"[The information of a message can] be defined as the 'minimum number of binary decisions which enable the receiver to construct the message, on the basis of the data already available to him.' These data comprise both the convention regarding the symbols and the language used, and the knowledge available at the moment when the message started." (Dennis Gabor, "Optical transmission" in Information Theory : Papers Read at a Symposium on Information Theory, 1952)
"For a large class of cases - though not for all - in which we employ the word 'meaning' it can be defined thus: the meaning of a word is its use in language." (Ludwig Wittgenstein, "Philosophical investigations", 1953)
"Like everything metaphysical the harmony between thought and reality is to be found in the grammar of the language." (Ludwig Wittgenstein, "Philosophical Investigations", 1953)
"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)
"Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghost-like character of the real variable." (Alfred N Whitehead,"Essays in Science and Philosophy", 1948)
"What distinguishes the language of science from language as we ordinarily understand the word? […] What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data." (Albert Einstein, "Ideas and Opinions", 1954)
"Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment." (C West Churchman, "Costs, Utilities, and Values", 1956)
"Mathematics in this sense is a form of poetry, which has the same relation to the prose of practical mathematics as poetry has to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process." (Jacob Bronowski, "Science and Human Values", 1956)
"Understanding mathematical logic, or the theory of relativity, is not an indispensable attribute of the cultured mind. But if one wishes to learn anything about these subjects, one must learn something. It is necessary to master the rudiments of the language, to practice a technique, to follow step by step a characteristic sequence of reasoning and to see a problem through from beginning to end." (James R Newman, "The World of Mathematics" Vol. I, 1956)
"Cybernetics is likely to reveal a great number of interesting and suggestive parallelisms between machine and brain and society. And it can provide the common language by which discoveries in one branch can readily be made use of in the others. [...] [There are] two peculiar scientific virtues of cybernetics that are worth explicit mention. One is that it offers a single vocabulary and a single set of concepts suitable for representing the most diverse types of system. [...] The second peculiar virtue of cybernetics is that it offers a method for the scientific treatment of the system in which complexity is outstanding and too important to be ignored. Such systems are, as we well know, only too common in the biological world!" (W Ross Ashby, "An Introduction to Cybernetics", 1956)
"Mathematics in this sense is a form of poetry, which has the same relation to the prose of practical mathematics as poetry has to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process." (Jacob Bronowski, "Science and Human Values", 1956)
"The forms of a person’s thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language - shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family." (Benjamin L Whorf, 1956)
"We dissect nature along the lines laid down by our native languages. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds - and this means largely by the linguistic systems in our minds. […] We are thus introduced to a new principle of relativity, which holds that all observers are not led by the same physical evidence to the same picture of the universe, unless their linguistic backgrounds are similar or can in some way be calibrated." (Benjamin L Whorf, 1956)
"The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analysing visible motions it has developed two ways of representing them by elementary processes; moving particles and waves. There is no other way of giving a pictorial description of motions - we have to apply it even in the region of atomic processes, where classical physics breaks down." (Max Born, "Atomic Physics", 1957)
"Both science and art form in the course of the centuries a human language by which we can speak about the more remote parts of reality, and the coherent sets of concepts as well as the different styles of art are different words or groups of words in this language." (Werner K Heisenberg, "Physics and Philosophy", 1958)
"Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached." (Werner K Heisenberg, "Physics and Philosophy", 1958)
"If words are not things, or maps are not the actual territory, then, obviously, the only possible link between the objective world and the linguistic world is found in structure, and structure alone. The only usefulness of a map or a language depends on the similarity of structure between the empirical world and the map-languages. If the structure is not similar, then the traveller or speaker is led astray, which, in serious human life-problems, must become always eminently harmful. If the structures are similar, then the empirical world becomes 'rational' to a potentially rational being, which means no more than that verbal, or map-predicted characteristics, which follow up the linguistic or mapstructure, are applicable to the empirical world." (Alfred Korzybski, "Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics", 1958)
"We believe that student will come to understand mathematics when his textbook and teacher use unambiguous language and when he is enabled to discover generalizations by himself." (Max Beberman, "An Emerging Program of Secondary School Mathematics", 1958)
"As the sensations of motion and discreteness led to the abstract notions of the calculus, so may sensory experience continue thus to suggest problem for the mathematician, and so may she in turn be free to reduce these to the basic formal logical relationships involved. Thus only may be fully appreciated the twofold aspect of mathematics: as the language of a descriptive interpretation of the relationships discovered in natural phenomena, and as a syllogistic elaboration of arbitrary premise." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)
"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)
"There is a logic of language and a logic of mathematics. The former is supple and lifelike, it follows our experience. The latter is abstract and rigid, more ideal. The latter is perfectly necessary, perfectly reliable: the former is only sometimes reliable and hardly ever systematic. But the logic of mathematics achieves necessity at the expense of living truth, it is less real than the other, although more certain. It achieves certainty by a flight from the concrete into abstraction." (Thomas Merton, "The Secular Journal of Thomas Merton", 1959)
"We are always looking for metaphors in which to express our ideas of life, for our language is inadequate for all its complexities. Life is a labyrinth.[...] Life is a machine.[...] Life is a laboratory.[...] It is but a metaphor. When we speak of ultimate things we can, maybe, speak only in metaphors. Life is a dance, a very elaborate and complex dance [...]." (Charles Singer, "A Short History of Scientific Ideas to 1900", 1959)
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