"[a pictorial representation] is not a faithful record of a visual experience, but the faithful construction of a relational model […] Such a model can be constructed to any required degree of accuracy . What is decisive here is clearly the word 'required'. The form of a representation cannot be divorced from its purpose and the requirements of the society in which the given visual language gains currency." (Ernst H Gombrich," Art and illusion", 1960)
"By a symbol I do not mean an allegory or a sign, but an image that describes in the best possible way the dimly discerned nature of the spirit. A symbol does not define or explain; it points beyond itself to a meaning that is darkly divined yet still beyond our grasp, and cannot be adequately expressed in the familiar words of our language." (Carl G Jung, "The Structure And Dynamics Of The Psyche", 1960)
"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." (Eugene P Wigner,"The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)
"Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. [...] The student's task in learning set theory is to steep himself in unfamiliar but essentially shallow generalities till they become so familiar that they can be used with almost no conscious effort. In other words, general set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some, and here it is; read it, absorb it, and forget it [...] the language and notation are those of ordinary informal mathematics. A more important way in which the naive point of view predominates is that set theory is regarded as a body of facts, of which the axioms are a brief and convenient summary; in the orthodox axiomatic view the logical relations among various axioms are the central objects of study. (Paul R Halmos, "Naive Set Theory", 1960)
"Language, in its origin and essence, is simply a system of signs or symbols that denote real occurrences or their echo in the human soul." (Carl G Jung, "The Structure And Dynamics Of The Psyche", 1960)
"Numbers are the landmarks which enable us to speak in a language common to all men, of successive moments of duration." (Félix E Borel, "Space and Time", 1960)
"Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefor objective in the sense that it can be unambiguously communicated in ordinary human language." (Niels Bohr, "The Unity of Human Knowledge", 1960)
"The enormous usefulness of mathematics in natural sciences is something bordering on the mysterious, and there is no rational explanation for it. It is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," 1960)
"The mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. This shows that the mathematical language has more to commend it than being the only language which we can speak; it shows that it is, in a very real sense, the correct language." (Eugene P Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications in Pure and Applied Mathematics 13 (1), 1960)
"Every economic and social situation or problem is now described in statistical terms, and we feel that it is such statistics which give us the real basis of fact for understanding and analysing problems and difficulties, and for suggesting remedies. In the main we use such statistics or figures without any elaborate theoretical analysis; little beyond totals, simple averages and perhaps index numbers. Figures have become the language in which we describe our economy or particular parts of it, and the language in which we argue about policy." (Ely Devons, "Essays in Economics", 1961)
"The two most important characteristics of the language of statistics are first, that it describes things in quantitative terms, and second, that it gives this description an air of accuracy and precision. The limitations, as well as the advantages, of the statistical approach arise from these two characteristics. For a description of the quantitative aspect of events never gives us the whole story; and even the best statistics are never, and never can be, completely accurate and precise. To avoid misuse of the language we must, therefore, guard against exaggerating the importance of the elements in any situation that can be described quantitatively, and we must know sufficient about the error and inaccuracy of the figures to be able to use them with discretion." (Ely Devons, "Essays in Economics", 1961)
"Indeed the language of statistics is rarely as objective as we imagine. The way statistics are presented, their arrangement in a particular way in tables, the juxtaposition of sets of figures, in itself reflects the judgment of the author about what is significant and what is trivial in the situation which the statistics portray." (Ely Devons, "Essays in Economics", 1961)
"The art of using the language of figures correctly is not to be over-impressed by the apparent air of accuracy, and yet to be able to take account of error and inaccuracy in such a way as to know when, and when not, to use the figures. This is a matter of skill, judgment, and experience, and there are no rules and short cuts in acquiring this expertness." (Ely Devons, "Essays in Economics", 1961)
"The two most important characteristics of the language of statistics are first, that it describes things in quantitative terms, and second, that it gives this description an air of accuracy and precision." (Ely Devons, "Essays in Economics", 1961)
"We all know that in economic statistics particularly, true precision, comparability and accuracy is extremely difficult to achieve, and it is for this reason that the language of economic statistics is so difficult to handle." (Ely Devons, "Essays in Economics", 1961)
