Motivation
What is the “organizing principle” of the universe? What is common among particle physics, chemistry, biology, psychology, sociology and economics? Can this answer help us know the nature of God?
Content
Emergent Phenomena seems like an obscure topic to highlight here but in fact it is so common in our world that it may be called the organizing principle of the universe. In the simplest terms it is any phenomena where a complex system arises from the interactions of simpler components where the complex system has properties that are almost impossible to predict by just observing the properties of the simpler components.
Confused? Let us illustrate by an example. The figure below shows one approximate chain of increasing complexity which has been built upon multiple levels of Emergence of complex systems which themselves become the building blocks of the next stage. At each stage there are rules for how the components in that box interact with each other. For example Hydrogen and Oxygen are Atoms and they have their individual properties (like boiling point, viscosity, combustibility etc) and rules of interacting with each other. But when they combine to form H2O (water) it has properties completely different from either of them and it would be difficult to predict all its properties by just studying the properties of Hydrogen and Oxygen. Similar leaps of complexity are seen at other levels like individual human behavior studied by psychology to behavior of social groups studied by sociology .
How does this happen? Does this happen according to some grand plan?
Well, the success of the Theory of Evolution by Natural Selection in explaining the journey from Single Cellular Life to Humans gives us some clues on how simple rules and a lot of time for them to play out can lead to the arising of complexity in the absence of any grand designs. But when emergence happens it is very difficult to take the final result and try to trace it back to the initial conditions or take any initial conditions and predict the final result because many intermediate steps happen by chance or non-linear interactions. But it can be said that whatever survives one stage of rule based interaction is in someways “stable enough” to not disappear and it is “unstable enough” to not become totally static and continues interacting with its environment to build the next level of rules. (See Technical Notes for a walk through the “simplest complex” system called Cellular Automaton shown below )
Technical Notes
It might still be hard to imagine what terms like emergence, complexity, rules, stability, etc mean in this context and so we will walk through a system called Cellular Automaton which is the “simplest complex” system we can use to explain these concepts.
The Game of Life is a Cellular Automaton created by mathematician John Convay. The universe of the Game of Life is an infinite two-dimensional grid of square cells, each of which is in one of two possible states, alive (green) or dead (black). Every cell interacts with its eight neighbours, which are the cells that are horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:
- Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies, as if by overpopulation.
- Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
An initial pattern constitutes the seed of the system. The first generation is created by applying the above rules simultaneously to every cell in the seed. The rules continue to be applied repeatedly to create further generations. From a random initial state of black and green dots, with luck and time, the game can automatically generate stable patterns like the ones shown below and many more that look “alive”. If the initial state is not conducive for “life”, it can also produce a blank canvas or static patterns that do not change.
Below is a roughly 1 minute animation of the rules above starting with the initial state of a 3-4 green boxes in the center, exploding to multitude of different changing shapes and finally settling into a few static patterns (on screen)
Below is a compilation of some dramatic patterns that emerge when these rules are allowed to play for a long time with different initial conditions
References
Stanford Professor Robert Sapolsky gives a lecture on emergence and complexity
