"The mathematical and computing techniques for making programmed decisions replace man but they do not generally simulate him." (Herbert A Simon, "Corporations 1985", 1960)
"The main object of cybernetics is to supply adaptive, hierarchical models, involving feedback and the like, to all aspects of our environment. Often such modelling implies simulation of a system where the simulation should achieve the object of copying both the method of achievement and the end result. Synthesis, as opposed to simulation, is concerned with achieving only the end result and is less concerned (or completely unconcerned) with the method by which the end result is achieved. In the case of behaviour, psychology is concerned with simulation, while cybernetics, although also interested in simulation, is primarily concerned with synthesis." (Frank H George, "Soviet Cybernetics, the militairy and Professor Lerner", New Scientist, 1973)
"Computer based simulation is now in wide spread use to analyse system models and evaluate theoretical solutions to observed problems. Since important decisions must rely on simulation, it is essential that its validity be tested, and that its advocates be able to describe the level of authentic representation which they achieved." (Richard Hamming, 1975)
"When a real situation involves chance we have to use probability mathematics to understand it quantitatively. Direct mathematical solutions sometimes exist […] but most real systems are too complicated for direct solutions. In these cases the computer, once taught to generate random numbers, can use simulation to get useful answers to otherwise impossible problems."
"The real leverage in most management situations lies in understanding dynamic complexity, not detail complexity. […] Unfortunately, most 'systems analyses' focus on detail complexity not dynamic complexity. Simulations with thousands of variables and complex arrays of details can actually distract us from seeing patterns and major interrelationships. In fact, sadly, for most people 'systems thinking' means 'fighting complexity with complexity', devising increasingly 'complex' (we should really say 'detailed') solutions to increasingly 'complex' problems. In fact, this is the antithesis of real systems thinking."
"A model for simulating dynamic system behavior requires formal policy descriptions to specify how individual decisions are to be made. Flows of information are continuously converted into decisions and actions. No plea about the inadequacy of our understanding of the decision-making processes can excuse us from estimating decision-making criteria. To omit a decision point is to deny its presence - a mistake of far greater magnitude than any errors in our best estimate of the process." (Jay W Forrester, "Policies, decisions and information sources for modeling", 1994)
"A field of study that includes a methodology for constructing computer simulation models to achieve better under-standing of social and corporate systems. It draws on organizational studies, behavioral decision theory, and engineering to provide a theoretical and empirical base for structuring the relationships in complex systems." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Casual Loops", 1997)
"What it means for a mental model to be a structural analog is that it embodies a representation of the spatial and temporal relations among, and the causal structures connecting the events and entities depicted and whatever other information that is relevant to the problem-solving talks. […] The essential points are that a mental model can be nonlinguistic in form and the mental mechanisms are such that they can satisfy the model-building and simulative constraints necessary for the activity of mental modeling." (Nancy J Nersessian, "Model-based reasoning in conceptual change", 1999)
"A neural network is a particular kind of computer program, originally developed to try to mimic the way the human brain works. It is essentially a computer simulation of a complex circuit through which electric current flows." (Keith J Devlin & Gary Lorden, "The Numbers behind NUMB3RS: Solving crime with mathematics", 2007)
"[...] a model is a tool for taking decisions and any decision taken is the result of a process of reasoning that takes place within the limits of the human mind. So, models have eventually to be understood in such a way that at least some layer of the process of simulation is comprehensible by the human mind. Otherwise, we may find ourselves acting on the basis of models that we don’t understand, or no model at all.” (Ugo Bardi, “The Limits to Growth Revisited”, 2011)
"Not only the mathematical way of thinking, but also simulations assisted by mathematical methods, is quite effective in solving problems. The latter is utilized in various fields, including detection of causes of troubles, optimization of expected performances, and best possible adjustments of usage conditions. Conversely, without the aid of mathematical methods, our problem-solving effort will get stuck most probably [...]" (Shiro Hiruta, "Mathematics Contributing to Innovation of Management", [in "What Mathematics Can Do for You"] 2013)
"System dynamics [...] uses models and computer simulations to understand behavior of an entire system, and has been applied to the behavior of large and complex national issues. It portrays the relationships in systems as feedback loops, lags, and other descriptors to explain dynamics, that is, how a system behaves over time. Its quantitative methodology relies on what are called 'stock-and-flow diagrams' that reflect how levels of specific elements accumulate over time and the rate at which they change. Qualitative systems thinking constructs evolved from this quantitative discipline." (Karen L Higgins, "Economic Growth and Sustainability: Systems Thinking for a Complex World", 2015)
"Optimization is more than finding the best simulation results. It is itself a complex and evolving field that, subject to certain information constraints, allows data scientists, statisticians, engineers, and traders alike to perform reality checks on modeling results." (Chris Conlan, "Automated Trading with R: Quantitative Research and Platform Development", 2016)
"But [bootstrap-based] simulations are clumsy and time-consuming, especially with large data sets, and in more complex circumstances it is not straightforward to work out what should be simulated. In contrast, formulae derived from probability theory provide both insight and convenience, and always lead to the same answer since they don’t depend on a particular simulation. But the flip side is that this theory relies on assumptions, and we should be careful not to be deluded by the impressive algebra into accepting unjustified conclusions." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)
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