Here is a brief summary of some of the key principles of the complexity sciences, aka system sciences or network sciences.
Once one understands these principles using examples from any discipline - physics, chemistry, biology, physiology, ecology, economics, sociology, geology, geography, geometry, astronomy, cosmology, cognitive sciences, climatology, meteorology, astronomy ... - then one can apply them to virtually any system from any discipline. This allows students of one discipline to intuitively understand the behavior of systems studied in other disciplines without detailed knowledge of those disciplines.
Thus, for the first time in the history of western science, students and scientists from radically different disciplines - say physics and climatology - can communicate,
sharing knowledge about their respective systems in an understandable way.
• Systems or networks : groups of coupled (linked), interacting parts operating by simple rules (rule sets) that lead to remarkably complex behavior. "System" and "network" are not synonyms. In my view, a network is a connected set.A system is a self-bounding network with a physical-chemical boundary.Examples of networks include microbial mats and animal intestines,
ecosystems, economies, political systems, the Internet, and galaxies.Examples of systems include cells and Earth's metabolism and homeostasis.
• States (or 'attractors') : Systems do not demonstrate just any kind of behavior. Instead, system dynamics (or behavior over time) fall into a limited number of types called "states" or "attractors", so named because it is as if a system is "attracted" to a particular type of behavior. There are effectively four types of system states, designated classes 1 - 4.
◦ Class 1 is very static and unchanging; this is characteristic of "dead" systems.
◦ Class 2 systems are repetitive, or periodic, with behavioral characteristics repeating at very regular and predictable time intervals.
◦ Class 3 is called chaos (which some confuse with randomness, which is different.
◦ Class 4 - far and away most common in nature, and also most complex and interesting - is a mixture of classes 2 and 3, of order and chaos. Class 4 is often referred to as "the edge of chaos" or the "chaord". Human physiology - including healthy hearts and brains - ecosystems, economies, traffic patterns, extinction events, earthquakes and avalanches, ocean waves ... all are class 4.
• Non-linearity: Dynamics (behavior) of systems resulting from class 3 & 4 rules is non-linear; that is not linear, regular, orderly and well-behaved, but operating near “the edge of chaos” where accurate, long-term quantitative predictions are rare, and surprises in the form of unexpected, rapidly-shifting, even catastrophic behavior are common. This record of Antarctic temperatures and other variables over a few hundred thousand years from the Vostok ice core exemplifies non-linearity quite well. The long term behavior of most (class 4) systems in nature and human societies look similar. Just think of stock market trends.
• Feedback: The most important factor leading to non-linear behavior, where the actions of a part feed back to it through the network. Negative feedback reverses changes, stabilizing systems. Positive feedback accelerates changes, destabilizing systems, sometimes causing them to "jump" to a new behavioral state at critical thresholds (tipping points or bifurcations). In healthy, stable systems, positive & negative feedback work in concert.
• Fractals: Structures in natural class 4 systems are rarely regular geometric objects described by classic (Euclidean) geometry, but fractals, which are objects in which the parts of a system on multiple size scales look similar to the whole. That is, in plain English, the parts of parts of parts of parts still look like the whole. A branch of an oak tree has the same general form as the whole tree.
A small part of a cloud (or a cliff face on a mountain) has the same general shape as the whole cloud (or of the entire mountain). A lightning bolt isn't a straight line, but a complex collection of zig zag branches, which are fractal. The most famous "artificial" (or mathematical) fractal is called the Mandelbrot set, a tiny portion of which is shown on the right.
• Power law distributions: Behavior (dynamics) in class 4 systems are described by power law distributions, in which the size of changes are inversely proportional to their frequency; that is, small changes are frequent, while large changes are infrequent.
• Energy gradients & self-organization: When exposed to energy gradients (energy flows), matter can spontaneously organize – or “self-organize” - into remarkably complex systems; examples include vortices, convection cells, chemical clocks (like the BZ reaction & natural heart pacemakers), living systems, societies with economies and politics, and galaxies. The proper study of these concepts is non-equilibrium thermodynamics, or NET, which is actually easier to understand than pronounce, and far easier to comprehend for educated lay people than classical, equilibrium thermodynamics.
• Emergence: Systems demonstrate emergent properties, characteristics that cannot be fully explained by the properties of the parts but that are logically consistent with the properties of the parts; that is, they demonstrate emergence. (Note: Emergence is not “mystical”, but a function of system complexity that does not allow simple “cause and effect” explanations.)
• Symbiogenesis: In living systems, evolution occurs not only by natural selection and mutations, but also very often as a result of symbiogenesis, the emergence of new cells, organs or species via symbiosis among two or more existing species living in close physical contact. The image on the right is of Mixotricha paradoxa, a microbe that is actually five (or probably more) microbes living symbiotically. Other famous examples of symbiogenesis include green worms (have no digestive tract, but feed via photosynthetic algae in their skin); legumes (able to fix nitrogen only by bacteria living in their roots); and cows (that can digest their plant food only with a healthy microbial community living in their gut).
• Gaia: Earth's planetary-scale metabolism and homeostasis composed of our linked atmosphere, oceans, freshwater, surface rocks & all life forms. That is, it has a metabolism - the complex set of chemical reactions occurring inside of all of your cells that are at the root of your life, similar to your metabolism, but much more complex – and homeostasis - automatic (without conscious thought) self-regulation of temperature and chemical composition of Earth's air, water and even surface rocks, which cannot be explained by physics and chemistry alone (even though explanations include and are consistent with physics and chemistry).