"If we study the history of science we see happen two inverse phenomena […] Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities. […] No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations." (Henri Poincaré, "Science and Hypothesis", 1901)
"The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it’." (Alfred N Whitehead, "The Concept of Nature", 1919)
"[Disorganized complexity] is a problem in which the number of variables is very large, and one in which each of the many variables has a behavior which is individually erratic, or perhaps totally unknown. However, in spite of this helter-skelter, or unknown, behavior of all the individual variables, the system as a whole possesses certain orderly and analyzable average properties. [...] [Organized complexity is] not problems of disorganized complexity, to which statistical methods hold the key. They are all problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole. They are all, in the language here proposed, problems of organized complexity." (Warren Weaver, "Science and Complexity", American Scientist Vol. 36, 1948)
"Nor does complexity deny the valid simplification which is part of the process of analysis, and even a method of achieving complex architecture itself." (Robert Venturi, "Complexity and Contradiction in Architecture", 1966)
"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos." (Herbert A Simon, "The Sciences of the Artificial", 1969)
"At each level of complexity, entirely new properties appear. [And] at each stage, entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one." (Herb Anderson, 1972)
"In general, complexity and precision bear an inverse relation to one another in the sense that, as the complexity of a problem increases, the possibility of analysing it in precise terms diminishes. Thus 'fuzzy thinking' may not be deplorable, after all, if it makes possible the solution of problems which are much too complex for precise analysis." (Lotfi A Zadeh, "Fuzzy languages and their relation to human intelligence", 1972)
"Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius - and a lot of courage to move in the opposite direction." (Ernst F Schumacher, "Small is Beautiful", 1973)
"The aim of the model is of course not to reproduce reality in all its complexity. It is rather to capture in a vivid, often formal, way what is essential to understanding some aspect of its structure or behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation", 1976)
"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves at each level of system." (James G Miller, "Living Systems", 1978)
"Simplicity does not precede complexity, but follows it." (Alan J Perlis, "Epigrams on Programming", 1982)
"Organized simplicity occurs where a small number of significant factors and a large number of insignificant factors appear initially to be complex, but on investigation display hidden simplicity." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)
"The state of development of mathematical theory in relation to some attributes of complexity is a clear measure of our ability/inability to deal with that attribute […]" (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)
"Complexity is not an objective factor but a subjective one. Supersignals reduce complexity, collapsing a number of features into one. Consequently, complexity must be understood in terms of a specific individual and his or her supply of supersignals. We learn supersignals from experience, and our supply can differ greatly from another individual's. Therefore there can be no objective measure of complexity." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)
"Modeling in its broadest sense is the cost-effective use of something in place of something else for some [cognitive] purpose. It allows us to use something that is simpler, safer, or cheaper than reality instead of reality for some purpose. A model represents reality for the given purpose; the model is an abstraction of reality in the sense that it cannot represent all aspects of reality. This allows us to deal with the world in a simplified manner, avoiding the complexity, danger and irreversibility of reality." (Jeff Rothenberg, "The Nature of Modeling. In: Artificial Intelligence, Simulation, and Modeling", 1989)
"A measure that corresponds much better to what is usually meant by complexity in ordinary conversation, as well as in scientific discourse, refers not to the length of the most concise description of an entity (which is roughly what AIC [algorithmic information content] is), but to the length of a concise description of a set of the entity’s regularities. Thus something almost entirely random, with practically no regularities, would have effective complexity near zero. So would something completely regular, such as a bit string consisting entirely of zeroes. Effective complexity can be high only a region intermediate between total order and complete." (Murray Gell-Mann, "What is Complexity?", Complexity Vol 1 (1), 1995)
"The larger, more detailed and complex the model - the less abstract the abstraction – the smaller the number of people capable of understanding it and the longer it takes for its weaknesses and limitations to be found out." (John Adams, "Risk", 1995)
"Complexity is that property of a model which makes it difficult to formulate its overall behaviour in a given language, even when given reasonably complete information about its atomic components and their inter-relations." (Bruce Edmonds, "Syntactic Measures of Complexity", 1999)
"Falling between order and chaos, the moment of complexity is the point at which self-organizing systems emerge to create new patterns of coherence and structures of behaviour." (Mark C Taylor, "The Moment of Complexity: Emerging Network Culture", 2001)
"[…] most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)
"The urge to tinker with a formula is a hunger that keeps coming back. Tinkering almost always leads to more complexity. The more complicated the metric, the harder it is for users to learn how to affect the metric, and the less likely it is to improve it." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)
More on "Complexity" at the-web-of-knowledge.blogspot.com.
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