Richard Brodie - Collected Quotes

"A belief system, through its memes, can spread in a way that looks just like a conspiracy without any conscious intention on the part of the participants." (Richard Brodie, "Virus of the Mind", 2009)

"A meme is a replicator that uses the medium of our minds to replicate. Meme evolution happens because our minds are good at copying and innovating - ideas, behaviors, tunes, shapes, structures, and so on." (Richard Brodie, "Virus of the Mind", 2009)

"A mind is a terrible thing to waste." (Richard Brodie, "Virus of the Mind", 2009)

"A mutation is an error in copying. It produces a defective -  or possibly improved in some sense - copy instead of an exact duplicate of the original." (Richard Brodie, "Virus of the Mind", 2009)

"A virus is anything that takes external copying equipment and puts it to work making copies of itself." (Richard Brodie, "Virus of the Mind", 2009)

"A virus of the mind is something out in the world that infects people with memes. Those memes, in turn, influence the infected people’s behavior so that they help perpetuate and spread the virus." (Richard Brodie, "Virus of the Mind", 2009)

"All cultural institutions, regardless of their initial design or intention (if any), evolve to have but one goal: to perpetuate themselves." (Richard Brodie, "Virus of the Mind", 2009)

"Associations are connections between memes. When you are programmed with an association-meme, the presence of one thing triggers a thought or feeling about something else. This causes a change in your behavior, which can ultimately spread the meme to another mind." (Richard Brodie, "Virus of the Mind", 2009)

"Beliefs are like cow paths. The more often you walk down a path, the more it looks like the right way to go." (Richard Brodie, "Virus of the Mind", 2009)

"Complicated things arise naturally out of the forces of evolution. No conscious intention is necessary." (Richard Brodie, "Virus of the Mind", 2009)

"Evolution is a scientific model of how things become more complex; entropy describes how things become simpler. They are the creative and the destructive forces of the universe." (Richard Brodie, "Virus of the Mind", 2009)

"Evolution requires two things: replication, with a certain degree of fidelity; and innovation, or a certain degree of infidelity." (Richard Brodie, "Virus of the Mind", 2009)

"Gaining someone’s trust is an effective way to bypass their skepticism and make it possible to program them with new memes." (Richard Brodie, "Virus of the Mind", 2009)

"If we want to combat the mind viruses responsible for the decline of culture, we need to be conscious of our own programming, consciously adopting memes that take us in the direction we want to go." (Richard Brodie, "Virus of the Mind", 2009)

"If you currently believe in any concepts or subcultures or dogmas that meet these requirements, and you didn’t consciously choose to program yourself with these memes, you are infected with a mind virus." (Richard Brodie, "Virus of the Mind", 2009)

"Memes enter our minds without our permission. They become part of our mental programming and influence our lives without our even being aware of it." (Richard Brodie, "Virus of the Mind", 2009)

"Memetics is the study of the workings of memes: how they interact, replicate, and evolve." (Richard Brodie, "Virus of the Mind", 2009)

"One of the ways the memes you are programmed with greatly affect your future is through self-fulfilling prophecy." (Richard Brodie, "Virus of the Mind", 2009)

"Strategies are beliefs about cause and effect. When you are programmed with a strategy-meme, you unconsciously believe behaving a certain way is likely to produce a certain effect. That behavior may trigger a chain of events that results in spreading the strategy-meme to another mind." (Richard Brodie, "Virus of the Mind", 2009)

"Taking over bits of your mind and pulling you in different directions, mind viruses distract you from what’s most important to you in life and cause confusion, stress, and even despair." (Richard Brodie, "Virus of the Mind", 2009)

"The evolution of ideas, culture, and society revolves around the selfish meme just as the evolution of species revolves around the selfish gene." (Richard Brodie, "Virus of the Mind", 2009)

"The most interesting thing about memes is not whether they’re true or false; it’s that they are the building blocks of your mind." (Richard Brodie, "Virus of the Mind", 2009)

"The most popular and prevalent parts of our culture are the most effective at copying memes." (Richard Brodie, "Virus of the Mind", 2009)

"The universe contains many mechanisms for copying and dispersing information, and viruses are some of the things that are often copied and dispersed." (Richard Brodie, "Virus of the Mind", 2009)

"The very act of asking people a question can cause them to create or reinforce a meme in their minds. Asking enough of the right questions can actually change someone’s belief system, and therefore influence the person’s behavior." (Richard Brodie, "Virus of the Mind", 2009)

"The world is full of memes spread by mind viruses, all competing for a share of your mind, your perception, your attention. They care nothing for your well-being, but instead add to your confusion and subtract from your fulfillment." (Richard Brodie, "Virus of the Mind", 2009)

"Those new memes conflict with your old ones, and a mental tension is created. Your mind wants to resolve the conflict. It does so by creating a new meme." (Richard Brodie, "Virus of the Mind", 2009)

"Truth is not one of the strong selectors for memes." (Richard Brodie, "Virus of the Mind", 2009)

"Viewed through memetics, all values, morals, traditions, and ideas with respect to God and rights are the result of meme evolution. And meme evolution is guided by our genetic tendencies, which in turn evolved around sex." (Richard Brodie, "Virus of the Mind", 2009)

"We can either give up on the hope of having a fulfilling life and a better world or consciously choose which memes to program ourselves with and which we want to spread." (Richard Brodie, "Virus of the Mind", 2009)

"We have an enormous hunger to understand the world around us, which was extremely useful when the world was simple and mostly consisted of physical rewards and dangers. In the society of memes, however, we are constantly trying to make sense of things that simply have no sense." (Richard Brodie, "Virus of the Mind", 2009)

"You can be conditioned, through repetition, to acquire new distinction-memes that make reality look different to you and provide reinforcing evidence that keeps those distinction-memes in place." (Richard Brodie, "Virus of the Mind", 2009)

On Culture (Unsourced)

"[...] every culture in the world has had its own unique history and we can not therefore say that any culture observable in the present day world is an earlier form of any other." (Charles W Hart)

"He who cherishes the values of culture cannot fail to be a pacifist." (Albert Einstein)

"Human creative work is by excellence one of expression. The deep human desire is to be understood by other peoples. This expression which succeeds to be communicated is just what we call culture." (Grigore C Moisil)

"More and more, science has become not only increasingly necessary as a foundation for professional skill, but has come to be regarded as the most valuable instrument of culture." (Henry P Smith)

"Our models of communication [...] create what we disingenuously pretend they merely describe. As a result our science is [...] a reflexive one. We not only describe behavior; we create a particular corner of culture - culture that determines, in part, the kind of communicative world we inhabit." (James W Carey)

"Our will and testament has come about out of a vigorous conviction that a nation that does not highly esteem mathematical thought can never be capable of achieving the highest cultural goals and thereby enjoy the international respect which, in the long term, is an effective means of maintaining our position in the world, as well as asserting our right to live our own lives." (M Gustav Mittag-Leffler)

"Science with its strict analysis of the facts, its persevering search for new, more consummate truths, and its relentless struggle against discovered mistakes and prejudices - science must saturate all or technics, our culture, and everyday life." (Abram F Joffe)

"The acquiring of culture is the developing of an avid hunger for knowledge and beauty." (Jesse L Bennett [attributed])

"The highest culture is not obtained from the teacher when at school or college, so much as by our ever-diligent self-education when we become men." (Samuel Smiles)

"The mathematics of rhythm are universal. They don't belong to any particular culture." (John McLaughlin)

"The trademark of modern culture is science; if you can fake this, you’ve got it made." (Mario Bunge)

"We are caged by our cultural programming. Culture is a mass hallucination, and when you step outside the mass hallucination you see it for what it’s worth." (Terence McKenna)

On Culture (From Fiction to Science Fiction)

"The great law of culture is: Let each become all that he was created capable of being." (Thomas Carlyle, "Jean Paul Friedrich Richter" (1827)

"This history of culture will explain to us the motives, the conditions of life, and the thought of the writer or reformer." (Lev N Tolstoy, "War and Peace", 1867)

"Culture is then properly described not as having its origin in curiosity, but as having its origin in the love of perfection; it is a study of perfection." (Matthew Arnold, "Culture and Anarchy", 1869)

"Not a having and a resting, but a growing and a becoming is the character of perfection as culture conceives it." (Matthew Arnold, "Culture and Anarchy", 1869)

"The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language." (Anton Chekhov, [letter to A.S. Suvorin] 1892)

