Feedback Loops

There is an important difference between a random state and a chaotic state. In a random state each new state is totally unrelated to the previous step. This means there can be no predictability within a random system. What happens now is totally unrelated to what happened before, or what might happen later, or what might happen in another part of the system, but in a chaotic system, how it changes each time depends on how the system was the time step before. An iterating of system states allows many interesting and unusually properties to develop in chaotic systems that are not seen in random systems. Life cannot proceed out of randomness, which falls prey to entropy, but it can proceed out of chaos.

A feedback loop is formed where an event occurs in an environment to which a system responds, and that response has an effect back on the environment. This effect then forms a new event, to which there is a further response. We can see that this can happen in a chaotic system, but not in a random system This loop then continues so the input from the environment becomes the output which is itself the new input. The loop goes round and round. An example of a feedback loop is a person driving a car. They drive at a speed that suits the conditions and the road rules. From moment to moment they may speed up or slow down as they respond to a changing environment.

There are two types of feedback loop; negative feedback loops and positive feedback loops. A positive feedback loop is a loop where the change in a system is increased at each iteration so the system grows over time. The growth of population can be an example of positive feedback. If there are more children in each generation, the population just increases and increases. Before long the population will grow extremely large. A system the doubles at each iteration is an example of exponential growth. If we take a large piece of paper and fold it over in half, then in half again and again until we have folded it fifty times, the pile will surprisingly reach from the earth to the sun. This illustrates how dramatically a system can change under the influence of a positive feedback loop. The top graph shows a positive feedback loop increasing over time.

A thermostatically controlled heater is an example of a negative feedback loop. The temperature is monitored. If it drops down to a certain level, the heater is turned on increasing the heat. Eventually it will reach an upper level and the heater is turned off. The result is that the temperature is kept within certain limits. Positive feedback loops change the nature of a system, while negative feedback loops tend to maintain the system as it is and resist perturbations from the outside. the bottom graph  shows a negative feedback loop where the system moves to a single value or single range and then does not change from that.

Often more than one feedback loop operates in a system. Taking the population growth example and place it on a previously undiscovered island. The initial settlers will soon grow as their numbers increase under the influence of a positive feedback loop. Eventually the population reaches the point where the island is no longer able to support a growing population and a negative loop will kick in.

An important consequence of feedback loops is that the law we looked at previously with the one-kilogram rocks breaks down. We usually assume that a small change in a system will create a small result and if we want to a large change, then a large amount of work is needed. When a positive feedback loop is operating a small change can get amplified time after time looping through the system so that it has a major effect.

A negative feedback loop will keep a system stable, so it tends to remain the same irrespective of outside influences.