On Images (1980-1989)

"A mental image occurs when a representation of the type created during the initial phases of perception is present but the stimulus is not actually being perceived; such representations preserve the perceptible properties of the stimulus and ultimately give rise to the subjective experience of perception." (Stephen M Kosslyn, "Image and Mind", 1980)

"It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings." (Stephen Kosslyn, "Image and Mind", 1980)

"Like pictures, images seem to depict information about interval spatial extents. The scanning experiments support the claim that portions of images depict corresponding portions of the represented objects, and that the spatial relations between portions of the image index the spatial relations between the corresponding portions of the imaged objects." (Stephen Kosslyn," Image and Mind", 1980)

"My suggestion is that at each state the proper order of operation of the mind requires an overall grasp of what is generally known, not only in formal logical, mathematical terms, but also intuitively, in images, feelings, poetic usage of language, etc." (David Bohm,"Wholeness and the Implicate Order Wholeness and the Implicate Order", 1980)

"[…] statistics is the science that deals with distributions and proportions in actual" (large but finite) classes" (also called ‘populations’, ‘aggregates’, ‘ensembles’) of actual things." (Bas C van Frassen,"The Scientic Image", 1980)

"These organizational processes result in our perceptions being structured into units corresponding to objects and properties of objects. It is these larger units that may be stored and later assembled into images that are experienced as quasi-pictorial, spatial entities resembling those evoked during perception itself [...] It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings." (Stephen Kosslyn, "Image and Mind", 1980)

"This is why thought as power which has not always existed, is born from an outside [duration] more distant than an external world, and, as power which does not yet exist, confronts an inside, an un thinkable or unthought, deeper than any internal world. […] Thought outside itself and this unthought within thought." (Gilles Deleuze, "Cinema 2: The Time-Image", 1980)

"What is in the present is what the image ‘represents‘, but not the image itself which, in cinema as in painting, is never to be confused with what it represents. The image itself is the system of the relationships between its elements, that is, a set of relationships from which the variable present only flows. […] What is specific in the image, as soon as it is creative, is to make perceptible, to make visible, relationships of time which cannot be seen in the represented object and do not allow them - selves to be reduced to the present." (Gilles Deleuze, "Cinema 2: The Time-Image", 1980)

"A person who thinks by images becomes less and less capable of thinking by reasoning, and vice versa. The intellectual process based on images is contradictory to the intellectual process of reasoning that is related to the word. There are two different ways of dealing with an object. They involve not only different approaches, but even more important, opposing mental attitudes. This is not a matter of complementary processes, such as analysis and synthesis or logic and dialectic. These processes lack any qualitative common denominator." (Jacques Ellul, "The Humiliation of the Word", 1981)

"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)

"That is to say, intuition is not a direct perception of something existing externally and eternally. It is the effect in the mind of certain experiences of activity and manipulation of concrete objects" (at a later stage, of marks on paper or even mental images). As a result of this experience, there is something" (a trace, an effect) in the pupil's mind which is his representation of the integers. But his representation is equivalent to mine, in the sense that we both get die same answer to any question you ask - or if we get different answers, we can compare notes and figure out what's right. We do this, not because we have been taught a set of algebraic rules, but because our mental pictures match each other." (Philip J Davis & Reuben Hersh, "The Mathematical Experience", 1981)

"The formalist makes a distinction between geometry as a deductive structure and geometry as a descriptive science. Only the first is regarded as mathematical. The use of pictures or diagrams, or even mental imagery, all are non- mathematical. In principle, they should be unnecessary. Consequently. he regards them as inappropriate in a mathematics text, perhaps even in a mathematics class." (Philip J Davis & Reuben Hersh, "The Mathematical Experience", 1981)

"The thinking person goes over the same ground many times. He looks at it from varying points of view - his own, his arch-enemy’s, others’. He diagrams it, verbalizes it, formulates equations, constructs visual images of the whole problem, or of troublesome parts, or of what is clearly known. But he does not keep a detailed record of all this mental work, indeed could not. […] Deep understanding of a domain of knowledge requires knowing it in various ways. This multiplicity of perspectives grows slowly through hard work and sets the state for the re-cognition we experience as a new insight." (Howard E Gruber, "Darwin on Man", 1981)

"Vision is a process that produces from images of the external world a description that is useful to the viewer and not cluttered with irrelevant information." (David Marr, "Vision", 1982)

