🧭🚥Business Intelligence: Key Performance Indicators [KPI] (Between Certainty and Uncertainty)

Business Intelligence Series

Despite the huge collection of documented Key Performance Indicators (KPIs) and best practices on which KPIs to choose, choosing a reliable set of KPIs that reflect how the organization performs in achieving its objectives continues to be a challenge for many organizations. Ideally, for each objective there should be only one KPIs that reflects the target and the progress made, though is that realistic?

Let's try to use the driver's metaphor to exemplify several aspects related to the choice of KPIs. A driver's goal is to travel from point A to point B over a distance d in x hours. The goal is SMART (Specific, Measurable, Achievable, Relevant, and Time-bound) if the speed and time are realistic and don't contradict Physics, legal or physical laws. The driver can define the objective as "arriving on time to the destination". 

One can define a set of metrics based on the numbers that can be measured. We have the overall distance and the number of hours planned, from which one can derive an expected average speed v. To track a driver's progress over time there are several metrics that can be thus used: e.g., (1) the current average speed, (2) the number of kilometers to the destination, (3) the number of hours estimated to the destination. However, none of these metrics can be used alone to denote the performance alone. One can compare the expected with the current average speed to get a grasp of the performance, and probably many organizations will use only (1) as KPI, though it's needed to use either (2) or (3) to get the complete picture. So, in theory two KPIs should be enough. Is it so?

When estimating (3) one assumes that there are no impediments and that the average speed can be attained, which might be correct for a road without traffic. There can be several impediments - planned/unplanned breaks, traffic jams, speed limits, accidents or other unexpected events, weather conditions (that depend on the season), etc. Besides the above formula, one needs to quantify such events in one form or another, e.g., through the perspective of the time added to the initial estimation from (3). However, this calculation is based on historical values or navigator's estimation, value which can be higher or lower than the final value. 

Therefore, (3) is an approximation for which is needed also a confidence interval (± t hours). The value can still include a lot of uncertainty that maybe needs to be broken down and quantified separately upon case to identify the deviation from expectations, e.g. on average there are 3 traffic jams (4), if the road crosses states or countries there may be at least 1 control on average (5), etc. These numbers can be included in (3) and the confidence interval, and usually don't need to be reported separately, though probably there are exceptions. 

When planning, one needs to also consider the number of stops for refueling or recharging the car, and the average duration of such stops, which can be included in (3) as well. However, (3) slowly becomes  too complex a formula, and even if there's an estimation, the more facts we're pulling into it, the bigger the confidence interval's variation will be. Sometimes, it's preferable to have instead two-three other metrics with a low confidence interval than one with high variation. Moreover, the longer the distance planned, the higher the uncertainty. One thing is to plan a trip between two neighboring city, and another thing is to plan a trip around the world. 

Another assumption is that the capability of the driver/car to drive is the same over time, which is not always the case. This can be neglected occasionally (e.g. one trip), though it involves a risk (6) that might be useful to quantify, especially when the process is repeatable (e.g. regular commuting). The risk value can increase considering new information, e.g. knowing that every a few thousand kilometers something breaks, or that there's a traffic fine, or an accident. In spite of new information, the objective might also change. Also, the objective might suffer changes, e.g. arrive on-time safe and without fines to the destination. As the objective changes or further objectives are added, more metrics can be defined. It would make sense to measure how many kilometers the driver covered in a lifetime with the car (7), how many accidents (8) or how many fines (9) the driver had. (7) is not related to a driver's performance, but (8) and (9) are. 

As can be seen, simple processes can also become very complex if one attempts to consider all the facts and/or quantify the uncertainty. The driver's metaphor applies to a simple individual, though once the same process is considered across the whole organization (a group of drivers), the more complexity is added and the perspective changes completely. E.g., some drivers might not even reach the destination or not even have a car to start with, and so on. Of course, with this also the objectives change and need to be redefined accordingly. 