"Cybernetics is concerned primarily with the construction of theories and models in science, without making a hard and fast distinction between the physical and the biological sciences. The theories and models occur both in symbols and in hardware, and by 'hardware’ we shall mean a machine or computer built in terms of physical or chemical, or indeed any handleable parts. Most usually we shall think of hardware as meaning electronic parts such as valves and relays. Cybernetics insists, also, on a further and rather special condition that distinguishes it from ordinary scientific theorizing: it demands a certain standard of effectiveness. In this respect it has acquired some of the same motive power that has driven research on modern logic, and this is especially true in the construction and application of artificial languages and the use of operational definitions. Always the search is for precision and effectiveness, and we must now discuss the question of effectiveness in some detail. It should be noted that when we talk in these terms we are giving pride of place to the theory of automata at the expense, at least to some extent, of feedback and information theory." (Frank H George, "The Brain As A Computer", 1962)
"All our language is composed of brief little dreams; and the wonderful thing is that we sometimes make of them strangely accurate and marvelously reasonable thoughts. […] What should we be without the help of that which does not exist? Very little. And our unoccupied minds would languish if fables, mistaken notions, abstractions, beliefs, and monsters, hypotheses, and the so-called problems of metaphysics did not people with beings and objectless images our natural depths and darkness. Myths are the souls of our actions and our loves. We cannot act without moving towards a phantom. We can love only what we create." (Paul Valéry, "The Outlook for Intelligence", 1962)
"The problems are the ones that we have always known. The little gods are still with us, under different names. There is conformity: of technique, leading to repetition; of language, encouraging if not imposing conformity of thought. There is popularity: it is so easy to ride along on an already surging tide; to plant more seed in an already well-ploughed field; so hard to drive a new furrow into stony ground. There is laxness: the disregard of small errors, of deviations, of the unexpected response; the easy worship of the smooth curve. There is also fear: the fear of speculation; the overprotective fear of being wrong. We are forgetful of the curious and wayward dialectic of science, whereby a well-constructed theory even if it is wrong, can bring a signal advance." (Dickinson W Richards, Transactions of the Association of American Physicians Vol. 75, 1962)
"There is folk poetry in the common names; but science, devoted to order and systematic knowledge, insists on classifying and defining. The poet’s buttercup is the botanist’s Ranunculus. If you would walk with scientist as well as poet, learn both languages." (Hal Borland, "Beyond Your Doorstep: A Handbook to the Country", 1962)
"We must include in any language with which we hope to describe complex data-processing situations the capability for describing data." (Grace Hopper, "Management and the Computer of the Future", 1962)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 1963)
"This language controls by reducing the linguistic forms and symbols of reflection, abstraction, development, contradiction; by substituting images for concepts. It denies or absorbs the transcendent vocabulary; it does not search for but establishes and imposes truth and falsehood." (Herbert Marcuse, "One-Dimensional Man", 1964)
"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. […] If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." (Richard P Feynman, "The Character of Physical Law", 1965)
"The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply." (Clifford Truesdell & Walter Noll, "The Non-Linear Field Theories of Mechanics", 1965)
"In the language of cybernetics, maintaining reactions can be outlined as follows: the sensing material receives information about the external environment in the form of coded signals. This information is reprocessed and sent in the form of new signals through defined channels, or networks. This new information brings about an internal reorganization of the system which contributes to the preservation of its integrity. The mechanism which reprocesses the information is called the control system. It consists of a vast number of input and output elements, connected by channels through which the signals are transmitted. The information can be stored in a recall or memory system, which may consist of separate elements, each of which can be in one of several stable states. The particular state of the element varies, under the influence of the input signals. When a number of such elements are in certain specified states, information is, in effect, recorded in the form of a text of finite length, using an alphabet with a finite number of characters. These processes underlie contemporary electronic computing machines and are, in a number of respects, strongly analogous to biological memory systems." (Carl Sagan, "Intelligent Life in the Universe", 1966)