"As the traveller who has been once from home is wiser than he who has never left his own door step, so a knowledge of one other culture should sharpen our ability to scrutinise more steadily, to appreciate more lovingly, our own." (Margaret Mead, "Coming of Age in Samoa", 1928)

"The worst difficulties from which we suffer do not come from without. They come from within [...] They come from a peculiar type of brainy people, always found in our country, who if they add something to our culture, take much from its strength. Our difficulties come from the mood of unwarrantable self-abasement into which we have been cast by a powerful section of our own intellectuals." (Winston Churchill, [speech] 1933)

"There are and have been worlds and cultures without end, each nursing the proud illusion that it is unique in space and time. There have been men without number suffering from the same megalomania; men who imagined themselves unique, irreplaceable, irreproducible. There will be more [...] more plus infinity. (Alfred Bester, "The Demolished Man", 1953)

"You don't have to burn books to destroy a culture. Just get people to stop reading them." (Ray Bradbury, "Fahrenheit 451", 1953)

"No one person can change a whole culture." (Poul Anderson, "Ghetto", 1954)

"When two alien cultures meet, the stronger must transform the weaker with love or hate." (Damon Knight, "Stranger Station", 1956)

"The meeting between ignorance and knowledge, between brutality and culture - it begins in the dignity with which we treat our dead." (Frank Herbert, "Dune", 1965)

"Homo can truly be called sapiens when he practices his specialty of being unspecialized. His repeated attempts to freeze himself into an all-answering pattern or culture or ideology, or whatever he has named it, have repeatedly brought ruin. Give him the pragmatic business of making his living, and he will usually do rather well. He adapts, within broad limits." (Poul Anderson, "The Queen of Air and Darkness", 1971)

"No culture as yet has actually forgotten history because no culture has really possessed more than fragments of it." (Edgar Pangborn, "Mount Charity", 1971)

"When one culture has the big guns and the other has none, there is a certain predictability about the outcome." (Joanna Russ, ‘"When It Changed", 1972)

"Man creates culture and through culture creates himself." (Pope John Paul II, "Osservatore Romano", 1980)

"A dying culture invariably exhibits personal rudeness. Bad manners. Lack of consideration for others in minor matters. A loss of politeness, of gentle manners, is more significant than is a riot." (Robert A. Heinlein, "Friday", 1982)

"Love was always a word that covered too much territory, from loving a spouse to loving a hobby or abstract justice, and the emotion-mongers of popular entertainment portrayed it as everlasting and exclusive. In a culture under stress the truth could not be concealed by sentimental fluff. The Greenhouse people learned to appreciate love without glorifying it." (George Turner, "Drowning Towers", 1987)

"Some cultures send their young people to the desert to seek visions and guidance, searching for true thinking spawned by the openness of the place, the loneliness, the beauty of emptiness." (Pat Murphy, "Rachel in Love", 1987)

"Most people don’t listen. They use the time when someone else is speaking to think of what they’re going to say next. True Listeners have always been revered among oral cultures, and prized for their rarity value." (Terry Pratchett, "Pyramids", 1989)

"As the soil, however rich it may be, cannot be productive without culture, so the mind without cultivation can never produce good fruit." (Seneca)

"Culture is acquainting ourselves with the best that has been known and said in the world, and thus with the history of the human spirit." (Matthew Arnold)

"Culture is the arts elevated to a set of beliefs." (Thomas Wolfe)

"Culture of the mind must be subservient to the heart." (Mohandas Gandhi)

"In rhetoric, this art of omission is a chief secret of power, and, in general, it is proof of high culture, to say the greatest matters in the simplest way. Veracity first of all, and forever." (Ralph W Emerson)

"It surprises me how our culture can destroy curiosity in the most curious of all animals - human beings." (Paul Maclean)

"Language is the road of a culture. It tells you where its people come from and where they are going." (Rita Mae Brown)

"No culture can live if it attempts to be exclusive." (Mohandas Gandhi)

"Noble life demands a noble architecture of noble uses of noble men. Lack of culture means what it has always meant: ignoble civilization and therefore imminent downfall." (Frank Lloyd Wright)

On Culture (1970-1979)

"If observation be the soil, reading is the manure of intellectual culture." (Daniel Drake, "Physician to the West: Selected Writings of Daniel Drake on Science and Society", 1970)

"Surely one of the most important characteristics of a scientific, introverted, specialized, hence infinitely intellectual culture is its drive toward, and faith in, total “awareness”. Awareness of almost every conceivable factor influencing almost every conceivable situation is our characteristic panacea or cure-all. In this sense, gnosis, the total consciousness, and self-consciousness are the major goals of our secular culture. We really believe that if we know or are aware of everything, if we can understand all relevant causes and factors, we can control everything." (Langdon Gilkey, "Religion and the Scientific Future: Reflections on Myth, Science, and Theology", 1970)

"What a lost person needs is a map of the territory, with his own position marked on it so he can see where he is in relation to everything else. Literature is not only a mirror; it is also a map, a geography of the mind. Our literature is one such map, if we can learn to read it as our literature, as the product of who and where we have been. We need such a map desperately, we need to know about here, because here is where we live. For the members of a country or a culture, shared knowledge of their place, their here, is not a luxury but a necessity. Without that knowledge we will not survive." (Margaret Atwood, "Survival: A Thematic Guide to Canadian Literature", 1972)

"[…] science is not sacrosanct. The restrictions it imposes (and there are many such restrictions though it is not easy to spell them out) are not necessary in order to have general coherent and successful views about the world. There are myths, there are the dogmas of theology, there is metaphysics, and there are many other ways of constructing a worldview. It is clear that a fruitful exchange between science and such ‘nonscientific’ world-views will be in even greater need of anarchism than is science itself. Thus, anarchism is not only possible, it is necessary both for the internal progress of science and for the development of our culture as a whole." (Paul Feyerabend, "Against Method", 1975)

"The ‘culture’ of a group or class, is the peculiar and distinctive ‘way of life’ of the group or class, the meanings, values and ideas embodied in institutions, in social relations, in systems of beliefs, in mores and customs, in the uses of objects and material life. Culture is the distinctive shapes in which this material and social organization of life expresses itself. A culture includes the ‘maps of meaning’ which make things intelligible to its members. These ‘maps of meaning’ are not simply carried around in the head: they are objectivated in the patterns of social organization and relationship through which the individual becomes a ‘social individual’. Culture is the way the social relations of a group are structured and shaped: but it is also the way those shapes are experienced, understood and interpreted." (John Clark et al "Subcultures, Cultures and Class", 1975)

"The influence of modern physics goes beyond technology. It extends to the realm of thought and culture where it has led to a deep revision in man's conception of the universe and his relation to it." (Fritjof Capra, "The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism", 1975)

"I think the most significant creative activities of our or any other human culture - legal and ethical systems, art and music, science and technology - were made possible only through the collaborative work of the left and right cerebral hemispheres. [...] We might say that human culture is the function of corpus callosum." (Carl Sagan, "The Dragons of Eden: Speculations on the Evolution of Human", 1977)

"It is hard for us today to assimilate all the new ideas that are being suggested in response to the new information we have. We must remember that our picture of the universe is based not only on our scientific knowledge but also on our culture and our philosophy. What new discoveries lie ahead no one can say. There may well be civilizations in other parts of our galaxy or in other galaxies that have already accomplished much of what lies ahead for mankind. Others may just be beginning. The universe clearly presents an unending challenge." (Necia H Apfel & J Allen Hynek, "Architecture of the Universe", 1979)

On Culture (-1949)

"It is the destiny of our race to become united into one great body, thoroughly connected in all its parts, and possessed of similar culture. Nature, and even the passions and vices of Man, have from the beginning tended towards this end. A great part of the way towards it is already passed, and we may surely calculate that it will in time be reached." (Johann G Fichte, "The Vocation of Man", 1800)

"The highest possible stage in moral culture is when we recognize that we ought to control our thoughts." (Charles Darwin, "The Descent of Man", 1871)

"The man who is guided by concepts and abstractions only succeeds by such means in warding off misfortune, without ever gaining any happiness for himself from these abstractions. And while he aims for the greatest possible freedom from pain, the intuitive man, standing in the midst of a culture, already reaps from his intuition a harvest of continually inflowing illumination, cheer, and redemption - in addition to obtaining a defense against misfortune. To be sure, he suffers more intensely, when he suffers; he even suffers more frequently, since he does not understand how to learn from experience and keeps falling over and over again into the same ditch." (Friedrich Nietzsche," On Truth and Lie in an Extra-Moral Sense", 1873)

