A Picture's Worth

"The drawing shows me at a glance what would be spread over ten pages in a book." (Ivan Turgenev, 1862) [2]

"Sometimes, half a dozen figures will reveal, as with a lighting-flash, the importance of a subject which ten thousand labored words with the same purpose in view, had left at last but dim and uncertain." (Mark Twain, "Life on the Mississippi", 1883) 

"One good picture is worth many pages of written description." (William Sproston Caine, 1891) [2]

"One look is worth a thousand words" (Kathleen Caffyn, 1903) 

"Use a picture. It's worth a thousand words." (Arthur Brisbane, The Post-Standard, 1911)

"One Look Is Worth A Thousand Words" ([advertisement] 1913)

"A picture is worth ten thousand words. If you can’t see the truth in these pictures you are among the vast majority that must learn only by experience." (Arthur Brisbane, 1915)

"One picture is worth ten thousand words." (Frederick R Barnard, Printer’s Ink, 1921)

"One Picture Worth Ten Thousand Words" ([Chinese proverb] 1927)

"In many instances, a picture is indeed worth a thousand words. To make this true in more diverse circumstances, much more creative effort is needed to pictorialize the output from data analysis. Naive pictures are often extremely helpful, but more sophisticated pictures can be both simple and even more informative." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"One word is worth a thousand pictures. If it's the right word." (Edward Abbey, "Beyond the Wall: Essays from the Outside", 1984)

"A picture may be worth a thousand words, a formula is worth a thousand pictures." (Edsger Dijkstra, [conference at ETH Zurich] 1994)

"A magnificent picture is never worth a thousand perfect words." (John Dunning, "The Bookman's Wake", 1995)

"A picture tells a thousand words. But you get a thousand pictures from someone's voice." (Paul Fleischman, "Seek", 2001)

"If a picture is worth a thousand words, a metaphor is worth a thousand pictures." (Daniel H Pink, "A Whole New Mind: Why Right-Brainers Will Rule the Future", 2005)

"A picture may be worth a thousand words, but not all pictures are readable, interpretable, meaningful, or relevant." (Kristen Sosulski, "Data Visualization Made Simple: Insights into Becoming Visual", 2018)

"A good metaphor is worth a thousand pictures." (Anon) 

"As the Chinese say, 1001 words is worth more than a picture." (John McCarthy [source]) 

References:
[1] Wikipedia (2024) A picture is worth a thousand words [link]
[2] Quote Investigator (2022) A Picture Is Worth Ten Thousand Words [link] 
[3] SQL-Troubles (2024) Charts vs. Thousand Words [link]

Out of Context: On Image (Definitions)

"An image is, after all, a reminder; it is to the illiterate what a book is to the literate, and what the word is to the hearing, the image is to sight." (John of Damascus, cca. 8th century)

"[...] images are like sensuous contents except in that they contain no matter." (Aristotle, "De Anima", cca. 350 BC)

"[…] the image is not a symbol or idea. It is itself a fact, or else the facts eject it." (Francis H Bradley, "Principles of Logic", 1883)

"[…] the image is an act which envisions an absent or non-existent object as a body, by means of a physical or mental content which is present only as an 'analogical representative' of the object envisioned." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)

"[…] inner images are rather psychic manifestations of the archetypes which, however, would also have to put forth, create, condition anything lawlike in the behavior of the corporeal world." (Wolfgang Pauli, [letter to Markus Fierz] 1948)

"Thus a word or an image is symbolic when it implies something more than its obvious and immediate meaning." (Carl G Jung, "Man and His Symbols", 1964)

"Imagining is not perceiving, but images are indeed derivatives of perceptual activity. In particular, they are the anticipatory phases of that activity, schemata that the perceiver has detached from the perceptual cycle for other purposes." (Ulrich Neisser, "Cognition and Reality" 1976)

"The paradox of reality is that no image is as compelling as the one which exists only in the mind's eye." (Shana Alexander, "Talking Woman", 1976)

"The image is our attempt to reach the non-existent or absent object in our thoughts as we concentrate on this or that aspect of it, its visible appearance, its sound, its smell. […] The images themselves are not separate from our interpretations of the world; they are our way of thinking of objects in the world." (Mary Warnock, "Imagination", 1978)

"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)

"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)

"Images are defined to be information structures, with different kind of images representing different kind of information about what the actor is doing, why and how, and what kind of progress is being made." (Terence R. Mitchell & Lee R Beach, "Organizational behavior and human decision processes", 1990)

"[...] images are probably the main content of our thoughts, regardless of the sensory modality in which they are generated and regardless of whether they are about a thing or a process involving things; or about words or other symbols, in a given language, which correspond to a thing or process." (Antonio R Damasio, "Descartes' Error. Emotion, Reason, and the Human Brain", 1994)

"But because of the way in which depictions represent, there is a correspondence between parts and spatial relations of the representation and those of the object; this structural mapping, which confers a type of resemblance, underlies the way images convey specific content. In this respect images are like pictures. Unlike words and symbols, depictions are not arbitrarily paired with what they represent." (Stephen Kosslyn et al, "The Case for Mental Imagery", 2006)