The driver's metaphor is good for considering planning activities in which a volume of work needs to be completed in a given time and where a set of constraints apply. Therefore, for some organizations, just using two numbers might be enough for getting a feeling for what's happening. However, as soon one needs to consider other aspects like safety or compliance (considered in aggregation across many drivers), there might be other metrics that qualify as KPIs.

It's tempting to add two numbers and consider for example (8) and (9) together as the two are events that can be cumulated, even if they refer to different things that can overlap (an accident can result in a fine and should be counted maybe only once). One needs to make sure that one doesn't add apples with juice - the quantified values must have the same unit of measure, otherwise they might need to be considered separately. There's the tendency of mixing multiple metrics in a KPI that doesn't say much if the units of measure of its components are not the same. Some conversions can still be made (e.g. how much juice can be obtained from apples), though that's seldom the case.

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🔭Data Science: Method (Just the Quotes)

"There are two aspects of statistics that are continually mixed, the method and the science. Statistics are used as a method, whenever we measure something, for example, the size of a district, the number of inhabitants of a country, the quantity or price of certain commodities, etc. […] There is, moreover, a science of statistics. It consists of knowing how to gather numbers, combine them and calculate them, in the best way to lead to certain results. But this is, strictly speaking, a branch of mathematics." (Alphonse P de Candolle, "Considerations on Crime Statistics", 1833)

"The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

"As systematic unity is what first raises ordinary knowledge to the rank of science, that is, makes a system out of a mere aggregate of knowledge, architectonic is the doctrine of the scientific in our knowledge, and therefore necessarily forms part of the doctrine of method." (Immanuel Kant, "Critique of Pure Reason", 1871)

"Nothing is more certain in scientific method than that approximate coincidence alone can be expected. In the measurement of continuous quantity perfect correspondence must be accidental, and should give rise to suspicion rather than to satisfaction." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"The object of statistical science is to discover methods of condensing information concerning large groups of allied facts into brief and compendious expressions suitable for discussion. The possibility of doing this is based on the constancy and continuity with which objects of the same species are found to vary." (Sir Francis Galton, "Inquiries into Human Faculty and Its Development, Statistical Methods", 1883)

"Physical research by experimental methods is both a broadening and a narrowing field. There are many gaps yet to be filled, data to be accumulated, measurements to be made with great precision, but the limits within which we must work are becoming, at the same time, more and more defined." (Elihu Thomson, "Annual Report of the Board of Regents of the Smithsonian Institution", 1899)

"A statistical estimate may be good or bad, accurate or the reverse; but in almost all cases it is likely to be more accurate than a casual observer’s impression, and the nature of things can only be disproved by statistical methods." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"A method is a dangerous thing unless its underlying philosophy is understood, and none more dangerous than the statistical. […] Over-attention to technique may actually blind one to the dangers that lurk about on every side- like the gambler who ruins himself with his system carefully elaborated to beat the game. In the long run it is only clear thinking, experienced methods, that win the strongholds of science." (Edwin B Wilson, "The Statistical Significance of Experimental Data", Science, Volume 58 (1493), 1923)

"[…] the methods of statistics are so variable and uncertain, so apt to be influenced by circumstances, that it is never possible to be sure that one is operating with figures of equal weight." (Havelock Ellis, "The Dance of Life", 1923)

"Statistics may be regarded as (i) the study of populations, (ii) as the study of variation, and (iii) as the study of methods of the reduction of data." (Sir Ronald A Fisher, "Statistical Methods for Research Worker", 1925)

"Science is but a method. Whatever its material, an observation accurately made and free of compromise to bias and desire, and undeterred by consequence, is science." (Hans Zinsser, "Untheological Reflections", The Atlantic Monthly, 1929)