"The culture of the geometric imagination, tending to produce precision in remembrance and invention of visible forms will, therefore, tend directly to increase the appreciation of works of belles-letters." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)

"The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language." (Anton Chekhov, [letter to A.S. Suvorin] 1892) 

"Our science, in contrast with others, is not founded on a single period of human history, but has accompanied the development of culture through all its stages. Mathematics is as much interwoven with Greek culture as with the most modern problems in Engineering. She not only lends a hand to the progressive natural sciences but participates at the same time in the abstract investigations of logicians and philosophers." (Felix Klein, "Klein und Riecke: Ueber angewandte Mathematik und Physik" 1900)

"It is true that mathematics, owing to the fact that its whole content is built up by means of purely logical deduction from a small number of universally comprehended principles, has not unfittingly been designated as the science of the self-evident. Experience however, shows that for the majority of the cultured, even of scientists, mathematics remains the science of the incomprehensible." (Alfred Pringsheim, "Jahresbericht der Deutschen Mathematiker Vereinigung Ueber Wert and angeblichen Unwert der Mathematik", 1904)

"The goal is nothing other than the coherence and completeness of the system not only in respect of all details, but also in respect of all physicists of all places, all times, all peoples, and all cultures." (Max Planck, "Acht Vorlesungen", 1910)

"Only in a free society is man able to create the inventions and cultural values which make life worthwhile to modern man." (Albert Einstein, "Science and Civilization", [speech] 1933)

"Science, unguided by a higher abstract principle, freely hands over its secrets to a vastly developed and commercially inspired technology, and the latter, even less restrained by a supreme culture saving principle, with the means of science creates all the instruments of power demanded from it by the organization of Might." (Johan Huizinga, "In the Shadow of Tomorrow", 1936)

"I see the tasks of social sciences to discover what kinds of order actually do exist in the whole range of the behavior of human beings; what kind of functional relationships between different parts of culture exist in space and over time, and what functionally more useful kinds of order can be created." (Robert S Lynd, "Knowledge of What?", 1939)

"[...] science, if given its head, is not just cold efficiency; its attitude is tolerant, friendly and humane. It has already become the dominant inspiration of human culture, so that modern poetry, painting and architecture derive their most constructive ideas from scientific thought." (Conrad H Waddington, "The Scientific Attitude", 1941)

"Science can give us only the tools in the box, these mechanical miracles that it has already given us. But of what use to us are miraculous tools until we have mastered the humane, cultural use of them? We do not want to live in a world where the machine has mastered the man; we want to live in a world where man has mastered the machine." (Frank L Wright, "Frank Lloyd Wright on Architecture: Selected Writings 1894-1940", 1941)

"A culture is an historically created system of explicit and implicit designs for living, which tends to be shared by all or specially designated members of a group at a specified point in time." (Clyde Kluckhohn & W H Kelley, "The Concept of Culture", 1945)

"[...] science is truly one of the highest expressions of human culture - dignified and intellectually honest, and withal a never-ending adventure. Personally, I feel much the same with regard to the more ecstatic moments in science as I do with regard to music. I see little difference between the thrill of scientific discovery and what one experiences when listening to the opening bars of the Ninth Symphony." (William T Astbury, "Science in Relation to the Community", School Science Review Nr. 109, 1948)

On Culture (1950-1959)

"A social system consists in a plurality of individual actors interacting with each other in a situation which has at least a physical or environmental aspect, actors who are motivated in terms of a tendency to the 'optimization of gratification' and whose relation to their situations, including each other, is defined and mediated in terms of a system of culturally structured and shared symbols." (Talcott Parsons, "The Social System", 1951)

"Culture consists of patterns, explicit and implicit, of and for behavior acquired and transmitted by symbols, constituting the distinctive achievement of human groups, including their embodiments in artifacts; the essential core of culture consists of traditional (i.e., historically derived and selected) ideas and especially their attached values; culture systems may, on the one hand, be considered as products of action, on the other as conditioning elements of further action." (Alfred L Kroeber & Clyde Kluckhohn, "Culture", 1952)

"[...] mathematics is what we make it; not by each of us acting without due regard for what constitutes mathematics in our culture, but by seeking to build up new theories in the light of the old, and to solve outstanding problems generally recognized as valuable for the progress of mathematics as we know it. Until we make it, it fails to 'exist'. And, having been made, it may at some future time even fail to be 'mathematics' any longer." (Raymond L Wilder, "Introduction to the Foundations of Mathematics", 1952)

"Rich in its past, dynamic in the present, prodigious for the future, replete with simple and yet profound ideas and methods, surely mathematics can give something to anyone’s culture." (Rudolph E Langer, "The Things I Should Have Done, I Did Not Do", The American Mathematical Monthly, Vol. 59 (7), 1952)

"The principal mathematical element in the culture, embodying the living and growing mass of modern mathematics, will be chiefly possessed by the professional mathematicians. True, certain professions, such as engineering, physics, and chemistry, which employ a great deal of mathematics, carry a sizable amount of the mathematical tradition, and in some of these, as in the case of physics and engineering research, some individuals contribute to the growth of the mathematical element in the culture. But, in the main, the mathematical element of our culture is dependent for its existence and growth on the class of those individuals known as ‘mathematicians’." (Raymond L Wilder, "Introduction to the Foundations of Mathematics", 1952)

"[...] there is a tendency to forget that all science is bound up with human culture in general, and that scientific findings, even those which at the moment appear the most advanced and esoteric and difficult to grasp, are meaningless outside their cultural context." (Erwin Schrödinger, "Are There Quantum Jumps?", The British Journal for the Philosophy of Science Vol. 3, 1952)

"'World view' differs from culture, ethos, mode of thought, and national character. It is the picture the members of a society have of the properties and characters upon their stage of action. While 'national character' refers to the way these people look to the outsider looking in on them, 'world view' refers to the way the world looks to that people looking out. Of all that is connoted by 'culture', 'world view' attends especially to the way a man, in a particular society, sees himself in relation to all else. It is the properties of existence as distinguished from and related to the self. It is, in short, a man's idea of the universe. It is that organization of ideas which answers to a man the questions: Where am I? Among what do I move? What are my relations to these things? (Robert Redfield, "The Primitive World View", 1952)

"The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify. Statistical methods and statistical terms are necessary in reporting the mass data of social and economic trends, business conditions, 'opinion' polls, the census. But without writers who use the words with honesty and understanding and readers who know what they mean, the result can only be semantic nonsense." (Darell Huff, "How to Lie with Statistics", 1954)

"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)

"The separation between the two cultures has been getting deeper under our eyes; there is now precious little communication between them. [...] The traditional culture [...] is, of course, mainly literary [...] the scientific culture is expansive, not restrictive." (Charles P Snow, New Statesman, 1956)

"A good many times I have been present at gatherings of people who, by the standards of traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative." (Charles P Snow, "The Two Cultures", [lecture] 1959)

"Mathematics is an aspect of culture as well as a collection of algorithms." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)

On Culture (1960-1969)

"A world view is not merely a philosophical by-product of each culture, like a shadow, but the very skeleton of concrete cognitive assumptions on which the flesh of customary behavior is hung. World view, accordingly, may be expressed, more or less systematically in cosmology, philosophy, ethics, religious ritual, scientific belief, and so on, but it is implicit in almost every act. In Parsonian terms, it constitutes the set of cognitive orientations of the members of a society." (Anthony F C Wallace, "Culture and Personality", 1961)

"Rigorous proofs are the hallmark of mathematics, they are an essential part of mathematics’ contribution to general culture." (George Pólya, "Mathematical Discovery", 1962)

"When technology extends one of our senses, a new translation of culture occurs as swiftly as the new technology is interiorized." (Marshall McLuhan, "The Gutenberg Galaxy", 1962)

"Science contributes to our culture in many ways, as a creative intellectual activity in its own right, as the light which has served to illuminate man’s place in the universe, and as the source of understanding of man’s own nature." (John F Kennedy, Address to the National Academy of Sciences Washington, D.C., 1963)

"Any culture is a series of related structures which comprise social forms, values, cosmology, the whole of knowledge and through which all experience is mediated." (Mary Douglas, "Purity and Danger", 1966)

