On Semiotics: On Signs (trivia)

"Science will persevere just as long as we retain a faculty we show no signs of losing: the ability to conceive — in no matter how imperfect or rudimentary a form - what the truth might be and retain also the inclination to ascertain whether our imaginings correspond to real life or not." (Peter B Medawar, "The Limits of Science". 1984)

"Nature is a vast tablet, inscribed with signs, each of which has its own signifi cancy, and becomes poetry in the mind when read; and geology is simply the key by which myriads of these signs, hitherto indecipherable, can be unlocked and perused, and thus a new province added to the poetical domain." (Hugh Miller, "Sketch-Book of Popular Geology", 1880)

"In a universe whose size is beyond human imagining, where our world floats like a dust mote in the void of night, men have grown inconceivably lonely. We scan the time scale and the mechanisms of life itself for portents and signs of the invisible. As the only thinking mammals on the planet - perhaps the only thinking animals in the entire sidereal universe - the burden of consciousness has grown heavy upon us. We watch the stars, but the signs are uncertain. We uncover the bones of the past and seek for our origins. There is a path there, but it appears to wander. The vagaries of the road may have a meaning, however; it is thus we torture ourselves." (Loren C Eiseley, "The Immense Journey", 1957)

"We seem to be entering a new world of technology, but the vehicle which is carrying us - science - shows dangerous signs of inadequacy for the voyage ahead. (Barry Commoner, "Science and Survival", 1966)

"[...] the picture of the universe presented by astronomy is one of dismal stretches of time and space and unparalled desolation. In the eternal abyss of space - bleak, cold, and dark - there are no signs of a Cosmic Consciousness." (Woolsey Teller, "The Atheism of Astronomy", 1972)

"Nature talks in signs and, to understand its language, one has to pay attention to similarities in form." (Jeremy Narby, "The Cosmic Serpent: DNA and the Origins of Knowledg", 1998)

"This notion of 'being due' - what is sometimes called the gambler’s fallacy - is a mistake we make because we cannot help it. The problem with life is that we have to live it from the beginning, but it makes sense only when seen from the end. As a result, our whole experience is one of coming to provisional conclusions based on insufficient evidence: read ing the signs, gauging the odds." (John Haigh," Taking Chances: Winning With Probability", 1999)

On Semiotics: On Signs (-1799)

"It was ordained at the beginning of the world that certain signs should prefigure certain events." (Marcus Tullius Cicero, "De Divinatione" ["Concerning Divination"], 44 BC) 

"It would be a sign of great simplicity to think that the world was created in six days, or indeed at all in time; [...] Time is a thing posterior to the world. Therefore it would be correctly said that the world was not created in time, but that time had its existence in consequence of the world. For it is the motion of the heaven that has displayed the nature of time." (Philo Judaeus, "Allegories of the Sacred Laws" ["Legum allegoriae"], 1st century AD) 

"All things are filled full of signs, and it is a wise man who can learn about one thing from another." (Plotinus, "Enneads", cca. 270 AD)

"We are meant to take them [the words ‘increase and multiply’] in a figurative sense. […] It is only in the case of signs outwardly given that we find increase and multiplication in the sense that a single truth can be expressed by several different means […] that a single expression can be interpreted in several different ways." (St. Augustine,"Confessions", 397- 400)

"Letters are signs of things, symbols of words, whose power is so great that without a voice they speak to us the words of the absent; for they introduce words by the eye, not by the ear." (Isidore of Seville, "Etymologiae", cca. 800-625)

"The Imagination that is raised in man (or any other creature imbued with the faculty of imagining) by words, or other voluntary signs, is that we generally call Understanding; and is common to Man and Beasts." (Thomas Hobbes, "Leviathan: Or, The Matter, Forme, & Power of a Common-wealth Ecclesiasticall and Civill", 1651)

"The signs of science are, some certain and infallible; some, uncertain. Certain, when he that pretendeth the science of anything, can teach the same; that is to say, demonstrate the truth thereof perspicuously to another; uncertain, when only some particular events answer to his pretence, and upon many occasions prove so as he says they must. " (Thomas Hobbes, "Leviathan: Or, The Matter, Forme, & Power of a Common-wealth Ecclesiasticall and Civill", 1651)

