# 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 networks.

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. Youâ€™ll also get a sense of how these topics fit together to help explain how complexity arises and evolves in nature, society, and technology.

## 1. The Course

### 1.1. Unit 1: What is Complexity?

Some examples of complex systems given are ant colonies, the brain, social networks, 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.

#### 1.1.1. 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

#### 1.1.2. Core Disciplines, Goals, and Methodologies of the Sciences of Complexity

##### 1.1.2.1. 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

##### 1.1.2.2. 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?

##### 1.1.2.3. methodologies

- experimental work
- theoretical work
computer simulation

This course has a focus on computer simulation of complex systems.

#### 1.1.3. Definitions of complexity

Hard to define… lots of definitions. We'll look at Shannon information and Fractal dimension.

##### 1.1.3.1. 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

##### 1.1.3.2. 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?

#### 1.1.4. 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?

#### 1.1.5. 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.

### 1.2. Unit 2: Dynamics and chaos

#### 1.2.1. 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.

##### 1.2.1.1. 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

##### 1.2.1.2. 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

##### 1.2.1.3. 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?

#### 1.2.2. 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

#### 1.2.3. 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

## 2. Elsewhere

### 2.1. In my garden

Notes that link to this note (AKA backlinks).