
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, selforganizing, nonlinear, 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 interacting
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. 
Inclusive
of; 
•
Automota
Theory  the mathematical study of abstract
computing machines (especially Turing
machines) and the analysis of algorithms used by such machines. 
• Autopoiesis  the fundamental process of living systems, essentially
the mechanism by which living systems continually produce themselves
as autonomous unities. 
•
Cybernetics
 communication and control in living beings and
in the machines built by humans. 
•
Emergence  indication of the arising patterns, structures,
or properties, that do not seem adequately explained by referring
to the system's preexisting components and their interactions. 
• Feedback  a process whereby some proportion or in general,
function, of the output signal of a system is passed (fed back)
to the input. In biological systems such as organisms, ecosystems,
or the biosphere, most parameters must stay under control within
a narrow range around a certain optimal level under certain environmental
conditions. The deviation of the optimal value of the controlled
parameter can result from the changes in internal and external
environments. 
•
Network

systems of interconnected components 
•
NonLinear
Dynamical Systems 
exhibit a completely unpredictable behavior, which might seem to be
random (in deterministic systems). This unpredictable behaviour has
been called chaos.
•
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 selfsimilar
(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.
•
NonLinearity
 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. 
•
Gaia
Theory (Geophysiology)  broadly inclusive
name for a group of ideas that living organisms on a planet modify
the nature of the planet to make it more suitable for life. This set
of theories holds that all organisms on a planet regulate the biosphere
to the benefit of the whole. 
• SelfOrganization  the various mechanisms by which pattern,
structure and order emerge spontaneously in complex systems. Examples;
sand ripples, the coordinated movements of flocks of birds or
schools of fish, nests of termites, seashells, fingerprints, and
the galaxy. 
•
Symbiogenesis  a interaction between two organisms living together
in more or less intimate association or even the merging of two dissimilar
organisms. 
holography
and heirarchy
commonalities ?
reductionistic and holistic complements ?
mutualism, competition, parasiticism ?
statistical analysis ? deterministic ? random ?
chaos,
order, control ? fractal
commonalities ? 
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. 
Catastrophe Theory • Evolution Theory • Scientific Complexity
Experimental Mathematics • General Systems Theory
A.I. ? ? ?
• A.L. ? ? ? • Nanotech ? ? ? • Statistical Mechanics ? ? ? 
Simplicity: The property, condition, or quality of being simple or uncombined. It often denotes beauty, purity or clarity. Simple things are usually easier to explain and understand than complicated ones. Also refered to as Occom's Razor, or simple living lifestyle.
"Our life is frittered away by detail.... Simplify, simplify."
~ Henry David Thoreau
"Simplicity is the ultimate sophistication."
~ Leonardo Da Vinci
"I would have written a shorter letter, but I did not have the time."
~ Blaise Pascal, Mark Twain, T.S. Eliot....