"It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters, insofar as they are subject to reasoning, all that we can do in arithmetic and geometry." (Gottfried W Leibniz, 1677) 

"In signs, one sees an advantage for discovery that 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 Tschirnhaus] cca. 1686)

"As arithmetic and algebra are sciences of great clearness, certainty, and extent, which are immediately conversant about signs, upon the skillful use whereof they entirely depend, so a little attention to them may possibly help us to judge of the progress of the mind in other sciences, which, though differing in nature, design, and object, may yet agree in the general methods of proof and inquiry." (George Berkeley, "Alciphron: or the Minute Philosopher", 1732)

"[…] the sciences that are expressed by numbers or by other small signs, are easily learned; and without doubt this facility rather than its demonstrability is what has made the fortune of algebra." (Julien Offray de La Mettrie,"Man a Machine", 1747)

"Algebra is a general Method of Computation by certain Signs and Symbols which have been contrived for this Purpose, and found convenient. It is called an Universal Arithmetic, and proceeds by Operations and Rules similar to those in Common Arithmetic, founded upon the same Principles." (Colin Maclaurin,"A Treatise on Algebra", 1748)

"All abstract sciences are nothing but the study of relations between signs." (Denis Diderot, "Lettre sur les sourds et muets" ["Letter on the Deaf and Dumb"], 1751) 

On Semiotics: On Signs (1950-)

"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)

"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))

"The symbol is the tool which gives man his power, and it is the same tool whether the symbols are images or words, mathematical signs or mesons." (Jacob Bronowski, "The Reach of Imagination", 1967) 

"If 'model' is taken to mean visual representation or analogy with familiar experience, then clearly not every theory involves a model. Thus field theories, whether classical or quantal, are hardly visualisable. And if 'model' is taken to mean mechanism - either in a narrow mechanical sense or in a wide sense including nonmechanical mechanisms such as the meson field mechanism of nuclear forces - then some theories do contain models of this kind while others do not. [...] On the other hand in a third sense every physical theory is a model, namely of the underlying mathematical formalism. Moreover a physical theory is twice a model in the model-theoretic sense: once because every one of its basic signs has a particular interpretation within mathematics, another time because the same sign may have a physical interpretation as well - as is the case with all the referential primitives." (Mario Bunge, "Philosophy of Physics", 1973)

"Information is carried by physical entities, such as books or sound waves or brains, but it is not itself material. Information in a living system is a feature of the order and arrangement of its parts, which arrangement provides the signs that constitute a ‘code’ or ‘language’." (John Z Young, "Programs of the Brain", 1978)

"In a modern professional vocabulary a hypothesis is an imaginative preconception of what might be true in the form of a declaration with verifiable deductive consequences. It no longer tows ‘gratuitous’, ‘mere’, or ‘wild’ behind it, and the pejorative usage" (‘Evolution is a mere hypothesis’, ‘It is only a hypothesis that smoking causes lung cancer’) is one of the outward signs of little learning." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)

"Signs are not empirical objects. Empirical objects become signs (or they are looked at as signs) only from the point of view of a philosophical decision." (Umberto Eco, "Semiotics and the Philosophy of Language", 1984)

"When semiotics posits such concepts as 'sign', it does not act like a science; it acts like philosophy when it posits such abstractions as subject, good and evil, truth or revolution."  (Umberto Eco, "Semiotics and the Philosophy of Language", 1984)

"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)

"Maps, due to their melding of scientific and artistic approaches, always involve complex interaction between the denotative and the connotative meanings of signs they contain." (Alan M MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"When visualization tools act as a catalyst to early visual thinking about a relatively unexplored problem, neither the semantics nor the pragmatics of map signs is a dominant factor. On the other hand, syntactics (or how the sign-vehicles, through variation in the visual variables used to construct them, relate logically to one another) are of critical importance." (Alan M MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"In both quantum theory and general relativity, we encounter predictions of physically sensible quantities becoming infinite. This is likely the way that nature punishes impudent theorists who dare to break her unity. […] If infinities are signs of missing unification, a unified theory will have none. It will be what we call a finite theory." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"[…] in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; […]" (John Ruskin,"The Stones of Venice: The Sea Stories", 2013)

