 According to Wikipedia, emergence is conceived as a process whereby larger entities, patterns and regularities arise through interactions among smaller or simpler entities that themselves do not exhibit such properties. In the previous section we discussed how synergistic relations give rise to the phenomena of two or more elements having a greater combined output or effect than the simple product of each in isolation. This process whereby the interaction between elements gives rise to something that is greater than the sum of their parts is called emergence. So whereas when we were talking about synergies, we simply said that the combined effect was greater than its parts in isolation. The concept of emergence though implies that what is created out of these synergistic relations is not just quantitatively different, it is in fact qualitatively different. That is to say, none of the elements that contribute to the emergence of this new phenomena have its qualities when taken in isolation. There are many examples of this, but maybe the simplest is the example of water. Water is made up of hydrogen and oxygen atoms. Other of these two elements that make up the system have the property or quality of wetness, but when we combine them we get a substance called water that has the quality of being wet. This property of wetness has emerged out of the interaction of the system's elements and it only exists on the system's level. Another often cited example of emergence is the phenomena of life. Physical systems such as a plant cell consist of a set of inanimate molecules, none of which in isolation have the property of life, but it is the particular way that these elements are arranged into structures and processes that enable the emergent phenomena of the living system as an entirety. Our world is full of examples of emergence that we could cite, from ant colonies to galaxies and cultures, but all of these are types of structures, whereas emergence is really a process. These systems are then the product of a process of emergence that has played out to create two qualitatively different levels to the system. Emergence then is a process through which systems develop or we might say grow. During this process, unassociated elements interact, synchronized to form synergies, and out of this emerges some new and novel phenomena that previously did not exist. In order to create some qualitatively different and new phenomena, the system must go through what we call a phase transition. A phase transition is an often rapid or accelerated period during the process of a system's development, either side of which the fundamental parameters with which we describe the system can change qualitatively. Again, there are lots of examples of this, such as the phase transition between solid and liquid that a substance goes through when heated, but maybe the most dramatic example is the metamorphosis of a butterfly, from being a caterpillar to a mature adult. Not only does the system's morphology change, but the whole set of parameters that we define it with are so drastically altered prior and post the phase transition that we give the creature a whole new name. This illustration helps to bring us to another important theme within emergence, that is the distinction between what is called strong and weak emergence. Strong emergence describes how the emergent phenomena can be traced back to the individual elements, meaning we can predict and observe higher level emergent phenomena just by looking at individual components. In contrast, strong emergence, also known as irreducible emergence, states that these phenomena cannot be reduced to the individual components. Instead, the emergent phenomena are traced back to the interactions between the multiple components so, quite literally, cannot be predicted in any sense by looking at the components on their own. Consciousness is often cited as an example of strong emergence. It would appear that without prior knowledge or experience of what consciousness is, it would be virtually impossible to understand the vastly complex and subtle system that is human consciousness by analyzing the properties of the very simple neurons that formulate it. This distinction between strong and weak emergence may also be formulated within the language of information theory, where weakly emergent phenomena are essentially computable. That is to say, if we had sufficient information, we could simulate them. In contrast with strongly emergent phenomena, no amount of information could predict or formulate the end result of the process prior to its completion. The discussion of strong and weak emergence leads us to another key theme in system theory that is hierarchy, the distinction between micro and macro and top-down versus bottom-up causality, all of which we will be talking about in the next lecture.