"The most important application of the theory of probability is to what we may call 'chance-like' or 'random' events, or occurrences. These seem to be characterized by a peculiar kind of incalculability which makes one disposed to believe - after many unsuccessful attempts - that all known rational methods of prediction must fail in their case. We have, as it were, the feeling that not a scientist but only a prophet could predict them. And yet, it is just this incalculability that makes us conclude that the calculus of probability can be applied to these events." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"The fundamental difference between engineering with and without statistics boils down to the difference between the use of a scientific method based upon the concept of laws of nature that do not allow for chance or uncertainty and a scientific method based upon the concepts of laws of probability as an attribute of nature." (Walter A Shewhart, 1940)

"[Statistics] is both a science and an art. It is a science in that its methods are basically systematic and have general application; and an art in that their successful application depends to a considerable degree on the skill and special experience of the statistician, and on his knowledge of the field of application, e.g. economics." (Leonard H C Tippett, "Statistics", 1943)

"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition 'natural phenomena' includes all the happenings of the external world, whether human or not " (Sir Maurice G Kendall, "Advanced Theory of Statistics", Vol. 1, 1943)

"We can scarcely imagine a problem absolutely new, unlike and unrelated to any formerly solved problem; but if such a problem could exist, it would be insoluble. In fact, when solving a problem, we should always profit from previously solved problems, using their result or their method, or the experience acquired in solving them." (George Polya, 1945)

"The enthusiastic use of statistics to prove one side of a case is not open to criticism providing the work is honestly and accurately done, and providing the conclusions are not broader than indicated by the data. This type of work must not be confused with the unfair and dishonest use of both accurate and inaccurate data, which too commonly occurs in business. Dishonest statistical work usually takes the form of: (1) deliberate misinterpretation of data; (2) intentional making of overestimates or underestimates; and (3) biasing results by using partial data, making biased surveys, or using wrong statistical methods." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1951)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"The methods of science may be described as the discovery of laws, the explanation of laws by theories, and the testing of theories by new observations. A good analogy is that of the jigsaw puzzle, for which the laws are the individual pieces, the theories local patterns suggested by a few pieces, and the tests the completion of these patterns with pieces previously unconsidered." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)

"We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning." (Werner K Heisenberg, "Physics and Philosophy: The revolution in modern science", 1958)

"We are committed to the scientific method, and measurement is the foundation of that method; hence we are prone to assume that whatever is measurable must be significant and that whatever cannot be measured may as well be disregarded." (Joseph W Krutch, "Human Nature and the Human Condition", 1959)

"Scientific method is the way to truth, but it affords, even in principle, no unique definition of truth. Any so-called pragmatic definition of truth is doomed to failure equally." (Willard v O Quine, "Word and Object", 1960)

"Observation, reason, and experiment make up what we call the scientific method." (Richard Feynman, "Mainly mechanics, radiation, and heat", 1963)

"Engineering is the art of skillful approximation; the practice of gamesmanship in the highest form. In the end it is a method broad enough to tame the unknown, a means of combing disciplined judgment with intuition, courage with responsibility, and scientific competence within the practical aspects of time, of cost, and of talent." (Ronald B Smith, "Professional Responsibility of Engineering", Mechanical Engineering Vol. 86 (1), 1964)

"Statistics is a body of methods and theory applied to numerical evidence in making decisions in the face of uncertainty." (Lawrence Lapin, "Statistics for Modern Business Decisions", 1973)

"Statistical methods of analysis are intended to aid the interpretation of data that are subject to appreciable haphazard variability." (David V. Hinkley & David Cox, "Theoretical Statistics", 1974)

"Scientists use mathematics to build mental universes. They write down mathematical descriptions - models - that capture essential fragments of how they think the world behaves. Then they analyse their consequences. This is called 'theory'. They test their theories against observations: this is called 'experiment'. Depending on the result, they may modify the mathematical model and repeat the cycle until theory and experiment agree. Not that it's really that simple; but that's the general gist of it, the essence of the scientific method." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"But our ways of learning about the world are strongly influenced by the social preconceptions and biased modes of thinking that each scientist must apply to any problem. The stereotype of a fully rational and objective ‘scientific method’, with individual scientists as logical (and interchangeable) robots, is self-serving mythology." (Stephen J Gould, "This View of Life: In the Mind of the Beholder", Natural History Vol. 103, No. 2, 1994)

