On Mind: Mirrors II

"Conscious apprehension seems to exist […] as happens in a mirror-image when the smooth and bright surface is peaceful." (Plotinus, "Enneads", cca. 270 AD)

"[…] the mind orders nothing by its own motions, but lies merely receptive under the impressions of bodies, reflecting empty images in a mirror in place of reality." (Anicius Manlius Severinus Boethius, "The Consolation of Philosophy", cca. 524)

"In the same way as regards the soul, when that kind of thing in us which mirrors the images of thought and intellect is undisturbed, we see them and know them in a way parallel to sense-perception, along with the prior knowledge that it is intellect and thought that are active. But when this is broken because the harmony of the body is upset, thought and intellect operate without an image, and then intellectual activity takes place without a mind-picture." (Plotinus, "Enneads", cca. 270 AD)

"The noetic act is without parts and has not, so to speak, come out into the open, but remains unobserved within, but the verbal expression unfolds its content and brings it out of the noetic act into the image making power, and so shows the noetic act as if in a mirror, and this is how there is conscious apprehension and persistence and memory of it." (Plotinus, "Enneads", cca. 270 AD)

"This interconnection or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe." (Gottfried W Leibniz,  "Monadology", 1714)

"Let the poet confine his use of individual models to what is necessary to make his subject alive and convincing. As for all the rest, let him rely on the living world as mirrored in his bosom." (Johann Wolfgang von Goethe, 1789)

"The symbol. It is the thing without being the thing, and yet the thing: an image concentrated in the mirror of the mind and yet identical with the object. How inferior is allegory by comparison. Though it may have wit and subtle conceit, it is for the most part rhetorical and conventional. It always improves in proportion to its approach to what we call symbol." (Johann Wolfgang von Goethe, "Addenda on the Paintings of Philostratus", 1820) 

"A human being, what is a human being? Everything and nothing. Through the power of thought it can mirror everything it experiences. Through memory and knowledge it becomes a microcosm, carrying the world within itself. A mirror of things, a mirror of facts. Each human being becomes a little universe within the universe!" (Guy de Maupassant, [in "The Journal of a Madman"] 1851)

"Observation is like a piece of glass, which, as a mirror, must be very smooth, and must be very carefully polished, in order that it may reflect the image pure and undistorted." (Justus von Liebig, "The Study of the Natural Sciences", 1853) 

"In her manifold opportunities Nature has thus helped man to polish the mirror of [man’s] mind, and the process continues. Nature still supplies us with abundance of brain-stretching theoretical puzzles and we eagerly tackle them; there are more worlds to conquer and we do not let the sword sleep in our hand; but how does it stand with feeling? Nature is beautiful, gladdening, awesome, mysterious, wonderful, as ever, but do we feel it as our forefathers did?" (Sir John A Thomson, "The System of Animate Nature", 1920)

"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)

"Even a tarnished mirror will shine like a jewel if it is polished. A mind which presently is closed by illusions originating from the innate darkness of life is like a tarnished mirror, but once it is polished it will become clear, reflecting the enlightenment of immutable truth." (Nichiren Daishonin,"On Attaining Buddhahood", 1999)

"Thinking involves reasoning about a situation, and to do that we must have some kind of dynamic "model" of the situation in our heads. Any changes we make to this mental model of the world should ideally mirror changes in the real world." (S Ian Robertson, "Problem Solving", 2001)

"'Mental models' are deeply ingrained assumptions, generalizations, or even pictures or images that influence how we understand the world and how we take action. Very often, we are not consciously aware of our mental models or the effects they have on our behavior. […] The discipline of working with mental models starts with turning the mirror inward; learning to unearth our internal pictures of the world, to bring them to the surface and hold them rigorously to scrutiny. It also includes the ability to carry on ‘learningful’ conversations that balance inquiry and advocacy, where people expose their own thinking effectively and make that thinking open to the influence of others.” (Jossey-Bass Publishers, “The Jossey-Bass Reader on Educational Leadership”, 2nd Edi. 2007)

"If intelligence is a capacity that is gradually acquired as a result of development and learning, then a machine that can learn from experience would have, at least in theory, the capacity to carry out intelligent behavior. [...] Humans have created machines that imitate us - that provide mirrors to see ourselves and measure our strength, our intellect, and even our creativity." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Language accelerates learning and creation by permitting communication and coordination. A new idea can be spread quickly if someone can explain it and communicate it to others before they have to discover it themselves. But the chief advantage of language is not communication but autogeneration. Language is a trick that allows the mind to question itself; a magic mirror that reveals to the mind what the mind thinks; a handle that turns a mind into a tool." (Kevin Kelly, "What Technology Wants", 2010)

"It is a right, yes a duty, to search in cautious manner for the numbers, sizes, and weights, the norms for everything [God] has created. For He himself has let man take part in the knowledge of these things […] For these secrets are not of the kind whose research should be forbidden; rather they are set before our eyes like a mirror so that by examining them we observe to some extent the goodness and wisdom of the Creator." (Johannes Kepler)

On Mistakes, Blunders and Errors VI: Mind

"Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them." (J B Joseph Fourier, "The Analytical Theory of Heat", 1822)

"It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"All experience attests the strength of the tendency to mistake mental abstractions, even negative ones, for substantive realities; and the Permanent Possibilities of sensation which experience guarantees arc so extremely unlike in many of their properties to actual sensations, that since we are capable of imagining something which transcends sensations, there is a great natural probability that we should suppose these to be it." (Hippolyte Taine, "On intelligence", 1871)

"Perfect readiness to reject a theory inconsistent with fact is a primary requisite of the philosophic mind. But it, would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent. (William S Jevons, "The Principles of Science", 1874)

"Most mistakes in philosophy and logic occur because the human mind is apt to take the symbol for the reality." (Albert Einstein, "Cosmic Religion: With Other Opinions and Aphorisms", 1931)

"Since we have no systematic way to avoid all the inconsistencies of commonsense logic, each person must find his own way by building a private collection of 'cognitive censors' to suppress the kinds of mistakes he has discovered in the past." (Marvin Minsky, "Jokes and their Relation to the Cognitive Unconscious", 1980)

"There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation." (Charles Hermite, The Mathematical Intelligencer, Vol. 5, No. 4, 1983)

"In specific cases, we think by applying mental rules, which are similar to rules in computer programs. In most of the cases, however, we reason by constructing, inspecting, and manipulating mental models. These models and the processes that manipulate them are the basis of our competence to reason. In general, it is believed that humans have the competence to perform such inferences error-free. Errors do occur, however, because reasoning performance is limited by capacities of the cognitive system, misunderstanding of the premises, ambiguity of problems, and motivational factors. Moreover, background knowledge can significantly influence our reasoning performance. This influence can either be facilitation or an impedance of the reasoning process." (Carsten Held et al, "Mental Models and the Mind", 2006)

"A border is a completely imaginary line on a paper or cybernetic map that has no genuine counterpart in the real world. Do not mistake it for a property line. It is possible, in some instances, for a border to be congruent with a property line, but they are not the same thing at all. One represents the geographical limit of a military and political claim to authority over a given territory. The other is part of the description of something - in this case, land - lawfully owned by an individual or a voluntary and contractual association of individuals." (L Neil Smith, "Only Nixon", 2010)

"The human mind delights in finding pattern - so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it." (Stephen J Gould, "The Flamingo's Smile: Reflections in Natural History", 2010)

"Mental models represent possibilities, and the theory of mental models postulates three systems of mental processes underlying inference: (0) the construction of an intensional representation of a premise’s meaning – a process guided by a parser; (1) the building of an initial mental model from the intension, and the drawing of a conclusion based on heuristics and the model; and (2) on some occasions, the search for alternative models, such as a counterexample in which the conclusion is false. System 0 is linguistic, and it may be autonomous. System 1 is rapid and prone to systematic errors, because it makes no use of a working memory for intermediate results. System 2 has access to working memory, and so it can carry out recursive processes, such as the construction of alternative models." (Sangeet Khemlania & P.N. Johnson-Laird, "The processes of inference", Argument and Computation, 2012)