"Using maps as communication tools masks their complexity as a mode of thinking. Maps act like language: we attribute the signs or marks in the map to a natural extension of thought. But post-structuralism exposed maps (like language) as artificial signs whose meaning is tethered to time, place, culture, gesture, smell - in short, a plethora of cognitive and phenomenal attributes of our communication ecology." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)

"When dealing with meaningful visual representation, aspects of a representation's meaning can be altered by modifying its visual characteristics; these characteristics are extensively explored in semiotics, the study of signs and symbols and their use or interpretation." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

 

On Semiotics: On Signs (1850-1899)

"Observe this: the abstraction of the philosopher is meant to keep the object itself, with its perturbing suggestions, out of sight, allowing only one quality to fill the field of vision; whereas the abstraction of the poet is meant to bring the object itself into more vivid relief, to make it visible by means of the selected qualities. In other words, the one aims at abstract symbols, the other at picturesque effects. The one can carry on his deductions by the aid of colourless signs, X or Y. The other appeals to the emotions through the symbols which will most vividly express the real objects in their relations to our sensibilities." (George H Lewes, "The Principles of Success in Literature", 1865)

"The degree in which each mind habitually substitutes signs for images will be, CETERIS PARIBUS [with other conditions remaining the same], the degree in which it is liable to error. This is not contradicted by the fact that mathematical, astronomical, and physical reasonings may, when complex, be carried on more successfully by the employment of signs; because in these cases the signs themselves accurately represent the abstractness of the relations. Such sciences deal only with relations, and not with objects; hence greater simplification ensures greater accuracy. But no sooner do we quit this sphere of abstractions to enter that of concrete things, than the use of symbols becomes a source of weakness. Vigorous and effective minds habitually deal with concrete images." (George H Lewes, "The Principles of Success in Literature", 1865)

"I believe, therefore, that there can be no possible sense at all in speaking of any other truth for our representations except a practical [truth]. Our representations of things can be nothing else at all except symbols, naturally given signs for things, that we learn to use for the regulation of our motions and actions. When we have correctly learned to read such a symbol, we are then capable of so adjusting our actions with its help that they have the desired result, that is, the expected new sensations occur. Another comparison between representations and things not only fails to exist in actuality – here all schools agree – but any other kind of comparison is in no way thinkable and has no sense at all." (Hermann von Helmholtz, "Handbuch der Physologieschen Optik", 1867)

"The being of a sign is merely being represented. Now really being and being represented are very different. Giving to the word sign the full scope that reasonably belongs to it for logical purposes, a whole book is a sign; and a translation of it is a replica of the same sign. A whole literature is a sign." (Charles S Peirce," What Is a Sign?", 1894) 

"In algebra we perform, as far as possible, all numerical operations which are identical in form once for all, so that only a remnant of work is left for the individual case. The use of the signs of algebra and analysis, which are merely symbols of operations to be performed, is due to the observation that we can materially disburden the mind in this way and spare its powers for more important and more difficult duties, by imposing all mechanical operations upon the hand." (Ernst Mach, "The Economical Nature of Physical Enquiry", Popular Scientific Lectures, 1895)

"Strange as it may sound, the power of mathematics rests upon its evasion of all unnecessary thought and on its wonderful saving of mental operation. Even those arrangement-signs which we call numbers are a system of marvelous simplicity and economy. When we employ the multiplication-table in multiplying numbers of several places, and so use the results of old operations of counting instead of performing the whole of each operation anew; when we consult our table of logarithms, replacing and saving thus new calculations by old ones already performed; when we employ determinants instead of always beginning afresh the solution of a system of equations; when we resolve new integral expressions into familiar old integrals; we see in this simply a feeble reflexion of the intellectual activity of a Lagrange or a Cauchy, who, with the keen discernment of a great military commander, substituted new operations for whole hosts of old ones. No one will dispute me when I say that the most elementary as well as the highest mathematics are economically-ordered experiences of counting, put in forms ready for use." (Ernst Mach, "Popular Scientific Lectures", 1895)