"The methods of science include controlled experiments, classification, pattern recognition, analysis, and deduction. In the humanities we apply analogy, metaphor, criticism, and (e)valuation. In design we devise alternatives, form patterns, synthesize, use conjecture, and model solutions." (Béla H Bánáthy, "Designing Social Systems in a Changing World", 1996) 

"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 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)

"Scientists pursue ideas in an ill-defined but effective way that is often called the scientific method. There is no strict rule of procedure that will lead you from a good idea to a Nobel prize or even to a publishable discovery. Some scientists are meticulously careful; others are highly creative. The best scientists are probably both careful and creative. Although there are various scientific methods in use, a typical approach consists of a series of steps." (Peter Atkins et al, "Chemical Principles: The Quest for Insight" 6th ed., 2013)

"Science, at its core, is simply a method of practical logic that tests hypotheses against experience. Scientism, by contrast, is the worldview and value system that insists that the questions the scientific method can answer are the most important questions human beings can ask, and that the picture of the world yielded by science is a better approximation to reality than any other." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

"The general principles of starting with a well-defined question, engaging in careful observation, and then formulating hypotheses and assessing the strength of evidence for and against them became known as the scientific method." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

🔭Data Science: Laws (Just the Quotes)

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

"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)

"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

"But law is no explanation of anything; law is simply a generalization, a category of facts. Law is neither a cause, nor a reason, nor a power, nor a coercive force. It is nothing but a general formula, a statistical table." (Florence Nightingale, "Suggestions for Thought", 1860)

"The process of discovery is very simple. An unwearied and systematic application of known laws to nature, causes the unknown to reveal themselves. Almost any mode of observation will be successful at last, for what is most wanted is method." (Henry D Thoreau, "A Week on the Concord and Merrimack Rivers", 1862)

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

"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)

"The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe." (Sir James G Frazer, "The Golden Bough: A Study in Magic and Religion", 1890)

"Even one well-made observation will be enough in many cases, just as one well-constructed experiment often suffices for the establishment of a law." (Émile Durkheim, "The Rules of Sociological Method", "The Rules of Sociological Method", 1895)

"An experiment is an observation that can be repeated, isolated and varied. The more frequently you can repeat an observation, the more likely are you to see clearly what is there and to describe accurately what you have seen. The more strictly you can isolate an observation, the easier does your task of observation become, and the less danger is there of your being led astray by irrelevant circumstances, or of placing emphasis on the wrong point. The more widely you can vary an observation, the more clearly will be the uniformity of experience stand out, and the better is your chance of discovering laws." (Edward B Titchener, "A Text-Book of Psychology", 1909)

"It is well to notice in this connection [the mutual relations between the results of counting and measuring] that a natural law, in the statement of which measurable magnitudes occur, can only be understood to hold in nature with a certain degree of approximation; indeed natural laws as a rule are not proof against sufficient refinement of the measuring tools." (Luitzen E J Brouwer, "Intuitionism and Formalism", Bulletin of the American Mathematical Society, Vol. 20, 1913)

"[…] as the sciences have developed further, the notion has gained ground that most, perhaps all, of our laws are only approximations." (William James, "Pragmatism: A New Name for Some Old Ways of Thinking", 1914)

"Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages." (Bertrand A Russell, "The Analysis of Matter", 1927)

"Science is the attempt to discover, by means of observation, and reasoning based upon it, first, particular facts about the world, and then laws connecting facts with one another and (in fortunate cases) making it possible to predict future occurrences." (Bertrand Russell, "Religion and Science, Grounds of Conflict", 1935)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"The world is not made up of empirical facts with the addition of the laws of nature: what we call the laws of nature are conceptual devices by which we organize our empirical knowledge and predict the future." (Richard B Braithwaite, "Scientific Explanation", 1953)

