Ancient and Current Chaos Theories

Interdisciplinary Description of Complex Systems 4(1), 1-18, 2006 ANCIENT AND CURRENT CHAOS THEORIES Güngör Gündüz Department of Chemical Engineering, Middle East Technical University Ankara, Turkey Regular paper Received: 8. February, 2006. Accepted: 31. May, 2006. SUMMARY Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists) and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated. KEY WORDS chaos, randomness, dynamical systems, natural philosophy, ancient philosophy, information, biological evolution, nonlinearity CLASSIFICATION PACS: 01.70.+w, 89.75.-k *Corresponding author, η: ; (90) 312 210 26 16; Kimya Mühendisliği Bölümü, Orta Doğu Teknik Üniversitesi, Ankara 06531, Turkey G. Gündüz INTRODUCTION In the last three decades, the chaos theories have born, grown, matured, and revolutionized our understanding of natural phenomena. Classical physics, statistical physics, electromagnetism, quantum theory, and relativity also had great revolutionary impacts in explaining natural phenomena, but none of these had so rapid influence on the fields other than basic physics. In the past, it usually took some decades for the application of physical laws in applied sciences and engineering after their discovery. However, chaos theories soon found applications in almost all branches of technical, medical, and social fields, and also in arts. The term chaos is first seen in the Sumerian epic of Gilgamesh which is the oldest script strongly touching the fundamentals of human psychology and human’s understanding of the earthly and heavenly events. In one of the paragraphs of the epic, the Earth God complains to other Gods about humans, and says ‘humans have gotten so overcrowded, and they have run into dearth, starvation, and chaos, and they do not respect me; something has to be done’. Gods then decided to send water flood to extinct them. The flood of Noah in religious scripts is based on this story. In terms of chaos current theories, it is true that anything that multiplies can cause overcrowding and thus chaos, then the components becomes pretty much free from the general rules (the rules of the system or of Gods) [1]. It is possible to control the chaos, and to get out from it by external intervention of physical forces, i.e. Gods’ intervention in Gilgamesh epic. The chaos concept has been a fundamental metaphor for both natural and social events, and cosmogony in ancient societies. According to a Mesopotamian cosmogony, the conjunction of male Apsu which represents freshwater and of female Tiamat which represents seawater gives birth to Goddess Mummu who represents the chaotic fog and clouds. Mummu then gave birth to primitive ocean and water. First Gods came out from the primitive water, and one of them then became a creative God and created earth, stars, and all living things [2]. The Sumerians used to believe that the earth and stars were floating soil on water [3]. Similarly, the Egyptians also used to believe in that the universe was essentially water, and all stars were surrounded by water. There is also a phrase in Cor’an stating that the essence of all things is water. The Egyptians attributed a kind of philosophical meaning to the word chaos and thought that it is the primordial state before genesis, and it is the medium for the coexistence of form and structure. It is in fact a kind of reservoir in which all kinds of field forces and forms dissolve in infinitesimal time. In Genesis, it is understood as a coarse but homogeneous structure with feasibility [4]. In Hesiod’s Theogony, chaos meant an empty space or matter not yet formed. It was believed that order (i.e. cosmos) came out from chaos, which was also the beginning of time. RATIONAL THINKING The predominating elements of Middle East cosmology before rational thinking were: (i) unlimited and infinity, (ii) the basic element of all things, and (iii) chaos and order. In this respect, water was believed to represent all the properties described as such; and the first natural philosopher, Thales of Miletus, considered water as the element of everything [5]. He also thought that the earth rests on water as in the Sumerian cosmogony. Thales considered water to be an element, and also as something that all other things can be reduced into [6]. He used to visualize water together with a force that revives or moves it. In other words, the mover and the moving are not separated and they coexist in the same object [7]. Water as the sole material principle, has been objected by Anaximander, the second philosopher of Miletus. He introduced the concept of ‘apeiron, the unlimited or infinity’ and proposed that it is both a principle (arche) and an element. Apeiron is a kind of reservoir 2 Ancient and Current Chaos Theories where all varieties are not yet differentiated; they are entangled in the form of a composite state. Apeiron is like a tank of all qualities, and it serves to conserve all beings. He rejected the idea of a single element (like water) to be the founding principle of all existing. He claimed that the single element wouldn’t allow the appearance of others. According to him, any ‘elemental stuff’ can change into one or more of the other elemental stuffs, and every ‘coming into being’ is due to the change of a pre-existent. He, in fact, is the founder of a dynamic universe model by claiming the continuous generation of new things. Anaximander thought that the contradictions like earth (dry), water (wet), fire (hot), and air (cold) pre-existed before apeiron, and they were at fight (i.e. competition) with each other. He thus pointed the importance of four-stuff long before Empedocles. Anaximander also thought that the need for earth’s stability like water bears in some problems, and one needs something stronger than an analogy and deeper than a cushion of water [5]. He in fact thought the earth to be at rest at mid-space. He also claimed a kind of primitive biological evolution theory. The third philosopher of Miletus, Anaximenes, did not respect much the uncertainty in the apeiron concept, and he returned to more concrete basic e (...truncated)