"External images act on me, transmit movement to me, and I return movement: how could images be in my consciousness since I am myself image, that is, movement?" (Gilles Deleuze, "Cinema 1: The Movement Image", 1983)

"Myth is the system of basic metaphors, images, and stories that in-forms the perceptions, memories, and aspirations of a people; provides the rationale for its institutions, rituals and power structure; and gives a map of the purpose and stages of life." (Sam Keen, "The Passionate Life", 1983)

"Since mental models can take many forms and serve many purposes, their contents are very varied. They can contain nothing but tokens that represent individuals and identities between them, as in the sorts of models that are required for syllogistic reasoning. They can represent spatial relations between entities, and the temporal or causal relations between events. A rich imaginary model of the world can be used to compute the projective relations required for an image. Models have a content and form that fits them to their purpose, whether it be to explain, to predict, or to control." (Philip Johnson-Laird, "Mental models: Toward a cognitive science of language, inference, and consciousness", 1983)

"The physicist […] engages in complex and difficult calculations, involving the manipulating of ideal, mathematical quantities that, at first glance, are wholly lacking in the music of the living world and the beauty of the resplendent cosmos. It would seem as if there exists no relationship between these quantities and reality. Yet these ideal numbers that cannot be grasped by one's senses, these numbers that only are meaningful from within the system itself, only meaningful as part of abstract mathematical functions, symbolize the image of existence. […] As a result of scientific man's creativity there arises an ordered, illumined, determined world, imprinted with the stamp of creative intellect, of pure reason and clear cognition. From the midst of the order and lawfulness we hear a new song, the song of the creature to the Creator, the song of the cosmos to its Maker." (Joseph B Soloveitchik, "Halakhic Man", 1983)

"The thing and the perception of the thing are one amid the same thing, one and the same image, but related in one or other of two systems of reference. The thing is the image as it is in itself, as it is related to all the other images to whose action it completely submits and on which it reacts immediately. But the perception of the thing is the same image related to another special image which frames it, and which only retains a partial action from it, and only reacts to it mediately." (Gilles Deleuze, "Cinema 1: The Movement Image", 1983)

"In medical science arguments are going on between behaviorists who perceive the function of brain as a multitude of simple and unconscious conditioned reflexes, and cognitivists who insist that humans sensing the surrounding world create its mental image which can be considered as memory of facts." (Yevgeniy Chazov, "Tragedy and Triumph of Reason", 1985)

"That is to say, intuition is not a direct perception of something existing externally and eternally. It is the effect in the mind of certain experiences of activity and manipulation of concrete objects" (at a later stage, of marks on paper or even mental images)." (Philip J Davis & Reuben Hersh,"The Mathematical Experience", 1985)

"Any system that insulates itself from diversity in the environment tends to atrophy and lose its complexity and distinctive nature." (Gareth Morgan, "Images of Organization", 1986)

"Organizations are complex and paradoxical phenomena that can be understood in many different ways. Many of our taken-for-granted ideas about organizations are metaphorical, even though we may not recognize them as such. For example, we frequently talk about organizations as if they were machines designed to achieve predetermined goals and objectives, and which should operate smoothly and efficiently. And as a result of this kind of thinking, we often attempt to organize and manage them in a mechanistic way, forcing their human qualities into a background role. By using different metaphors to understand the complex and paradoxical character of organizational life, we are able to manage and design organizations in ways that we may not have thought possible before." (Gareth Morgan, "Images of Organization", 1986)

"An image of thought called philosophy has been formed historically and it effectively stops people from thinking." (Gilles Deleuze,"Dialogues II", 1987)

"[...] modern mathematics is rich with vivid images and provocative ideas." (Ivars Peterson, "The Mathematical Tourist", 1988)

"To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas." (Ivars Peterson, "The Mathematical Tourist", 1988)

"What were the needs that led me to single out a few of these monsters, calling them fractals, to add some of their close or distant kin, and then to build a geometric language around them? The original need happens to have been purely utilitarian. That links exist between usefulness and beauty is, of course, well known. What we call the beauty of a flower attracts the insects that will gather and spread its pollen. Thus the beauty of a flower is useful - even indispensable - to the survival of its species. Similarly, it was the attractiveness of the fractal images that first brought them to the attention of many colleagues and then of a wide world." (Benoît B Mandelbrot, "Fractals and an Art for the Sake of Science", Leonardo [Supplemental Issue], 1989)