Donald J Wheeler - Collected Quotes

"Averages, ranges, and histograms all obscure the time-order for the data. If the time-order for the data shows some sort of definite pattern, then the obscuring of this pattern by the use of averages, ranges, or histograms can mislead the user. Since all data occur in time, virtually all data will have a time-order. In some cases this time-order is the essential context which must be preserved in the presentation." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Before you can improve any system you must listen to the voice of the system (the Voice of the Process). Then you must understand how the inputs affect the outputs of the system. Finally, you must be able to change the inputs (and possibly the system) in order to achieve the desired results. This will require sustained effort, constancy of purpose, and an environment where continual improvement is the operating philosophy." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Data are collected as a basis for action. Yet before anyone can use data as a basis for action the data have to be interpreted. The proper interpretation of data will require that the data be presented in context, and that the analysis technique used will filter out the noise."  (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions taken may be totally inconsistent with the data. Thus, the proper use of data requires that you have simple and effective methods of analysis which will properly separate potential signals from probable noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"No comparison between two values can be global. A simple comparison between the current figure and some previous value and convey the behavior of any time series. […] While it is simple and easy to compare one number with another number, such comparisons are limited and weak. They are limited because of the amount of data used, and they are weak because both of the numbers are subject to the variation that is inevitably present in weak world data. Since both the current value and the earlier value are subject to this variation, it will always be difficult to determine just how much of the difference between the values is due to variation in the numbers, and how much, if any, of the difference is due to real changes in the process." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"No matter what the data, and no matter how the values are arranged and presented, you must always use some method of analysis to come up with an interpretation of the data.

While every data set contains noise, some data sets may contain signals. Therefore, before you can detect a signal within any given data set, you must first filter out the noise." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Since the average is a measure of location, it is common to use averages to compare two data sets. The set with the greater average is thought to ‘exceed’ the other set. While such comparisons may be helpful, they must be used with caution. After all, for any given data set, most of the values will not be equal to the average." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"The purpose of analysis is insight. The best analysis is the simplest analysis which provides the needed insight." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"We analyze numbers in order to know when a change has occurred in our processes or systems. We want to know about such changes in a timely manner so that we can respond appropriately. While this sounds rather straightforward, there is a complication - the numbers can change even when our process does not. So, in our analysis of numbers, we need to have a way to distinguish those changes in the numbers that represent changes in our process from those that are essentially noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"When a system is predictable, it is already performing as consistently as possible. Looking for assignable causes is a waste of time and effort. Instead, you can meaningfully work on making improvements and modifications to the process. When a system is unpredictable, it will be futile to try and improve or modify the process. Instead you must seek to identify the assignable causes which affect the system. The failure to distinguish between these two different courses of action is a major source of confusion and wasted effort in business today." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"When a process displays unpredictable behavior, you can most easily improve the process and process outcomes by identifying the assignable causes of unpredictable variation and removing their effects from your process." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"While all data contain noise, some data contain signals. Before you can detect a signal, you must filter out the noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Without meaningful data there can be no meaningful analysis. The interpretation of any data set must be based upon the context of those data. Unfortunately, much of the data reported to executives today are aggregated and summed over so many different operating units and processes that they cannot be said to have any context except a historical one - they were all collected during the same time period. While this may be rational with monetary figures, it can be devastating to other types of data." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"[…] you simply cannot make sense of any number without a contextual basis. Yet the traditional attempts to provide this contextual basis are often flawed in their execution. [...] Data have no meaning apart from their context. Data presented without a context are effectively rendered meaningless." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Data analysis is not generally thought of as being simple or easy, but it can be. The first step is to understand that the purpose of data analysis is to separate any signals that may be contained within the data from the noise in the data. Once you have filtered out the noise, anything left over will be your potential signals. The rest is just details." (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"Descriptive statistics are built on the assumption that we can use a single value to characterize a single property for a single universe. […] Probability theory is focused on what happens to samples drawn from a known universe. If the data happen to come from different sources, then there are multiple universes with different probability models. If you cannot answer the homogeneity question, then you will not know if you have one probability model or many. [...] Statistical inference assumes that you have a sample that is known to have come from one universe." (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"In order to be effective a descriptive statistic has to make sense - it has to distil some essential characteristic of the data into a value that is both appropriate and understandable. […] the justification for computing any given statistic must come from the nature of the data themselves - it cannot come from the arithmetic, nor can it come from the statistic. If the data are a meaningless collection of values, then the summary statistics will also be meaningless - no arithmetic operation can magically create meaning out of nonsense. Therefore, the meaning of any statistic has to come from the context for the data, while the appropriateness of any statistic will depend upon the use we intend to make of that statistic." (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"The four questions of data analysis are the questions of description, probability, inference, and homogeneity. Any data analyst needs to know how to organize and use these four questions in order to obtain meaningful and correct results. [...] 

THE DESCRIPTION QUESTION: Given a collection of numbers, are there arithmetic values that will summarize the information contained in those numbers in some meaningful way?

THE PROBABILITY QUESTION: Given a known universe, what can we say about samples drawn from this universe? [...] 

THE INFERENCE QUESTION: Given an unknown universe, and given a sample that is known to have been drawn from that unknown universe, and given that we know everything about the sample, what can we say about the unknown universe? [...] 

THE HOMOGENEITY QUESTION: Given a collection of observations, is it reasonable to assume that they came from one universe, or do they show evidence of having come from multiple universes?" (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

Stephen Few - Collected Quotes

"An effective dashboard is the product not of cute gauges, meters, and traffic lights, but rather of informed design: more science than art, more simplicity than dazzle. It is, above all else, about communication." (Stephen Few, "Information Dashboard Design", 2006)

"Most dashboards fail to communicate efficiently and effectively, not because of inadequate technology (at least not primarily), but because of poorly designed implementations. No matter how great the technology, a dashboard's success as a medium of communication is a product of design, a result of a display that speaks clearly and immediately. Dashboards can tap into the tremendous power of visual perception to communicate, but only if those who implement them understand visual perception and apply that understanding through design principles and practices that are aligned with the way people see and think." (Stephen Few, "Information Dashboard Design", 2006)

"A signal is a useful message that resides in data. Data that isn’t useful is noise. […] When data is expressed visually, noise can exist not only as data that doesn’t inform but also as meaningless non-data elements of the display (e.g. irrelevant attributes, such as a third dimension of depth in bars, color variation that has no significance, and artificial light and shadow effects)." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Apart from the secondary benefits of digital data, which are many, such as faster and cheaper information collection and distribution, the primary benefit is better decision making based on evidence. Despite our intellectual powers, when we allow our minds to become disconnected from reliable information about the world, we tend to screw up and make bad decisions." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Data contain descriptions. Some are true, some are not. Some are useful, most are not. Skillful use of data requires that we learn to pick out the pieces that are true and useful. [...] To find signals in data, we must learn to reduce the noise - not just the noise that resides in the data, but also the noise that resides in us. It is nearly impossible for noisy minds to perceive anything but noise in data." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Signals always point to something. In this sense, a signal is not a thing but a relationship. Data becomes useful knowledge of something that matters when it builds a bridge between a question and an answer. This connection is the signal." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"The term data, unlike the related terms facts and evidence, does not connote truth. Data is descriptive, but data can be erroneous. We tend to distinguish data from information. Data is a primitive or atomic state (as in ‘raw data’). It becomes information only when it is presented in context, in a way that informs. This progression from data to information is not the only direction in which the relationship flows, however; information can also be broken down into pieces, stripped of context, and stored as data. This is the case with most of the data that’s stored in computer systems. Data that’s collected and stored directly by machines, such as sensors, becomes information only when it’s reconnected to its context."  (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"Everything that informs us of something useful that we didn't already know is a potential signal. If it matters and deserves a response, its potential is actualized." (Stephen Few)

