Synchronization is a state of coordination between two or more elements within a system, whereby their variables are correlated in some fashion. The mathematician Steven Strogatz talks about synchronization as such. “sync is maybe one of…the most pervasive drives in all of nature. It extends from the subatomic scale to the furthest reaches of the cosmos. It’s a deep tendency towards order in nature that opposes what we’ve all been taught about entropy…(it is) the tendency towards spontaneous order. “ Any form of organization within a system is going to derive ultimately from elements assuming some coordination between their states this coordination can be understood in terms of some correlation between their state variables. There are just three different types of correlation, firstly we can have a random correlation, meaning there is no relation between the variables, they are independent, secondly we can have a positive correlation, meaning the values associated with the different elements move in the same direction, lastly we can have a negative correlation, where the two variables move in different directions.
When elements or agents act completely independently, we will get a random correlation between their states, for example, me choosing to go to the swimming pool on Friday has absolutely no correlation to whether my neighbor will go shopping the following Monday, these two events are randomly correlated. Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable. For example, if we took a large enough group of people and randomly assigned connections between them, and then went and plotted a graph of how many connections each person had, we would get a normal or Gaussian distribution, where some would have few connections, some many, but most would tend towards the average and the more connections we added the closer we could predict what this average would be, this is called the law of large number. If this is truly a random system, any individual event is perfectly random, totally unpredictable, but as we go to the limit of infinity we get an outcome that is perfectly predictable, thus the further we go towards infinity the more it will tend towards this predictable outcome.
If the values are negatively correlated we have what is called a negative causal link within system dynamics. A negative link is a relationship between two variables where they change in the opposite direction, such that as the value of one variable increases, the other decreases, and vice versa. An example of this might be the financial relationship between the owner of a business and the employees, if all other things are equal, the more the owner pays the employees the less profit for the owner, thus elements within this type of relation are going in the opposite direction creating a counterbalancing dynamic.
Positive causal links between values associated with different elements means they both move in the same direction. Thus if one variable increases, the other one also increases or if one decreases the other also decreases. Positive links represent relations of deep interdependency, everyone wins or losses together. We get this positive link by two things interacting in either a constructive fashion meaning they both increase or a destructive fashion meaning they both decrease. By constructive we mean the two variables are moving in the positive direction, by two countries signing a trade agreement their two economies may grow and this is essentially a synergistic interaction, by both increasing together they are adding value to the overall system. Inversely with a destructive interaction the two variables move in the downward direction together an arms race between to nations might be an example of this, through this interaction the value of the whole system is decreasing, this may be called a negative synergy or interference in the way that two sound waves can cancel each other out making the combined output to the system less than a simple summation of its inputs.
Positive links are nonlinear, when we add and subtract the gains and losses to all agents in the interaction they do not sum to zero thus defying the additivity principle. This nonlinear nature to positive links makes these phenomena less well studied and understood. Wherever we have synergies or interference within a system we will get nonlinearity, this might be the synergy between two partners in a relationship, between to businesses engaged in a merger, different drugs taken at the same time or between to creatures within an ecosystem, these nonlinear phenomena are ubiquitous in our world and form the foundation for our understanding of synchronizations.