Friday, April 13, 2012

Example of an Emergent Phenomena : Fireflies


"At the heart of the universe is a steady, insistent beat: the sound of cycles in sync. It pervades nature at every scale from the nucleus to the cosmos. Every night along the tidal rivers of Malaysia, thousands of fireflies congregate in the mangroves and flash in unison, without any leader or cue from the environment. Trillions of electrons march in lockstep in a superconductor, enabling electricity to flow through it with zero resistance. In the solar system, gravitational synchrony can eject huge boulders out of the asteroid belt and toward Earth; the cataclysmic impact of one such meteor is thought to have killed the dinosaurs. Even our bodies are symphonies of rhythm, kept alive by the relentless, coordinated firing of thousands of pacemaker cells in our hearts. In every case, these feats of synchrony occur spontaneously, almost as if nature has an eerie yearning for order."
--- A quote from Sync - The Emerging Science of Spontaneous Order by Steven Strogatz 

One of the most intriguing phenomena within complexity science is that of emergence.  It is a salient feature of complex systems, so much so that definitions of complex systems include the quality of exhibiting emergence.  Many exciting solutions to the world’s bigger problems can be understood through collective dynamics and emergence.

What is Emergence?


Emergence is when behavior at a smaller scale of a system produces global behavior that is not entirely intuitive given the behavior at the smaller scale.  The global behavior is not directly programmed in the behavior at the local level. Something surprising happens at the larger scale.  From simple local interactions, we can arrive at global behavior that is immensely complex, sometimes seemingly random.
Another way to think of emergence involves the notion that the whole is greater than the sum of its parts. The behavior of the system is a result of not only its parts, but their interactions. The actions at the level of the individual do not imply that of the behavior of the system. We need to understand not only the system at the individual level, but at the level of multiple individuals to observer the effect of their interactions.
One of the most exciting examples of emergence involves evolution. At a smaller scale we have natural selection, species in a population surviving or dying over time based on selection pressures from the environment, with possible species variations through reproduction and sexual selection and the random chance of mutation. At a larger scale we have the development of biodiversity, a wide range of organisms from bacteria to whales, and an environment with so many different species able to thrive within different niches. Global biodiversity is not programmed in the local interactions; it is an emergent property. 

Why is it important to study the emergence of a system?

Understanding emergence is essential when working with complex systems. For the most part, complex systems exist because they are grown, i.e. they have evolved to be what they are. They are composed of many parts that interact across scales, from individuals to groups to the whole. When we think of a city, it grows through the interaction of all of the individuals and organizations which comprise the city. The city is not formed by a single individual, it is formed by its population. Emergent behavior can be difficult to understand, since by its very nature it is unintuitive and unpredictable (the very reason why it has received so much attention). In understanding global behaviors of a system, it helps to understand how individual interactions led to the global behaviors. In this way, one can attempt to reproduce the global behaviors through recreating the individual interactions. 

Example of Emergent Behavior: Fireflies

Fireflies can spontaneously synchronize their flashing: this phenomenon is one of the most popular example that illustrates emergent phenomena. The question surrounding the synchronization among fireflies is that when there is no head firefly, who has the ability to communicate with all the rest, so how is it possible that all fireflies flash in synchronization, when no firefly can see all of the rest?
Efforts have been made in the direction of developing a model that introduces a mechanism of simple interactions between the fireflies which operate locally [1]. Through this local interaction, the global behavior is that of synchrony. The key concept with respect to emergence is that the local interactions do not mention anything about synchronizing.
The analysis of this phenomena can be done using the following mathematical model.
Each firefly can be assumed to be an oscillator with time period of T, saying it fires at time T, and resets to zero only to fire again at time T. All of the fireflies have the same period T, but start at different times in their period. At each step, all of the fireflies increment in their period.
Also,, any firefly can see only within a certain detection radius. When one of the neighbors of a firefly flashes, the firefly increments in its period, leading it closer to flashing. The nature of this firing response is important. Say that a firefly is at time t’ in its period. The firing response is defined as follows: the amount of increment increases as t’ increases. So if a firefly is later in its period, the increment will be higher. If its just beginning its period, the increment will be lower. The next is not so important for the concepts, but mathematically it can be more accurately stated as such:

                                               
Here, t” is the new internal time if a firefly experiences a flash at time t’. As defined in the model, f is the firing function and epsilon is a small constant < 1 .
From a simple rule given a neighbour flashing, organization emerges as the fireflies flash as a group. The group is able to act as a whole through local interactions.

The above example of fireflies is useful for synchronising distributed systems like a wireless sensor networks, etc.

How can we go about studying the Emergent Behaviour of a System?

Think about environments that your are in or have seen, and reframe them in the systems perspective. How do the parts combine to form the whole. Is the emergent behavior obvious given local interactions?
What if there is a particular global quality we want to achieve. What are ways in which local interactions can achieve those global qualities? Because the global behavior can be unpredictable, it can become a difficult problem to determine the local interactions. But other times, those interactions can be found through the ingenuity of a group and global behaviors can be achieved. The question then also becomes, how do you create and environment that will promote such creativity? This is a question of emergence, in designing local interactions to promote global creativity.
References:

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