"One of the great purposes of education today is to help us filter the data, to reduce it to what's true and useful." (Stephen Few)

On Definitions V

"The use of a mathematical definition is, to deduce from it the properties of the thing defined […]" (Robert Woodhouse," On the necessary Truth of certain Conclusions obtained by Means of imaginary Quantities", 1801)

"The language of mathematics, permitting great sharpness and accuracy of definition, conduces largely to their power of drawing necessary conclusions. Language is not only a means of recording the results of our thinking; it is an instrument of thought, and that of the highest value." (Thomas Hill, "The Imagination in Mathematics", The North American Review Vol. 85 (176), 1857)

"The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it." (Thomas Hill, "Uses of Mathesis", Bibliotheca Sacra Vol. 32, 1875)

"The apodictic quality of mathematical thought, the certainty and correctness of its conclusions, are due, not to a special mode of ratiocination, but to the character of the concepts with which it deals. What is that distinctive characteristic? I answer: precision, sharpness, completeness of definition. But how comes your mathematician by such completeness? There is no mysterious trick involved; some ideas admit of such precision, others do not; and the mathematician is one who deals with those that do." (Cassius J Keyser, "The Universe and Beyond", Hibbert Journal Vol. 3, 1904–1905)

"[…] mathematics is a science whose concepts are too breakable, too dry, too precisely limited. The disciplines of life and society, of human thinking, are fluid disciplines, with some flexibility, with concepts that are not clearly defined, but which are able to include things less strictly delimited than a mathematical definition does it." (Grigore C Moisil, 1968)

"Because mathematical proofs are long, they are also difficult to invent. One has to construct, without making any mistakes, long chains of assertions, and see what one is doing, see where one is going. To see means to be able to guess what is true and what is false, what is useful and what is not. To see means to have a feeling for which definitions one should introduce, and what the key assertions are that will allow one to develop a theory in a natural manner." (David Ruelle, "Chance and Chaos", 1991)

"It is not surprising to find many mathematical ideas interconnected or linked. The expansion of mathematics depends on previously developed ideas. The formation of any mathematical system begins with some undefined terms and axioms (assumptions) and proceeds from there to definitions, theorems, more axioms and so on. But history points out this is not necessarily the route that creativity" (Theoni Pappas, "More Joy of Mathematics: Exploring mathematical insights & concepts", 1991)

"This absolutist view of mathematical knowledge is based on two types of assumptions: those of mathematics, concerning the assumption of axioms and definitions, and those of logic concerning the assumption of axioms, rules of inference and the formal language and its syntax. These are local or micro-assumptions. There is also the possibility of global or macro-assumptions, such as whether logical deduction suffices to establish all mathematical truths." (Paul Ernest, "The Philosophy of Mathematics Education", 1991)

"The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument." (Yuri I Manin, "Mathematics as Metaphor: Selected Essays of Yuri I. Manin", 2007)

"As students, we learned mathematics from textbooks. In textbooks, mathematics is presented in a rigorous and logical way: definition, theorem, proof, example. But it is not discovered that way. It took many years for a mathematical subject to be understood well enough that a cohesive textbook could be written. Mathematics is created through slow, incremental progress, large leaps, missteps, corrections, and connections." (Richard S Richeson, "Eulers Gem: The Polyhedron Formula and the birth of Topology", 2008)

On Definitions IV

"Definitions might be good if we did not employ words in making them." (Jean-Jacques Rousseau, "Emile, or, Treatise on Education", 1762)

"The mathematician pays not the least regard either to testimony or conjecture, but deduces everything by demonstrative reasoning, from his definitions and axioms. Indeed, whatever is built upon conjecture, is improperly called science; for conjecture may beget opinion, but cannot produce knowledge." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"It is the essence of a scientific definition to be causative, not by introduction of imaginary somewhats, natural or supernatural, under the name of causes, but by announcing the law of action in the particular case, in subordination to the common law of which all the phenomena are modifications or results." (Samuel T Coleridge, "Hints Towards the Formation of a More Comprehensive Theory of Life, The Nature of Life", 1847)

"The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing-glass of theory, and screw it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world." (James C Maxwell, "Are There Real Analogies in Nature?", 1856)

"A Weltanschauung [worldview] is an intellectual construction which solves all the problems of our existence uniformly on the basis of one overriding hypothesis, which, accordingly, leaves no question unanswered and in which everything that interests us finds its fixed place [...] the worldview of science already departs noticeably from our definition. It is true that it too assumes the uniformity of the explanation of the universe; but it does so only as a programme, the fulfillment of which is relegated to the future." Sigmund Freud, "New introductory lectures on psycho-analysis", 1932)

"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)

"The view is often defended that sciences should be built up on clear and sharply defined basal concepts. In actual fact no science, not even the most exact, begins with such definitions. The true beginning of scientific activity consists rather in describing phenomena and then in proceeding to group, classify and correlate them." (Sigmund Freud, "General Psychological Theory", 1963)

"This other world is the so-called physical world image; it is merely an intellectual structure. To a certain extent it is arbitrary. It is a kind of model or idealization created in order to avoid the inaccuracy inherent in every measurement and to facilitate exact definition." (Max Planck, "The Philosophy of Physics", 1963)

"Concepts form the basis for any science. These are ideas, usually somewhat vague (especially when first encountered), which often defy really adequate definition. The meaning of a new concept can seldom be grasped from reading a one-paragraph discussion. There must be time to become accustomed to the concept, to investigate it with prior knowledge, and to associate it with personal experience. Inability to work with details of a new subject can often be traced to inadequate understanding of its basic concepts." (William C Reynolds & Harry C Perkins, "Engineering Thermodynamics", 1977)

"Definitions are temporary verbalizations of concepts, and concepts - particularly difficult concepts - are usually revised repeatedly as our knowledge and understanding grows." (Ernst Mayr, "The Growth of Biological Thought", 1982)

On Definitions III

"In every new and growing science there are many working hypotheses that never attain to any sort of reality. On the other hand, in the old and abstract sciences of mathematics, where it is hard to tell how much is mere definition or convention, the problem of reality is not so much doubtful as it is meaningless." (Gilbert N Lewis, "The Anatomy of Science", 1926)

"Scientific Ideas can often be adequately exhibited for all the purposes of reasoning, by means of Definitions and Axioms; all attempts to reason by means of Definitions from common Notions, lead to empty forms or entire confusion." (William Whewell, "History of the Inductive Sciences from the Earliest to the Present Time", 1937)

"The view is often defended that sciences should be built up on clear and sharply defined basal concepts. In actual fact no science, not even the most exact, begins with such definitions. The true beginning of scientific activity consists rather in describing phenomena and then in proceeding to group, classify and correlate them." (Sigmund Freud, "Collected Papers", 1950)

"Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments." (Gerald Holton, "Introduction to Concepts and Theories in Physical Science", 1952)

"The exact verbal definition of qualitative concepts is more often the province of philosophy than of physical science." (Ronnie Bell, "The Proton in Chemistry", 1959)