"Mathematics gives the young man a clear idea of demonstration and habituates him to form long trains of thought and reasoning methodically connected and sustained by the final certainty of the result; and it has the further advantage, from a purely moral point of view, of inspiring an absolute and fanatical respect for truth. In addition to all this, mathematics, and chiefly algebra and infinitesimal calculus, excite to a high degree the conception of the signs and symbols - necessary instruments to extend the power and reach of the human mind by summarizing an aggregate of relations in a condensed form and in a kind of mechanical way. These auxiliaries are of special value in mathematics because they are there adequate to their definitions, a characteristic which they do not possess to the same degree in the physical and mathematical [natural?] sciences. There are, in fact, a mass of mental and moral faculties that can be put in full play only by instruction in mathematics; and they would be made still more available if the teaching was directed so as to leave free play to the personal work of the student." (M P Berthelot, "Science as an Instrument of Education", Popular Science Monthly, 1897)

"All our ideas and concepts are only internal pictures, or if spoken, combinations of sounds. The task of our thinking is so to use and combine them that by their means we always most readily hit upon the correct actions and guide others likewise. In this, metaphysics follows the most down-to-earth and practical point of view, so that extremes meet. The conceptual signs that we form thus exist only within us, we cannot measure external phenomena by the standard of our ideas. We can therefore pose such formal questions as whether only matter exists and force is a property of it, or whether force exists independently of matter or conversely whether matter is a product of force but none of these questions are significant since all these concepts are only mental pictures whose purpose is to represent phenomena correctly." (Ludwig Boltzmann, 1899)

"[…] no theory can be objective, actually coinciding with nature, but rather that each theory is only a mental picture of phenomena, related to them as sign is to designatum. From this it follows that it cannot be our task to find an absolutely correct theory but rather a picture that is, as simple as possible and that represents phenomena as accurately as possible. One might even conceive of two quite different theories both equally simple and equally congruent with phenomena, which therefore in spite of their difference are equally correct. (Ludwig Boltzmann, "On the development of the methods of theoretical physics", 1899)

On Semiotics: On Signs (1800-1849)

"It has been already observed, that demonstration ultimately depends on observations made on individual objects, and that a conclusion expressed by certain characters and signs, if general, must be true 'in each particular case that presents itself, on assigning specific values to the signs." (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)

"Algebra is a species of short-hand writing; a language, or system of characters or signs, invented for the purpose of facilitating the comparison and combination of ideas." (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)

"It has been already observed, that demonstration ultimately depends on observations made on individual objects, and that a conclusion expressed by certain characters and signs, if general, must be true 'in each particular case that presents itself, on assigning specific values to the signs." (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)

"The theory of which we have just given an overview may be considered from a point of view apt to set aside the obscure in what it presents, and which seems to be the primary aim, namely: to establish new notions on imaginary quantities. Indeed, putting to one side the question of whether these notions are true or false, we may restrict ourselves to viewing this theory as a means of research, to adopt the lines in direction only as signs of the real or imaginary quantities, and to see, in the usage to which we have put them, only the simple employment of a particular notation. For that, it suffices to start by demonstrating, through the first theorems of trigonometry, the rules of multiplication and addition given above; the applications will follow, and all that will remain is to examine the question of didactics. And if the employment of this notation were to be advantageous? And if it were to open up shorter and easier paths to demonstrate certain truths? That is what fact alone can decide." (Jean-Robert Argand, "Essai sur une manière de représenter les quantités imaginaires, dans les constructions géométriques", Annales Tome IV, 1813)

"The diversity of languages is not a diversity of signs and sounds but a diversity of views of the world." (Wilhelm von Humboldt, 1820)