On Constructs VII - Mind

"Ideas are substitutions which require a secondary process when what is symbolized by them is translated into the images and experiences it replaces; and this secondary process is frequently not performed at all, generally only performed to a very small extent. Let anyone closely examine what has passed in his mind when he has constructed a chain of reasoning, and he will be surprised at the fewness and faintness of the images which have accompanied the ideas." (George H Lewes "Problems of Life and Mind", 1873)

"The mind of man, learning consciously and unconsciously lessons of experience, gradually constructs a mental image of its surroundings - as the mariner draws a chart of strange coasts to guide him in future voyages, and to enable those that follow after him to sail the same seas with ease and safety." (William C Dampier, "The Recent Development of Physical Science", 1904)

"[…] we can only study Nature through our senses - that is […] we can only study the model of Nature that our senses enable our minds to construct; we cannot decide whether that model, consistent though it be, represents truly the real structure of Nature; whether, indeed, there be any Nature as an ultimate reality behind its phenomena." (William C Dampier, "The Recent Development of Physical Science", 1904)

"While the stuff from which our world picture is build is yielded exclusively from the sense organs as organs of the mind, so that every man's world picture is and always remains a construct of his mind and cannot be proved to have any other existence […]" (Erwin Schrodinger, "What is Life?", 1944)

"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience." (Northrop Frye, "The Educated Imagination", 1964)

"We never have any understanding of any subject matter except in terms of our own mental constructs of 'things' and 'happenings' of that subject matter." (Douglas T Ross, "Structured analysis (SA): A language for communicating ideas", IEEE Transactions on Software Engineering Vol. 3 (1), 1977)

"Perhaps we all lose our sense of reality to the precise degree to which we are engrossed in our own work, and perhaps that is why we see in the increasing complexity of our mental constructs a means for greater understanding, even while intuitively we know that we shall never be able to fathom the imponderables that govern our course through life." (Winfried G Sebald, "The Rings of Saturn", 1995)

"The seemingly stable scene you normally see is really a mental model that you construct - the eyes are actually darting all around, producing a retinal image as jerky as an amateur video, and some of what you thought you saw was instead filled in from memory." (William H Calvin, "How Brains Think", 1996)

"A general limitation of the human mind is its imperfect ability to reconstruct past states of knowledge, or beliefs that have changed. Once you adopt a new view of the world (or any part of it), you immediately lose much of your ability to recall what you used to believe before your mind changed." (Daniel Kahneman, "Thinking, Fast and Slow", 2011)

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 Mind: The Mind of God

"[…] what is physical is subject to the laws of mathematics, and what is spiritual to the laws of God, and the laws of mathematics are but the expression of the thoughts of God." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)

"It is true that impatience, the mother of stupidity, praises brevity, as if such persons had not life long enough to serve them to acquire a complete knowledge of one single subject, such as the human body; and then they want to comprehend the mind of God in which the universe is included, weighing it minutely and mincing it into infinite parts, as if they had to dissect it!" (Leonardo da Vinci, "The Notebooks of Leonardo da Vinci", 1888) 

"Toward the end of the last century, many physicists felt that the mathematical description of physics was getting ever more complicated. Instead, the mathematics involved has become ever more abstract, rather than more complicated. The mind of God appears to be abstract but not complicated. He also appears to like group theory." (Anthony Zee, "Fearful Symmetry: The Search for Beauty in Modern Physics", 1986)

"[…] the search for a Theory of Everything also raises interesting philosophical questions. Some physicists, [Stephen] Hawking among them, would regard the construction of a Theory of Everything as being, in some sense, reading the mind of God. Or at least unravelling the inner secrets of physical reality. Others simply argue that a physical theory is just a description of reality, rather like a map." (Peter Coles, "Hawking and the Mind of God", 2000)

"To look at the development of physics since Newton is to observe a struggle to define the limits of science. Part of this process has been the intrusion of scientific methods and ideas into domains that have traditionally been the province of metaphysics or religion. In this conflict, Hawking’s phrase ‘to know the Mind of God’ is just one example of a border infringement. But by playing the God card, Hawking has cleverly fanned the flames of his own publicity, appealing directly to the popular allure of the scientist-as-priest." (Peter Coles, "Hawking and the Mind of God", 2000)

"The universe is a symphony of strings, and the mind of God that Einstein eloquently wrote about for thirty years would be cosmic music resonating through eleven-dimensional hyper space." (Michio Kaku, "Parallel Worlds: A journey through creation, higher dimensions, and the future of the cosmos", 2004)

"I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details." (Albert Einstein)

"The laws of nature are but the mathematical thoughts of God." (Euclid)

"Time and the heavens came into being at the same instant, in order that, if they were ever to dissolve, they might be dissolved together. Such was the mind and thought of God in the creation of time." (Plato)

"Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes." (Johannes Kepler)

Rudy Rucker - Collected Quotes

"In the initial stages of research, mathematicians do not seem to function like theorem-proving machines. Instead, they use some sort of mathematical intuition to ‘see’ the universe of mathematics and determine by a sort of empirical process what is true. This alone is not enough, of course. Once one has discovered a mathematical truth, one tries to find a proof for it." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"The study of infinity is much more than a dry academic game. The intellectual pursuit of the absolute infinity is, as Georg Cantor realized, a form of the soul's quest for God. Whether or not the goal is ever reached, an awareness of the process brings enlightenment." (Rudy Rucker, "Infinity and the Mind: The science and philosophy of the infinite", 1982)

"At the most elemental level, reality evanesces into something called Schröedinger's Wave Function: a mathematical abstraction which is best represented as a pattern in an infinite-dimensional space, Hilbert Space. Each point of the Hilbert Space represents a possible state of affairs. The wave function for some one physical or mental system takes the form of, let us say, a coloring in of Hilbert Space. The brightly colored parts represent likely states for the system, the dim parts represent less probable states of affairs." (Rudy Rucker, "The Sex Sphere", 1983)

"The space of our universe is the hypersurface of a vast expanding hypersphere." (Rudy Rucker, "The Sex Sphere", 1983)

"What is the shape of space? Is it flat, or is it bent? Is it nicely laid out, or is it warped and shrunken? Is it finite, or is it infinite? Which of the following does space resemble more: (a) a sheet of paper, (b) an endless desert, (c) a soap bubble, (d) a doughnut, (e) an Escher drawing, (f) an ice cream cone, (g) the branches of a tree, or (h) a human body?" (Rudy Rucker, "The Fourth Dimension: Toward a Geometry of Higher Reality", 1984)

"A photon is a wavy yet solid little package that can zip through empty space without the benefit of any invisible jelly vibrating underfoot." (Rudy Rucker, "The Fourth Dimension: Toward a Geometry of Higher Reality", 1984)

"The world is colors and motion, feelings and thought [...] and what does math have to do with it? No much, if "math" means being bored in high school, but in truth mathematics is the one universal science. Mathematics is the study of pure pattern, and everything in the cosmos is a kind of pattern." (Rudy Rucker, "Mind Tools", 1987)

On Precision IV: Mind

"It has never yet been supposed, that all the facts of nature, and all the means of acquiring precision in the computation and analysis of those facts, and all the connections of objects with each other, and all the possible combinations of ideas, can be exhausted by the human mind." (Nicolas de Condorcet, "Outlines of an Historical View of the Progress of the Human Mind", 1795)

"An icon is a representamen of what it represents and for the mind that interprets it as such, by virtue of its being an immediate image, that is to say by virtue of characters which belong to it in itself as a sensible object, and which it would possess just the same were there no object in nature that it resembled, and though it never were interpreted as a sign. It is of the nature of an appearance, and as such, strictly speaking, exists only in consciousness, although for convenience in ordinary parlance and when extreme precision is not called for, we extend the term icon to the outward objects which excite in consciousness the image itself." (Charles S Peirce, "On Existential Graphs, Euler's Diagrams, and Logical", 1903)

"Now, a symbol is not, properly speaking, either true or false; it is, rather, something more or less well selected to stand for the reality it represents, and pictures that reality in a more or less precise, or a more or less detailed manner." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1906)

"All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life but only to an imagined celestial existence." (Bertrand Russell, 1923)