"If all the theories pertinent to systems engineering could be discussed within a common framework by means of a standard set of nomenclature and definitions, many separate courses might not be required." (A Wayne Wymore, "A Mathematical Theory of Systems Engineering", 1967)

"When terms [...] evolve and change definition with time; and when the social reality which terms are intended to organize and render intelligible is also seen to be in flux, capturing the truth in a net of words becomes a matter of intuition and style more than of any scientific method that can be replicated by others and made to achieve the same result every time someone asks the same question, or undertakes the same operations." (William H McNeill, "Discrepancies among the Social Sciences", 1981)

"Every physical concept must be given a definition such that one can in principle describe, in virtue of this definition, whether or not it applies in each particular case." (Albert Einstein)

"Physics shares with mathematics the advantages of succinct description and of brief, compendious definition, which precludes confusion, even in ideas where, with no apparent burdening of the brain, hosts of others are contained." (Ernst Mach)

"We begin to reason from sensible objects, and definition is the end and epilogue of science. It is not the beginning of our knowing, but only of our teaching." (Tommaso Campanella)

On Definitions II

"The errors of definitions multiply themselves according as the reckoning proceeds; and lead men into absurdities, which at last they see but cannot avoid, without reckoning anew from the beginning." (Thomas Hobbes, "The Moral and Political Works of Thomas Hobbes of Malmesbury", 1750)

"A definition is nothing else but an explication of the meaning of a word, by words whose meaning is already known. Hence it is evident that every word cannot be defined; for the definition must consist of words; and there could be no definition, if there were not words previously understood without definition." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"There is nothing more difficult than a good definition, for it is scarcely possible to express, in a few words, the abstracted view of an infinite variety of facts." (Humphry Davy, "Consolations in Travel, or the Last Days of a Philosopher" , 1830)

"Questions of Definition are of the very highest importance in Philosophy, and they need to be watched accordingly." (George Campbell, "A Fourth State of Matter, Nature", 1880)

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

"A definition is the enclosing a wilderness of idea within a wall of words." (Samuel Butler, "The Note-Books of Samuel Butler", 1912)

"Definitions are the guardians of rationality, the first line of defense against the chaos of mental disintegration. (Ayn Rand, The Romantic Manifesto, 1969)

"Definitions, like questions and metaphors, are instruments for thinking. Their authority rests entirely on their usefulness, not their correctness. We use definitions in order to delineate problems we wish to investigate, or to further interests we wish to promote. In other words, we invent definitions and discard them as suits our purposes." (Neil Postman, "Language Education in a Knowledge Context", 1980)

"A full definition of an object must include the whole of human experience, both as a criterion of truth and a practical indicator of its connection with human wants." (Vladimir Lenin) 

"Fundamental definitions do not arise at the start but at the end of the exploration, because in order to define a thing you must know what it is and what it is good for." (Hans Freudenthal)

On Definitions I

"Rules for Demonstrations. I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it. II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated. III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions." (Blaise Pascal, "Pensées", 1670)

"Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition; Not to employ in definitions any but terms perfectly known or already explained. […] A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading." (Blaise Pascal, "Pensées", 1670)

"The science [mathematics], once fairly established on the foundation of a few axioms and definitions, as upon a rock, has grown from age to age, so as to become the most solid fabric that human reason can boast." (Thomas Reid, "Essays on the Intellectual Powers of Man", 1785)

"Mathematics is an experimental science, and definitions do not come first but later on." (Oliver Heaviside, "On Operators in Physical Mathematics", Proceedings of the Royal Society of London, Series A Vol. 54, 1854)

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

"The whole history of the development of mathematics has been a history of the destruction of old definitions […] old hobbies, old idols." (David E Smith, American Mathematical Monthly Vol. 1 (1), 1894)

"If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. [...] Hence the question of whether axioms are a priori becomes pointless since they are arbitrary." (Hans Reichenbach, "The Philosophy of Space and Time", 1928) 

"The word 'definition' has come to have a dangerously reassuring sound, owing no doubt to its frequent occurrence in logical and mathematical writings." (Willard van Orman Quine, "From a Logical Point of View", 1953)

"In order that a mathematical science of any importance may be founded upon conventional definitions, the entities created by them must have properties which bear some affinity to the properties of existing things."(John H C Whitehead, A Treatise on Universal Algebra, with Applications, 1960)

"The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity." (Richard Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

On Causality (1700-1799)

"All effects follow not with like certainty from their supposed causes." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"It is universally allowed that nothing exists without a cause of its existence, and that chance, when strictly examined, is a mere negative word, and means not any real power which has anywhere a being in nature." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"We only find, that the one does actually, in fact, follow the other. The impulse of one billiard-ball is attended with motion in the second. This is the whole that appears to the outward senses. The mind feels no sentiment or inward impression from this succession of objects: consequently, there is not, in any single, particular instance of cause and effect, any thing which can suggest the idea of power or necessary connexion." (David Hume, "An Enquiry Concerning Human Understanding", 1748)

"[…] chance, that is, an infinite number of events, with respect to which our ignorance will not permit us to perceive their causes, and the chain that connects them together. Now, this chance has a greater share in our education than is imagined. It is this that places certain objects before us and, in consequence of this, occasions more happy ideas, and sometimes leads us to the greatest discoveries […]" (Claude Adrien Helvetius, "On Mind", 1751)

"[...] for no more by the law of reason than by the law of nature can anything occur without a cause." (Jean J Rousseau, "The Social Contract", 1762)

"The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road." (Gottfried W Leibniz, "New Essays Concerning Human Understanding", 1704) [published 1765]

"One of the most intimate of all associations in the human mind is that of cause and effect. They suggest one another with the utmost readiness upon all occasions; so that it is almost impossible to contemplate the one, without having some idea of, or forming some conjecture about the other." (Joseph Priestley, "The History and Present State of Electricity", 1767)

"To endeavor at discovering the connections that subsist in nature, is no way inconsistent with prudence; but it is downright folly to push these researches too far; as it is the lot only of superior Beings to see the dependence of events, from one end to the other, of the chain which supports them." (Pierre Louis Maupertuis, "An Essay Towards a History of the Principal Comets Since 1742", 1769)

"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)

"If an event can be produced by a number n of different causes, the probabilities of the existence of these causes, given the event (prises de l'événement), are to each other as the probabilities of the event, given the causes: and the probability of each cause is equal to the probability of the event, given that cause, divided by the sum of all the probabilities of the event, given each of the causes.” (Pierre-Simon Laplace, "Mémoire sur la Probabilité des Causes par les Événements", 1774)

"The word ‘chance’ then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.” (Pierre-Simon Laplace, "Mémoire sur les Approximations des Formules qui sont Fonctions de Très Grands Nombres", 1783)

"The laws of nature are the rules according to which the effects are produced; but there must be a cause which operates according to these rules." (Thomas Reid, "Essays on the Active Powers of Man", 1785)

"Pure mathematics can never deal with the possibility, that is to say, with the possibility of an intuition answering to the conceptions of the things. Hence it cannot touch the question of cause and effect, and consequently, all the finality there observed must always be regarded simply as formal, and never as a physical end." (Immanuel Kant, "The Critique of Judgement", 1790)

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On Causality (1800-1899)

"We know the effects of many things, but the causes of few; experience, therefore, is a surer guide than imagination, and inquiry than conjecture." (Charles C Colton, "Lacon", 1820)

"Primary causes are unknown to us; but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy." (Jean-Baptiste-Joseph Fourier, "The Analytical Theory of Heat", 1822)

