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