"As our mental eye penetrates into smaller and smaller distances and shorter and shorter times, we find nature behaving so entirely differently from what we observe in visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be ‘true’. A complete satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think of it, but however we think it, it is wrong; not perhaps quite as meaningless as a ‘triangular circle’, but more so than a ‘winged lion’." (Erwin Schrödinger, "Science and Humanism", 1952)

"Concepts are inventions of the human mind used to construct a model of the world. They package reality into discrete units for further processing, they support powerful mechanisms for doing logic, and they are indispensable for precise, extended chains of reasoning. […] A mental model is a cognitive construct that describes a person's understanding of a particular content domain in the world." (John Sown, "Conceptual Structures: Information Processing in Mind and Machine", 1984)

"A formal system consists of a number of tokens or symbols, like pieces in a game. These symbols can be combined into patterns by means of a set of rules which defines what is or is not permissible (e.g. the rules of chess). These rules are strictly formal, i.e. they conform to a precise logic. The configuration of the symbols at any specific moment constitutes a ‘state’ of the system. A specific state will activate the applicable rules which then transform the system from one state to another. If the set of rules governing the behaviour of the system are exact and complete, one could test whether various possible states of the system are or are not permissible." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"A mental model represents a possibility, or, to be precise, the structure and content of the model capture what is common to the different ways in which the possibility could occur [...]" (Philip N Johnson-Laird, Mental Models, Sentential Reasoning, and Illusory Inferences, [in "Mental Models and the Mind"], 2006)

"Human language is a vehicle of truth but also of error, deception, and nonsense. Its use, as in the present discussion, thus requires great prudence. One can improve the precision of language by explicit definition of the terms used. But this approach has its limitations: the definition of one term involves other terms, which should in turn be defined, and so on. Mathematics has found a way out of this infinite regression: it bypasses the use of definitions by postulating some logical relations (called axioms) between otherwise undefined mathematical terms. Using the mathematical terms introduced with the axioms, one can then define new terms and proceed to build mathematical theories. Mathematics need, not, in principle rely on a human language. It can use, instead, a formal presentation in which the validity of a deduction can be checked mechanically and without risk of error or deception." (David Ruelle, "The Mathematician's Brain", 2007)

On Networks (1970-1979)

"Nature is a network of happenings that do not unroll like a red carpet into time, but are intertwined between every part of the world; and we are among those parts. In this nexus, we cannot reach certainty because it is not there to be reached; it goes with the wrong model, and the certain answers ironically are the wrong answers. Certainty is a demand that is made by philosophers who contemplate the world from outside; and scientific knowledge is knowledge for action, not contemplation. There is no God’s eye view of nature, in relativity, or in any science: only a man’s eye view." (Jacob Bronowski, "The Identity of Man", 1972)

"In the province of the mind, what one believes to be true is true or becomes true, within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the mind, there are no limit. […] In the province of connected minds, what the network believes to be true, either is true or becomes true within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the network's mind there are no limits." (John C Lilly, "The Human Biocomputer", 1974)

"As with any graphic, networks are used in order to discover pertinent troups of to inform others of the groups and structures discovered. It is a good means of displaying structures, However, it ceases to be a means of discovery when the elements are numerous. The figure rapidly becomes complex, illegible and untransformable." (Jacques Bertin, "Graphics and graphic information processing", 1977)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 1979)

Hannah Arendt - Collected Quotes

"The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle." (Hannah Arendt, "The Human Condition", 1958)

"Storytelling reveals meaning without committing the error of defining it." (Hannah Arendt, "Men in Dark Times", 1968)

"Predictions of the future are never anything but projections of present automatic processes and procedures, that is, of occurrences that are likely to come to pass if men do not act and if nothing unexpected happens; every action, for better or worse, and every accident necessarily destroys the whole pattern in whose frame the prediction moves and where it finds its evidence." (Hannah Arendt, "On Violence", 1970)

"It interrupts any doing, any ordinary activities, no matter what they happen to be. All thinking demands a stop-and-think." (Hannah Arendt, "The Life of the Mind", 1977)

"It was mathematics, the non-empirical science par excellence, wherein the mind appears to play only with itself, that turned out to be the science of sciences, delivering the key to those laws of nature and the universe that are concealed by appearances." (Hannah Arendt, "The Life of the Mind", 1977)

"Metaphysical fallacies contain the only clues we have to what thinking means to those who engage in it." (Hannah Arendt, "The Life of the Mind", 1977)

"The need of reason is not inspired by the quest for truth but by the quest for meaning. And truth and meaning are not the same. The basic fallacy, taking precedence over all specific metaphysical fallacies, is to interpret meaning on the model of truth." (Hannah Arendt, "The Life of the Mind", 1977)

"To expect truth to come from thinking signifies that we mistake the need to think with the urge to know." (Hannah Arendt, "The Life of the Mind", 1977)

"What science and the quest for knowledge are after is irrefutable truth; that is, propositions that human beings are not free to reject — that are compelling. They are of two kinds, as we have known since Leibnitz: truths of reasoning and truths of fact." (Hannah Arendt, The New Yorker, 1977)

"Analogies, metaphors, and emblems are the threads by which the mind holds on to the world even when, absentmindedly, it has lost direct contact with it, and they guarantee the unity of human experience. Moreover, in the thinking process itself they serve as models to give us our bearings lest we stagger blindly among experiences that our bodily senses with their relative certainty of knowledge cannot guide us through." (Hannah Arendt, "The Life of the Mind", 1981)

On Perception: The Filtering Mind

"Nothing is easier than self-deceit. For what each man wishes, that he also believes to be true." (Demosthenes, "Olynthiac", 349 BC)

"Men willingly believe what they wish to be true." (Julius Caesar,"De Bello Gallico", Book III, 58–49 BC)

"Man prefers to believe what he prefers to be true." (Francis Bacon,"Novum Organum", 1620)

"The human understanding resembles not a dry light, but admits a tincture of the will and passions, which generate their own system accordingly; for man always believes more readily that which he prefers." (Sir Francis Bacon, "Novum Organum", 1620)

"People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive." (Blaise Pascal, "De l'Art de persuader" ["On the Art of Persuasion"], 1658)

"It is hard to prevent oneself from believing what one so keenly desires, and who can doubt that the interest we have in admitting or denying the reality of the Judgement to come determines the faith of most men in accordance with their hopes and fears." (Jean-Jacques Rousseau,"Reveries of the Solitary Walker", 1782)

"Because of the extended time image and the extended relationship images, man is capable of ‘rational behavior,’ that is to say, his response is not to an immediate stimulus but to an image of the future filtered through an elaborate value system.  His image contains not only what is, but what might be." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)

"We say the map is different from the territory. But what is the territory? Operationally, somebody went out with a retina or a measuring stick and made representations which were then put on paper. What is on the paper map is a representation of what was in the retinal representation of the man who made the map; and as you push the question back, what you find is an infinite regress, an infinite series of maps. The territory never gets in at all. […] Always, the process of representation will filter it out so that the mental world is only maps of maps, ad infinitum." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"In the province of the mind, what one believes to be true is true or becomes true, within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the mind, there are no limit. […] In the province of connected minds, what the network believes to be true, either is true or becomes true within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the network's mind there are no limits." (John C Lilly, "The Human Biocomputer", 1974)

"Nature is not ‘given’ to us - our minds are never virgin in front of reality. Whatever we say we see or observe is biased by what we already know, think, believe, or wish to see. Some of these thoughts, beliefs and knowledge can function as an obstacle to our understanding of the phenomena." (Anna Sierpinska, "Understanding in Mathematics", 1994)

"The abstractions of science are stereotypes, as two-dimensional and as potentially misleading as everyday stereotypes. And yet they are as necessary to the process of understanding as filtering is to the process of perception." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)

"We all would like to know more and, at the same time, to receive less information. In fact, the problem of a worker in today's knowledge industry is not the scarcity of information but its excess. The same holds for professionals: just think of a physician or an executive, constantly bombarded by information that is at best irrelevant. In order to learn anything we need time. And to make time we must use information filters allowing us to ignore most of the information aimed at us. We must ignore much to learn a little." (Mario Bunge, "Philosophy in Crisis: The Need for Reconstruction", 2001)

