"Presumably, one can become a mathematical genius only if one has an outstanding capacity for forming vivid mental representations of abstract mathematical concepts - mental images that soon turn into an illusion, eclipsing the human origins of mathematical objects and endowing them with the semblance of an independent existence." (Stanislas Dehaene," The Number Sense: How the Mind Creates Mathematics", 2011)
"The second law states that a general tendency in the universe" (as a closed system) is toward elimination of all differences. Thus, the ultimate state is sameness and randomness, a chaotic simplicity. Entropy" (S), the measure of randomness, will therefore always increase. However, we know that living systems are neg-entropic" (–S). They are able not only to negate this formidable process by differentiation, but also to move toward a predefined order, an organized complexity. Using the formula I = –S, which indicates that a neg-entropic system must have information, one might conclude that movement toward complexity and order is only possible if the system has a means of knowing and an internal image of what it wants to be." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"A theory is a purely mental image of how something should be. In other words, the thought in the dark" (with eyes closed) comes first, and the comparison with nature" (eyes open) comes later. If the imagined agrees with the real, then the theory is correct." (Adrian Bejan, [interview] 2012)
"Image theory is an attempt to describe decision making as it actually occurs. […] The concept of images is central to the theory. They represent visions held by individuals and organisations that constitute how they believe the world should exist. When considering individuals, the theory refers to these images as the value image, trajectory image and strategic image. The value image is based on an individual’s ethics, morals and beliefs. The trajectory images encompass the decision maker’s goals and aspirations. Finally, for each trajectory image, a decision maker may have one or more strategic images that contain their plans, tactics and forecasts for their goal. […] In an organisational decision-making setting, these images are referred to as culture, vision and strategy." (Christopher B Stephenson, "What causes top management teams to make poor strategic decisions?", 2012)
"The concept of infinity embedded in fractals' identity provides an infinity of possibilities to explore in a single image. The repetition of a formula is the key to becoming more familiar with it. When trying a completely new formula, all fractal artists are engaged in the same activity - a random playing around." (Mehrdad Garousi, "The Postmodern Beauty of Fractals", Leonardo Vol. 45" (1), 2012)
"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 2013)
"Thus, when we speak of a mathematical concept, we speak not of a single isolated mental image, but rather of a family of mutually correcting mental images. They are privately owned, but publicly checked, examined, corrected, and accepted or rejected. This is the role of the mathematical research community, how it indoctrinates and certifies new members, how it reviews, accepts or rejects proposed publication, how it chooses directions of research to follow and develop, or to ignore and allow to die. All these social activities are based on a necessary condition: that the individual members have mental models that fit together, that yield the same answers to test questions. A new branch of mathematics is established when consensus is reached about the possible test questions and their answers. That collection of possible questions and answers" (not necessarily explicit) becomes the means of accepting or rejecting proposed new members." (Reuben Hersh,"Mathematical Intuition: Poincaré, Pólya, Dewey" [in"The Courant–Friedrichs–Lewy" (CFL) Condition", 2013])
"To know how scientists engage in visual imagery is to understand how they think creatively." (Edward O Wilson, "Letters to a Young Scientist", 2013)
"We identify and analyze distorting mental models that constitute experience in a manner that occludes the moral dimension of situations from view, thereby thwarting the first step of ethical decision-making. Examples include an unexamined moral self-image, viewing oneself as merely a bystander, and an exaggerated conception of self-sufficiency. These mental models, we argue, generate blind spots to ethics, in the sense that they limit our ability to see facts that are right before our eyes – sometimes quite literally, as in the many examples of managers and employees who see unethical behavior take place in front of them, but do not recognize it as such." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)
"Mental imagery is often useful in problem solving. Verbal descriptions of problems can become confusing, and a mental image can clear away excessive detail to bring out important aspects of the problem. Imagery is most useful with problems that hinge on some spatial relationship. However, if the problem requires an unusual solution, mental imagery alone can be misleading, since it is difficult to change one’s understanding of a mental image. In many cases, it helps to draw a concrete picture since a picture can be turned around, played with, and reinterpreted, yielding new solutions in a way that a mental image cannot." (James Schindler, "Followership", 2014)
"A mental representation is a mental structure that corresponds to an object, an idea, a collection of information, or anything else, concrete or abstract, that the brain is thinking about. […] Because the details of mental representations can differ dramatically from field to field, it’s hard to offer an overarching definition that is not too vague, but in essence these representations are preexisting patterns of information - facts, images, rules, relationships, and so on - that are held in long-term memory and that can be used to respond quickly and effectively in certain types of situations." (Anders Ericsson & Robert Pool," Peak: Secrets from the New Science of Expertise", 2016)
"Geometric pattern repeated at progressively smaller scales, where each iteration is about a reproduction of the image to produce completely irregular shapes and surfaces that can not be represented by classical geometry. Fractals are generally self-similar" (each section looks at all) and are not subordinated to a specific scale. They are used especially in the digital modeling of irregular patterns and structures in nature." (Mauro Chiarella, "Folds and Refolds: Space Generation, Shapes, and Complex Components", 2016)
"Most of us have difficulty figuring probabilities and statistics in our heads and detecting subtle patterns in complex tables of numbers. We prefer vivid pictures, images, and stories. When making decisions, we tend to overweight such images and stories, compared to statistical information. We also tend to misunderstand or misinterpret graphics." (Daniel J Levitin, "Weaponized Lies", 2017)
"Images are generally resistant to change and ignore messages that do not conform to their internal settings. Sometimes, however, they do react and can alter in an incremental or even revolutionary manner. Humans can talk about and share their images and, in the symbolic universe they create, reflect upon what is and what might be." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)
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