"Images are not just minor variations on perception and thought, of negligible theoretical interest; they are a robust mental category in need of independent investigation." (Colin McGinn, Mindsight, 2009)

"Images are generally resistant to change and ignore messages that do not conform to their internal settings." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)

John D Barrow - Collected Quotes

"A more interesting problem is the extent to which the brain is qualitatively adapted to understand the Universe. Why should its categories of thought and understanding be able to cope with the scope and nature of the real world? Why should be Theory of Everything be written in a 'language' that our minds can decode? Why has the process of natural selection so over-endowed us with mental faculties that we can understand the whole fabric of the Universe far beyond anything required for our past and present survival?"  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. [...] whilst leaving some underlying theme unchanged. [...] for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time [...] the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation [...] discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play [...]"  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Everywhere […] in the Universe, we discern that closed physical systems evolve in the same sense from ordered states towards a state of complete disorder called thermal equilibrium. This cannot be a consequence of known laws of change, since […] these laws are time symmetric- they permit […] time-reverse. […] The initial conditions play a decisive role in endowing the world with its sense of temporal direction. […] some prescription for initial conditions is crucial if we are to understand […]"  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"In practice, the intelligibility of the world amounts to the fact that we find it to be algorithmically compressible. We can replace sequences of facts and observational data by abbreviated statements which contain the same information content. These abbreviations we often call 'laws of Nature.' If the world were not algorithmically compressible, then there would exist no simple laws of nature. Instead of using the law of gravitation to compute the orbits of the planets at whatever time in history we want to know them, we would have to keep precise records of the positions of the planets at all past times; yet this would still not help us one iota in predicting where they would be at any time in the future. This world is potentially and actually intelligible because at some level it is extensively algorithmically compressible. At root, this is why mathematics can work as a description of the physical world. It is the most expedient language that we have found in which to express those algorithmic compressions." (John D Barrow, "New Theories of Everything", 1991)

"It is enigma enough that the world is described by mathematics; but by simple mathematics, of the sort that a few years energetic study now produces familiarity with, this is an enigma within an enigma."   (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"It is simplest to think of mathematics as the catalogue of all possible patterns. [...] When viewed in this way, it is inevitable that the world is described by mathematics. [...] In many ways the search for a Theory of Everything is a manifestation of a faith that this compression goes all the way down to the bedrock of reality [...]"  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Somehow the breathless world that we witness seems far removed from the timeless laws of Nature which govern the elementary particles and forces of Nature. The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"String theory promises to take a further step beyond that taken by Einstein's picture of force subsumed within curved space and time geometry. Indeed, string theory contains Einstein's theory of gravitation within itself. Loops of string behave like the exchange particles of the gravitational forces, or 'gravitons' as they are called in the point-particle picture of things. But it has been argued that it must be possible to extract even the geometry of space and time from the characteristics of the strings and their topological properties. At present, it is not known how to do this and we merely content ourselves with understanding how strings behave when they sit in a background universe of space and time."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"The inflationary period of expansion does not smooth out irregularity by entropy-producing processes like those explored by the cosmologies of the seventies. Rather it sweeps the irregularity out beyond the Horizon of our visible Universe, where we cannot see it . The entire universe of stars and galaxies on view to us. […] on this hypothesis, is but the reflection of a minute, perhaps infinitesimal, portion of the universe's initial conditions, whose ultimate extent and structure must remain forever unknowable to us. A theory of everything does not help here. The information contained in the observable part of the universe derives from the evolution of a tiny part of the initial conditions for the entire universe. The sum total of all the observations we could possibly make can only tell us about a minuscule portion of the whole."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"The scope of Theories of Everything is infinite but bounded; they are necessary parts of a full understanding of things but they are far from sufficient to reveal everything about a Universe like ours. In the pages of this book, we have seen something of what a Theory of Everything might hope to teach us about the unity of the Universe and the way in which it may contain elements that transcend our present compartmentalized view of Nature's ingredients. But we have also learnt that there is more to Everything than meets the eye. Unlike many others that we can imagine, our world contains prospective elements. Theories of Everything can make no impression upon predicting these prospective attributes of reality; yet, strangely, many of these qualities will themselves be employed in the human selection and approval of an aesthetically acceptable Theory of Everything. There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight. For, to see through everything, would leave us seeing nothing at all."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"There is one qualitative aspect of reality that sticks out from all others in both profundity and mystery. It is the consistent success of mathematics as a description of the workings of reality and the ability of the human mind to discover and invent mathematical truths."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Three laws governing black hole changes were thus found, but it was soon noticed that something unusual was going on. If one merely replaced the words 'surface area' by 'entropy' and 'gravitational field' by 'temperature', then the laws of black hole changes became merely statements of the laws of thermodynamics. The rule that the horizon surface areas can never decrease in physical processes becomes the second law of thermodynamics that the entropy can never decrease; the constancy of the gravitational field around the horizon is the so-called zeroth law of thermodynamics that the temperature must be the same everywhere in a state of thermal equilibrium. The rule linking allowed changes in the defining quantities of the black hole just becomes the first law of thermodynamics, which is more commonly known as the conservation of energy."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"That is, the physicist likes to learn from particular illustrations of a general abstract concept. The mathematician, on the other hand, often eschews the particular in pursuit of the most abstract and general formulation possible. Although the mathematician may think from, or through, particular concrete examples in coming to appreciate the likely truth of very general statements, he will hide all those intuitive steps when he comes to present the conclusions of his thinking to outsiders. It presents the results of research as a hierarchy of definitions, theorems and proofs after the manner of Euclid; this minimizes unnecessary words but very effectively disguises the natural train of thought that led to the original results."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Topology is that branch of mathematics which is interested in the forms of things aside from their size and shape. Two things are said to be topologically equivalent if one can be deformed smoothly into the other without sticking, cutting, or puncturing it in any way. Thus an egg is equivalent to a sphere."  (John D Barrow, "New Theories of Everything: The Quest for Ultimate Explanation", 1991)