"The receiver decodes the symbols to interpret the meaning of the message. Encoding and decoding are potential sources for communication errors because knowledge, attitudes, and context act as filters and create noise when translating from symbols to meaning. Finally, feedback occurs when the receiver responds to the sender’s communication with a return message. Without feedback, the communication is one-way; with feedback, it is two-way. Feedback is a powerful aid to communication effectiveness because it enables the sender to determine whether the receiver correctly interpreted the message." (Richard L Daft & Dorothy Marcic, "Understanding Management" 5th Ed., 2006)

"Your mental models shape the way you see the world. They help you to quickly make sense of the noises that filter in from outside, but they can also limit your ability to see the true picture." (Colin Cook & Yoram R Wind, "The Power of Impossible Thinking: Transform the Business of Your Life and the Life of Your Business", 2006)

"Great stories agree with our worldview. The best stories don't teach people anything new. Instead the best stories agree with what the audience already believes and makes the members of the audience feel smart and secure when reminded how right they were in the thirst place." (Seth Godin, "All Marketers are Liars", 2009)

"Actually, around 80% of the data we use to make decisions is already in our heads before we engage with a situation. Our power to perceive is governed and limited by cognitive filters, sometimes termed our ‘mental model’. Mental models are formed as a result of past experience, knowledge and attitudes. They are deeply ingrained, often subconscious, structures that limit what we perceive and also colour our interpretation of supposed facts." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010) 

"[…] our strong mental models tend to make us blind to certain possibilities, and therefore we unknowingly engage in biased listening. Whenever we interpret information, we subconsciously access three filters based upon how we feel about the content, the information source and situation (or context) in which we receive the information." (Robina Chatham & Brian Sutton, "Changing the IT Leader’s Mindset", 2010)

"Perception and memory are imprecise filters of information, and the way in which information is presented, that is, the frame, influences how it is received. Because too much information is difficult to deal with, people have developed shortcuts or heuristics in order to come up with reasonable decisions. Unfortunately, sometimes these heuristics lead to bias, especially when used outside their natural domains." (Lucy F Ackert & Richard Deaves, "Behavioral Finance: Psychology, Decision-Making, and Markets", 2010)

"When people believe a conclusion is true, they are also very likely to believe arguments that appear to support it, even when these arguments are unsound." (Daniel Kahneman, "Thinking, Fast and Slow", 2011)

"Mental models bind our awareness within a particular scaffold and then selectively can filter the content we subsequently receive. Through recalibration using revised mental models, we argue, we cultivate strategies anew, creating new habits, and galvanizing more intentional and evolved mental models. This recalibration often entails developing a strong sense of self and self-worth, realizing that each of us has a range of moral choices that may deviate from those in authority, and moral imagination." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

"In the absence of clear information - in the absence of reliable statistics - people did what they had always done: filtered available information through the lens of their worldview." (Zachary Karabell, "The Leading Indicators: A short history of the numbers that rule our world", 2014)

"We are genetically predisposed to look for patterns and to believe that the patterns we observe are meaningful. […] Don’t be fooled into thinking that a pattern is proof. We need a logical, persuasive explanation and we need to test the explanation with fresh data." (Gary Smith, "Standard Deviations", 2014)

"Images are generally resistant to change and ignore messages that do not conform to their internal settings. Sometimes, however, they do react and can alter in an incremental or even revolutionary manner. Humans can talk about and share their images and, in the symbolic universe they create, reflect upon what is and what might be." (Michael C Jackson, "Critical Systems Thinking and the Management of Complexity", 2019)

"Confirmation bias is the tendency to notice, believe, and share information that is consistent with our preexisting beliefs. When a claim confirms our beliefs about the world, we are more prone to accept it as true and less inclined to challenge it as possibly false." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"The contradiction between what we see with our own eyes and what the statistics claim can be very real. […] The truth is more complicated. Our personal experiences should not be dismissed along with our feelings, at least not without further thought. Sometimes the statistics give us a vastly better way to understand the world; sometimes they mislead us. We need to be wise enough to figure out when the statistics are in conflict with everyday experience - and in those cases, which to believe." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"We filter new information. If it accords with what we expect, we’ll be more likely to accept it. […] Our brains are always trying to make sense of the world around us based on incomplete information. The brain makes predictions about what it expects, and tends to fill in the gaps, often based on surprisingly sparse data." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"[…] mathematicians and poets are people who believe in the power of words, of concepts and giving names to concepts." (Cédric Villani)

"Nothing is so easy as to deceive one's self; for what we wish, that we readily believe." (Democritus)

"The human brain is a complex organ with the wonderful power of enabling man to find reasons for continuing to believe whatever it is that he wants to believe." (Voltaire)

Out of Context: On Mind (Definitions)

"Mind is the limit and measure of all things [...]" (Nicolas of Cusa [Nicolaus Cusanus], "Idiota de mente" ["The Layman: About Mind"], 1450)

"You know how the divine Simplicity enfolds all things. Mind is the image of this enfolding Simplicity." (Nicolas of Cusa [Nicolaus Cusanus], "Idiota de mente: The Layman: About Mind", 1450)

"Man's mind is so formed that it is far more susceptible to falsehood than to truth." (Desiderius Erasmus, "Praise of Folly", 1509)

"The mind is so constituted that it does not willingly rest in facts and immediate causes, but seeks always after a knowledge of the remoter links in the chain of causation." (Thomas H Huxley, "Discourses Biological and Geological", 1894)

"The true scientific mind is not to be tied down by its own conditions of time and space. It builds itself an observatory erected upon the border line of present, which separates the infinite past from the infinite future." (Arthur C Doyle, "The Poison Belt", 1913)

"A truthful mind is necessary for the discovery of truth in Nature." (Sir Richard A Gregory, "Discovery; or, The Spirit and Service of Science", 1916)

"No human mind is capable of grasping in its entirety the meaning of any considerable quantity of numerical data." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"Mind is the first and most direct thing in our experience; all else is remote inference." (Arthur Eddington, "Science and the Unseen World", 1929)

The truly scientific mind is altogether unafraid of the new [...]" (Wilfred Trotter, "Observation and Experiment and Their Use in the Medical Sciences", British Medical Journal Vol. 2, 1930)

"Most mistakes in philosophy and logic occur because the human mind is apt to take the symbol for the reality." (Albert Einstein, "Cosmic Religion: With Other Opinions and Aphorisms", 1931)

"The eye sees only what the mind is prepared to comprehend." (Robertson Davies, "Tempest-Tost", 1951)

"We are part of nature, and our mind is the only instrument we have, or can conceive of, for learning about nature or about ourselves." (Conrad H Waddington, "The Nature of Life", 1960)

"The mind is defined as the sum total of all the programs and the metaprograms of a given human computer, whether or not they are immediately elicitable, detectable, and visibly operational to the self or to others." (John C Lilly "Programming and Metaprogramming in the Human Biocomputer" 2nd Ed., 1972)

"The human mind is constantly drawn to anything that embodies some aspect of symmetry." (Marcus du Sautoy, "Symmetry: A Journey into the Patterns of Nature", 2008)

"The human mind is not capable of grasping the Universe." (Albert Einstein)

On Mind (Unsourced)

"A fact is not novel if it has an analogue which could have some interest. A fact which does not fit in with a series of known facts is a fact which deserves particular attention. If the mind had to retain all individual facts, it could not manage and science would not exist; but when these facts can be connected by general laws and by theories, when a large number of these facts can be represented by a single one, one can remember them more easily, one can generalise one’s ideas, one can compare one general fact with another general fact and discoveries can succeed each other. It is only when laws can be introduced into a science that it assumes the true character of science." (Joseph L Gay-Lussac)

"Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind." (Hermann Weyl)

"By observation, facts are distinctly and minutely impressed in the mind; by analogy, similar facts are connected ; by experiment, new facts are discovered ; and, in the progression of knowledge, observation, guided by analogy, leads to experiment, and analogy, confirmed by experiment, becomes scientific truth." (Sir Humphry Davy)

"Cognitive psychology has shown that the mind best understands facts when they are woven into a conceptual fabric, such as a narrative, mental map, or intuitive theory. Disconnected facts in the mind are like unlinked pages on the Web: They might as well not exist." (Steven Pinker)

"Disclaimer: Even if the below quotes are translations that reflect maybe a more or less modern language used to interpret them, their importance as first attempts to define the inner workings of the mind remains.