"Culture, in the sense of the public, standardised values of a community, mediates the experience of individuals. It provides in advance some basic categories, a positive pattern in which ideas and values are tidily ordered. And above all, it has authority, since each is induced to assent because of the assent of others." (Mary Douglas, "Purity and Danger", 1966)

"Human action is ‘cultural’ in that meanings and intentions concerning acts are formed in terms of symbolic systems (including the codes through which they operate in patterns) that focus most generally about the universal of human societies, language." (Talcott Parsons, "Societies: Evolutionary and Comparative Perspectives" 1966)

"After all, Greek thought is expressed not only mythically, in fiction, but also directly, in theorems. The gate through which the Greek world may be discussed - and without the knowledge of which, in my opinion, one’s culture can not be deemed complete - is not necessarily Homer. Greek geometry is a wider gate, through which the eye might grasp an austere, yet essential landscape." (Dan Barbilian, 1967)

"Any understanding of social and cultural change is impossible without a knowledge of the way media works as environments." (Marshall McLuhan, "The Medium is the Massage: An inventory of effects", 1967)

"There isn’t a scientific community. It is a culture. It is a very undisciplined organization." (Isidor Isaac Rabi, "The Politics of Pure Science", 1967)

"No science of any kind can be divorced from ethical considerations [...] Science is a human learning process which arises in certain subcultures in human society and not in others, and a subculture as we seen is a group of people defined by acceptance of certain common values, that is, an ethic which permits extensive communication between them." (Kenneth E Boulding, "Economics As A Moral Science", 1969)

On Culture (1980-1989)

"Culture is the collective programming of the mind distinguishing the members of one group or category of people from others." (Geert Hofstede, "Culture's consequences: International differences in work-related values", 1980)

"Science, since people must do it, is a socially embedded activity. It progresses by hunch, vision, and intuition. Much of its change through time does not record a closer approach to absolute truth, but the alteration of cultural contexts that influence it so strongly. Facts are not pure and unsullied bits of information; culture also influences what we see and how we see it. Theories, moreover, are not inexorable inductions from facts. The most creative theories are often imaginative visions imposed upon facts; the source of imagination is also strongly cultural." (Stephen J Gould, "The Mismeasure of Man", 1980)

"The dominant culture of a complex society is never a homogeneous structure. It is layered, reflecting different interests within the dominant class (e.g. an aristocratic versus a bourgeois outlook), containing different traces from the past (e.g. religious ideas within a largely secular culture), as well as emergent elements in the present. Subordinate cultures will not always be in open conflict with it. They may, for long periods, coexist with it, negotiate the spaces and gaps in it, make inroads into it, ‘warrening it from within’. However, though the nature of this struggle over culture can never be reduced to a simple opposition, it is crucial to replace the notion of ‘culture’ with the more concrete, historical concept of ‘cultures’; a redefinition which brings out more clearly the fact that cultures always stand in relations of domination - and subordination - to one another, are always, in some sense, in struggle with one another." (Stuart Hall et al, "Encoding, Decoding’, 1980)

"However, for most of us, science functions like myth in that we have no personal experience in the matter. We put our trust in the scientific view given us by our culture and enshrined in its myths. If asked why leaves are green, most of us would probably mutter something about “chlorophyll.” But unless we were specialists, we would simply be repeating the story of someone else’s experience." (Wallace B Clift, "Jung and Christianity", 1982)

"Culture [is] a pattern of basic assumptions invented, discovered, or developed by a given group as it learns to cope with its problems of external adaptation and internal integration that has worked well enough to be considered valid and, therefore, to be taught to new members as the correct way to perceive, think, and feel in relation to those problems." (Edgar H Schein, "Organizational Culture and Leadership", 1985)

"[…] paradigms, the core of the culture of science, are transmitted and sustained just as is culture generally: scientists accept them and become committed to them as a result of training and socialization, and the commitment is maintained by a developed system of social control." (Barry Barnes, "Thomas Kuhn", 1985)

"[...] without imagination, heightened awareness, moral sense, and some reference to the general culture, the engineering experience becomes less meaningful, less fulfilling than it should be." (Samuel C Florman, "The Civilized Engineer", 1985)

"Science develops best when its concepts and conclusions are integrated into the broader human culture and its concerns for ultimate meaning and value." (Pope John Paul II, [letter to Father George V Coyne], 1988)

"A culture may be conceived as a network of beliefs and purposes in which any string in the net pulls and is pulled by the others, thus perpetually changing the configuration of the whole. If the cultural element called morals takes on a new shape, we must ask what other strings have pulled it out of line. It cannot be one solitary string, nor even the strings nearby, for the network is three-dimensional at least." (Jacques Barzun, "The Culture We Deserve", 1989)

On Culture (1990-1999)

"Science is an integral part of culture. It’s not this foreign thing, done by an arcane priesthood. It’s one of the glories of the human intellectual tradition." (Stephen J Gould, Independent (London), 1990)

"Works of science are ways of understanding created through human effort which, like works of art, can be interrogated for what they say about ourselves and our development. By finding out about our science we find out about ourselves." (Joseph Schwartz, "The Creative Moment: How Science Made Itself Alien to Modern Culture", 1992)

"Mathematics was born and nurtured in a cultural environment. Without the perspective which the cultural background affords, a proper appreciation of the content and state of present-day mathematics is hardly possible." (Raymond L Wilder, American Mathematical Monthly, 1994)

"New knowledge is not science until it is made social. The scientific culture can be defined as new verifiable knowledge secured and distributed with fair credit meticulously given." (Edward O Wilson, "Naturalist", 1994)

"Culture in the broadest sense is a form of highly participatory activity, in which people create their societies and identities. Culture shapes individuals, drawing out and cultivating their potentialities and capacities for speech, action, and creativity." (Douglas Kellner, "Media Culture", 1995)

"Human mind and culture have developed a formal system of thought for recognizing, classifying, and exploiting patterns. We call it mathematics. By using mathematics to organize and systematize our ideas about patterns, we have discovered a great secret: nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)

"Networks constitute the new social morphology of our societies, and the diffusion of networking logic substantially modifies the operation and outcomes in processes of production, experience, power, and culture. While the networking form of social organization has existed in other times and spaces, the new information technology paradigm provides the material basis for its pervasive expansion throughout the entire social structure." (Manuel Castells, "The Rise of the Network Society", 1996)

"Any global tradition needs to begin with a shared worldview - a culture-independent, globally accepted consensus as to how things are." (Ursula Goodenough, "The Sacred Depths of Nature", 1998)

"Despite being partly familiar to all, because of these contradictory aspects, mathematics remains an enigma and a mystery at the heart of human culture. It is both the language of the everyday world of commercial life and that of an unseen and perfect virtual reality. It includes both free-ranging ethereal speculation and rock-hard certainty. How can this mystery be explained? How can it be unraveled? The philosophy of mathematics is meant to cast some light on this mystery: to explain the nature and character of mathematics. However this philosophy can be purely technical, a product of the academic love of technique expressed in the foundations of mathematics or in philosophical virtuosity. Too often the outcome of philosophical inquiry is to provide detailed answers to the how questions of mathematical certainty and existence, taking for granted the received ideology of mathematics, but with too little attention to the deeper why questions." (Paul Ernest, "Social Constructivism as a Philosophy of Mathematics", 1998)

"Even revolutionaries conserve; all cultures are conservative. This is so because it is a systemic phenomenon: all systems exist only as long as there is conservation of that which defines them." (Humberto M Romesin & Pille Bunnell, "Biosphere, Homosphere, and robosphere: What has that to do with Business?", Society for Organizational Learning, 1998)

"[Mathematics is] a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context." (Reuben Hersh, "What Is Mathematics, Really?", 1998)

"Cultural archetypes are the unconscious models that help us make sense of the world: they are the myths, narratives, images, symbols, and files into which we organize the data of our life experience" (Clotaire Rapaille, "Cultural Imprints", Executive Excellence Vol. 16 (10), 1999)

"Every culture has a shared pattern of thinking. It is the cement that holds a culture together, gives it unity. A culture's characteristic way of thinking is imbedded in its concept of the nature of reality, its world view. […] A change of world view not only brings about profound cultural changes, but also is responsible for what historians call a ‘change of age’. An age is a period of time in which the prevailing world view has remained relatively unchanged." (Russell L Ackoff,"Re-Creating the Corporation", 1999)

