# Introduction to Complexity URL : https://www.complexityexplorer.org/courses/119-introduction-to-complexity I enrolled on this in August 2021. I see it as a bit of a refresher on what I did in [[Evolutionary and adaptive systems]]. And to give me a fun intro to [[agent-based modelling]] with [[NetLogo]]. And then, the aim would be, to be followed up by some study of [[Systems thinking]]. They're related, but slightly different. See [[Complex Adaptive Systems, Systems Thinking, and Agent-Based Modeling]]. That I can then apply to questions around [[political organisation]], [[climate change]], and [[social network]]s. > In this course you'll learn about the tools used by scientists to understand [[complex systems]]. The topics you'll learn about include dynamics, chaos, fractals, information theory, self-organization, agent-based modeling, and networks. You’ll also get a sense of how these topics fit together to help explain how complexity arises and evolves in nature, society, and technology. ## The Course ### Unit 1: What is Complexity? Some examples of complex systems given are [[ant colonies]], [[the brain]], [[social network]]s, the web, the human genome, the economy, [[food webs]], the [[immune system]], cities. I'm probably most interested in the [[networks]] complex systems. But they're all interesting. Biological, social, technological. #### Properties common to complex systems - [[agents]] - [[nonlinear]] interactions - no central control ([[decentralisation]]) - [[self-organisation]] - [[emergence]] (emergent behaviours) - hierarchical organisation - information processing - complex dynamics - e.g. foraging trails in ants - e.g. stock prices - evolution and learning #### Core Disciplines, Goals, and Methodologies of the Sciences of Complexity ##### disicplines dynamics : the study of continually changing structure and behaviour of systems information : the study of representation, symbols, and communication computation : the study of how systems process information and act on the results evolution : the study of how systems adapt to constantly changing environments ##### goals - cross-disciplinary insights into complex systems - e.g how does information processing in ant colonies relate to information processing in cities - e.g. how is information flow in the brain simalar to information flow in an economic network - general theory - is it possible? ##### methodologies - experimental work - theoretical work - computer simulation This course has a focus on computer simulation of complex systems. #### Definitions of complexity Hard to define… lots of definitions. We'll look at [[Shannon information]] and [[Fractal dimension]]. ##### [[Warren Weaver]] - problems of simplicity - a few variables, e.g. pressure and temperature; current, resistance, voltage; population vs time - problems of disorganized complexity - billions or trillions of variables - e.g. laws of temperature and pressure - averages, statistical mechanics - we assume little interaction between variables - problems of organized complexity - moderate to large number of variables - strong non linear interactions - can't be averaged meaningfully - ##### Problems of organized complexity - what makes an evening primrose open when it does? - what is aging? - what is a gene? - on what does the price of wheat depend? - how can you explain the behaviour of e.g. a labour union? #### What are Complex Systems? The Experts Weigh In - something where there's no simple compact way of describing the system - systems that encode long histories - sophisticated internal architecture of how it stores information - interacting things with emergent behaviour - evolution and adaptation is a key part of complex systems? - and feedback? #### Introduction to NetLogo NetLogo is super simple to set up and get running the demos. The Ants model is very cool - foraging for food sources and finding the closest thanks to pheromone trails. This is the kind of thing I faffed around with graphics programming on in my Masters, surely would have been easier to use a pre-built system for it. I wonder why we didn't… I really like the way it's presented, in that it gets you thinking about how the agent-based models might run and their dynamics. And it also makes you make predictions as to how changes in parameters and behaviours might change the dynamics. Thinking a bit more scientifically about it. Making a prediction and testing it with an experiment. I also love the NetLogo agent-based modelling stuff because it is very much thinking visually. When some result isn't what you expected, you actually view the behaviour on screen. ### Unit 2: Dynamics and chaos #### Introduction to dynamics [[Dynamics]] is the science of how systems change over time. How does behaviour unfold and how does it change over time. e.g. planetary dynamics; fluid dynamics; electrical dynamics; climate dynamics; crowd dynamics; population dynamics; financial dynamics; group dynamics; dynamics of conflicts and dynamics of cooperation. ##### Dynamical systems theory - branch of maths of how systems change over time - calculus - diff eqs - iterated maps - etc - dynamics of a system - manner in which the system changes - gives us vocabularly and set of tools for describing dynamics ##### Brief history - (in the west) Aristotle - one set of laws for the earth, one for the heavens - copernicus - sun is stationary - galileo - experimental method - proved aristotle laws were false - newton - founder of modern science of dynamics - laws of motion same on earth and in heavens - laplace - proponent of newtonian reductionism - thought you could have complete prediction of the future - poincare - small differences in intial conditions produce very great ones in the final phenonema - "sensitive dependence on initial conditions" - so-called butterfly effect ##### Chaos - one particular type of dynamics of a system - defined as "sensitive dependence on initial conditions" - chaos is present in lots of places in nature - solar system orbits, weather and climate, computer networks, population growth and dynamics, and more - we'll look at population growth - what is the difference between chaos and randomness? #### Iteration - Doing something again and again. - population growth is iterative - iterative part is we take last years pop to calculate this years pop - we have a linear equation because we have a linear system - linear equation because no interaction between bunnies - independence yields linearity #### Linear vs non-linear systems - what happens when the parts interact in a non-linear way? - linearity: "the whole **is** the sum of the parts" - for non-linear - we add in death through overcrowding - plus a death rate - this gives us the "[[logistic model]]" - with non-linear systems, the whole **is not** the sum of the parts