"Do not train a child to learn by force or harshness; but direct them to it by what amuses their minds, so that you may be better able to discover with accuracy the peculiar bent of the genius of each." (Plato)

"Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion’." (Albert Einstein)

"Educating the mind without educating the heart is no education at all." (Aristotle)

"Education is not learning, but the training of the mind that it may learn." (Sir William W Gull)

"Education's purpose is to replace an empty mind with an open one." (Malcolm S Forbes)

"Either mathematics is too big for the human mind, or the human mind is more than a machine." (Kurt Gödel)

"Human beings suffer from a 'centralized mindset'; they would like to assign the coordination of activities to a central command. But the way social insects form highways and other amazing structures such as bridges, chains, nests (by the way, African fungus-growing termites have invented air conditioning) and can perform complex tasks (nest building, defense, cleaning, brood care, foraging, etc) is very different: they self-organize through direct and indirect interactions." (Eric Bonabeau)

"I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of daily life." (Michael Faraday)

"Imaginary numbers have an intuitive explanation: they 'rotate' numbers, just like negatives make a 'mirror image' of a number. […] Seeing imaginary numbers as rotations gives us a new mindset to approach problems; the 'plug and chug' formulas can make intuitive sense, even for a strange topic like complex numbers." (Kalid Azal, Math, Better Explained)

"Imagination, as well as reason, is necessary to perfection in the philosophical mind. A rapidity of combination, a power of perceiving analogies, and of comparing them by facts, is the creative source of discovery." (Sir Humphry Davy)

"Indeed, when in the course of a mathematical investigation we encounter a problem or conjecture a theorem, our minds will not rest until the problem is exhaustively solved and the theorem rigorously proved; or else, until we have found the reasons which made success impossible and, hence, failure unavoidable. Thus, the proofs of the impossibility of certain solutions plays a predominant role in modern mathematics; the search for an answer to such questions has often led to the discovery of newer and more fruitful fields of endeavour." (David Hilbert)

"Intuition is the conception of an attentive mind, so clear, so distinct, and so effortless that we cannot doubt what we have so conceived." (René Descartes)

"[…] it is only through Mathematics that we can thoroughly understand what true science is. Here alone can we find in the highest degree simplicity and severity of scientific law, and such abstraction as the human mind can attain." (Auguste Comte)

"It is the mark of an educated mind to rest satisfied with the degree of precision which the nature of the subject admits and not to seek exactness where only an approximation is possible." (Aristotle)

"It is very helpful to represent these things in this fashion since nothing enters the mind more readily than geometric figures." (René Descartes)

"It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature." (Albert Einstein)

"Learn just enough of the subject [metaphysics] to enable your mind to get rid of it." (Benjamin Jowett)

"Mathematical inquiry lifts the human mind into closer proximity with the divine than is attainable through any other medium." (Hermann Weyl)

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate." (Leonhard Euler)

"Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man." (Maria Goeppert-Mayer)

"Mathematics is a spirit of rationality. It is this spirit that challenges, simulates, invigorates and drives human minds to exercise themselves to the fullest. It is this spirit that seeks to influence decisively the physical, normal and social life of man, that seeks to answer the problems posed by our very existence, that strives to understand and control nature and that exerts itself to explore and establish the deepest and utmost implications of knowledge already obtained." (Morris Kline)

"Mathematics is music for the mind; Music is mathematics for the soul." (Stanley Gudder)

"Mathematics is the science that yields the best opportunity to observe the working of the mind. Its study is the best training of our abilities as it develops both the power and the precision of our thinking. Mathematics is valuable on account of the number and variety of its applications. And it is equally valuable in another respect: By cultivating it, we acquire the habit of a method of reasoning which can be applied afterwards to the study of any subject and can guide us in life's great and little problems." (Nicolas de Condorcet)

"Mathematics originates in the mind of an individual, as it doubtless originated historically in the collective life of mankind, with the recognition of certain recurrent abstract features in common experience, and the development of processes of counting, measuring, and calculating, by which order can be brought into the manipulations of these features. It originated in this manner, indeed; but already at a very early stage it begins to transcend the practical sphere and its character undergoes a corresponding change. Intellectual curiosity progressively takes charge, despite the fact that practical considerations may for long continue to be the main source of interest and may indeed never cease to stimulate the creation of new concepts and new methods. As mathematics breaks from its early dependence on practical utility, its ‘immediate’ significance is at the same time lost and the goal is to discover what it is that makes 'emancipated' mathematics valid. (Geoffrey T Kneebone)

"Metaphysics, in whatever latitude the term be taken, is a science or complement of sciences exclusively occupied with mind." (Sir William Hamilton)

"Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity." (Mary Somerville)

"Nothing stimulates great minds to work on enriching knowledge with such force as the posing of difficult but simultaneously interesting problems." (John Bernoulli)

"Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude." (Alfred N Whitehead)

"Science is the labor and handicraft of the mind; poetry can only be considered its recreation." (Sir Francis Bacon)

"Show all these fanatics a little geometry, and they learn it quite easily. But, strangely enough, their minds are not thereby rectified. They perceive the truths of geometry, but it does not teach them to weighp robabilities. Their minds have set hard. They will reason in a topsy-turvy wall all their lives, and I am sorry for it." (Voltaire)

"The aim of education should be to convert the mind into a living fountain not a reservoir." (John Mason)

"The business of education is not to make the young perfect in any one of the sciences, but so to open their minds as may best make them capable of any, when they shall apply themselves to it." (John Locke)

"The essence of engineering consists not so much in the mere construction of the spectacular layouts or developments, but in the invention required - the analysis of the problem, the design, the solution by the mind which directs it all." (William Hood)

"The idea of a universal mind or Logos would be, I think, a fairly plausible inference from the present state of scientific theory." (Arthur Eddington)

"The laws of thought, and especially of number, must hold good in heaven, whether it is a place or a state of mind; for they are independent of any particular sphere of existence, essential to Being itself, to God’s being as well as ours, laws of His mind before we learned them. The multiplication table will hold good in heaven […]" (Hilda P Hudson)

"The man of science will acts as if this world were an absolute whole controlled by laws independent of his own thoughts or act; but whenever he discovers a law of striking simplicity or one of sweeping universality or one which points to a perfect harmony in the cosmos, he will be wise to wonder what role his mind has played in the discovery, and whether the beautiful image he sees in the pool of eternity reveals the nature of this eternity, or is but a reflection of his own mind." (Tobias Dantzig)

"[…] the notion of the infinite […] forces itself upon our mind and yet is incomprehensible. When this notion takes possession of the understanding we have only to bow before it." (Louis Pasteur)

"The sole aim of science is the honor of the human mind, and from this point of view a question about numbers is as important as a question about the system of the world." (Carl Gustav Jacobi)

"The teacher, if indeed wise, does not bid you to enter the house of their wisdom, but leads you to the threshold of your own mind." (Kahil Gibran)

"The truth of a theory is in your mind, not in your eyes." (Albert Einstein)

"There is a great difference between the spirit of Mathematics and the spirit of Observation. In the former, the principles are palpable, but remote from common use; so that from want of custom it is not easy to turn our head in that direction; but if it be thus turned ever so little, the principles are seen fully confessed, and it would argue a mind incorrigibly false to reason inconsequentially on principles so obtrusive that it is hardly possible to overlook them." (Blaise Pascal)

"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth." (Proclus Lycaeus, cca 5th century)

"‘Tis of singular use, rightly to understand, and carefully to distinguish from hypotheses or mere suppositions, the true and certain consequences of experimental and mathematical philosophy; which do, with wonderful strength and advantage, to all such as are capable of apprehending them, confirm, establish, and vindicate against all objections, those great and fundamental truths of natural religion, which the wisdom of providence has at the same time universally implanted, in some degree, in the minds of persons even of the meanest capacities, not qualified to examine demonstrative proofs." (Samuel Clarke)