"Imagining the unseeable is hard, because imagining means having an image in your mind. And how can you have a mental image of something you have never seen? Like perception itself, the models of science are embedded inextricably in the current worldview we call culture." (K C Cole, "First You Build a Cloud", 1999)

On Culture (2000-2009)

"Numeracy is the ability to process, interpret and communicate numerical, quantitative, spatial, statistical, even mathematical information, in ways that are appropriate for a variety of contexts, and that will enable a typical member of the culture or subculture to participate effectively in activities that they value." (Jeff Evans, "Adults´ Mathematical Thinking and Emotion", 2000)

"The stunning variety of life forms that surround us, as well as the beliefs, practices, techniques, and behavioral forms that constitute human culture, are the product of evolutionary dynamics." (Herbert Gintis, "Game Theory Evolving", 2000)

"A scientific theory or other product is creative only if the innovation gains the acceptance of a field of experts and so transforms the culture." (Jeanne Nakamura & Mihaly Csikszentmihalyi, "Catalytic creativity: The case of Linus Pauling", 2001)

"All human knowledge - including statistics - is created  through people's actions; everything we know is shaped by our language, culture, and society. Sociologists call this the social construction of knowledge. Saying that knowledge is socially constructed does not mean that all we know is somehow fanciful, arbitrary, flawed, or wrong. For example, scientific knowledge can be remarkably accurate, so accurate that we may forget the people and social processes that produced it." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Ecological rationality uses reason – rational reconstruction – to examine the behavior of individuals based on their experience and folk knowledge, who are ‘naïve’ in their ability to apply constructivist tools to the decisions they make; to understand the emergent order in human cultures; to discover the possible intelligence embodied in the rules, norms and institutions of our cultural and biological heritage that are created from human interactions but not by deliberate human design. People follow rules without being able to articulate them, but they can be discovered." (Vernon L Smith, "Constructivist and ecological rationality in economics", 2002)

"A meme is to thinking what a gene is to evolution. A meme is defined as any idea, behavior, or skill. Like a gene, it can replicate by transferring from one person to another by imitation: stories, fashions, inventions, recipes, songs, ways of plowing a field or throwing a baseball or making a sculpture. Like a gene, it competes with other memes, as ideas and behavior compete in a culture and between cultures." (Didier Sornette, "Why Stock Markets Crash: Critical Events in Complex Financial Systems", 2003)

"Just because people doing science are embedded in a particular social and cultural milieu, it doesn’t follow that science is not universal." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"Art is constructivist in nature, aimed at the deliberate refinement and elaboration of mental models and worldviews. These are the natural products of cognition itself, the outcome of the brain’s tendency to strive for the integration of perceptual and conceptual material over time. […] human culture is essentially a distributed cognitive system within which worldviews and mental models are constructed and shared by the members of a society. Artists are traditionally at the forefront of that process, and have a large influence on our worldviews and mental models." (Mark Turner, "The Artful Mind : cognitive science and the riddle of human creativity", 2006)

"Mathematics can be as effortless as humming a tune, if you know the tune. But our culture does not prepare us for appreciation of mathematics as it does for appreciation of music. Though we start hearing music very early in life, the same cannot be said of mathematics, even though the two subjects are twins. This is a shame; to know music without knowing its mathematics is like hearing a melody without its accompaniment." (Gareth Loy, "Musimathics: The Mathematical Foundations of Music" Vol. 1, 2006)

"The principle of informed responsibility: no culture is justified in creating a cultural separation of its own area; it is the responsibility of each culture to inform other cultures about their own developments and be informed about developments of other cultures." (Andrzej P. Wierzbicki et al, "Creative Space: Models of Creative Processes for the Knowledge Civilization Age", Studies in Computational Intelligence Vol. 10, 2006)

"The principle of systemic integration: whenever needed, knowledge from and about diverse cultures and disciplines might be synthesized by systemic methods, be they soft or hard, without a prior prejudice against any of them, following the principles of open and informed systemic integration." (Andrzej P. Wierzbicki et al, "Creative Space: Models of Creative Processes for the Knowledge Civilization Age", Studies in Computational Intelligence Vol. 10, 2006)

"When great learning comes up against an unsupportive organizational culture, the culture wins every time." (Marc J Rosenberg, "Beyond E-Learning", 2006)

"Beneath the problems that often seem so ‘given’ lie cultural norms and practices and ultimately whole worldviews. Our problems have contexts, backgrounds, roots. These in turn can be shifted and reconstructed. Problems can be circumvented or at least reshaped so that they arise in more manageable forms." (Anthony Weston, "How to Re-Imagine the World", 2007)

"Mathematical good taste, then, consists of using intelligently the concepts and results available in the ambient mathematical culture for the solution of new problems. And the culture evolves because its key concepts and results change, slowly or brutally, to be replaced by new mathematical beacons." (David Ruelle, "The Mathematician's Brain", 2007)

"Our generational perspective contributes to the mental models we hold about ourselves, the world, and the way things ‘should’ be. These beliefs create blind spots that can become our undoing as we pursue our values and seek to accomplish our goals. Likewise, they can have a powerful effect on our culture." (Deborah Gilburg,"Empowering Multigenerational Collaboration in the Workplace", The Systems Thinker Vol. 18 No. 4, 2007)

"A theory is a speculative explanation of a particular phenomenon which derives it legitimacy from conforming to the primary assumptions of the worldview of the culture in which it appears. There can be more than one theory for a particular phenomenon that conforms to a given worldview. […] A new theory may seem to trigger a change in worldview, as in this case, but logically a change in worldview must precede a change in theory, otherwise the theory will not be viable. A change in worldview will necessitate a change in all theories in all branches of study." (M G Jackson, "Transformative Learning for a New Worldview: Learning to Think Differently", 2008)

"Many mathematical game theorists dislike the dependence of an outcome on historical, cultural, or linguistic aspects of the game or on purely arbitrary devices like round numbers; they would prefer the solution be determined purely by the abstract mathematical facts about the game - the number of players, the strategies available to each, and the payoffs to each in relation to the strategy choices of all. We disagree. We think it entirely appropriate that the outcome of a game played by humans interacting in a society should depend on the social and psychological aspects of the game." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Our culture, obsessed with numbers, has given us the idea that what we can measure is more important than what we can't measure. Think about that for a minute. It means that we make quantity more important than quality." (Donella Meadows, "Thinking in Systems: A Primer", 2008)

"The brain seems to be making choices according to some stubborn timing pattern, undoubtedly influenced by both culture and gene." (John Medina, "Brain Rules", 2008)

"If we want to combat the mind viruses responsible for the decline of culture, we need to be conscious of our own programming, consciously adopting memes that take us in the direction we want to go." (Richard Brodie, "Virus of the Mind", 2009)

"If you currently believe in any concepts or subcultures or dogmas that meet these requirements, and you didn’t consciously choose to program yourself with these memes, you are infected with a mind virus." (Richard Brodie, "Virus of the Mind", 2009)

"Mathematicians seek a certain kind of beauty. Perhaps mathematical beauty is a constant - as far as the contents of mathematics are concerned - and yet the forms this beauty takes are certainly cultural. And while the history of mathematics surely is many stranded, one of its most important strands is formed by such cultural forms of mathematical beauty." (Reviel Netz, "Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic", 2009)

"The most popular and prevalent parts of our culture are the most effective at copying memes." (Richard Brodie, "Virus of the Mind", 2009)

"Truth in mathematics is totally dependent on pure thought, with no component of data to be added. This is unique. Associated with truth in mathematics is an absolute certainty in its validity. Why does this matter, and why does it go beyond a cultural oddity of our profession? The answer is that mathematics is deeply embedded in the reasoning used within many branches of knowledge. That reasoning often involves conjectures, assumptions, intuition. But whatever aspect has been reduced to mathematics has an absolute validity. As in other subjects search for truth, the mathematical components embedded in their search are like the boulders in the stream, providing a solid footing on which to cross from one side to the other." (James Glimm, "Reflections and Prospectives", 2009)

On Culture (2010-)

"The answers to the human problems of ecology are to be found in economy. And the answers to the problems of economy are to be found in culture and character. To fail to see this is to go on dividing the world falsely between guilty producers and innocent consumers." (Wendell Berry, "What Are People For?: Essays", 2010)

