"[…] a complex system is incomprehensible unless we can simplify it by using alternative levels of description." (John L Casti, "On System Complexity: Identification, Measurement, and Management" [in "Complexity, Language, and Life: Mathematical Approaches"] 1986)
"Coping with complexity involves the creation of faithful models of not only the system to be managed. but also of the management system itself." (John L Casti, "On System Complexity: Identification, Measurement, and Management" [in "Complexity, Language, and Life: Mathematical Approaches"] 1986)
"[…] complexity emerges from simplicity when alternative descriptions of a system are not reducible to each other. For a given observer, the more such inequivalent descriptions he or she generates, the more complex the system appears. Conversely, a complex system can be simplified in one of two ways: reduce the number of potential descriptions (by restricting the observer's means of interaction with the system) and/or use a coarser notion of system equivalence, thus reducing the number of equivalence classes." (John L Casti, "On System Complexity: Identification, Measurement, and Management" [in "Complexity, Language, and Life: Mathematical Approaches"] 1986)
"Simple systems generally involve a small number of components. with self-interaction dominating the mutual interaction of the variables. […] Besides involving only a few variables. simple systems generally have very few feedback/feedforward loops. Such loops enable the system to restructure. or at least modify. the interaction pattern of its variables. thereby opening-up the possibility of a wider range of potential behavior patterns." (John L Casti, "On System Complexity: Identification, Measurement, and Management" [in "Complexity, Language, and Life: Mathematical Approaches"] 1986)
"[…] a model is a mathematical representation of the modeler's reality, a way of capturing some aspects of a particular reality within the framework of a mathematical apparatus that provides us with a means for exploring the properties of the reality mirrored in the model." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)
"Basically, the point of making models is to be able to bring a measure of order to our experiences and observations, as well as to make specific predictions about certain aspects of the world we experience." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)
"Reliable information processing requires the existence of a good code or language, i.e., a set of rules that generate information at a given hierarchical level, and then compress it for use at a higher cognitive level. To accomplish this, a language should strike an optimum balance between variety (stochasticity) and the ability to detect and correct errors (memory)."(John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)
"Skewness is a measure of symmetry. For example, it's zero for the bell-shaped normal curve, which is perfectly symmetric about its mean. Kurtosis is a measure of the peakedness, or fat-tailedness, of a distribution. Thus, it measures the likelihood of extreme values." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)
"[…] the complexity of a given system is always determined relative to another system with which the given system interacts. Only in extremely special cases, where one of these reciprocal interactions is so much weaker than the other that it can be ignored, can we justify the traditional attitude regarding complexity as an intrinsic property of the system itself." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)
"The core of a decision problem is always to find a single method that can be applied to each question, and that will always give the correct answer for each individual problem." (John L Casti, "Mathematical Mountaintops: The Five Most Famous Problems of All Time", 2001)
"[…] according to the bell-shaped curve the likelihood of a very-large-deviation event (a major outlier) located in the striped region appears to be very unlikely, essentially zero. The same event, though, is several thousand times more likely if it comes from a set of events obeying a fat-tailed distribution instead of the bell-shaped one." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"[…] both rarity and impact have to go into any meaningful characterization of how black any particular [black] swan happens to be." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"Due to the problem of predicting outlier events, they are not usually factored into the design of systems." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"Forecasting models […] ordinarily are based only on past data, which is generally a tiny sample of the total range of possible outcomes. The problem is that those 'experts' who develop the models often come to believe they have mapped the entire space of possible system behaviors, which could not be further from the truth. Worse yet, when outliers do crop up, they are often discounted as 'once in a century' events and are all but ignored in planning for the future. […] the world is much more unpredictable than we’d like to believe."(John L Casti, "X-Events: The Collapse of Everything", 2012)
"If you want a system - economic, social, political, or otherwise - to operate at a high level of efficiency, then you have to optimize its operation in such a way that its resilience is dramatically reduced to unknown - and possibly unknowable - shocks and/or changes in its operating environment. In other words, there is an inescapable price to be paid in efficiency in order to gain the benefits of adaptability and survivability in a highly uncertain environment. There is no escape clause!" (John L Casti, "X-Events: The Collapse of Everything", 2012)
"Sustainability is a delicate balancing act calling upon us to remain on the narrow path between organization and chaos, simplicity and complexity." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"The first path of increasing complexity via innovation often faces limits as to how much complexity can be added or reduced in a given system. This is because if you change the complexity level in one place, a compensating change in the opposite direction generally occurs somewhere else." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"[…] the law of requisite complexity […] states that in order to fully regulate/control a system, the complexity of the controller has to be at least as great as the complexity of the system that’s being controlled. To put it in even simpler terms, only complexity can destroy complexity." (John L Casti, "X-Events: The Collapse of Everything", 2012)
"What is and isn’t complex depends to a large degree not only on a target system, but also on the system(s) the target interacts with, together with the overall context in which the interacting systems are embedded." (John L Casti, "X-Events: The Collapse of Everything", 2012)
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