"To educate a man in mind and not in morals is to educate a menace to society." (Theodore Roosevelt)

"What else can the human mind hold besides numbers and magnitudes? These alone we apprehend correctly, and if piety permits to say so, our comprehension is in this case of the same kind as God’s, at least insofar as we are able to understand it in this mortal life." (Johannes Kepler)

"What, after all, is mathematics but the poetry of the mind, and what is poetry but the mathematics of the heart?" (David E Smith)

"You know how the divine Simplicity enfolds all things. Mind is the image of this enfolding Simplicity. If, then, you called this divine Simplicity infinite Mind, it will be the exemplar of our mind. If you called the divine mind the totality of the truth of things, you will call our mind the totality of the assimilation of things, so that it may be a totality of ideas. In the divine Mind conception is the production of things; in our mind conception is the knowledge of things. If the divine Mind is absolute Being, then its conception is the creation of beings; and conception in the human mind is the assimilation of beings." (Nicholas of Cusa)

On Mind (-1599)

"Beholding beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities (for he has hold not of an image but of a reality) [...]." (Plato, "The Symposium", cca. 385–370 BC)

"The same ideas, one must believe, recur in men’s minds not once or twice but again and again." (Aristotle, "De Caelo" ["On the Heavens"], cca. 350 BC)

"Since it seems that there is nothing outside and separate in existence from sensible spatial magnitudes, the objects of thought are in the sensible forms, viz. both the abstract objects and all the states and affections of sensible things. Hence no one can learn or understand anything in the absence of sense, and when the mind is actively aware of anything it is necessarily aware of it along with an image; for images are like sensuous contents except in that they contain no matter. Imagination is different from assertion and denial; for what is true or false involves a synthesis of thoughts. In what will the primary thoughts differ from images? Must we not say that neither these nor even our other thoughts are images, though they necessarily involve them?" (Aristotle, "De Anima", cca. 350 BC)

"As infinite kinds of almost identical images arise continually from the innumerable atoms and flow out to us from the gods, so we should take the keenest pleasure in turning and bending our mind and reason to grasp these images, in order to understand the nature of these blessed and eternal beings." (Marcus Tullius Cicero, "De Natura Deorum" ["On the Nature of the Gods"], 45 BC)

"Nothing has such power to broaden the mind as the ability to investigate systematically and truly all that comes under thy observation in life." (Marcus Aurelius, "Meditations", cca. 121–180 AD)

"In the same way as regards the soul, when that kind of thing in us which mirrors the images of thought and intellect is undisturbed, we see them and know them in a way parallel to sense-perception, along with the prior knowledge that it is intellect and thought that are active. But when this is broken because the harmony of the body is upset, thought and intellect operate without an image, and then intellectual activity takes place without a mind-picture." (Plotinus, "Enneads", cca. 270 AD)

"We both are, and know that we are, and delight in our being, and our knowledge of it. Moreover, in these three things no true-seeming illusion disturbs us; for we do not come into contact with these by some bodily sense, as we perceive the things outside of us of all which sensible objects it is the images resembling them, but not themselves which we perceive in the mind and hold in the memory, and which excite us to desire the objects. But, without any delusive representation of images or phantasms, I am most certain that I am, and that I know and delight in this." (Aurelius Augustinus, "The City of God", early 400s)

"[…] the mind orders nothing by its own motions, but lies merely receptive under the impressions of bodies, reflecting empty images in a mirror in place of reality." (Anicius Manlius Severinus Boethius, "The Consolation of Philosophy", cca. 524)

"An image is, after all, a reminder; it is to the illiterate what a book is to the literate, and what the word is to the hearing, the image is to sight. All this is the approach through the senses: but it is with the mind that we lay hold on the image." (John of Damascus, cca. 8th century)

"The objection we are dealing with argues from the standpoint of an agent that presupposes time and acts in time, but did not institute time. Hence the question about 'why God's eternal will produces an effect now and and not earlier' presupposes that time exists; for 'now' and 'earlier' are segments of time. With regard to the universal production of things, among which time is also to be counted, we should not ask, 'Why now and not earlier?' Rather we should ask: 'Why did God wish this much time to intervene?' And this depends on the divine will, which is perfectly free to assign this or any other quantity to time. The same may be noted with respect to the dimensional quantity of the world. No one asks why God located the material world in such and such a place rather than higher up or lower down or in some other position; for there is no place outside the world. The fact that God portioned out so much quantity to the world that no part of it would be beyond the place occupied in some other locality, depends on the divine will. However, although there was no time prior to the world and no place outside the world, we speak as if there were. Thus we say that before the world existed there was nothing except God, and that there is no body lying outside the world. But in thus speaking of 'before' and 'outside,' we have in mind nothing but time and place as they exist in our imagination." (Thomas Aquinas, "Compendium Theologiae" ["Compendium of Theology"], cca. 1265 [unfinished])

"Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience."(Roger Bacon, "Opus Majus", cca. 1267)

"The truth of voice perishes with the sound; truth latent in the mind is hidden wisdom and invisible treasure; but the truth which illuminates books desires to manifest itself to every disciplinable sense. Let us consider how great a commodity of doctrine exists in books, - how easily, how secretly, how safely, they expose the nakedness of human ignorance without putting it to shame. These are the masters that instruct us without rods and ferules, without hard words and anger, without clothes or money. If you approach them, they are not asleep; if, investigating, you interrogate them, they conceal nothing; if you mistake them, they never grumble; if you are ignorant, they cannot laugh at you." (Richard de Burry, "Philobiblon", 1344)

"Geometry enlightens the intellect and sets one's mind right. All of its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence." (Ibn Khaldun, cca. 14th century)

"Man's mind is so formed that it is far more susceptible to falsehood than to truth." (Desiderius Erasmus, "Praise of Folly", 1509)

"There are certain pleasures which only fill the outward senses, and there are others also which pertain only to the mind or reason; but music is a delectation so put in the midst that both by the sweetness of the sounds it moveth the senses, and by the artificiousness of the number and proportions it delighteth reason itself." (John Northbrooke , "Against Dicing", 1577)

""Nature that framed us of four elements, Warring within our breasts for regiment, Doth teach us all to have aspiring minds: Our souls, whose faculties can comprehend The wondrous architecture of the world: And measure every wand’ring planet’s course, Still climbing after knowledge infinite, And always moving as the restless spheres, Wills us to wear ourselves and never rest, Until we reach the ripest fruit of all, That perfect bliss and sole felicity, The sweet fruition of an earthly crown.""  (Christopher Marlowe, ""Tamburlaine the Great"", 1590)

"[W]hatsoever the Philosopher saith should be done, [the poet] gives a perfect picture of it by some one, by who he presupposeth it was done, so as he coupleth the generall notion with the particuler example. A perfect picture I say, for hee yeeldeth to the powers of the minde an image of that whereof the Philosopher bestoweth but a wordish description, which doth neither strike, pearce, nor possesse the sight of the soule so much, as that other doth." (Sir Philip Sidney, "Defence of Poesie", 1595)

"The diversity of the phenomena of Nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment." (Johannes Kepler, "Mysterium Cosmographicum", 1596)

On Mind (1600-1699)

"Man, as the minister and interpreter of nature, dies and understands as much as his observations on the order of nature, either with regard to things or the mind permit him, and neither knows or is capable of more." (Francis Bacon, "Novum Organum", 1620)

"No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed." (Sir Francis Bacon, "Novum Organum" Book 2, 1620)

"The entire method consists in the order and arrangement of the things to which the mind's eye must turn so that we can discover some truth." (René Descartes, "Rules for the Direction of the Mind", 1628)

"[…] it is astonishing and incredible to us, but not to Nature; for she performs with utmost ease and simplicity things which are even infinitely puzzling to our minds, and what is very difficult for us to comprehend is quite easy for her to perform." (Galileo Galilei, "Dialog Concerning the Two World Systems", 1630)