"A less inflexible picture of mathematics is one that focuses on the fact that it is an open-ended human activity. Inventionism is the belief that mathematics is nothing more than what mathematicians do. …We invent mathematics; we do not discover it. [...] The independent discovery of the same mathematical theorems by different mathematicians from totally different economic, cultural, and political backgrounds - often at widely separated times in history - argues against such a simple view. The inventionist could respond by pointing to the universality of human languages. [...]One might expect that those aspects of this universal grammar that share features of logic, and hence counting, would also make counting appear instinctive. In fact, although simple counting [...] is fairly universal in ancient and primitive cultures, virtually none of them went on to carry out mathematical operations more sophisticated than counting. This suggests that these higher mathematical operations are not genetically programmed into the human brain [...] They are more likely to be by-products of multi-purpose pattern-recognition capabilities." (John D Barrow, "The Artful Universe", 1995)

"Highly correlated brown and black noise patterns do not seem to have seem to have attractive counterparts in the visual arts. There, over-correlation is the order of the day, because it creates the same dramatic associations that we find in attractive natural scenery, or in the juxtaposition of symbols. Somehow, it is tediously predictable when cast in a one-dimensional medium, like sound." (John D Barrow, "The Artful Universe", 1995)

"The laws of Nature are based upon the existence of a pattern, linking one state of affairs to another; and where there is pattern, there is symmetry. Yet. [...] the symmetries that the laws enshrine are broken in [...] outcomes. Suppose that we balance a needle on its point and then release it. The law of gravity, which governs its subsequent motion, is perfectly democratic. It has no preference for any particular direction in the Universe: it is symmetrical in this respect. Yet, when the needle falls, it must fall in a particular direction. The directional symmetry of the underlying law is broken, therefore [...] By the same token, the fallen needle hides the symmetry of the law. [...] Such 'symmetry-breaking' governs much of what we see in the Universe... It allows a Universe governed by a small number of symmetrical laws to manifest an infinite diversity of complex, asymmetrical states. This is how the Universe can be at once, simple and complicated." (John D Barrow, "The Artful Universe", 1995)

"Where there is life there is a pattern, and where there is a pattern there is mathematics. Once that germ of rationality and order exists to turn a chaos into a cosmos, then so does mathematics. There could not be a non-mathematical Universe containing living observers."  (John D Barrow, "The Artful Universe", 1995)

"The physicist's concept of nothing - the vacuum [...] began as empty space - the void… turned into a stagnant ether through which all the motions of the Universe swam, vanished in Einstein's hands, then re-emerged in the twentieth-century quantum picture of how Nature works." (John D Barrow, "The Book of Nothing", 2000)

"Images and pictures [...] have played a key role in shaping our scientific picture of the world. [...] Carefully constructed families of pictures can act as a calculus all their own. Like any successful systems of symbols, with an appropriate grammar they enlarge the number of things that we can do without consciously thinking." (John D Barrow, "Cosmic Imagery: Key Images in the History of Science" 2008)

"Scientific pictures are often not just about science. They may [...] have an undeniable aesthetic quality. They may even have been primarily works of art that possess a scientific message." (John D Barrow, "Cosmic Imagery: Key Images in the History of Science" 2008)

"The advent of small, inexpensive computers with superb graphics has changed the way many sciences are practiced, and the way that all sciences present the results of experiments and calculations." (John D Barrow, "Cosmic Imagery: Key Images in the History of Science", 2008)

"If one looks at the special problems that were the mainsprings of progress along the oldest and most persistent lines of human inquiry, then one finds Nothing, suitably disguised as something, never far from the centre of things." ( John D Barrow, "The Book of Nothing", 2009)

"While we have no reason to expect that our position in the universe is special in every way, we would be equally misled were we to assume that it could not be special in any way." (John D Barrow, "The Book of Universes: Exploring the Limits of the Cosmos", 2011)