 In this last lecture to the course, we're going to wrap things up by giving an overview to the application of systems theory to the various domains of science, what is called systems science. Systems theory is a formal language, meaning like other formal languages such as mathematics, it is independent from external reference to any subject matter and thus is solely dependent upon its own internal logic. If this logic is consistent then it works. If there are logical inconsistencies within the syntax of the language then it does not work. The same should be true for any formal language such as the algorithms that run your computer. If there is an error in the program's logic then it will crash the system. Although the term science in its broadest definition may be used to include the formal languages, it is essentially an empirical endeavor, meaning that it is dependent upon reference to some subject matter in order for its validation. Thus the vast majority of people who call themselves scientists spend their time amassing or analyzing empirical data. Whereas the formal languages are independent from empirical science, science works best when it is supported by some formal language and mathematics as we know is the formal language that supports most of modern science. Mathematical proofs are considered the gold standard in terms of scientific validation. Since the turn of the 20th century, set theory has been the de facto foundation to mainstream mathematics. As we have discussed previously, set theory and reductionism paradigm are suited to the modeling of certain types of systems. Thus, modern science supported by mathematics does a very good job of describing the simple deterministic systems that we have to deal with in the natural sciences. Areas like chemistry and, particularly physics, represent powerful, sophisticated and well developed frameworks. But other areas of science, most notably the social sciences that have to deal with non-deterministic, highly interconnected and emergent systems, either try to mimic the natural sciences as mainstream economics does or are left with very little in the way of formal foundations out of which to build any kind of robust framework. Another aspect to the way modern science has developed under the reductionist paradigm is its fractured nature. Science is today a highly specialized and compartmentalized activity. Of course, there is nothing wrong with specialization, but when the knowledge and expertise of one domain are very disconnected from those of another, then science as a body of knowledge can become too focused on the trees without seeing the forest. Science serves a function within society and ultimately a society needs answers to not only these analytical questions, but also to bigger questions, such as the nature of order and chaos in our universe or how the different domains of knowledge really relate to each other. The reductionist paradigm offers us limited means to approaching these bigger questions and if science can't provide society with plausible answers, then people will look elsewhere and it would have failed in providing us with an integrated picture of how the world works and not just a one-sided picture that reduces everything to some simple interaction between physical components. This is where system science comes in. With its holistic approach, it lets us focus less on specialized knowledge within specific domains and more on how these domains fit together, often through the idea of integrative levels. Thus, system science is a much more interdisciplinary form of science, being more relevant when we are dealing with phenomena that cross the traditional domains, such as ecology that doesn't confine itself to dealing with biological systems, but also recognizes the important interplay between human industrial activity, the biosphere, and the abiotic geosphere. Thus, the area of system ecology has proven one of the most successful areas within the system sciences. Another interdisciplinary domain system science is proving particularly relevant too, is in the study of the interaction between people and technology. What are called socio-technical systems, whereas modern science has supported a technocratic view of the world, system science crosses the two boundaries to recognize the importance of the interaction between people and technology. This leads up to what can possibly be the system sciences greatest contribution to our scientific framework. For centuries, people have been trying to apply the success of modern physics to studying social systems with limited results. Traditional science rests upon an objective view of the world, that is to say removing the subjective interpretation of the view from the model. This works fine when dealing with inanimate objects, but of course there is a subjective dimension to almost everything that humans do. System science is philosophically sophisticated enough to deal with the difficult questions surrounding the subjective nature of the human condition that are required to truly tackle areas like psychology, cultural studies, and sociology. System science and traditional science are often cast in contrary terms, but of course they are two sides of the same coin. Developing a scientific framework powerful enough to describe our world in all its richness will require both the qualitative capacities of system science that allow us to properly contextualize things and the rigorous quantitative methods of analysis that allow us to properly compute this information with the net result being hopefully a fuller picture of how our extraordinary world works.