"Cultures are never merely intellectual constructs. They take form through the collective intelligence and memory, through a commonly held psychology and emotions, through spiritual and artistic communion." (Tariq Ramadan, "Islam and the Arab Awakening", 2012)

"Scientific method is the gateway into scientific discoveries that in turn prompt technological advances and cultural influences." (Hugh G Gauch Jr., "Scientific Method in Brief", 2012)

"A mathematical entity is a concept, a shared thought. Once you have acquired it, you have it available, for inspection or manipulation. If you understand it correctly (as a student, or as a professional) your ‘mental model’ of that entity, your personal representative of it, matches those of others who understand it correctly. (As is verified by giving the same answers to test questions.) The concept, the cultural entity, is nothing other than the collection of the mutually congruent personal representatives, the ‘mental models’, possessed by those participating in the mathematical culture." (Reuben Hersh, "Experiencing Mathematics: What Do We Do, when We Do Mathematics?", 2014)

"Culture is fuzzy, easy to caricature, amenable to oversimplifications, and often used as a catchall when all other explanations fail." (Zachary Karabell, "The Leading Indicators: A short history of the numbers that rule our world", 2014)

"All cultures organize themselves around a story, which tells them how the world came into being - a creation myth." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)

"Paradigm change necessarily involves a discontinuous jump. Reality is singular and each paradigm evokes its own reality. This is the reason that scientific paradigms are not changed without a great deal of conflict; the reason why deep thinking is so difficult and involves overcoming so much resistance both in the individual and in the larger culture. In fact it has been said that a scientist never really gives up the paradigm within which she has been trained." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)

"When a culture is founded on the principle of immediacy of experience, there is no need for numeracy. It is impossible to consume more than one thing at a time, so differentiating between 'a small amount', 'a larger amount' and 'many' is enough for survival." (The Open University, "Understanding the environment: learning and communication", 2016)

"History of mathematics is done by mathematicians as well as historians. History models mathematics as a segment of the ongoing story of human culture. Mathematicians are likely to see the past through the eyes of the present, and ask, ‘Was it important? natural? deep? surprising? elegant?’ The historian sees mathematics as a thread in the ever-growing web of human life, intimately interwoven with finance and technology, with war and peace. Today's mathematics is the culmination of all that has happened before now, yet to future viewpoints it will seem like a brief, outmoded stage of the past." (Reuben Hersh, "Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)

On Perfection (1800-1899)

"[…] we must not measure the simplicity of the laws of nature by our facility of conception; but when those which appear to us the most simple, accord perfectly with observations of the phenomena, we are justified in supposing them rigorously exact." (Pierre-Simon Laplace, "The System of the World", 1809)

"Geometry is a true natural science: - only more simple, and therefore more perfect than any other. We must not suppose that, because it admits the application of mathematical analysis, it is therefore a purely logical science, independent of observation. Everybody studied by geometers presents some primitive phenomena which, not being discoverable by reasoning, must be due to observation alone." (Auguste Comte,"Course of Positive Philosophy", 1830)

"A mathematician is only perfect insofar as he is a perfect man, sensitive to the beauty of truth." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"The man who insists upon seeing with perfect clearness before he decides, never decides." (Henri-Frédéric Amiel, [journal entry] 1856)

"It often happens that the pursuit of the beautiful and appropriate, or, as it may be otherwise expressed, the endeavor after the perfect, is rewarded with a new insight into the true." (James J Sylvester, "Separation of the Roots of an Algebraical Equation", Philosophical Magazine, 1866)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"In abstract mathematical theorems the approximation to absolute truth is perfect, because we can treat of infinitesimals. In physical science, on the contrary, we treat of the least quantities which are perceptible." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"The more progress physical sciences makes, the more they tend to enter the domain of mathematics, which is a kind of center to which they all converge. We may even judge of the degree of perfection to which a science has arrived by the facility with which it may be submitted to calculation." (Adolphe Quetelet, "Annual Report of the Board of Regents of the Smithsonian Institution", 1874)

"[…] it is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician." (Karl Weierstrass, [Letter to Sofia Kovalevskaya], 1883)

"Mathematics is perfectly free in its development and is subject only to the obvious consideration, that its concepts must be free from contradictions in themselves, as well as definitely and orderly related by means of definitions to the previously existing and established concepts." (Georg Cantor," Grundlagen einer allgemeinen Manigfaltigkeitslehre", 1883)

"I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them on the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge, - knowledge mingled with ignorance, producing doubt." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1887)

"Geometry exhibits the most perfect example of logical stratagem." (Henry T Buckle,"History of Civilization in England" Vol. 2, 1891)

"[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity." (Hermann von Helmholtz, "Über das Verhältnis der Naturwissenschaften zur Gesammtheit der Wissenschaft", 1896)

On Perfection (-1799)

"The mathematician is perfect only in so far as he is a perfect man, in so far as he senses in himself the beauty of truth; only then will his work be thorough, transparent, prudent, pure, clear, graceful, indeed elegant." (Plato, "Republic", cca. 375 BC)

"If in a discussion of many matters […] we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability." (Plato, "Timaeus", cca. 360 BC)

"But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end." (Aristotle, "Generation of Animals", cca 4th century BC)

"[…] he who wishes to attain to human perfection, must therefore first study Logic, next the various branches of Mathematics in their proper order, then Physics, and lastly Metaphysics." (Moses Maimonides, "The Guide for the Perplexed", 1190)

"Sound is generated by motion, since it belongs to the class of successive things. For this reason, while it exists when it is made, it no longer exists once it has been made. […] All music, especially mensurable music, is founded in perfection, combining in itself number and sound." (Jean de Muris,"Ars novae musicae", 1319)

"Nature is not at variance with art nor art with nature, they both being the servants of his providence: art is the perfection of nature." (Sir Thomas Browne," Religio Medici", 1643)

"And thus many are ignorant of mathematical truths, not out of any imperfection of their faculties, or uncertainty in the things themselves, but for want of application in acquiring, examining, and by due ways comparing those ideas." (John Locke, "An Essay Concerning Human Understanding", 1689)

"There is nothing in Nature that does more show the piercing Force of Human Understanding, the sublimity of its Speculations and deep researchers, than true Astronomy. It raises our Minds above our Senses, and even in contradiction to them, shows us the true System of the World: the faculty of Reason by which we have made these great discoveries in the Heavens must needs be derived from Heaven, since no Earthly Principle can attain so great a Perfection." (John Keill, "An Introduction to the True Astronomy", 1721)

"For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear." (Leonhard Euler, "De Curvis Elasticis", 1744)

"[...] one day the precision of the data might be brought to such perfection that the mathematician in his study would be able to calculate any phenomenon of chemical combination in the same way…as he calculates the movement of the heavenly bodies." (Antoine-Laurent Lavoisier, "Memories de l’Académie Royale des Sciences", 1782 [Published 1785])

"As long as algebra and geometry proceeded along separate paths, their advance was slow and their applications limited. But when these sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace toward perfection." (Joseph-Louis de Lagrange, "Leçons Élémentaires de Mathématiques", 1795)

On Perfection (2000-)

"Prediction is rarely perfect. There are usually many unmeasured variables whose effect is referred to as 'noise'. But the extent to which the model box emulates nature's box is a measure of how well our model can reproduce the natural phenomenon producing the data." (Leo Breiman, "Statistical Modeling: The Two Cultures", Statistical Science 16(3), 2001)

[...] an apparently random universe could be obeying every whim of a deterministic deity who chooses how the dice roll; a universe that has obeyed perfect mathematical laws for the last ten billion years could suddenly start to play truly random dice. So the distinction is about how we model the system, and what point of view seems most useful, rather than about any inherent feature of the system itself. (Ian Stewart, "Does God Play Dice: The New Mathematics of Chaos", 2002)

"[...] the view that math provides absolute certainty and is static and perfect while physics is tentative and constantly evolving is a false dichotomy. Math is actually not that different from physics. Both are attempts of the human mind to organize, to make sense, of human experience; in the case of physics, experience in the laboratory, in the physical world, and in the case of math, experience in the computer, in the mental mindscape of pure mathematics. And mathematics is far from static and perfect; it is constantly evolving, constantly changing, constantly morphing itself into new forms. New concepts are constantly transforming math and creating new fields, new viewpoints, new emphasis, and new questions to answer. And mathematicians do in fact utilize unproved new principles suggested by computational experience, just as a physicist would." (Gregory Chaitin, "Meta Math: The Quest for Omega", 2005)

