Symmetries in Images on Ancient Seals

Symmetries in Images on Ancient Seals Amelia Carolina Sparavigna Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy E-mail: amelia.sparavigna@polito.it Abstract: We discuss the presence of symmetries in images engraved on ancient seals, in particular on stamp seals. Used to stamp decorations, to secure the containers from tampering and for owner's identification, we can find seals that can be dated from Neolithic times. Earliest seals were engraved with lines, dots and spirals. Nevertheless, these very ancient stamp seals, in the small circular or ovoid space of their bases, possess bilateral and rotational symmetries. The shape of the base seems to determine the symmetries of images engraved on it. We will also discuss what could be the meaning of antisymmetry and broken symmetry for images on seals. Keywords: Symmetry, Seals, Antisymmetry. 1. Introduction We can find symmetries in human artifacts across time and cultures. As widely discussed, this is considered as due to a biological significance of symmetry [1,2]. The simplest symmetry, the bilateral one, seems to be deeply connected with the human perception of health and then beauty of living beings. Humans are very sensitive to the presence of symmetry in images [3] and many speculations about the mechanisms underlying the vision of symmetry have been proposed as proposed [4,5]. This human sensitivity to symmetries not only gives rise to an aesthetic sense of pleasure, when good proportioned and balanced forms are observed [6], but also stimulates the use of symmetries in science [1]. In physics symmetry means the invariance of the physical laws under specific transformations. Conservation of energy, momentum and angular momentum can be viewed as a consequence of symmetry for continuous translations in time and space and for rotation, according to the Noether's Theorem. In quantum mechanics, wave functions can be either symmetric or antisymmetric, depending on particles' spin. Particles with antisymmetric wave functions are called fermions and obey the Pauli exclusion principle. Particles with integer spin have a symmetric wave function and are called bosons. In solid state physics, discrete symmetries govern oscillations of the atomic structure and mechanisms of charge and energy transport. Studies on the symmetries in pottery decorations have been already performed. Important to identify the period of a certain culture, symmetries have a practical use in the restoration of damaged materials. In this paper, we will discuss the presence of symmetry in other ancient artefacts, the stamp seals. Considered as a form of art of non-primary importance, engraved images can be not only beautiful but also rather important for archaeological studies, because, as pottery, they are durable artefacts. Ancient stamp seals and cylinder seals were made of a hard material and used to press an engraved figure into soft clay, for securing purposes [8], or, as for early Neolithic seals, to stamp decorations on leather and textile. It is possible that they were used to stamp non-permanent tattoo, as guessed for seals found at Çatalhöyük (7500-5700 BCE) [9]. This use is guessed also for pre-Columbian seals [10]. Cylinders firstly appeared in Mesopotamia in the late 4th millennium BCE, then widespread in Syria and Egypt and in the Aegean area. Stamp seals preceded cylinders. Early stamp seals were used in Persia, northern Syria, and Anatolia [8]. In Egypt, the scarab seals largely replaced cylinder seals early in the 2nd millennium BCE and continued as the main type, till they were replaced by the signet ring in Roman period. For Egyptians, the scarab seal was not only an impression seal: it was also an amulet with images and symbols engraved to protect the owner [11-14]. Egyptian scarabs have inscriptions, human and animals figures. Many scarabs of the Middle Kingdom Period have the base decorated with coils and entanglements of cords: these seals display bilateral and two-fold rotational symmetries (see Fig.1). Seals collections are seldom published in public domain, then it is impossible to be exhaustive in describing symmetries displayed by these objects. In this paper, which is just an introduction to more detailed researches, let us try to follow a time-line to see if any evolution in decoration symmetries was present and what are the constrains imposed by the shape of the seal. Figure 1. Seals of the Middle Kingdom with spiral coils and crosses, at the Egyptian Museum of Torino. 2. Symmetries and seals Images on stamp seals can display symmetries adequate with the shape of their bases. Mirror or bilateral symmetry occurs when the two halves of a whole are each other's mirror images. Rotational symmetries occur with respect to rotations in the space: rotations are about an axis perpendicular to the 2 plane of the image. We find a two-fold sy

…(Full text truncated)…

This content is AI-processed based on ArXiv data.