"Science sees signs: poetry, the thing signified." (Julius C Hare, "Guesses at Truth", 1827)

"The mutual interdependence of thought and word illuminates clearly the truth that languages are not really means for representing already known truths, but are rather instruments for discovering previously unrecognised ones. The differences between languages are not those of sounds and signs but those of differing  worldviews […] objective truth always rises from the entire energy of subjective individuality." (Wilhelm von Humboldt, "Über die Verschiedenheit des menschlichen Sprachbaues und ihren Einfluss auf die geistige Entwickelung des Menschengeschlechts" ["On the Diversity of Human Language Structure and Its Influence on the Mental Development of the Human Race"], 1836) 

On Semiotics: On Signs (1900-1949)

"All our thinking is performed upon signs of some kind or other, either imagined or actually perceived. The best thinking, especially on mathematical subjects, is done by experimenting in the imagination upon a diagram or other scheme, and it facilitates the thought to have it before one’s eyes." (Charles S Peirce, “The Principles of Mathematics”, cca. 1902) 

"A sign is a thing which is the representative, or deputy, of another thing for the purpose of affecting a mind. […] The utility of icons is evidenced by the diagrams of the mathematician, whether they involve continuity, like geometrical figures, or are arrays of discrete objects like a body of algebraical formulae, all of which are icons. Icons have to be used in all thinking." (Charles S Peirce, [manuscript] 1903)

"Many diagrams resemble their objects not at all in looks; it is only in respect to the relations of their parts that their likeliness consists. […] When, in algebra, we write equations under one another in a regular array, especially when we put resembling letters for corresponding coefficients, the array is an icon. […] In fact, every algebraic equation is an icon, in so far as it exhibits, by means of the algebraic signs (which are not themselves icons), the relations of the quantities concerned." (Charles S Peirce, "New Elements", 1904)

"The edifice of science is not raised like a dwelling, in which the foundations are first firmly laid and only then one proceeds to construct and to enlarge the rooms. Science prefers to secure as soon as possible comfortable spaces to wander around and only subsequently, when signs appear here and there that the loose foundations are not able to sustain the expansion of the rooms, it sets about supporting and fortifying them. This is not a weakness, but rather the right and healthy path of development." (David Hilbert, "The Logical Principles of Mathematical Thinking", 1905)

"It is important to understand what I mean by semiosis. All dynamic action, or action of brute force, physical or psychical, either takes place between two subjects, - whether they react equally upon each other, or one is agent and the other patient, entirely or partially, — or at any rate is a resultant of such actions between pairs. But by 'semiosis' I mean, on the contrary, an action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs." (Charles S Peirce,"Pragmatism", 1907) 

"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, "Symbols for the transformation", 1912)

"I call the combination of a concept and a sound-image a sign, but in current usage the term generally designates only a sound-image, a word, for example" (arbor, etc.). One tends to forget that arbor is called a sign only because it carries the concept ‘tree’, with the result that the idea of the sensory part implies the idea of the whole." (Ferdinand de Saussure, "Course in General Linguistics", 1915

"The logic of things, i.e., of the material concepts and relations on which the structure of a science rests, cannot be separated by the logic of signs. For the sign is no mere accidental cloak of the idea, but its necessary and essential organ. It serves not merely to communicate a complete and given thought content, but is an instrument, by means of which this content develops and fully defines itself. […] Consequently, all truly strict and exact thought is sustained by the symbolic and semiotics on which it is based." (Ernst Cassirer, "The Philosophy of Symbolic Forms", 1923)

"The words in a poem, (or more exactly, syllables) are vocal signs that convey an intangible essence (the pattern of feeling) that vanishes the moment we approach it with an analytical intelligence." (Herbert Read, "What is a Poem", 1926)

"The words of the language, as they are written or spoken, do not seem to play any role in any mechanism of thought. The physical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced or combined. […] But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought - before there is any connection with logical construction in words or other kinds of signs which can be communicated to others. The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will." (Albert Einstein, [letter to Hadamard, in" (Jacques Hadamard, "The Psychology of Invention in the Mathematical Field,1945)])