"Things of all kinds are subject to a universal law which may be called the law of large numbers. It consists in the fact that, if one observes very considerable numbers of events of the same nature, dependent on constant causes and causes which vary irregularly, sometimes in one direction, sometimes in the other, it is to say without their variation being progressive in any definite direction, one shall find, between these numbers, relations which are almost constant." (Siméon-Denis Poisson, "Poisson’s Law of Large Numbers", 1837)

"Cause and effect, means and ends, seed and fruit cannot be severed; for the effect already blooms in the cause, the end preexists in the means, the fruit in the seed." (Ralph W Emerson, "Essays", 1841)

"An hypothesis being a mere supposition, there are no other limits to hypotheses than those of the human imagination; we may, if we please, imagine, by way of accounting for an effect, some cause of a kind utterly unknown, and acting according to a law altogether fictitious." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"The truth that every fact which has a beginning has a cause, is coextensive with human experience." (John S Mill, "System of Logic, Ratiocinative and Inductive", 1843)

"Causes are often disproportionate to effects." (Hannah F S Lee, "The Log Cabin, or, The World before You", 1844)

"First causes are outside the realm of science; they forever escape us in the sciences of living as well as in those of inorganic bodies." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

“Man’s mind cannot grasp the causes of events in their completeness, but the desire to find those causes is implanted in man’s soul. And without considering the multiplicity and complexity of the conditions any one of which taken separately may seem to be the cause, he snatches at the first approximation to a cause that seems to him intelligible and says: ‘This is the cause!’” (Leo Tolstoy, “War and Peace”, 1867)

"The accidental causes of science are only 'accidents' relatively to the intelligence of a man." (Chauncey Wright, "The Genesis of Species", North American Review, 1871)

"It is surprising to learn the number of causes of error which enter into the simplest experiment, when we strive to attain rigid accuracy." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)

"If statistical graphics, although born just yesterday, extends its reach every day, it is because it replaces long tables of numbers and it allows one not only to embrace at glance the series of phenomena, but also to signal the correspondences or anomalies, to find the causes, to identify the laws." (Émile Cheysson, cca. 1877)

"Before we can completely explain a phenomenon we require not only to find its true cause, its chief relations to other causes, and all the conditions which determine how the cause operates, and what its effect and amount of effect are, but also all the coincidences." (George Gore, "The Art of Scientific Discovery", 1878)

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Victor Hugo - Collected Quotes

"A stand can be made against invasion by an army; no stand can be made against invasion by an idea." (Victor Hugo, "The History of a Crime", 1851–1852)

"Nihilism has no substance. There is no such thing as nothingness, and zero does not exist. Everything is something. Nothing is nothing." (Victor Hugo, "Les Misérables", 1862)

"Philosophy is the microscope of thought. Everything desires to flee from it, but nothing escapes it." (Victor Hugo, "Les Misérables", 1862)

"[...] the small is great, the great is small; all is in equilibrium in necessity […]" (Victor Hugo, "Les Misérables", 1862)

"The straight line, a respectable optical illusion which ruins many a man." (Victor Hugo, Les Misérables, 1862)

"Who then understands the reciprocal flux and reflux of the infinitely great and the infinitely small, the echoing of causes in the abysses of being, and the avalanches of creation?" (Victor Hugo, "Saint Denis", 1862) 
"In Science, all tends to stir, to change, to form fresh surfaces. All denies, destroys, creates, replaces all. What was ground yesterday is put into the hopper again today. The colossal machine, Science, never rests. It is never satisfied; it is insatiable for improvement, of which the absolute knows nothing." (Victor Hugo, "William Shakespeare", 1864)

"Science seeks perpetual motion. She has found it: it is Science herself." (Victor Hugo, "William Shakespeare", 1864)


"Science has but the right to put a visa on facts; she should verify and distinguish." (Victor Hugo, "William Shakespeare", 1864)

"Science is ignorant, and has no right to laugh: a savant who laughs at the possible, is very near being an idiot." (Victor Hugo, "William Shakespeare", 1864)

"The unexpected ought always to be expected by Science. Her duty is to stop it in its course and search it, rejecting the chimerical, establishing the real." (Victor Hugo, "William Shakespeare", 1864)

"The mission of Science is to study and sound everything." (Victor Hugo, "William Shakespeare", 1864)

"An ant weighs upon the earth; a star can well weigh upon the universe." (Victor Hugo, "The Toilers of the Sea", 1866)

"Arithmetic, like the sea, is an undulation without any possible end." (Victor Hugo, "The Toilers of the Sea", 1866)

"Chance, if such a thing exists, is far-seeing." (Victor Hugo, "The Toilers of the Sea", 1866)

"Every fact is a logarithm; one added term ramifies it until it is thoroughly transformed. In the general aspect of things, the great lines of creation take shape and arrange themselves into groups; beneath lies the unfathomable." (Victor Hugo, "The Toilers of the Sea", 1866)

"One microscopic glittering point; then another; and another, and still another; they are scarcely perceptible, yet they are enormous. This light is a focus; this focus, a star; this star, a sun; this sun, a universe; this universe, nothing. Every number is zero in the presence of the infinite." (Victor Hugo, "The Toilers of the Sea", 1874)

"Phenomena may well be suspected of anything, are capable of anything. Hypothesis proclaims the infinite; that is what gives hypothesis its greatness. Beneath the surface fact it seeks the real fact. It asks creation for her thoughts, and then for her second thoughts. The great scientific discoverers are those who hold nature suspect." (Victor Hugo, "The Toilers of the Sea", 1874)

"Nature eludes calculation. Number is a grim pullulation. Nature is the thing that cannot be numbered." (Victor Hugo, "The Toilers of the Sea", 1874)

"To put everything in balance is good, to put everything in harmony is better." (Victor Hugo, "Ninety-Three", 1874)

"For true poetry, complete poetry, consists in the harmony of contraries. Hence, it is time to say aloud - and it is here above all that exceptions prove the rule - that everything that exists in nature exists in art." (Victor Hugo, "Dramas", 1896)

"Science says the first word on everything, and the last word on nothing." (Victor Hugo, "Things of the Infinite: Intellectual Autobiography", 1907)

Jules Verne - Collected Quotes

"In the cause of science men are expected to suffer." (Jules Verne, "A Journey to the Center of the Earth", 1864)

"Science, great, mighty and in the end unerring [...] science has fallen into many errors - errors which have been fortunate and useful rather than otherwise, for they have been the stepping stones to truth." (Jules Verne, "A Journey to the Center of the Earth", 1864)

"When science has sent forth her fiat - it is only to hear and obey." (Jules Verne, "A Journey to the Center of the Earth", 1864)

"We cannot prevent equilibrium from producing its effects. We may brave human laws, but we cannot resist natural ones." (Jules Verne, "Twenty Thousand Leagues Under the Sea", 1870)

"All things are simple […] when you know how to do them." (Jules Verne, "Twenty Thousand Leagues Under the Sea", 1870)

"Either my calculation is correct, or there is no truth in figures." (Jules Verne, "A Journey to the Center of the Earth", 1864)

"Reality provides us with facts so romantic that imagination itself could add nothing to them." (Jules Verne, "The Fur Country", 1873)

"Civilization never recedes; the law of necessity ever forces it onwards." (Jules Verne, "The Mysterious Island", 1875)

Mental Models L

"[…] 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)