"To apply oneself to great inventions, starting from the smallest beginnings, is no task for ordinary minds; to divine that wonderful arts lie hid behind trivial and childish things is a conception for superhuman talents." (Galileo Galilei, "Dialogue Concerning the Two Chief World Systems", 1632)

"[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited; but this […] is wrong, for we cannot speak of infinite quantities as being the one greater or less than or equal to another." (Galileo Galilei, "Two New Sciences", 1638)

"What is big is easy to perceive: what is small is difficult to perceive. In short, it is difficult for large numbers of men to change position, so their movements can be easily predicted. An individual can easily change his mind, so his movements are difficult to predict."(Miyamoto Musashi, "The Book of Five Rings" , 1645)

"Whatever we imagine is finite. Therefore, there is no idea or conception of anything we call finite. No man can have in his mind an image of infinite magnitude; nor conceive infinite swiftness, infinite time, or infinite force, or inmate power." (Thomas Hobbes, "Of Man", 1658)

"The highest endeavor of the mind, and the highest virtue, it to understand things by intuition." (Baruch Spinoza, "The Road to Inner Freedom: The Ethics" , 1667)

"For the Mind feels those things that it conceives in understanding no less than those it has in the memory. For the eyes of the mind, by which it sees and observes things, are demonstrations [descriptions] themselves." (Baruch Spinoza, "Ethics, Demonstrated in Geometrical Order", 1677)

"Men judge things according to the disposition of their minds, and had rather imagine things than understand them." (Baruch Spinoza, "Ethics", Book I, 1677)

"The images of things are affections of the human body whose ideas represent external bodies as present to us. […] the affections of the human body whose ideas present external bodies as present to us, we shall call things, though they do not reproduce [external] figures of things. And when the mind regards bodies in this way, we shall say that it imagines." (Baruch Spinoza, "Ethics", 1677)

"As in a block of marble all possible figures are potentially contained in it, and can be drawn out of it by the movement or by the action of the chisel, so in the same way all intelligible figures are potentially in intelligible extension and are discovered in it according to the different ways in which this extension is represented to the mind, as a consequence of the general laws which God has established according to which he continuously acts in us. " (Nicolas Malebranche , "Dialogues On Metaphysics And Religion", 1688)

"Probability is the appearance of agreement upon fallible proofs. As demonstration is the showing the agreement or disagreement of two ideas by the intervention of one or more proofs, which have a constant, immutable, and visible connexion one with another; so probability is nothing but the appearance of such an agreement or disagreement by the intervention of proofs, whose connexion is not constant and immutable, or at least is not perceived to be so, but is, or appears for the most part to be so, and is enough to induce the mind to judge the proposition to be true or false, rather than the contrary." (John Locke, "An Essay Concerning Human Understanding", Book IV, 1689)

"Sometimes the mind perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other; and this, I think, we may call intuitive knowledge. [...] Intuitive knowledge needs no probation, nor can have any, this being the highest of all human certainty." (John Locke, "An Essay Concerning Human Understanding", 1689)

"They that are ignorant of Algebra cannot imagine the wonders in this kind are to be done by it: and what further improvements and helps advantageous to other parts of knowledge the sagacious mind of man may yet find out, it is not easy to determine. This at least I believe, that the ideas of quantity are not those alone that are capable of demonstration and knowledge; and that other, and perhaps more useful, parts of contemplation, would afford us certainty, if vices, passions, and domineering interest did not oppose and menace such endeavors." (John Locke, "An Essay Concerning Human Understanding", 1689)

"[….] a great number of […] living and thinking Particles could not possibly by their mutual contract and pressing and striking compose one greater individual Animal, with one Mind and Understanding, and a Vital Consension of the whole Body: anymore than a swarm of Bees, or a crowd of Men and Women can be conceived to make up one particular Living Creature compounded and constituted of the aggregate of them all."(Richard Bentley, "The folly and unreasonableness of atheism", 1699)

On Mind (1700-1749)

"Mathematics make the mind attentive to the objects which it considers. This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the same thing to the understanding as music to the ear and beauty to the eye. The pursuit of it does really as much gratify a natural faculty implanted in us by our wise Creator as the pleasing of our senses: only in the former case, as the object and faculty are more spiritual, the delight is more pure, free from regret, turpitude, lassitude, and intemperance that commonly attend sensual pleasures." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"The mathematics are the friends to religion, inasmuch as they charm the passions, restrain the impetuosity of the imagination, and purge the mind from error and prejudice. Vice is error, confusion and false reasoning; and all truth is more or less opposite to it. Besides, mathematical truth may serve for a pleasant entertainment for those hours which young men are apt to throw away upon their vices; the delightfulness of them being such as to make solitude not only easy but desirable." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"[…] for the saving the long progression of the thoughts to remote and first principles in every case, the mind should provide itself several stages; that is to say, intermediate principles, which it might have recourse to in the examining those positions that come in its way. These, though they are not self-evident principles, yet, if they have been made out from them by a wary and unquestionable deduction, may be depended on as certain and infallible truths, and serve as unquestionable truths to prove other points depending upon them, by a nearer and shorter view than remote and general maxims. […] And thus mathematicians do, who do not in every new problem run it back to the first axioms through all the whole train of intermediate propositions. Certain theorems that they have settled to themselves upon sure demonstration, serve to resolve to them multitudes of propositions which depend on them, and are as firmly made out from thence as if the mind went afresh over every link of the whole chain that tie them to first self-evident principles." John Locke, "The Conduct of the Understanding", 1706)

"Nothing proves more clearly that the mind seeks truth, and nothing reflects more glory upon it, than the delight it takes, sometimes in spite of itself, in the driest and thorniest researches of algebra." (Bernard de Fontenelle, "Histoire du Renouvellement de l'Académie des Sciences", 1708)

"The ideas imprinted on the senses by the Author of Nature are called real things: and those excited in the imagination being less regular, vivid and constant, are more properly termed ideas, or images of things, which they copy and represent. But then our sensations, be they never so vivid and distinct, are nevertheless ideas, that is, they exist in the mind, or are perceived by it, as truly as the ideas of its own framing. The ideas of sense are allowed to have more reality in them, that is, to be more strong, orderly, and coherent than the creatures of the mind; but this is no argument that they exist without the mind. They are also less dependent on the spirit, or thinking substance which perceives them, in that they are excited by the will of another and more powerful spirit: yet still they are ideas, and certainly no idea, whether faint or strong, can exist otherwise than in a mind perceiving it." (George Berkeley, "Principles of Human Knowledge", 1710)

"To speak the truth, Philonous, I think there are two kinds of objects, the one perceived immediately, which are likewise called ideas, the other are real things or external objects perceived by the mediation of ideas, which are their images and representations. Now I own, ideas do not exist without the mind; but the latter sort of objects do." (George Berkeley, "Three Dialogues", 1713)

"[Mathematics] guides our minds in an orderly way, and furnishes us simple and rational principles by means of which ambiguities are clarified, disorder is converted into order, and complexities are analyzed into their component parts." (Johann B Mencken, "The Charlatanry of the Learned", 1715)

"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)

"By the very nature of poetry it is impossible for everyone to be at the same time a sublime poet and a sublime metaphysician, for metaphysics abstracts the mind from the senses, and the poetic faculty must submerge the whole mind in the senses. Metaphysics soars up to universals, and the poetic faculty must plunge deep into particulars." (Giambattista Vico, "The New Science", 1725)

"For chemistry is no science form’d à priori; ’tis no production of the human mind, framed by reasoning and deduction: it took its rise from a number of experiments casually made, without any expectation of what follow’d; and was only reduced into an art or system, by collecting and comparing the effects of such unpremeditated experiments, and observing the uniform tendency thereof. So far, then, as a number of experimenters agree to establish any undoubted truth; so far they may be consider'd as constituting the theory of chemistry." (Hermann Boerhaave, "A New Method of Chemistry", 1727)

