On Entropy: Definitions

"Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Clichés, for example, are less illuminating than great poems." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"Entropy is a measure of the heat energy in a substance that has been lost and is no longer available for work. It is a measure of the deterioration of a system." (William B. Sill & Norman Hoss (Eds.), "Popular Science Encyclopedia of the Sciences", 1963)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Entropy is not about speeds or positions of particles, the way temperature and pressure and volume are, but about our lack of information." (Hans C von Baeyer," Information, The New Language of Science", 2003)

"Entropy is a measure of amount of uncertainty or disorder present in the system within the possible probability distribution. The entropy and amount of unpredictability are directly proportional to each other." ("G Suseela & Y Asnath V Phamila, "Security Framework for Smart Visual Sensor Networks", 2019)

"In the physics [entropy is the] rate of system's messiness or disorder in a physical system. In the social systems theory - social entropy is a sociological theory that evaluates social behaviors using a method based on the second law of thermodynamics." (Justína Mikulášková et al, "Spiral Management: New Concept of the Social Systems Management", 2020)

Out of Context: On Patterns (Definitions)

"From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"When someone shows you a pattern, no matter how impressive the person’s credentials, consider the possibility that the pattern is just a coincidence. Ask why, not what. No matter what the pattern, the question is: Why should we expect to find this pattern?" (Gary Smith, "Standard Deviations", 2014)

"Don’t be fooled into thinking that a pattern is proof. We need a logical, persuasive explanation and we need to test the explanation with fresh data." (Gary Smith, "Standard Deviations", 2014)

"A pattern is a design or model that helps grasp something. Patterns help connect things that may not appear to be connected. Patterns help cut through complexity and reveal simpler understandable trends." (Anil K. Maheshwari, "Business Intelligence and Data Mining", 2015)

"By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"Thanks to their flexibility, the most complex models available to us can fit any patterns that appear in the data, but this means that they will also do so even when those patterns are mere phantoms and mirages in the noise." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)

Out of Context: On Diagrams (Definitions)

 "Diagrams are of great utility for illustrating certain questions of vital statistics by conveying ideas on the subject through the eye, which cannot be so readily grasped when contained in figures." (Florence Nightingale, "Mortality of the British Army", 1857)

"Diagrams are sometimes used, not merely to convey several pieces of information such as several time series on one chart, but also to provide visual evidence of relationships between the series." (Alfred R Ilersic, "Statistics", 1959)

"Diagrams, whether representational or symbolic, are meaningless unless attached to some body of theory. On the other hand theories are in no need of diagrams save for psychological purposes. Let us then keep theoretical models apart from visual analogues."  (Mario Bunge, "Philosophy of Physics", 1973)

"Schematic diagrams are more abstract than pictorial drawings, showing symbolic elements and their interconnection to make clear the configuration and/or operation of a system." (Ernest O Doebelin, "Engineering experimentation: planning, execution, reporting", 1995)

"[...] (4) Diagrams are psychologically useful, but prove nothing; (5) Diagrams can even be misleading [...]" (James R Brown,"Philosophy of Mathematics", 1999)

"A model diagram declares some sets and binary relations, and imposes some basic constraints on them. A diagram is a good way to convey the outline of a model, but diagrams aren’t expressive enough to include detailed constraints." (Daniel Jackson, "Software Abstractions", 2006) 

"[...] diagrams are models, graphical in nature, that are used to illustrate structure (e.g., how components are physically interconnected); they do not capture functional behavior of a system. "  (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)

On Diagrams: Definitions

"A diagram is a representamen [representation] which is predominantly an icon of relations and is aided to be so by conventions. Indices are also more or less used. It should be carried out upon a perfectly consistent system of representation, founded upon a simple and easily intelligible basic idea." (Charles S Peirce, 1903)

"A diagram is an icon or schematic image embodying the meaning of a general predicate; and from the observation of this icon we are supposed to construct a new general predicate." (Charles S Peirce, "New Elements" ["Kaina stoiceia"], 1904)

"[The diagram] is only an heuristic to prompt certain trains of inference; [...] it is dispensable as a proof-theoretic device; indeed, [...] it has no proper place in the proof as such. For the proof is a syntactic object consisting only of sentences arranged in a finite and inspectable array." (Neil Tennant, "The withering away of formal semantics", Mind and Language Vol. 1 (4), 1986)

"Diagrams are a means of communication and explanation, and they facilitate brainstorming. They serve these ends best if they are minimal. Comprehensive diagrams of the entire object model fail to communicate or explain; they overwhelm the reader with detail and they lack meaning." (Eric Evans, "Domain-Driven Design: Tackling complexity in the heart of software", 2003)

"A diagram is a graphic shorthand. Though it is an ideogram, it is not necessarily an abstraction. It is a representation of something in that it is not the thing itself. In this sense, it cannot help but be embodied. It can never be free of value or meaning, even when it attempts to express relationships of formation and their processes. At the same time, a diagram is neither a structure nor an abstraction of structure." (Peter Eisenman, "Written Into the Void: Selected Writings", 1990-2004, 2007)

"Diagrams are information graphics that are made up primarily of geometric shapes, such as rectangles, circles, diamonds, or triangles, that are typically (but not always) interconnected by lines or arrows. One of the major purposes of a diagram is to show how things, people, ideas, activities, etc. interrelate and interconnect. Unlike quantitative charts and graphs, diagrams are used to show interrelationships in a qualitative way." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)

"[...] diagrams are models, graphical in nature, that are used to illustrate structure (e.g., how components are physically interconnected); they do not capture functional behavior of a system. "  (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)