"Mathematics as done by mathematicians is not just heaping up statements logically deduced from the axioms. Most such statements are rubbish, even if perfectly correct. A good mathe￾matician will look for interesting results. These interesting re￾sults, or theorems, organize themselves into meaningful and natural structures, and one may say that the object of mathematics is to find and study these structures." (David Ruelle,"The Mathematician's Brain", 2007)

"We must be prepared to find that the perfection, purity, and simplicity that we love in mathematics is metaphorically related to a yearning for human perfection, purity, and simplicity. And this may explain why mathematicians often have a religious inclination. But we must also be prepared to find that our love of mathematics is not exempt from the usual human contradictions." (David Ruelle, "The Mathematician's Brain", 2007)

"Yet, with the discovery of the butterfly effect in chaos theory, it is now understood that there is some emergent order over time even in weather occurrence, so that weather prediction is not next to being impossible as was once thought, although the science of meteorology is far from the state of perfection." (Peter Baofu, "The Future of Complexity: Conceiving a Better Way to Understand Order and Chaos", 2007)

"Nature is complex, and almost all methods of observation and experiment are imperfect." (Victor Cohn & Lewis Cope, "News & Numbers: A writer’s guide to statistics" 3rd Ed, 2012)

"Ontological mathematics is operating in such a way as to organize itself into a zero-entropy structure - mathematical perfection. The 'Big Bang' is equivalent to the total scrambling of a cosmic Rubik’s Cube. The task of ontological mathematics is then to unscramble the Cube and return it to its original, pristine configuration. Emotionally, this amounts to returning to perfect Love and Bliss. Intellectually, it means reaching a state of perfect logic and reason [...] thinking perfectly." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)

On Perfection (1950-1974)

"[...] nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"If simple perfect laws uniquely rule the universe, should not pure thought be capable of uncovering this perfect set of laws without having to lean on the crutches of tenuously assembled observations? True, the laws to be discovered may be perfect, but the human brain is not. Left on its own, it is prone to stray, as many past examples sadly prove. In fact, we have missed few chances to err until new data freshly gleaned from nature set us right again for the next steps. Thus pillars rather than crutches are the observations on which we base our theories; and for the theory of stellar evolution these pillars must be there before we can get far on the right track." (Erwin Schrödinger & Martin Schwarzschild, "Structure and Evolution of the Stars", 1958)

"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)

"No theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1962)

"Perfect logic and faultless deduction make a pleasant theoretical structure, but it may be right or wrong; the experimenter is the only one to decide, and he is always right." (Léon Brillouin, "Scientific Uncertainty and Information", 1964)

"It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true." (Bertrand Russell, "Autobiography", 1967)

"But, really, mathematics is not religion; it cannot be founded on faith. And what was most important, the methods yielding such remarkable results in the hands of the great masters began to lead to errors and paradoxes when employed by their less talented students. The masters were kept from error by their perfect mathematical intuition, that subconscious feeling that often leads to the right answer more quickly than lengthy logical reasoning. But the students did not possess this intuition […]" (Naum Ya. Vilenkin, "Stories about Sets", 1968)

"The point is that every experiment involves an error, the magnitude of which is not known beforehand and it varies from one experiment to another. For this reason, no matter what finite number of experiments have been carried out, the arithmetic mean of the values obtained will contain an error. Of course, if the experiments are conducted under identical conditions and the errors are random errors, then the error of the mean will diminish as the number of experiments is increased, but it cannot be reduced to zero for a finite number of experiments. […] The choice of entities for an experiment must be perfectly random, so that even an apparently inessential cause could not lead to erroneous conclusions." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

On Perfection (1925-1949)

 "Science is a magnificent force, but it is not a teacher of morals. It can perfect machinery, but it adds no moral restraints to protect society from the misuse of the machine. It can also build gigantic intellectual ships, but it constructs no moral rudders for the control of storm tossed human vessel. It not only fails to supply the spiritual element needed but some of its unproven hypotheses rob the ship of its compass and thus endangers its cargo." (William J Bryan, "Undelivered Trial Summation Scopes Trial", 1925)

"The discovery that all mathematics follows inevitably from a small collection of fundamental laws is one which immeasurably enhances the intellectual beauty of the whole; to those who have been oppressed by the fragmentary and incomplete nature of most existing chains of deduction this discovery comes with all the overwhelming force of a revelation; like a palace emerging from the autumn mist as the traveler ascends an Italian hill-side, the stately stories of the mathematical edifice appear in their due order and proportion, with a new perfection in every part." (Bertrand A W Russell, "Mysticism and Logic and Other Essays", 1925)

"Mathematics then becomes the ladder by which we all may climb into the heaven of perfect insight and eternal satisfaction, and the solution of arithmetic and algebraic problems is connected with the salvation of our souls." (Scott Buchanan, "Poetry and Mathematics", 1929)

"Natural law is not applicable to the unseen world behind the symbols, because it is unadapted to anything except symbols, and its perfection is a perfection of symbolic linkage. You cannot apply such a scheme to the parts of our personality which are not measurable by symbols any more than you can extract the square root of a sonnet." (Arthur S Eddington, "Science and the Unseen World", 1929)

"The final truth about phenomena resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge is complete. We go beyond the mathematical formula at our own risk; we may find a [nonmathematical] model or picture that helps us to understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault." (James Jeans, "The Mysterious Universe", 1930)

"A circle no doubt has a certain appealing simplicity at the first glance, but one look at a healthy ellipse should have convinced even the most mystical of astronomers that that the perfect simplicity of the circle is akin to the vacant smile of complete idiocy. Compared to what an ellipse can tell us, a circle has nothing to say." (Eric T Bell, "The Handmaiden of the Sciences", 1937)

"Matter-of-fact is an abstraction, arrived at by confining thought to purely formal relations which then masquerade as the final reality. This is why science, in its perfection, relapses into the study of differential equations. The concrete world has slipped through the meshes of the scientific net." (Alfred N Whitehead, "Modes of Thought", 1938)

"Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection." (Herman Weyl, "Symmetry", 1938)

"In anything at all, perfection is finally attained not when there is no longer anything to add, but when there is no longer anything to take away [...]" (Antoine de Saint Exupéry, "Wind, Sand and Stars", 1939)

"Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science." (Richard Courant & Herbert Robbins, "What Is Mathematics?", 1941)

"If God has made the world a perfect mechanism, He has at least conceded so much to our imperfect intellect that in order to predict little parts of it, we need not solve innumerable differential equations, but can use dice with fair success." (Max Born, "Albert Einstein: Philosopher-Scientist", 1949)

On Perfection (1900-1924)

"And as the ideal in the whole of Nature moves in an infinite process toward an Absolute Perfection, we may say that art is in strict truth the apotheosis of Nature. Art is thus at once the exaltation of the natural toward its destined supernatural perfection, and the investiture of the Absolute Beauty with the reality of natural existence. Its work is consequently not a means to some higher end, but is itself a final aim; or, as we may otherwise say, art is its own end. It is not a mere recreation for man, a piece of by-play in human life, but is an essential mode of spiritual activity, the lack of which would be a falling short of the destination of man. It is itself part and parcel of man's eternal vocation." (George H Howison, "The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Idealism", 1901)

"The very possibility of mathematical science seems an insoluble contradiction. If this science is only deductive in appearance, from whence is derived that perfect rigour which is challenged by none? If, on the contrary, all the propositions which it enunciates may be derived in order by the rules of formal logic, how is it that mathematics is not reduced to a gigantic tautology? The syllogism can teach us nothing essentially new, and if everything must spring from the principle of identity, then everything should be capable of being reduced to that principle." (Henri Poincaré, "Science and Hypothesis", 1901)

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." (Bertrand Russell, 'The Study of Mathematics", 1902)

"There is not in Nature any system perfectly isolated, perfectly abstracted from all external action; but there are systems which are nearly isolated. If we observe such a system, we can study not only the relative motion of its different parts with respect to each other, but the motion of its centre of gravity with respect to the other parts of the universe." (Henri Poincaré, "Science and Hypothesis", 1902)