"The likeness of a visible thing is that in virtue of which sight sees. And the likeness of an intellectively cognized thing, an intelligible species, is the form in virtue of which intellect cognizes. […] That which is intellectively cognized first is the thing of which the intelligible species is a likeness." (Thomas Aquinas, "Quaestiones disputatae de veritate", cca. 1256-1259)

"One who doesn't perceive the essence and quiddity of a thing, but only its image, can't know the thing. For one who has seen only a picture of Hercules doesn't know Hercules. A human being, however, perceives nothing of a thing, except only its image, that is, a species received through the senses, which is an image of the thing and not the thing itself. For not the stone but a species of the stone is in the soul." (Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)

"[…] one ought to say that one may perceive the image of a thing in two ways. In one way, as the object of cognition. In this way it is true that one perceiving only the thing's image does not cognize the thing; for example, someone seeing the image of Hercules painted on a wall does not thereby either see or cognize Hercules. In another way, as the basis [ratio] of cognizing, and in this way the claim is not true. For through only a species perceived of a thing the thing is truly cognized - as a stone is truly seen through its sensible species alone, received in the eye, and is truly intellectively cognized through its intelligible species alone, received in intellect." (Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)

"Phantasms don't have the same manner of existing that the human intellect has [...] and so they cannot through their own power make an impression on the possible intellect. But through the power of the agent intellect, a kind of likeness results in the possible intellect as a result of agent intellect's turning toward the phantasms […] And this is how intelligible species are said to be abstracted from phantasms. It's not that some form that is numerically the same is first in phantasms and then produced in the possible intellect."(Thomas Aquinas, "Summa Theologiae", cca. 1266-1273)

"The attention will tend toward the species either in such a way that it would not pass beyond so as to attend to the object, or in such a way that it would pass beyond. If in the first way, then the thing will not be seen in itself but only its image will be seen as if it were the thing itself." (Peter J Olivi, "Quaestiones in secundum librum Sententiarum", cca. 1280- 1282)

"No prior assimilation through a species is required before an act of intellectively cognizing. Rather, the assimilation suffices that comes about through the act of intellectively cognizing, which is [itself] a likeness of the thing cognized." (William Ockham," Expositio in librum Perihermenias", cca. 1321-1324)

"Such an image or fictum was postulated for no other reason than to supposit for a thing in such a way that both a proposition might be composed out of it and it might be common to things. For these are denied of things." (William Ockham, "Expositio in librum Perihermenias", cca, 1321-1324)

"The thing represented needs to be cognized in advance - otherwise the representative would never lead to a cognition of the thing represented as to something similar." (William Ockham, "Expositio in librum Perihermenias", cca. 1321-1324)

"Within image theory, it is suggested that important components of decision-making processes are the different 'images' that a person may use to evaluate choice options. Images may represent a person's principles, goals, or plans. Decision options may then match or not match these images and be adopted, rejected, considered further, depending on circumstances." (Deborah J Terry & Michael A Hogg, "Attitudes, Behavior, and Social Context: The Role of Norms and Group Membership", 1999) 

Mental Models XLIX

"For imagination is different from either perceiving or discursive thinking, though it is not found without sensation, or judgement without it. That this activity is not the same kind of thinking as judgement is obvious. For imagining lies within our own power whenever we wish (e.g. we can call up a picture, as in the practice of mnemonics by the use of mental images), but in forming opinions we are not free: we cannot escape the alternative of falsehood or truth." (Aristotle, "De Anima", 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)

"Thinking is different from perceiving and is held to be in part imagination, in part judgement: we must therefore first mark off the sphere of imagination and then speak of judgement. If then imagination is that in virtue of which an image arises for us, excluding metaphorical uses of the term, is it a single faculty or disposition relative to images, in virtue of which we discriminate and are either in error or not? The faculties in virtue of which we do this are sense, opinion, knowledge, thought." (Aristotle, "De Anima", cca. 350 BC)

"As regards the question, therefore, what memory or remembering is, it has now been shown that it is the having of an image, related as a likeness to that of which it is an image; and as to the question of which of the faculties within us memory is a function, it has been shown that it is a function of the primary faculty of sense-perception, i.e. of that faculty whereby we perceive time."  (Aristotle," De Memoria et Reminiscentia" ["On Memory and Recollection"], 4th century BC)

"But since we have, in our work on the soul, treated of imagination, and the faculty of imagination is identical with that of sense-perception, though the being of a faculty of imagination is different from that of a faculty of sense-perception; and since imagination is the movement set up by a sensory faculty when actually discharging its function, while a dream appears to be an image (for which occurs in sleep - whether simply or in some particular way - is what we call a dream): it manifestly follows that dreaming is an activity of the faculty of sense-perception, but belongs to this faculty qua imaginative." (Aristotle, On Dreams, 4th century BC)

"For according to the arguments from the existence of the sciences there will be Forms of all things of which there are sciences, and according to the argument that there is one attribute common to many things there will be Forms even of negations, and according to the argument that there is an object for thought even when the thing has perished, there will be Forms of perishable things; for we can have an image of these." (Aristotle, "Metaphysics", 4th century BC)

"All that is required between cognizer and cognized is a likeness in terms of representation, not a likeness in terms of an agreement in nature. For it's plain that the form of a stone in the soul is of a far higher nature than the form of a stone in matter. But that form, insofar as it represents the stone, is to that extent the principle leading to its cognition." (Thomas Aquinas, "Quaestiones disputatae de veritate", cca. 1256-1259) 

"Imagery is not past but present. It rests with what we call our mental processes to place these images in a temporal order." (George H Mead, 1929)

"It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for, as has been remarked, it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience. Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme - the quantum theory - which seems entirely adequate for the treatment of atomic processes; for visualisation, however, we must content ourselves with two incomplete analogies - the wave picture and the corpuscular picture." (Werner Heisenberg, "On Quantum Physics", 1930)

"The solution of the difficulty is that the two mental pictures which experiment lead us to form - the one of the particles, the other of the waves - are both incomplete and have only the validity of analogies which are accurate only in limiting cases." (Werner Heisenberg,"On Quantum Mechanics", 1930)

Mental Models XLVII (Limitations VI)

"Every presentation of philosophy, whether oral or written, is to be taken and can only be taken in the sense of a means. Every system is only an expression or image of reason, and hence only an object of reason, an object which reason - a living power that procreates itself in new thinking beings - distinguishes from itself and posits as an object of criticism. Every system that is not recognized and appropriated as just a means, limits and warps the mind for it sets up the indirect and formal thought in the place of the direct, original and material thought." (Ludwig A Feuerbach, "Towards a Critique of Hegel's Philosophy", 1839) 

"[…] 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)

"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 model of the natural world we build in our minds by such a process will forever be inadequate, just a little cathedral in the mountains. Still it is better than no model at all." (Timothy Ferris, "The Red Limit: The Search for the Edge of the Universe", 1977)

"A person who thinks by images becomes less and less capable of thinking by reasoning, and vice versa. The intellectual process based on images is contradictory to the intellectual process of reasoning that is related to the word. There are two different ways of dealing with an object. They involve not only different approaches, but even more important, opposing mental attitudes. This is not a matter of complementary processes, such as analysis and synthesis or logic and dialectic. These processes lack any qualitative common denominator." (Jacques Ellul, "The Humiliation of the Word", 1981) 