"This whole illusion has its history in ways of thinking - in the images, models, myths, and language systems which we have used for thousands of years to make sense of the world. […] Idolatry is not the use of images, but confusing them with what they represent, and in this respect mental images and lofty abstractions can be more insidious than bronze idols." (Alan W. Watts," The Book on the Taboo Against Knowing Who You Are", 1966)
"[…] cybernetics studies the flow of information round a system, and the way in which this information is used by the system as a means of controlling itself: it does this for animate and inanimate systems indifferently. For cybernetics is an interdisciplinary science, owing as much to biology as to physics, as much to the study of the brain as to the study of computers, and owing also a great deal to the formal languages of science for providing tools with which the behaviour of all these systems can be objectively described." (A Stafford Beer, 1966)
"For cybernetics is an interdisciplinary science, owing as much to biology as to physics, as much to the study of the brain as to the study of computers, and owing also a great deal to the formal languages of science for providing tools with which the behaviour of all these systems can be objectively described." (A Stafford Beer, 1966)
"Just as no thing or organism exists on its own, it does not act on its own. Furthermore, every organism is a process: thus the organism is not other than its actions. To put it clumsily: it is what it does. More precisely, the organism, including its behavior, is a process which is to be understood only in relation to the larger and longer process of its environment. For what we mean by 'understanding' or 'comprehension' is seeing how parts fit into a whole, and then realizing that they don't compose the whole, as one assembles a jigsaw puzzle, but that the whole is a pattern, a complex wiggliness, which has no separate parts. Parts are fictions of language, of the calculus of looking at the world through a net which seems to chop it up into bits. Parts exist only for purposes of figuring and describing, and as we figure the world out we become confused if we do not remember this all the time." (Alan Watts, "The Book on the Taboo Against Knowing Who You Are", 1966)
"Rationality consists [of] the continuous adaptation of our language to our continually expanding world, and metaphor is one of the chief means by which this is accomplished." (Mary B Hesse, "Models and Analogies in Science", 1966)
"Graphic representation constitutes one of the basic sign-systems conceived by the human mind for the purposes of storing, understanding, and communicating essential information. As a 'language' for the eye, graphics benefits from the ubiquitous properties of visual perception. As a monosemic system, it forms the rational part of the world of images. […] Graphics owes its special significance to its double function as a storage mechanism and a research instrument." (Jacques Bertin, Semiology of graphics [Semiologie Graphique], 1967)
"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. […] If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." (Richard P Feynman,"The Character of Physical Law", 1967)
"Foundations and organization are similar in that both provide some sort of more systematic exposition. But a step in this direction may be crucial for organization, yet foundationally trivial, for instance a new choice of language when (i) old theorems are simpler to state but (ii) the primitive notions of the new language are defined in terms of the old, that is if they are logically dependent on the latter. Quite often, (i) will be achieved by using new notions with more ‘structure’, that is less analyzed notions, which is a step in the opposite direction to a foundational analysis. In short, foundational and organizational aims are liable to be actually contradictory." (Georg Kreisel & Jean-Louis Krivine, "Elements of Mathematical Logic: Model Theory", 1967)
"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. […] If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." (Richard P Feynman, "The Character of Physical Law", 1967)
"[Human] communication is rendered more complex by the use of differing sets of sound-symbols, called languages and by the fact that a given set of symbols tends to change with the passage of years to become an entirely new language." (Howard L Myers, "The Creatures of Man", 1968)
"In practice, let us note, the determination of sets by means of characterizing criteria runs into difficulty because of the ambiguity of our language. The task of separating the objects belonging to a set from those that do not is often made difficult by the large number of objects of intermediate type." (Naum Ya. Vilenkin, "Stories about Sets", 1968)
"Unfortunately, we are not in a position to give a rigorous definition of the fundamental concept of the theory : the concept of set. Of course, we could say that a set is a collection, a union, an ensemble, a family, a system, a class, etc. But this would not be a mathematical definition, but rather a misuse of the multitude of words available in the English language." (Naum Ya. Vilenkin, "Stories about Sets", 1968)
"Computer languages of the future will be more concerned with goals and less with procedures specified by the programmer." (Marvin Minsky, "Form and Content in Computer Science", [Turing Award lecture] 1969)
"Learning a language represents training in the delusions of that language." (Frank Herbert, "The Bureau of Sabotage: Whipping Star", 1969)
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