Quotable Mathematics

"Beliefs are generalizations about the past projected onto the present and future to shape it in the image of the past. [...] When we g...

"In general, we seem to associate complexity with anything we find difficult to understand." (Robert L Flood, "Complexity: a ...

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necess...

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

"It bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical oper...

"A higher-level formal language is an abstract machine." (Joseph Weizenbaum, "Computer power and human reason: From judgment ...

"The moral universe is so closely linked to the physical universe that it is scarcely likely that they are not one and the same machine...

"[Systems thinking is] A new way to view and mentally frame what we see in the world; a worldview and way of thinking whereby we see th...

"A mental model is a collection of 'connected' autonomous objects. Running  a mental model corresponds to modifying the paramet...

"Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently." (Benoît Ma...

  "Synergy is the only word in our language that means behavior of whole systems unpredicted by the separately observed behaviors of an...

"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...

"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...

"The first attempts to consider the behavior of so-called 'random neural nets' in a systematic way have led to a series of ...

"Ninety-nine [students] out of a hundred are automata, careful to walk in prescribed paths, careful to follow the prescribed custom. Th...

"Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonline...

"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 ...