"Whenever I have talked about mental models, audiences have readily grasped that a layout of concrete objects can be represented by an internal spatial array, that a syllogism can be represented by a model of individuals and identities between them, and that a physical process can be represented by a three-dimensional dynamic model. Many people, however, have been puzzled by the representation of abstract discourse; they cannot understand how terms denoting abstract entities, properties or relations can be similarly encoded, and therefore they argue that these terms can have only 'verbal' or propositional representations." (Philip Johnson-Laird,"Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness", 1983)

"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) 

"Faced with the overwhelming complexity of the real world, time pressure, and limited cognitive capabilities, we are forced to fall back on rote procedures, habits, rules of thumb, and simple mental models to make decisions. Though we sometimes strive to make the best decisions we can, bounded rationality means we often systematically fall short, limiting our ability to learn from experience." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The robustness of the misperceptions of feedback and the poor performance they cause are due to two basic and related deficiencies in our mental model. First, our cognitive maps of the causal structure of systems are vastly simplified compared to the complexity of the systems themselves. Second, we are unable to infer correctly the dynamics of all but the simplest causal maps. Both are direct consequences of bounded rationality, that is, the many limitations of attention, memory, recall, information processing capability, and time that constrain human decision making." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"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)

Collective Intelligence IV (Swarm Behavior)

"The best and noblest bees are generated and bred out of the Lion, and the Kings and Princes of them do derive their pedigree and descent from the brain of the Lion, being the most excellent part of his body: it is no wonder therefore if they proceeding and coming from so generous a flock, do assail the greatest beasts, and being endures with Lion-like courage, do fear nothing." (Thomas Moffett, "Theatre of Insects", 1634)

"[….] 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)

"Hence, following the comparison to a bee swarm, it is a whole stuck to a tree branch, by means of the action of many bees which must act in concert to hold on; some others become attached to the initial ones, and so on; all concur in forming a fairly solid body, yet each one has a particular action, apart from the others; if one of them gives way or acts too vigorously, the entire mass will be disturbed: when they all conspire to stick close, to mutually embrace, in the order of required proportions, they will comprise a whole which shall endure until they disturb one another." (Théophile de Bordeu," Recherches anatomiques sur la position des glandes et sur leur action", 1751)

"One could, following these authors, compare man to a flock of cranes which fly together, in a particular order, without mutually assisting or depending on one another. The Physicians or Philosophers who have studied and carefully observed man, have noticed this sympathy in all animal movements – this constant and necessary agreement in the interaction of the various parts, however disparate or distant from one another; they have also noticed the disturbance of the whole that results from the sensory disagreement of a single part. A famous physician [M. de Bordeu] and an illustrious physicist [M. de Maupertuis] likewise compared man, from this luminous and philosophical point of view, to a swarm of bees which strive together to hang to a tree branch. One can see them pressing and sustaining one another, forming a kind of whole, in which each living part contributes in its way, by the correspondence and direction of its movements, to sustain this kind of life of the whole body, if we may refer in this way to a mere connection of actions." (Ménuret de Chambaud, "Observation", Encyclopédie XI [by Diderot 318b-319a], cca. 1751 and 1772)

"Have you ever seen a swarm of bees leaving their hive? [...] The world, or the general mass of matter, is the great hive [...]. Have you seen them fly away and form a long cluster of little winged animals, hanging off the end of the branch of a tree, all clinging on to each other by their feet? [...] This cluster is a being, an individual, some sort of animal [...]. If one of these bees decides to pinch somehow the bee it is clinging onto, do you know what will happen? […] this one will pinch the next one; [...] as many pinching sensations will arise throughout the cluster as there are little animals in it; […] the whole cluster will stir, move and change position and shape […] someone who’d never seen the formation of a cluster like that would be tempted to think it was a single animal with five or six hundred heads and a thousand or twelve hundred wings [...]" (Denis Diderot," Rêve de D’Alembert", 1769)

"Ants exhibit a 'neuron-like' behavior insofar as inactive ants have a low propensity to become spontaneously active, but can become excited by other ants with whom they come into contact. [...] Conversely, ants are prone to lapse back into inactivity if their activation is not sufficiently reinforced, and even exhibit a short refractory period (similar to neurons) before they can be reactivated – a mechanism which keeps the swarm from getting permanently 'locked' into an excitatory state." (Georg Theiner & John Sutton, "The collaborative emergence of group cognition", 2014) 

Collective Intelligence IV - Swarm Intelligence

"At the other far extreme, we find many systems ordered as a patchwork of parallel operations, very much as in the neural network of a brain or in a colony of ants. Action in these systems proceeds in a messy cascade of interdependent events. Instead of the discrete ticks of cause and effect that run a clock, a thousand clock springs try to simultaneously run a parallel system. Since there is no chain of command, the particular action of any single spring diffuses into the whole, making it easier for the sum of the whole to overwhelm the parts of the whole. What emerges from the collective is not a series of critical individual actions but a multitude of simultaneous actions whose collective pattern is far more important. This is the swarm model." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"It is the great irony of life that a mindless act repeated in sequence can only lead to greater depths of absurdity, while a mindless act performed in parallel by a swarm of individuals can, under the proper conditions, lead to all that we find interesting." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995) 

"Just what valuable insights do ants, bees, and other social insects hold? Consider termites. Individually, they have meager intelligence. And they work with no supervision. Yet collectively they build mounds that are engineering marvels, able to maintain ambient temperature and comfortable levels of oxygen and carbon dioxide even as the nest grows. Indeed, for social insects teamwork is largely self-organized, coordinated primarily through the interactions of individual colony members. Together they can solve difficult problems (like choosing the shortest route to a food source from myriad possible pathways) even though each interaction might be very simple (one ant merely following the trail left by another). The collective behavior that emerges from a group of social insects has been dubbed 'swarm intelligence'." (Eric Bonabeau & Christopher Meyer, Swarm Intelligence: A Whole New Way to Think About Business, Harvard Business Review,2001)

"Through self-organization, the behavior of the group emerges from the collective interactions of all the individuals. In fact, a major recurring theme in swarm intelligence (and of complexity science in general) is that even if individuals follow simple rules, the resulting group behavior can be surprisingly complex - and remarkably effective. And, to a large extent, flexibility and robustness result from self-organization." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"[…] swarm intelligence is becoming a valuable tool for optimizing the operations of various businesses. Whether similar gains will be made in helping companies better organize themselves and develop more effective strategies remains to be seen. At the very least, though, the field provides a fresh new framework for solving such problems, and it questions the wisdom of certain assumptions regarding the need for employee supervision through command-and-control management. In the future, some companies could build their entire businesses from the ground up using the principles of swarm intelligence, integrating the approach throughout their operations, organization, and strategy. The result: the ultimate self-organizing enterprise that could adapt quickly - and instinctively - to fast-changing markets." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"Swarm intelligence is sometimes also referred to as mob intelligence. Swarm intelligence uses large groups of agents to solve complicated problems. Swarm intelligence uses a combination of accumulation, teamwork, and voting to produce solutions. Accumulation occurs when agents contribute parts of a solution to a group. Teamwork occurs when different agents or subgroups of agents accidentally or purposefully work on different parts of a large problem. Voting occurs when agents propose solutions or components of solutions and the other agents vote explicitly by rating the proposal’s quality or vote implicitly by choosing whether to follow the proposal." (Michael J North & Charles M Macal, "Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation", 2007)

