Quotable Mathematics

"[...] emergence is an integral part of the dynamics of open systems [...] " (Fritjof  Capra, "The Hidden Connections", ...

"Stability is commonly thought of as desirable, for its presence enables the system to combine of flexibility and activity in performan...

"[...] if the behavior points for the entire control surface are plotted and then connected, they form a smooth surface: the behavior s...

"To build matter itself from geometry - that in a sense is what string theory does. It can be thought of that way, especially in a theo...

"A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be s...

"In short, complex adaptive systems are characterized by perpetual novelty." (M Mitchell Waldrop, "Complexity: The Emerging S...

"Complexity is the characteristic property of complicated systems we don’t understand immediately. It is the amount of difficulties we ...

"Complexity must be grown from simple systems that already work."  (Kevin Kelly, "Out of Control: The New Biology of Machines...

"When one combines the new insights gained from studying far-from-equilibrium states and nonlinear processes, along with these comp...

"Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic...

"In complex systems cause and effect are often not closely related in either time or space. The structure of a complex system is not a ...

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The ...

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are ...

"The principle that whole entities exhibit properties which are meaningful only when attributed to the whole, not to its parts - e.g. t...

"The chaos theory will require scientists in all fields to, develop sophisticated mathematical skills, so that they will be able to bet...

"As perceivers we select from all the stimuli falling on our senses only those which interest us, and our interests are governed by a p...

"Every system of whatever size must maintain its own structure and must deal with a dynamic environment, i.e., the system must strike a...

"The systems approach to problems focuses on systems taken as a whole, not on their parts taken separately. Such an approach is concern...

"Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the ...