26 November 2020

On Representation (2010-2019)

"Mental models represent possibilities, and the theory of mental models postulates three systems of mental processes underlying inference: (0) the construction of an intensional representation of a premise’s meaning – a process guided by a parser; (1) the building of an initial mental model from the intension, and the drawing of a conclusion based on heuristics and the model; and (2) on some occasions, the search for alternative models, such as a counterexample in which the conclusion is false. System 0 is linguistic, and it may be autonomous. System 1 is rapid and prone to systematic errors, because it makes no use of a working memory for intermediate results. System 2 has access to working memory, and so it can carry out recursive processes, such as the construction of alternative models." (Sangeet Khemlania & P.N. Johnson-Laird, "The processes of inference", Argument and Computation, 2012)

"Simply put, a conceptual model is a simplified representation of reality, devised for a certain purpose and seen from a certain point of view." (David W Emble & Bernhard Thalheim, "Handbook of Conceptual Modeling", 2012)

"Representation is intrinsic to human life and engineering practice. We communicate with other people throughout the design and construction process by means of words, diagrams, and sketches. We create mental and computational models of materials, loads, and the arrangement of members. We develop building information models (BIM), drawings, and specifications to indicate how the various pieces and parts are to be assembled into the finished structure." (Jon A Schmidt, "Representation and Reality", Structure [magazine], 2015)

"The intent of these representations is to capture the relevant characteristics of reality, which may overlap but are not identical in each case. The engineer has to ascertain what those are, and then incorporate appropriate assumptions and simplifications accordingly. Two common strategies are abstraction, which involves neglecting certain aspects of reality in order to gain a better understanding of the remaining aspects; and idealization, which involves replacing a complicated and/or complex aspect of reality with a simplified version." (Jon A Schmidt, "Representation and Reality", Structure [magazine], 2015)

“A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, “Calculus: Early Transcedentals” 8th Ed., 2016)

“A mental model is not necessarily founded on facts or complete understanding of reality. Let's be honest, most of our mental models are flawed in many ways, and that's perfectly normal. They work because they are fast and simple and not because they are a complete representation of the reality. […] The most important thing about a person's mental model is that it's simplified and very limited compared to what it models.” (Peter W Szabo, “User Experience Mapping”, 2017)

"Once we understand our user's mental model, we can capture it in a conceptual model. The conceptual model is a representation of the mental model using elements, relationships, and conditions. Our design and final system will be the tangible result of this conceptual model." (Pau Giner & Pablo Perea, "UX Design for Mobile, 2017) 

"A model or conceptual model is a schematic or representation that describes how something works. We create and adapt models all the time without realizing it. Over time, as you gain more information about a problem domain, your model will improve to better match reality." (James Padolsey, "Clean Code in JavaScript", 2020)

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