"Swarm intelligence illustrates the complex and holistic way in which the world operates. Order is created from chaos; patterns are revealed; and systems are free to work out their errors and problems at their own level. What natural systems can teach humanity is truly amazing." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"These nature-inspired algorithms gradually became more and more attractive and popular among the evolutionary computation research community, and together they were named swarm intelligence, which became the little brother of the major four evolutionary computation algorithms." (Yuhui Shi, "Emerging Research on Swarm Intelligence and Algorithm Optimization", Information Science Reference, 2014)

"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)

"The most amazing thing about social insect colonies is that there's no individual in charge. If you look at a single ant, you may have the impression that it is behaving, if not randomly, at least not in synchrony with the rest of the colony. You feel that it is doing its own things without paying too much attention to what the others are doing." (Eric Bonabeau)

Collective Intelligence III - Swarm Intelligence

"Dumb parts, properly connected into a swarm, yield smart results." (Kevin Kelly, "New Rules for the New Economy", 1999) 

"It is, however, fair to say that very few applications of swarm intelligence have been developed. One of the main reasons for this relative lack of success resides in the fact that swarm-intelligent systems are hard to 'program', because the paths to problem solving are not predefined but emergent in these systems and result from interactions among individuals and between individuals and their environment as much as from the behaviors of the individuals themselves. Therefore, using a swarm-intelligent system to solve a problem requires a thorough knowledge not only of what individual behaviors must be implemented but also of what interactions are needed to produce such or such global behavior." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)

"[…] when software systems become so intractable that they can no longer be controlled, swarm intelligence offers an alternative way of designing an ‘intelligent’ systems, in which autonomy, emergence, and distributed functioning replace control, preprogramming, and centralization." (Eric Bonabeau et al, "Swarm Intelligence: From Natural to Artificial Systems", 1999)

"Agent subroutines may pass information back and forth, but subroutines are not changed as a result of the interaction, as people are. In real social interaction, information is exchanged, but also something else, perhaps more important: individuals exchange rules, tips, beliefs about how to process the information. Thus a social interaction typically results in a change in the thinking processes - not just the contents - of the participants." (James F Kennedy et al, "Swarm Intelligence", 2001)

"Swarm Intelligence can be defined more precisely as: Any attempt to design algorithms or distributed problem-solving methods inspired by the collective behavior of the social insect colonies or other animal societies. The main properties of such systems are flexibility, robustness, decentralization and self-organization." ("Swarm Intelligence in Data Mining", Ed. Ajith Abraham et al, 2006)

"Many ants, all obeying simple rules, create the order that we see in an ant colony. This is an example of what has come to be known as swarm intelligence: behaviour or design that emerges out of simple responses by many individuals. Understanding how this happens is important in designing systems of components that have to coordinate their behaviour to achieve a desired result. Knowledge of the way order emerges in an ant colony, for instance, has been applied to create the so-called ant sort algorithm, which is used in contexts where items need to be sorted constantly, without any knowledge of the overall best plan." (David G Green, "The Serendipity Machine: A voyage of discovery through the unexpected world of computers", 2004)

"The most familiar example of swarm intelligence is the human brain. Memory, perception and thought all arise out of the nett actions of billions of individual neurons. As we saw earlier, artificial neural networks (ANNs) try to mimic this idea. Signals from the outside world enter via an input layer of neurons. These pass the signal through a series of hidden layers, until the result emerges from an output layer. Each neuron modifies the signal in some simple way. It might, for instance, convert the inputs by plugging them into a polynomial, or some other simple function. Also, the network can learn by modifying the strength of the connections between neurons in different layers." (David G Green, "The Serendipity Machine: A voyage of discovery through the unexpected world of computers", 2004)

"It is not only a metaphor to transform the Internet to a superbrain with self-organizing features of learning and adapting. Information retrieval is already realized by neural networks adapting to the information preferences of a human user with synaptic plasticity. In sociobiology, we can 1 earn from populations of ants and termites how to organize traffic and information processing by swarm intelligence. From a technical point of view, we need intelligent programs distributed in the nets. There are already more or less intelligent virtual organisms {'agents'), learning, self-organizing and adapting to our individual preferences of information, to select our e-mails, to prepare economic transactions or to defend the attacks of hostile computer viruses, like the immune system of our body." (Klaus Mainzer, "Complexity Management in the Age of Globalization", 2006)

"How is it that an ant colony can organize itself to carry out the complex tasks of food gathering and nest building and at the same time exhibit an enormous degree of resilience if disrupted and forced to adapt to changing situations? Natural systems are able not only to survive, but also to adapt and become better suited to their environment, in effect optimizing their behavior over time. They seemingly exhibit collective intelligence, or swarm intelligence as it is called, even without the existence of or the direction provided by a central authority." (Michael J North & Charles M Macal, "Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation", 2007)

"Swarm intelligence can be effective when applied to highly complicated problems with many nonlinear factors, although it is often less effective than the genetic algorithm approach discussed later in this chapter. Swarm intelligence is related to swarm optimization […]. As with swarm intelligence, there is some evidence that at least some of the time swarm optimization can produce solutions that are more robust than genetic algorithms. Robustness here is defined as a solution’s resistance to performance degradation when the underlying variables are changed. (Michael J North & Charles M Macal, Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation, 2007)

Collective Intelligence II

"Civilization is to groups what intelligence is to individuals. It is a means of combining the intelligence of many to achieve ongoing group adaptation. […] Civilization, like intelligence, may serve well, serve adequately, or fail to serve its adaptive function. When civilization fails to serve, it must disintegrate unless it is acted upon by unifying internal or external forces." (Octavia E Butler, "Parable of the Sower", 1993)

"Great leaders reinforce the idea that accomplishment in our society comes from great individual acts. We credit individuals for outcomes that required teams and communities to accomplish." (Peter Block, "Stewardship", 1993)

"We must learn to think together in an integrated, synergistic fashion, rather than in fragmented and competitive ways." (Joanna Macy, Noetic Sciences Bulletin, 1994-1995)

"The leading edge of growth of intelligence is at the cultural and societal level. It is like a mind that is struggling to wake up. This is necessary because the most difficult problems we face are now collective ones. They are caused by complex global interactions and are beyond the scope of individuals to understand and solve. Individual mind, with its isolated viewpoints and narrow interests, is no longer enough." (Jeff Wright, "Basic Beliefs", [email] 1995)

"It [collective intelligence] is a form of universally distributed intelligence, constantly enhanced, coordinated in real time, and resulting in the effective mobilization of skills. I'll add the following indispensable characteristic to this definition: The basis and goal of collective intelligence is mutual recognition and enrichment of individuals rather than the cult of fetishized or hypostatized communities." (Pierre Levy, "Collective Intelligence", 1999)

The three basic mechanisms of averaging, feedback and division of labor give us a first idea of a how a CMM [Collective Mental Map] can be developed in the most efficient way, that is, how a given number of individuals can achieve a maximum of collective problem-solving competence. A collective mental map is developed basically by superposing a number of individual mental maps. There must be sufficient diversity among these individual maps to cover an as large as possible domain, yet sufficient redundancy so that the overlap between maps is large enough to make the resulting graph fully connected, and so that each preference in the map is the superposition of a number of individual preferences that is large enough to cancel out individual fluctuations. The best way to quickly expand and improve the map and fill in gaps is to use a positive feedback that encourages individuals to use high preference paths discovered by others, yet is not so strong that it discourages the exploration of new paths." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"With the growing interest in complex adaptive systems, artificial life, swarms and simulated societies, the concept of “collective intelligence” is coming more and more to the fore. The basic idea is that a group of individuals (e. g. people, insects, robots, or software agents) can be smart in a way that none of its members is. Complex, apparently intelligent behavior may emerge from the synergy created by simple interactions between individuals that follow simple rules." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