"The true mathematician is always a great deal of an artist, an architect, yes, of a poet. Beyond the real world, though perceptibly connected with it, mathematicians have created an ideal world which they attempt to develop into the most perfect of all worlds, and which is being explored in every direction. None has the faintest conception of this world except him who knows it; only presumptuous ignorance can assert that the mathematician moves in a narrow circle. The truth which he seeks is, to be sure, broadly considered, neither more nor less than consistency; but does not his mastership show, indeed, in this very limitation? To solve questions of this kind he passes unenviously over others." (Alfred Pringsheim, Jaresberichte der Deutschen Mathematiker Vereinigung Vol 13, 1904)

"The beautiful has its place in mathematics as elsewhere. The prose of ordinary intercourse and of business correspondence might be held to be the most practical use to which language is put, but we should be poor indeed without the literature of imagination. Mathematics too has its triumphs of the Creative imagination, its beautiful theorems, its proofs and processes whose perfection of form has made them classic. He must be a 'practical' man who can see no poetry in mathematics." (Wiliam F White, "A Scrap-book of Elementary Mathematics: Notes, Recreations, Essays", 1908)

"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s ‘blank form of a universe’ without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition." (Lawrence J Henderson, "The Order of Nature: An Essay", 1917)

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty, cold and austere, like that of a sculpture without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry." (Bertrand Russell, "The Study of Mathematics", 1919)

On Perfection (Unsourced)

"[Arithmetic] is another of the great master-keys of life. With it the astronomer opens the depths of the heavens; the engineer, the gates of the mountains; the navigator, the pathways of the deep. The skillful arrangement, the rapid handling of figures, is a perfect magician's wand." (Edward Everett)

"It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset." (Sir Arthur S Eddington)

"Mathematics is a way of expressing natural laws, it is the easiest and best way to describe a general law or the flow of a phenomenon, it is the most perfect language in which one can narrate a natural phenomenon." (Gheorghe Ţiţeica)

"So far as a theory is formed in the generalization of natural appearances, that theory must be just, although it may not be perfect, as having comprehended every appearance; that is to say, a theory is not perfect until it be founded upon every natural appearance; in which case, those appearances will be explained by the theory." (William Huggins)

"The mathematician's best work is art […] a high and perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch each other." (M Gustav Mittag-Leffler)

"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive, and even elegant." (Johann Wolfgang von Goethe)

"The part always has a tendency to reunite with its whole in order to escape from its imperfection." (Leonardo Da Vinci)

"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)

On Perfection: Perfect Symmetry

"The fact is that the beautiful, humanly speaking, is merely form considered in its simplest aspect, in its most perfect symmetry, in its most entire harmony with our make-up." (Victor Hugo, "Cromwell", 1909)

"Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty, and perfection." (Herman Weyl, "Symmetry", 1938)

"[...] nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop." (Chen-Ning Yang, "The Law of Parity Conservation and Other Symmetry Laws of Physics", [Nobel lecture] 1957)

"Nature is never perfectly symmetric. Nature's circles always have tiny dents and bumps. There are always tiny fluctuations, such as the thermal vibration of molecules. These tiny imperfections load Nature's dice in favour of one or other of the set of possible effects that the mathematics of perfect symmetry considers to be equally possible." (Ian Stewart & Martin Golubitsky,"Fearful Symmetry: Is God a Geometer?", 1992)

"Nature behaves in ways that look mathematical, but nature is not the same as mathematics. Every mathematical model makes simplifying assumptions; its conclusions are only as valid as those assumptions. The assumption of perfect symmetry is excellent as a technique for deducing the conditions under which symmetry-breaking is going to occur, the general form of the result, and the range of possible behaviour. To deduce exactly which effect is selected from this range in a practical situation, we have to know which imperfections are present (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"Skewness is a measure of symmetry. For example, it's zero for the bell-shaped normal curve, which is perfectly symmetric about its mean. Kurtosis is a measure of the peakedness, or fat-tailedness, of a distribution. Thus, it measures the likelihood of extreme values." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)

"Symmetry is basically a geometrical concept. Mathematically it can be defined as the invariance of geometrical patterns under certain operations. But when abstracted, the concept applies to all sorts of situations. It is one of the ways by which the human mind recognizes order in nature. In this sense symmetry need not be perfect to be meaningful. Even an approximate symmetry attracts one's attention, and makes one wonder if there is some deep reason behind it." (Eguchi Tohru & ‎K Nishijima ,"Broken Symmetry: Selected Papers Of Y Nambu", 1995)

"The possibility of translating uncertainties into risks is much more restricted in the propensity view. Propensities are properties of an object, such as the physical symmetry of a die. If a die is constructed to be perfectly symmetrical, then the probability of rolling a six is 1 in 6. The reference to a physical design, mechanism, or trait that determines the risk of an event is the essence of the propensity interpretation of probability. Note how propensity differs from the subjective interpretation: It is not sufficient that someone’s subjective probabilities about the outcomes of a die roll are coherent, that is, that they satisfy the laws of probability. What matters is the die’s design. If the design is not known, there are no probabilities." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"The word ‘symmetry’ conjures to mind objects which are well balanced, with perfect proportions. Such objects capture a sense of beauty and form. The human mind is constantly drawn to anything that embodies some aspect of symmetry. Our brain seems programmed to notice and search for order and structure. Artwork, architecture and music from ancient times to the present day play on the idea of things which mirror each other in interesting ways. Symmetry is about connections between different parts of the same object. It sets up a natural internal dialogue in the shape." (Marcus du Sautoy,"Symmetry: A Journey into the Patterns of Nature", 2008)

"Mathematical symmetry is an idealized model. However, slightly imperfect symmetry requires explanation; it’s not enough just to say ‘it’s asymmetric’." (Ian Stewart, "Symmetry: A Very Short Introduction", 2013)

On Symbols (2010-)

"In natural language, even the most carefully chosen words drag along concealed meanings that have the power to manipulate reasoning. [...] Symbols of mathematics too sometimes have concealed meanings, but their purpose is to bring along pure thought. It is possible to learn what a mathematical symbol stands for by context. We learn the meanings of mathematical symbols mostly from their definitions: Mostly, because in formal mathematics not everyone easily grasps definitions that are not linked to the familiar properties of experience." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"Unlike symbols in poetry, mathematical symbols begin as deliberate designs created by mathematicians. That does not stop symbols from performing the same function that a poem would: to make connections between experience and the unknown and to transfer metaphorical thoughts capable of conveying meaning. As in poetry, there are archetypes in mathematics. If there are such things as self-evident truths, then there probably are things we know about the world that come with the human package at birth." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"What is good mathematical notation? As it is with most excellent questions, the answer is not so simple. Whatever a symbol is, it must function as a revealer of patterns, a pointer to generalizations. It must have an intelligence of its own, or at least it must support our own intelligence and help us think for ourselves. It must be an indicator of things to come, a signaler of fresh thoughts, a clarifier of puzzling concepts, a help to overcome the mental fatigues of confusion that would otherwise come from rhetoric or shorthand." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"When it comes to algebra, visual conception is beyond any similarities in the physical world. That’s okay; as we’ve noted, it’s not the job of mathematics to be concerned with the physical world, nor with what we call 'reality'. Symbolic consistency and meaning are essentials of mathematics. So is certainty. So is imagination. So is the creative process. So is hypothesis. So is belief beyond experience. So is adventure of knowledge. And, in today’s complexity, there is no better way to do the job of mathematics than by symbolic envisagement." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"Yet there is a distinct difference between the writer’s art and the mathematician’s. Whereas the writer is at liberty to use symbols in ways that contradict experience in order to jolt emotions or to create states of mind with deep-rooted meanings from a personal life’s journey, the mathematician cannot compose contradictions, aside from the standard argument that establishes a proof by contradiction. Mathematical symbols have a definite initial purpose: to tidily package complex information in order to facilitate understanding." (Joseph Mazur, "Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers", 2014)

"Usually, diagrams contain some noise – information unrelated to the diagram’s primary goal. Noise is decorations, redundant, and irrelevant data, unnecessarily emphasized and ambiguous icons, symbols, lines, grids, or labels. Every unnecessary element draws attention away from the central idea that the designer is trying to share. Noise reduces clarity by hiding useful information in a fog of useless data. You may quickly identify noise elements if you can remove them from the diagram or make them less intense and attractive without compromising the function." (Vasily Pantyukhin, "Principles of Design Diagramming", 2015)

"Using symbols is one common way of applying semantics to help make sense of the world. Symbols provide clues to understanding experiences by conveying recognizable meanings that are shared by societies." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"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)