Chaos and Complexity Tutorial

Stephen Hawking has said that the science of this 21st century will be the science of complexity. When science has achieved so much, what could it be that could take us all on yet another enormous leap forward?

Science generally uses a system called reductionism to investigate our world. This means breaking down anything being examined into the parts that make it up. Reductionism proposes that if we understand the parts, we will understand how the whole system works. If you take a mechanical clock to pieces, you can see what each part does you can find out how it works. Some things, however, can't be investigated in this way. There is much to be learned by dissecting a rat, for example, but in dissecting it, we kill it and cannot learn what gives it life.

Sometimes we need to stand back and look at the whole system to understand how things work, rather than break it into pieces.

Chaos Theory looks at how very simple things can generate very complex outcomes that could not be predicted by just looking at the parts by themselves. You may have noticed the wonderful swirling patterns of birds flying together in the sky or fish schooling in the oceans. At first glance we would think the birds would have to be rather intelligent to work out how to fly in formation like that. We would probably also assume there must be a 'bird in charge' giving  instructions to all the others.

Research into swarms has shown, however, that all that is required is for each bird to maintain the distance between itself and its neighbours and fly in the average direction of its neighbours. From this alone the wonderful, swirling, complex patterns the birds or fish make are seen. Simple rules can generate complex behaviours that just seem to emerge out of nowhere. While each individual agent does not need much intelligence, the is swarm intelligence which resides with the collective.

Complexity Theory looks at how complex systems can generate simple outcomes. Consider the billions of cells that make up a person and yet they all manage to work together in such a way that the body works as a single unit. Our body works to keep us alive. We get hungry when we need food; we get thirsty when we need water. We can think and learn and we have a distinct personality. Something happens when large numbers of individual units come together and interact intensely with each other. New levels of operating just emerge through what is called self-organisation. By looking at a single human cell, you could not tell that it would be able to operate with other cells to form a human body.

A city also has a large number of intensely interacting units. This time human beings form the units. Once again, we would not know from examining a single human being that they would gather together in the millions to form cities. It is an emergent property, so that a city takes on a life or a personality of its own, which has self organised out of the interactions of all the people who live in the city.

We cannot predict what a complex system will evolve into. When we think about it, all life from the smallest cell to the largest animals are complex adaptive systems and life always provides us with a mystery . 

You can follow your way through the tutorial to learn about some of the many aspects of Chaos and Complexity. Chaos and Complexity is a new science looking at our world in a holistic way. The large number of calculations needed to explore complexity has meant that it has only been since the advent of the computer that we have been able to make real progress into understanding complexity. With the ever increasing ability of computers to undertake enormous calculations very quickly, we are making great leaps in our understanding of the complex nature of the world in which we live. We are still only at the beginning of the journey of developing complexity as a science.

You will learn about fractals, or patterns that are self-similar, that is a basic pattern repeated within itself over and over in the system. Once you know what to look for you will see fractals everywhere you look. They are in nature, they are in our cities, trees, vegetable and even in our brain.

Life is caught in the tension between order and chaos. If there is too much order, everything becomes the same and there is no room for creativity or anything new. Everything must fit the one pattern. If there is too much chaos nothing can last long enough to create anything useful; everything is just a jumble that destroys everything before it can get started. Between order and chaos is found the Edge of Chaos, the point where there is enough chaos for novelty and creativity, but also enough order for consistency and patterns to endure. This point is a magic point, where new and unimagined properties can emerge.

Linked to fractals are Power Law Distributions. Who would have imagined that the frequency of earthquakes, sand falling down a sand pile, the money in people's bank accounts, the number of people dying in wars, traffic jams, brain cells and the number of times particular words appear in a text all fit the same mathematical patterns and proportions.

Small World Networks are networks such as groups of people that interact. If there are not many links between the people, the group is not very effective. If there are too many links everyone spends so much time communicating that they do not get to get on with the group's tasks. As the number of links increases, there is a point where the effectiveness of the group increases dramatically.

If we take a network with many agents all linked and interacting heavily, and then can then take out agents one at a time, we can test how effective the system remains. We find that the system is remarkably resilient at first because other agents can take over the role of the lost agents. This means at first there is not much difference in effectiveness, but as more and more agents are taken out, the system reaches a  tipping point. At this point its effectiveness reduces suddenly as too many agents are missing and the remaining ones are finally overwhelmed. The system suddenly collapses. A human body can sustain serious damage and continue to function surprisingly well, but if the damage reaches the tipping point, the disintegration is quick and we can die quite suddenly.

The tipping point also works the other way such as in trying to market a product in the market. here we want to reach the tipping point. As the small world network gains agents and builds connections, it can eventually reaching the tipping point,. Suddenly sales task off. Sometimes we talk about reaching a critical mass.

A basic condition of a living system is that it is dissipative. That means it requires a flow of energy in and out. the energy is used to keep the organism alive and maintain the boundary between itself and the outside world

Living systems are examples of Complex Adaptive Systems. They exist within a wider environment interacting with it in complex, non-linear ways. Complex Adaptive Systems are such that they can improve their fitness in their environment by learning. As their environment changes, they adapt by taking new forms that work better. Often this means competing in an environment with other systems, each trying to improve to gain a larger share of the resources available in that environment. This is where complexity links to evolution and the concept of natural selection. Autpoiesis is another approach to understanding complex adaptive systems

Have you ever tried to find out about something, only to find out you are left with more questions than those with which you started? Instead of things becoming clearer when you look at them more closely they stay just as fuzzy. Fuzzy Logic explores this world and comes up with some surprisingly practical applications.

Genetic algorithms are another way of solving some problems where we choose a solution rather than find a solution. Cellular automata allows us to understand many natural systems.

This tutorial looks at all these topics to present  a new way of looking at the world we live in and, then, the life we live.

Welcome to this strange and wonderful new science that gives us penetrating insights into this magnificent world in which we all live.

You can choose between the full tutorial, or a shortened version, that still explains the main concepts of chaos and complexity.