 In a recent paper by the researcher Yannir Bar-Yam, he describes the study of complex systems as, a new approach to science studying how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships within its environment. For someone new to the subject, this might seem like a funny thing to be studying, but this definition goes to the heart of one of the key issues in complexity theory, what we call emergence. Emergence is of central interest to the study of complexity because complex systems are typically composed of many small parts distributed out without centralized coordination. In such systems, order is formed out of the local interactions that give rise to the overall organization, and we call this general process emergence. Thus, with complex systems, we do not search for global rules that govern the whole system, but instead how local rules give rise to emergent organization. To understand this better, we need to delve deeper into a discussion surrounding what we call holism and reductionism. Such a discussion is of critical importance to understanding the foundations to complexity theory as an alternative approach to scientific inquiry. One of the most basic observations that we can make about our universe is that things are made of parts. Almost everything that we are interested in is a composite of other things. If the workings of a whole system are not apparent to us, the obvious way to conduct some scientific inquiry would be to look at those parts and try to understand the whole by understanding these elementary components. But once we start to take things apart, we quickly find that those parts are also made of more basic elements. In trying to understand the human body, we have identified that it is made of different organs, which are a combination of tissues, which in turn are made of cells, which are formed of organelles, formed of molecules, which are formed of atoms, which are formed of elementary particles, and this quest for ever more elementary parts continues today in the search for little strings. The power of this approach is in looking for the most basic building blocks that are common to all kind of systems, and from which we would be able to form a description of all things in terms of some combination of a set of these elementary building blocks. This would then in some way fulfill the aim of science to create a unified description of our world. In this endeavor, we have made extraordinary progress. We now know that the same building blocks of elementary particles form the very wide variety of things that we encounter in our lives. From trees to cars to rocks to people to butterflies and waterfalls, all are made of the same fundamental particles. Physicists and biologists use these basic building blocks to form precise descriptions of how these systems work. In this scientific quest for a complete understanding of our world, we have come a long way and we have combined many previously disparate aspects of our world into a coherent picture of how they work as a function of some set of basic building blocks. This approach to scientific inquiry is called analytical reductionism, where we break systems down into their parts, study the parts in isolation, and then recombine them to form a description of the whole in terms of these elements. This is largely the story of modern science as it has developed over the past centuries and it is through analytical reductionism that we discovered the atom, that we developed the cell theory of biology, that we formulated the periodic table, that we have cured many diseases. Given the fundamental role that science has come to play within modern societies, this approach has come to extend our collective understanding of the world, how we manage organizations and design systems. For example, we divide universities up into different subjects. However, we have little understanding of how these different subjects are interrelated, for how they should be arranged so as to deliver an integrated learning experience for the student. This illustrates the limitations of the analytical approach. In focusing on the parts, it inherently downplays the significance of the relations between those parts and how they work as a whole. By becoming more analytical in focusing on the parts, we become more removed from the network of connections between things and the whole that they form. We get a detailed description of the trees and all the different types of creatures that might live there, but we fail to see the forest. To make a full-balanced inquiry, it is necessary to see from both the perspective of the parts and from the perspective of the relations that form the whole. A system is a set of elements and relationships between those elements through which they form a whole. Thus, when we look at a composite entity, like a tree or a chair, we could equally ask a different question from talking about the parts. We could ask how the parts are interrelated to form the whole organization. This is a very different way of looking at the world. This approach to reasoning about some entity is called synthesis. Where synthesis means the combination of components or elements to form a connected whole. This basic set of assumptions that support an approach to scientific inquiry is called a paradigm. Thus, we can identify these two different paradigms, one of analytical reductionism and the other of what we call synthetic holism. Synthetic holism, also called systems thinking. To understand why synthetic reasoning is of importance, we have to understand better this idea of emergence. Emergence is a process whereby novel properties, features, or structures are formed as we combine elementary parts. With emergence, when we put things together in a particular way, something new is formed that none of the parts has, and we call this newly combined organization an emergent phenomenon. For example, we can say that walking is a type of emergent phenomenon. In walking, we coordinate our two legs to enable our motion. However, with one leg, we cannot walk, we can only hop. But walking is not simply a combination of two hops. Walking is a qualitatively different form of motion from hopping. Walking as a system of motion is far more effective and efficient than two hops combined. This new pattern of motion that we call walking is an emergent phenomenon. The reason that walking is qualitatively different is that moving by taking two hops involves no coordination between the parts. While walking requires a very specific type of coordination where the legs are working together to enable the overall process to take place. We call this phenomenon where two or more elements are working together, a synergy. It is these synergistic interactions between the parts that adds or subtracts value from the whole organization and thus makes the whole something different from the parts. Such emergent properties are a product of the synergies between the parts and thus they cannot be seen to derive directly from the properties in interaction of the elementary parts but exist instead only as a global structure. In such a way, emergence gives rise to new levels with new properties, features and processes as we put component parts together. Such irreducible patterns of organization are called integrative levels. This idea of emergence reveals the need for synthetic reasoning and the inherent limitations of analytical reductionism. With analysis, we focus on the parts and assume that the whole is nothing more than the sum of the parts. Thus, traditionally areas like physics have focused primarily on component parts and not directly on higher level whole systems, tacitly assuming that such whole systems are nothing more than some combination of the parts. However, as soon as we recognize the emergence of new properties on different levels, this inherently requires us to switch our focus from not just studying the elements but also how those parts are interrelated into a whole and the new features and properties that emerge as we do this. How new whole social systems are formed out of relationships between people, the brain formed out of neurons, how financial bubbles are formed out of the interaction between traders, the weather formed out of air flows. Thus, we can understand how complexity theory really is on a fundamental level a new kind of science. One, that is Mr. Barr-Yam, puts it, studies how relationships between parts give rise to the collective behaviors of a system.