"Man's general way of thinking of the totality, i.e. his general world view, is crucial for overall order of the human mind itself. If he thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken and without border (for every border is a division or break) then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole." (David Bohm, "Wholeness and the Implicate Order", 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)
"A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks." (Gian-Carlo Rota, 1981)
"Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through." (Hannah Arendt, "The Life of the Mind", 1981)
"If explaining minds seems harder than explaining songs, we should remember that sometimes enlarging problems makes them simpler! The theory of the roots of equations seemed hard for centuries within its little world of real numbers, but it suddenly seemed simple once Gauss exposed the larger world of so-called complex numbers. Similarly, music should make more sense once seen through listeners' minds." (Marvin Minsky, "Music, Mind, and Meaning", 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 ‘eyes of the mind’ must be able to see in the phase space of mechanics, in the space of elementary events of probability theory, in the curved four-dimensional space-time of general relativity, in the complex infinite dimensional projective space of quantum theory. To comprehend what is visible to the ‘actual eyes’, we must understand that it is only the projection of an infinite dimensional world on the retina." (Yuri I Manin, "Mathematics and Physics", 1981)
"We often hear that mathematics consists mainly in ‘proving theorems’. Is a writer’s job mainly that of ‘writing sentences’? A mathematician’s work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more often than not a way of making sure that our minds are not playing tricks." (Gian-Carlo Rota, "Complicating Mathematics" in "Discrete Thoughts", 1981)
"[…] a mathematician's ultimate concern is that his or her inventions be logical, not realistic. This is not to say, however, that mathematical inventions do not correspond to real things. They do, in most, and possibly all, cases. The coincidence between mathematical ideas and natural reality is so extensive and well documented, in fact, that it requires an explanation. Keep in mind that the coincidence is not the outcome of mathematicians trying to be realistic - quite to the contrary, their ideas are often very abstract and do not initially appear to have any correspondence to the real world. Typically, however, mathematical ideas are eventually successfully applied to describe real phenomena […]"(Michael Guillen,"Bridges to Infinity: The Human Side of Mathematics", 1983)
"Intuition can be understood as the mind turning in on itself and apprehending the result of processes that have taken place outside of awareness." (Philip Goldberg, "The Intuitive Edge", 1983)
"The psychological core of understanding consists in your having a 'working model' of the phenomenon in your mind. If you understand inflation, a mathematical proof, the way a computer works, DNA or a divorce, then you have a mental representation that serves as a model of an entity in much the same way as, say, a clock functions as a model of the earth's rotation." (Philip Johnson-Laird, "Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness", 1983)
"The vision of the Universe that is so vivid in our minds is framed by a few iron posts of true observation - themselves resting on theory for their meaning - but most of all the walls and towers in the vision are of papier-mâché, plastered in between those posts by an immense labor of imagination and theory." (John A Wheeler & Wojciech H Zurek, "Quantum Theory and Measurement", 1983)
"There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation." (Charles Hermite, The Mathematical Intelligencer, Vol. 5, No. 4, 1983)
"Concepts are inventions of the human mind used to construct a model of the world. They package reality into discrete units for further processing, they support powerful mechanisms for doing logic, and they are indispensable for precise, extended chains of reasoning. […] A mental model is a cognitive construct that describes a person's understanding of a particular content domain in the world." (John Sown, "Conceptual Structures: Information Processing in Mind and Machine", 1984)
"The quantum is that embarrassing little piece of thread that always hangs from the sweater of space-time. Pull it and the whole thing unravels." (Fred A Wolf, "Star Wave: Mind Consciousness of Quantum Physics", 1984)
"The third model regards mind as an information processing system. This is the model of mind subscribed to by cognitive psychologists and also to some extent by the ego psychologists. Since an acquisition of information entails maximization of negative entropy and complexity, this model of mind assumes mind to be an open system." (Thaddus E Weckowicz, "Models of Mental Illness", 1984)
"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, "Biophilia", 1984)
"Under pressure from the computer, the question of mind in relation to machine is becoming a central cultural preoccupation." (Sherry Turkle, "The Second Self: Computers and the Human Spirit", 1984)
"Mathematics is not a topic that one can easily approach with a virgin mind." (Wilfrid Hodges, "Building Models by Games", 1985)
"We who are heirs to three recent centuries of scientific development can hardly imagine a state of mind in which many mathematical objects were regarded as symbols of spiritual truths or episodes in sacred history. Yet, unless we make this effort of imagination, a fraction of the history of mathematics is incomprehensible." (Philip J Davis & Rueben Hersh, "The Mathematical Experience", 1985)
"Artificial intelligence is based on the assumption that the mind can be described as some kind of formal system manipulating symbols that stand for things in the world. Thus it doesn't matter what the brain is made of, or what it uses for tokens in the great game of thinking. Using an equivalent set of tokens and rules, we can do thinking with a digital computer, just as we can play chess using cups, salt and pepper shakers, knives, forks, and spoons. Using the right software, one system (the mind) can be mapped onto the other (the computer)." (George Johnson, Machinery of the Mind: Inside the New Science of Artificial Intelligence, 1986)
"The hardest problems we have to face do not come from philosophical questions about whether brains are machines or not. There is not the slightest reason to doubt that brains are anything other than machines with enormous numbers of parts that work in perfect accord with physical laws. As far as anyone can tell, our minds are merely complex processes. The serious problems come from our having had so little experience with machines of such complexity that we are not yet prepared to think effectively about them." (Marvin Minsky, 1986)
"Although science literally means ‘knowledge’, the scientific attitude is concerned much more with rational perception through the mind and with testing such perceptions against actual fact, in the form of experiments and observations." (David Bohm & F David Peat, "Science, Order, and Creativity", 1987)
"Modeling underlies our ability to think and imagine, to use signs and language, to communicate, to generalize from experience, to deal with the unexpected, and to make sense out of the raw bombardment of our sensations. It allows us to see patterns, to appreciate, predict, and manipulate processes and things, and to express meaning and purpose. In short, it is one of the most essential activities of the human mind. It is the foundation of what we call intelligent behavior and is a large part of what makes us human. We are, in a word, modelers: creatures that build and use models routinely, habitually – sometimes even compulsively – to face, understand, and interact with reality." (Jeff Rothenberg, "The Nature of Modeling. In: Artificial Intelligence, Simulation, and Modeling", 1989)
"The common perception of science as a rational activity, in which one confronts the evidence of fact with an open mind, could not be more false. Facts assume significance only within a pre-existing intellectual structure, which may be based as much on intuition and prejudice as on reason." (Walter Gratzer, The Guardian, 1989)
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