EMERGING SYSTEMS
"THE INTERCONNECTEDNESS OF ALL THINGS"
Mathematics and Sciences addressing the new dimensions
and levels of understanding the great web of life.

"One of the principal sciences of the next century will be the study of
complex, autocatalytic, self-organizing, non-linear, adaptive systems..."

Systems Theory: An interdisciplinary field which studies systems as a whole. Systems theory was founded on principles from physics, biology and engineering and later grew into numerous fields including philosophy, sociology, organizational theory, management, psychotherapy (within family systems therapy) and economics among others. Cybernetics is a related field, sometimes considered as a part of systems theory.

Systemics: An emerging branch of science that studies holistic systems and tries to develop logical mathematical, engineering and philosophical frameworks. General Systems Theory and Systems science are related field.

Complexity Theory (Com*plex"i*ty): A new set of interdisciplinary sciences from which are emerging explanatory principles and models of complex dynamic systems composed of many inter-acting parts. It offers radical new views of accelerating global ecological, climatic, economic, social & political changes, evolution, health & healing, immunology, consciousness and more. Examples: Inter(connected)net(work), the brain and body, an ecosystem, and financial markets. Many leading scientists believe that that systems, perhaps even life itself, arise and thrive on the edge of chaos with just enough order to give them pattern, but not so much to slow their adaptation and learning.

• Cybernetics - communication and control in living beings and in the machines built by humans.

• Chaos Theory - deals with dynamical systems that, while in principle deterministic, have a high sensitivity to initial conditions, because their governing equations are nonlinear. Examples; the atmosphere, plate tectonics, economies, and population growth. 

• Fractal Geometry - images or objects that are self-similar (Koch snowflake) at many or all scales. Fractals look like the whole, as do parts of the parts (Mandelbrot set) (Julia set) (Abstract Expressionism)

• The Butterfly Effect - "Sensitive dependence on initial conditions" i.e. the flapping of a butterfly's wing will create a disturbance that will become amplified eventually to change the large scale atmospheric motion.

• Non-Linearity - the solutions to the equations do not form a vector space and cannot be superposed (added together) to produce new solutions. This makes solving the equations much harder than in linear systems.

Computational Equivalence - a question of translating inputs and outputs from one system to another. Systems found in the natural world can perform computations up to a maximal ("universal") level of computational power, and that most systems do in fact attain this maximal level of computational power. Consequently, most systems are computationally equivalent. For example, the workings of the human brain or the evolution of weather systems can, in principle, compute the same things as a computer.

Computational Irreducibility - the only way to determine the answer to a computationally irreducible question is to perform, or simulate, the computation. Some irreducible computations can be sped up by performing them on faster hardware, as the principle refers only to computation time.