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

"[…] recent researchers in artificial intelligence and computational methods use the term swarm intelligence to name collective and distributed techniques of problem solving without centralized control or provision of a global model. […] the intelligence of the swarm is based fundamentally on communication. […] the member of the multitude do not have to become the same or renounce their creativity in order to communicate and cooperate with each other. They remain different in terms of race, sex, sexuality and so forth. We need to understand, then, is the collective intelligence that can emerge from the communication and cooperation of such varied multiplicity." (Antonio Negri, "Multitude: War and Democracy in the Age of Empire", 2004)

"Collective Intelligence (CI) is the capacity of human collectives to engage in intellectual cooperation in order to create, innovate, and invent." (Pierre Levy, "Toward a Self-referential Collective Intelligence", 2009)

Collective Intelligence I

"We must therefore establish a form of decision-making in which voters need only ever pronounce on simple propositions, expressing their opinions only with a yes or a no. […] Clearly, if anyone’s vote was self-contradictory (intransitive), it would have to be discounted, and we should therefore establish a form of voting which makes such absurdities impossible." (Nicolas de Condorcet, "On the form of decisions made by plurality vote", 1788)

"Collective wisdom, alas, is no adequate substitute for the intelligence of individuals. Individuals who opposed received opinions have been the source of all progress, both moral and intellectual. They have been unpopular, as was natural." (Bertrand Russell, "Why I Am Not a Christian", 1927)

"The collective intelligence of any group of people who are thinking as a 'herd' rather than individually is no higher than the intelligence of the stupidest members. (Mary Day Winn, Adam's Rib, 1931)

"Learning is a property of all living organisms. […] Since organized groups can be looked upon as living entities, they can be expected to exhibit learning […]" (Winfred B. Hirschmann, "Profit from the Learning Curve", Harvard Business Review, 1964)

"A cardinal principle in systems theory is that all parties that have a stake in a system should be represented in its management." (Malcolm S Knowles, "The Adult Learner", 1973)

"Collective intelligence emerges when a group of people work together effectively. Collective intelligence can be additive (each adds his or her part which together form the whole) or it can be synergetic, where the whole is greater than the sum of its parts." (Trudy and Peter Johnson-Lenz, "Groupware: Orchestrating the Emergence of Collective Intelligence", cca. 1980)

"Cybernetic information theory suggests the possibility of assuming that intelligence is a feature of any feedback system that manifests a capacity for learning." (Paul Hawken et al, "Seven Tomorrows", 1982)

"The concept of organizational learning refers to the capacity of organizational complexes to develop experiential knowledge, instincts, and 'feel' or intuition which are greater than the combined knowledge, skills and instincts of the individuals involved." (Don E. Kash, "Perpetual Innovation", 1989)

"We haven't worked on ways to develop a higher social intelligence […] We need this higher intelligence to operate socially or we're not going to survive. […] If we don't manage things socially, individual high intelligence is not going to make much difference. [...] Ordinary thought in society is incoherent - it is going in all sorts of directions, with thoughts conflicting and canceling each other out. But if people were to think together in a coherent way, it would have tremendous power." (David Bohm, "New Age Journal", 1989)

Maurits C Escher - Collected Quotes

"The result of the struggle between the thought and the ability to express it, between dream and reality, is seldom more than a compromise or an approximation." (Maurits C. Escher, "On Being a Graphic Artist", 1953)

"In mathematical quarters, the regular division of the plane has been considered theoretically […] Does this mean that it is an exclusively mathematical question? In my opinion, it does not. [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it." (Maurits C Escher, 1957)

"In geometry, topology is the study of properties of shapes that are independent of size or shape and are not changed by stretching, bending, knotting, or twisting." (Maurits C Escher, 1971)

"The ideas that are basic to [my work] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us. He who wonders discovers that this is in itself a wonder. By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics." (Maurits C Escher, "The Graphic Work", 1978)

"Science and art sometimes can touch one another, like two pieces of the jigsaw puzzle which is our human life, and that contact may be made across the borderline between the two respective domains." (Maurits C Escher)

"The laws of mathematics are not merely human inventions or creations. They simply ‘are’ they exist quite independently of the human intellect. The most that any man with a keen intellect can do is to find out that they are there and to take cognizance of them." (Maurits C Escher)

Jacques Bertin - Collected Quotes

"A graphic should not only show the leaves, it should show the branches as well as the entire tree." (Jacques Bertin, "The Semiology of Graphics", 1967)

"Graphic representation constitutes one of the basic sign-systems conceived by the human mind for the purposes of storing, understanding, and communicating essential information. As a "language" for the eye, graphics benefits from the ubiquitous properties of visual perception. As a monosemic system, it forms the rational part of the world of images. […] Graphics owes its special significance to its double function as a storage mechanism and a research instrument."  (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"The aim of the graphic is to make the relationship among previously defined sets appear." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"The great difference between the graphic representation of yesterday, which was poorly dissociated from the figurative image, and the graphics of tomorrow, is the disappearance of the congential fixity of the image. […] When one can superimpose, juxtapose, transpose, and permute graphic images in ways that lead to groupings and classings, the graphic image passes from the dead image, the 'illustration,' to the living image, the widely accessible research instrument it is now becoming. The graphic is no longer only the 'representation' of a final simplification, it is a point of departure for the discovery of these simplifications and the means for their justification. The graphic has become, by its manageability, an instrument for information processing." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"The plane is the mainstay of all graphic representation. It is so familiar that its properties seem self-evident, but the most familiar things are often the most poorly understood. The plane is homogeneous and has two dimensions. The visual consequences of these properties must be fully explored." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"The problem that still remains to be solved is that of the orderable matrix, that needs the use of imagination […] When the two components of a data table are orderable, the normal construction is the orderable matrix. Its permutations show the analogy and the complementary nature that exist between the algorithmic treatments and the graphical treatments." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"There are as many types of questions as components in the information." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography." (Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)

"As with any graphic, networks are used in order to discover pertinent troups of to inform others of the groups and structures dis(Jacques Bertin, "The Semiology of graphics" ["Semiologie Graphique"], 1967)overed. 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)

"Computers are able to multiply useless images without taking into account that, by definition, every graphic corresponds to a table. This table allows you to think about three basic questions that go from the particular to the general level. When this last one receives an answer, you have answers for all of them. Understanding means accessing the general level and discovering significant grouping (patterns). Consequently, the function of a graphic is answering the three following questions:

Which are the X,Y, Z components of the data table? (What it’s all about?)

What are the groups in X, in Y that Z builds? (What the information at the general level is?

What are the exceptions?

These questions can be applied to every kind of problem. They measure the usefulness of whatever construction or graphical invention allowing you to avoid useless graphics." (Jacques Bertin, [interview] 2003)

"Data is transformed into graphics to understand. A map, a diagram are documents to be interrogated. But understanding means integrating all of the data. In order to do this it’s necessary to reduce it to a small number of elementary data. This is the objective of the 'data treatment' be it graphic or mathematic." (Jacques Bertin, [interview] 2003)

"The use of computers shouldn't ignore the objectives of graphics, that are: (1) Treating data to get information. (2) Communicating, when necessary, the information obtained." (Jacques Bertin, [interview] 2003)

"Graphics is the visual means of resolving logical problems." (Jacques Bertin, "Graphics and Graphic Information Processing", 2011)