Complexity: A Guided Tour
Quick summary
Melanie Mitchell’s definition of complexity
A system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution.
Once complexity as a concept is well enough defined we can think about ways to quantify how much complexity is in a system.
Notes
Part I - Background and History
There is still mystery about the forces that cause a community - ants, termites, humans - to self-organize and build intricate structures to reinforce a resiient, long-term collective outcome.
In complex systems there is no central control; instead, individual agents follow simple behaviors, interact, process information, then adapt.
The history of science, especially complex systems, is one of constructing and deconstructing the components that make up a whole - whether that be an abstract idea, a living organism, or society.
That journey from parts to whole and back is complex, often unpredictable, and somewhat mysterious - even if deterministic. (personal note - and therein lies the challenge (and fun) of systems science.)
The fundamental questions of complexity science is under what conditions does emergent self-organizing behavior comes about in the system under study.
Before complexity there was dynamics and before dynamics was Sir Isaac Newton. Newtownian physics describe change over time in deterministic, formulaic paths.
Laplace believed that with Newton’s laws it was theoretically possible to predict the path of every moleculte in the universe through the eternity of time.
Quantum mechanics and chaotic systems disproved this theory: sensitive dependence on intial conditions creates unpredictable outcomes, even in deterministic systems.
Complexity, chaos, and dynamics are measured using information and entropy.
The amount of complexity in a system a common measurement in complexity science. Examples of different ways to measure complexity: complexity as computational capacity, statistical complexity, complexity as system hierarchies,
The field of “complex systems” started with the earlier fields of cybernetics and systems science.
Part II - Life and Evolution in Computers
Biology, evolution, and origins of life provide natural examples of computational processes for complexity scientists to emulate using models.
Genetic algorithms are inspired by biological processes for evolution, adaptation, and optimization. Inputs to genetic algorithms have two parts:
- a set of programs with different problem solving strategies
- a fitness function that scores each program for its success on a particular task
Genetic algorithms mimic the process of evolution by combining strategies and introducing random mutations of existing strategies. Over time and many simulations an optimal strategy is discovered by the algorithm.
Genetic algorithms often produce strategies that are highly creative and unintuitive.
Part III - Computation Writ Large
Part IV - Network Thinking
Part V - Conclusion
Reflections
Are humans the most complex? If so, why? Because we can extract, communicate, build, and destroy with greater power and impact than other species? What if complexity calculation included sustainable existence within the environment one lived in? Would we then be the most complex?
Can life be measured with a scale? Is a complex creature also more alive than a simple one? For example, a single cell organism compared to a human being. Which is more alive?
I believe there are three discrete categories of life: alive, dead, inanimate. Alive or not is separated by a delicate threshold. The state transition into and out of life is likely complex or even chaotic.
However for that to be true these states and their transitions must be modeled.
Life is the existence of a mysterious process of perpetuating internal self-organization that gives the ability to interact and respond to the surrounding environment. That ability is truly delicate - it switches on, and eventually switches off. Having that ability is what separates organisms from objects.
References
Bibliography
- Mitchell, M. (2009). Complexity: A guided tour.