Welcome to our MOOC on complexity science created by the Complexity Institute at Nanyang Technological University in Singapore. I'm Steve Lansing. In this series of eight video lectures, you'll learn what complex systems are, their universal properties, and how we simulate, and model them. You'll also explore two practical areas where complexity science has greatly deepened our understanding of the world. In this first lecture, we'll start by providing a gentle introduction to complexity science. In an interview with a newspaper, the great physicist, Stephen Hawking was quoted as saying, "The 21st century will be the century of complexity." In one of his influential essays on science and society, Heinz Pagels wrote that, "The great unexplored frontier is Complexity." Adding, "that nations and people who mastered the new science of complexity will become the economic, cultural, political superpowers of the next century." To better understand why prominent scientists like Hawking and Pagels feel this way about complexity science, let's go back to Warren Weaver who, in 1948, wrote an essay entitled, Science and Complexity. In this essay, Warren Weaver broke the progress of science into three stages: problems of simplicity, problems of disorganised complexity, and problems of organised complexity. In the first stage, scientists around the time of Isaac Newton began to apply the mathematics of differential and integral calculus to understand problems of simplicity. An example of this achievement was to use the law of universal gravitation to explain the movement of planets around the sun. Solving the equation of motion for two masses, Newton showed that orbits around the sun are conic sections, circular or elliptical for planets, or parabolic or hyperbolic for comets and asteroids. When problems of simplicity became more or less exhausted about a century later, scientists like Maxwell, Boltzmann, and Gibbs began considering problems of disorganised complexity. An example of such a problem would be a rigid box containing an Avogadro's number of air molecules. These air molecules can be deflected when they collide with each other or with the walls of the box. Otherwise, they travel with uniform velocity as Newton's First Law predicts that they would. Each air molecule alone obeys Newton's law. But because of the very large number of air molecules in the box, exact mathematical solutions are not feasible. However, if we treat this problem probabilistically by assuming that the pressure, volume, or temperature are constant, then it's relatively easy to work out the velocity distribution of the air molecules. Although we may never know the position and velocity of individual air molecules, our understanding of how the distribution of molecular speeds changes when we vary the pressure, volume, or temperature, allows us to predict the macroscopic behavior of the gas accurately. Finally, Weaver discussed problems of organised complexity. An important example of this class of problems is the problem of life. In modern biology, the fundamental description of life begins with DNA. DNA consists of two complimentary strands of amino acids coiled around each other to form a double helix. Beyond this basic level of organization, the very long DNA molecule has to be compactified so that it can fit into the nucleus of a cell. In multicellular organisms like us, the cells are further differentiated and organised into tissues and regions. Our brain is an example of an organ that's highly complex in itself. Groups of organs and tissues are then organized into a higher level system, like our circulatory system. All the different systems in our body combine to make one human individual. Amazing as it is, the organization of humans doesn't stop at the level of individuals. To facilitate our social interactions, we're further organized into groups, clans, organizations, and societies. As we've just seen from these examples, complex systems arise with many heterogeneous components. These components interact with each other often in nonlinear ways. As a result of these interactions, structures emerge at different spatial and temporal scales. Because there is no blueprint, we say that they arise through self-organisation. More importantly, many different structures at smaller scales are conditionally combined to give rise to structures at larger scales. We say that complex systems are irreducible because the behaviors of the larger structures cannot be explained in terms of the behavior of their smaller constituent parts. That's why Nobel laureate, Phil Anderson, said that complex systems are more than and different from the sum of their parts. Some complex systems, for example, human societies, have the capacity to learn from and adapt to their environment. All complex systems, because of the conditional nature of their interactions, show strong history dependence in their behavior. So, why should we care about complex systems? We can care about them because they're so common in nature and in human societies. Scientifically, complex systems are intriguing because they seem to create order out of chaos, in contradiction to the Second Law of Thermodynamics. Understanding the fundamentals of complex systems will help us to understand ourselves, our past, and our present, as well as our interaction with other complex systems in nature. By understanding complex systems and learning to predict their behaviors, we begin to gain some degree of control over how they evolve over time, and we can integrate those insights into our social policies. In the next two video segments, you'll hear Professor Peyto Sloat explain, what complex systems are, the scientific progress that we've achieved in trying to understand them, and why people should care about complex systems. These are excerpts from our NTU Winter School in complexity.