed through the maximum length of day and night at a given place on earth, varying from 12 equinoctial hours on the terrestrial equator, to 24 equinoctial hours at each one of the terrestrial poles.
My paper will attempt a reconstruction of the method Eudoxus may have used in order to establish the maximum length of day and night at a given place on earth, based on the measurement of the equinoctial shadow of a gnomon. I will argue that Eudoxus used a purely geometrical model, approximating his results by means of a geometric construction called analemma. Though explicitly attested only in later sources (Vitruvius, Heron, Ptolemy), this simple construction was probably already well known to Hellenistic astronomers: in my opinion, its use can account for Eudoxus’ results in a way much less complicated than other arithmetical methods hitherto proposed.
Roman Exceptionalism? Concern to Know the Hour
The paper stems from a claim – evidently not articulated or explored in scholarship to date – that concern to know the hour throughout the day has been overlooked as a distinctively Roman preoccupation, a strong one moreover which long predates the generally recognized emergence of such concern in 14th/15th century Europe.
Three concise sections follow. First, a demonstration that there is insufficient cause to limit this Roman preoccupation (as some continue to maintain) in one way or other to the elite, or to urban contexts, or to just a very few among the 12 hours; by the same token, it does not matter that these hours are ‘flexible’ ones of varying length according to season. Second, comparison with the seemingly less marked attention paid to knowing the hour in earlier or contemporary societies of the Near East, Egypt (the concept of the hour having originated in either or both these regions) and Greece. Third, discussion of possible means and routes by which attention to knowing the hour was transmitted to Rome, as well as how, when and why this awareness became a preoccupation which spread throughout the Roman world and persisted there for centuries.
Nemroth mesuravit omnem causam celi per suum intellectum: Number and Measurement of the Universe in the Liber Nemroth
This declaration of the first chapter of Liber Nemroth immediately states that the central objective of this cosmological and computistic dialogue is to re-create the universe and to explain it by measurement and number, since its creation. This strange unedited work, written in a poor Latin, has experienced several redactions, including perhaps a Carolingian one, produced around the series of eclipses of 806-809. Two versions of a highly illustrated version with diagrams have reached us. The cosmological doctrines, the measurements of celestial magnitudes, and the methods of measuring space and time that they convey refer to techniques foreign to the Greek and Roman experience, with identifiable data of Syriac origin alongside more traditional elements of medieval computus.
The paper aims to gather and analyse many passages of the text that involve the measurement of time and space, the planetary distances and recurrences, the terrestrial cues and measurements, and to highlight methods and their cultural origin.
Cette déclaration du premier chapitre du Liber Nemroth annonce d’emblée que l’objectif central de ce dialogue cosmologique et computistique est de re-créer l’univers et de l’expliquer, depuis sa création, par la mesure et le nombre. Cette œuvre étrange et inédite, écrite dans un latin malhabile, a connu plusieurs rédactions, dont peut-être une carolingienne, produite autour de la série d’éclipses de 806-809. Deux versions d’une rédaction très illustrée de diagrammes nous sont parvenues. Les doctrines cosmologiques, les mesures des grandeurs célestes, et les procédés de mesure de l’espace et du temps qu’elles transmettent renvoient à des techniques étrangères à l’expérience gréco-romaine, où des données d’origine syriaques sont identifiables aux côtés d’éléments computistiques plus traditionnels dans l’Occident médiéval.
La communication vis à rassembler et analyser les nombreux passages du texte qui font appel à la mesure du temps et de l’espace, aux distances et récurrences planétaires, aux repères et mesures terrestres, et à mettre en évidence les procédés et leur origine culturelle.