Mental Models XXVII

"Beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality) [...]." (Plato, "The Symposium", cca. 385–370 BC)

"In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished." (Gottfried W Leibniz, [letter to Ehrenfried W von Tschirnhaus] cca. 1680)

"The eye of the intellect 'sees in all objects what it brought with it the means of seeing'" (Thomas Carlyle, [probably quoting Varnhagen von Ense] 1839)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)

“There are great differences in the power of forming pictures of objects in the mind's eye; in other words of visualising them. In some persons the faculty of perceiving these images is so feeble that they hardly visualise at all. […] Other persons perceive past scenes with a distinctness and an appearance of reality that differ little from actual vision. Between these wide extremes I have met with a mass of intermediate cases extending in an unbroken series.”  (Francis Galton, “Mental imagery”, 1880)

"[...] thought is the representative or cognitive apprehension of relations among notions; imagination is the affective or felt apprehension of relations among images.” (James M Baldwin,"Handbook of Psychology: Senses and Intellect", 1890) 

"The direct task of our cognitive apparatus is the formation of invariants, and namely invariants of perception, thinking and motives. […] Still, in the first place, exactly these invariants are, cybernetically speaking, enabling a stabilization of the relationship between humans and their environment and between humans themselves." (Georg Klaus, "Kybernetik und Erkenntnistheorie" ["Cybernetics and Epistemology"], 1966)

"Mathematics associates new mental images with […] physical abstractions; these images are almost tangible to the trained mind but are far removed from those that are given directly by life and physical experience." (Yuri I Manin, "Mathematics and Physics", 1981)

"In broad terms, a mental model is to be understood as a dynamic symbolic representation of external objects or events on the par. t of some natural or artificial cognitive system. Mental models are thought to have certain properties which make them stand out against other forms of symbolic representations." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)

"According to the representational format claim, images constitute a class of mental models that is particularly suited to represent visually perceptible information. More specifically, an image can be conceived of as a viewer centered projection of an underlying mental model which, in turn, represents spatiotemporal aspects of external objects or events. Unlike propositional or network representations, images depict, rather than describe, a particular state of affairs." (Gert Rickheit & Lorenz Sichelschmidt, „Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)