Complexity

"Common Properties of Complex Systems: When looked at in detail, these various systems are quite different, but viewed at an abstract level they have some intriguing properties in common:

1. Complex collective behavior: All the systems I described above consist of large networks of individual components (ants, B cells, neurons, stock-buyers, Website creators), each typically following relatively simple rules with no central control or leader. It is the collective actions of vast numbers of components that give rise to the complex, hard-to-predict, and changing patterns of behavior that fascinate us.
2. Signaling and information processing: All these systems produce and use information and signals from both their internal and external environments.
3. Adaptation: All these systems adapt—that is, change their behavior to improve their chances of survival or success—through learning or evolutionary processes.

Now I can propose a definition of the term complex system : 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. (Sometimes a differentiation is made between complex adaptive systems , in which adaptation plays a large role, and nonadaptive complex systems, such as a hurricane or a turbulent rushing river. In this book, as most of the systems I do discuss are adaptive, I do not make this distinction.)

Systems in which organized behavior arises without an internal or external controller or leader are sometimes called self-organizing . Since simple rules produce complex behavior in hard-to-predict ways, the macroscopic behavior of such systems is sometimes called emergent . Here is an alternative definition of a complex system : a system that exhibits nontrivial emergent and self-organizing behaviors . The central question of the sciences of complexity is how this emergent self-organized behavior comes about."

"The defining idea of chaos is that there are some systems— chaotic systems—in which even minuscule uncertainties in measurements of initial position and momentum can result in huge errors in long-term predictions of these quantities. This is known as “sensitive dependence on initial conditions.” In parts of the natural world such small uncertainties will not matter. If your initial measurements are fairly but not perfectly precise, your predictions will likewise be close to right if not exactly on target. For example, astronomers can predict eclipses almost perfectly in spite of even relatively large uncertainties in measuring the positions of planets. But sensitive dependence on initial conditions says that in chaotic systems, even the tiniest errors in your initial measurements will eventually produce huge errors in your prediction of the future motion of an object. In such systems (and hurricanes may well be an example) any error, no matter how small, will make long-term predictions vastly inaccurate."

"The art of model-building is the exclusion of real but irrelevant parts of the problem, and entails hazards for the builder and the reader. The builder may leave out something genuinely relevant; the reader, armed with too sophisticated an experimental probe or too accurate a computation, may take literally a schematized model whose main aim is to be a demonstration of possibility."

"The reason we humans can share so many genes with other creatures quite different from us is that, although the genes might be the same, the sequences making up switches have often evolved to be different. Small changes in switches can produce very different patterns of genes turning on and off during development. Thus, according to Evo-Devo, the diversity of organisms is largely due to evolutionary modifications of switches, rather than genes."

"As for complex systems, we don’t even know what corresponds to the elemental “stuff” or to a basic “force”; a unified theory doesn’t mean much until you figure out what the conceptual components or building blocks of that theory should be.

Deborah Gordon, the ecologist and entomologist voiced this opinion:

Recently, ideas about complexity , self-organization, and emergence—when the whole is greater than the sum of its parts—have come into fashion as alternatives for metaphors of control. But such explanations offer only smoke and mirrors, functioning merely to provide names for what we can’t explain; they elicit for me the same dissatisfaction I feel when a physicist says that a particle’s behavior is caused by the equivalence of two terms in an equation. Perhaps there can be a general apparently self-organizing systems is to focus on the details of specific systems. This will reveal whether there are general laws... The hope that general principles will explain the regulation of all the diverse complex dynamical systems that we find in nature can lead to ignoring anything that doesn’t fit a pre-existing model. When we learn more about the specifics of such systems, we will see where analogies between them are useful and where they break down."