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

"[...] things which do not now exist in the mind itself, can only be perceived, remembered, or imagined, by means of ideas or images of them in the mind, which are the immediate objects of perception, remembrance, and imagination. This doctrine appears evidently to be borrowed from the old system; which taught, that external things make impressions upon the mind, like the impressions of a seal upon wax; that it is by means of those impressions that we perceive, remember) or imagine them; and that those impressions must resemble the things from which they are taken. When we form our notions of the operations of the mind by analogy, this way of conceiving them seems to be very natural, and offers itself to our thoughts: for as every thing which is felt must make some impression upon the body, we are apt to think, that every thing which is understood must make some impression upon the mind." (Thomas Reid, "An Inquiry into the Human Mind", 1734)

"All the perceptions of the human mind resolve themselves into two distinct kinds, which I shall call impressions and ideas. The difference betwixt these consists in the degrees of force and liveliness, with which they strike upon the mind, and make their way into our thought or consciousness. Those perceptions, which enter with most force and violence, we may name impressions; and under this name I comprehend all our sensations, passions and emotions, as they make their first appearance in the soul. By ideas I mean the faint images of these in thinking and reasoning. I believe it will not be very necessary to employ many words in explaining this distinction." (David Hume, "A Treatise of Human Nature", 1738)

"But to form the idea of an object, and to form an idea simply is the same thing; the reference of the idea to an object being an extraneous denomination, of which in itself it bears no mark or character. Now as it is impossible to form an idea of an object, that is possessed of quantity and quality, and yet is possessed of no precise degree of either; it follows, that there is an equal impossibility of forming an idea, that is not limited and confined in both these particulars. Abstract ideas are therefore in themselves individual, however they may become general in their representation. The image in the mind is only that of a particular object, though the application of it in our reasoning be the same, as if it were universal." (David Hume, "Treatise of Human Nature", 1738)

"Mathematical knowledge adds vigour to the mind, frees it from prejudice, credulity, and superstition. This it does in two ways: 1st, by accustoming us to examine, and not to take thigs upon trust. 2nd By giving us a clear and extensive knowledge of the system of the world […]." (Dr. John Arbuthnot, "Usefulness of Mathematical Learning", 1745)

"Our mental vision or conception of ideas is nothing but a revelation made to us by our Maker. When we voluntarily turn our thoughts to any object, and raise up its image in the fancy, it is not the will which creates that idea: It is the universal Creator, who discovers it to the mind, and renders it present to us." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

On Mind (1750-1799)

"Things which do not now exist in the mind itself, can only be perceived, remembered, or imagined, by means of the ideas or images in the mind, which are the immediate objects of perception, remembrance, and imagination." (Thomas Reid, "An Inquiry into the Human Mind on the Principles", 1764)

"But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability." (Pierre-Simon Laplace, "Recherches, 1º, sur l'Intégration des Équations Différentielles aux Différences Finies, et sur leur Usage dans la Théorie des Hasards", 1773)

"Our knowledge springs from two fundamental sources of the mind; the first is the capacity of receiving representations (receptivity for impressions), the second is the power of knowing an object through these representations (spontaneity [in the production] of concepts)." (Immanuel Kant, "Critique of Pure Reason", 1781)

"It is impossible to disassociate language from science or science from language, because every natural science always involves three things: the sequence of phenomena on which the science is based; the abstract concepts which call these phenomena to mind; and the words in which the concepts are expressed. To call forth a concept a word is needed; to portray a phenomenon a concept is needed. All three mirror one and the same reality." (Antoine-Laurent Lavoisier, "Traite Elementaire de Chimie", 1789)

"But mathematics, certainly, does not play the smallest part in the charm and movement of the mind produced by music. Rather is it only the indispensable condition (conditio sine qua non) of that proportion of the combining as well as changing impressions which makes it possible to grasp them all in one and prevent them from destroying one another, and to let them, rather, conspire towards the production of a continuous movement and quickening of the mind by affections that are in unison with it, and thus towards a serene self-enjoyment." (Immanuel Kant, "The Critique of Judgment", 1790)

"If the human mind is nonetheless to be able even to think the given infinite without contradiction, it must have within itself a power that is supersensible, whose idea of the noumenon cannot be intuited but can yet be regarded as the substrate underlying what is mere appearance, namely, our intuition of the world." (Immanuel Kant, "Critique of Judgment", 1790)

"It has never yet been supposed, that all the facts of nature, and all the means of acquiring precision in the computation and analysis of those facts, and all the connections of objects with each other, and all the possible combinations of ideas, can be exhausted by the human mind." (Nicolas de Condorcet, "Outlines Of An Historical View Of The Progress Of The Human Mind", 1795)

On Mind (1800-1824)

"The introduction of impossible quantities, is assigned as a great and primary cause of the evils under which mathematical science labours. During the operation of these quantities, it is said, all just reasoning is suspended, and the mind is bewildered by exhibitions that resemble the juggling tricks of mechanical dexterity." (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)

"There cannot be design without a designer; contrivance without a contriver; order without choice; arrangement, without any thing capable of arranging; subserviency and relation to a purpose, without that which could intend a purpose; means suitable to an end, without the end ever having been contemplated, or the means accommodated to it. Arrangement, disposition of parts, subserviency of means to an end, relation of instruments to an use, imply the presence of intelligence and mind." (William Paley, "Natural Theology or Evidences of the Existence and Attributes of the Deity", 1802)

"Every negative quantity standing by itself is a mere creature of the mind and [...] those which are met with in calculations are only mere algebraical forms, incapable of representing any thing real and effective." (Lazare Carnot, "Geometrie de Position", 1803)

"At the beginning I would ask anyone who wants to introduce a new function in analysis to clarify whether he intends to confine it to real magnitudes (real values of the argument) and regard the imaginary values as just vestigial –or whether he subscribes to my fundamental proposition that in the realm of magnitudes the imaginary ones a+bv-1 = a+bi have to be regarded as enjoying equal rights with the real ones. We are not talking about practical utility here; rather analysis is, to my mind, a self-sufficient science. It would lose immeasurably in beauty and symmetry from the rejection of any fictive magnitudes. At each stage truths, which otherwise are quite generally valid, would have to be encumbered with all sorts of qualifications. " (Carl F Gauss, [letter to Bessel,] 1811)

"The foundations of chemical philosophy are observation, experiment, and analogy. By observation, facts are distinctly and minutely impressed on the mind. By analogy, similar facts are connected. By experiment, new facts are discovered; and, in the progression of knowledge, observation, guided by analogy, lends to experiment, and analogy confirmed by experiment, becomes scientific truth." (Sir Humphry Davy, "Elements of Chemical Philosophy" Vol. 4, 1812)

"The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account." (Pierre-Simon Laplace, "Analytical Theory of Probability, 1812)

"It seems to be like taking the pieces of a dissected map out of its box. We first look at one part, and then at another, then join and dove-tail them; and when the successive acts of attention have been completed, there is a retrogressive effort of mind to behold it as a whole. The poet should paint to the imagination, not to the fancy; and I know no happier case to exemplify the distinction between these two faculties." (Samuel T Coleridge," Biographia Literaria", 1817)

"Analogy, although it is not infallible, is yet that telescope of the mind by which it is marvellously assisted in the discovery of both physical and moral truth." (Charles C Colton, "Lacon", 1820)

"This is the test and triumph of originality, not to show us what has never been, and what we may therefore very easily never have dreamt of, but to point out to us what is before our eyes and under our feet, though we have had no suspicion of its existence, for want of sufficient strength of intuition, of determined grasp of mind to seize and retain it." (William Hazlitt, "Table Talk; or, Original Essays", 1821)

"Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes." (Baron Jean-Baptiste-Joseph Fourier, "Théorie Analytique de la Chaleur", 1822)

"Mathematical analysis is as extensive as nature itself; it defines all perceptible relations, measures times, spaces, forces, temperatures; this difficult science is formed slowly, but it preserves every principle which it has once acquired; it grows and strengthens itself incessantly in the midst of the many variations and errors of the human mind. It's chief attribute is clearness; it has no marks to express confused notations. It brings together phenomena the most diverse, and discovers the hidden analogies which unite them." (J B Joseph Fourier, "The Analytical Theory of Heat", 1822)

"Symmetry is a characteristic of the human mind." (Alexander Pushkin, 1825)