"The methods of science may be described as the discovery of laws, the explanation of laws by theories, and the testing of theories by new observations. A good analogy is that of the jigsaw puzzle, for which the laws are the individual pieces, the theories local patterns suggested by a few pieces, and the tests the completion of these patterns with pieces previously unconsidered." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)

"Can there be laws of chance? The answer, it would seem should be negative, since chance is in fact defined as the characteristic of the phenomena which follow no law, phenomena whose causes are too complex to permit prediction." (Félix E Borel, "Probabilities and Life", 1962)

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." (Richard Feynman, "The Feynman Lectures on Physics" Vol. 1, 1964)

"At each level of complexity, entirely new properties appear. [And] at each stage, entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one." (Herb Anderson, 1972)

"A good scientific law or theory is falsifiable just because it makes definite claims about the world. For the falsificationist, If follows fairly readily from this that the more falsifiable a theory is the better, in some loose sense of more. The more a theory claims, the more potential opportunities there will be for showing that the world does not in fact behave in the way laid down by the theory. A very good theory will be one that makes very wide-ranging claims about the world, and which is consequently highly falsifiable, and is one that resists falsification whenever it is put to the test." (Alan F Chalmers,  "What Is This Thing Called Science?", 1976)

"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicity states or which may be derived from it. [...[] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer Power and Human Reason", 1984)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985)

"A law explains a set of observations; a theory explains a set of laws. […] Unlike laws, theories often postulate unobservable objects as part of their explanatory mechanism." (John L Casti, "Searching for Certainty", 1990)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996) 

"A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

"[...] things that seem hopelessly random and unpredictable when viewed in isolation often turn out to be lawful and predictable when viewed in aggregate." (Steven Strogatz, "The Joy of X: A Guided Tour of Mathematics, from One to Infinity", 2012)

🔭Data Science: Probability (Just the Quotes)

"Probability is a degree of possibility." (Gottfried W Leibniz, "On estimating the uncertain", 1676)

"Probability, however, is not something absolute, [it is] drawn from certain information which, although it does not suffice to resolve the problem, nevertheless ensures that we judge correctly which of the two opposites is the easiest given the conditions known to us." (Gottfried W Leibniz, "Forethoughts for an encyclopaedia or universal science", cca. 1679)

"[…] the highest probability amounts not to certainty, without which there can be no true knowledge." (John Locke, "An Essay Concerning Human Understanding", 1689)

"As mathematical and absolute certainty is seldom to be attained in human affairs, reason and public utility require that judges and all mankind in forming their opinions of the truth of facts should be regulated by the superior number of the probabilities on the one side or the other whether the amount of these probabilities be expressed in words and arguments or by figures and numbers." (William Murray, 1773)

"All certainty which does not consist in mathematical demonstration is nothing more than the highest probability; there is no other historical certainty." (Voltaire, "A Philosophical Dictionary", 1881)

"Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution." (Max Planck, "The Atomic Theory of Matter", 1909)

"Sometimes the probability in favor of a generalization is enormous, but the infinite probability of certainty is never reached." (William Dampier-Whetham, "Science and the Human Mind", 1912)

"There can be no unique probability attached to any event or behaviour: we can only speak of ‘probability in the light of certain given information’, and the probability alters according to the extent of the information." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)

"[…] the statistical prediction of the future from the past cannot be generally valid, because whatever is future to any given past, is in tum past for some future. That is, whoever continually revises his judgment of the probability of a statistical generalization by its successively observed verifications and failures, cannot fail to make more successful predictions than if he should disregard the past in his anticipation of the future. This might be called the ‘Principle of statistical accumulation’." (Clarence I Lewis, "Mind and the World-Order: Outline of a Theory of Knowledge", 1929)

"Science does not aim, primarily, at high probabilities. It aims at a high informative content, well backed by experience. But a hypothesis may be very probable simply because it tells us nothing, or very little." (Karl Popper, "The Logic of Scientific Discovery", 1934)

"The most important application of the theory of probability is to what we may call 'chance-like' or 'random' events, or occurrences. These seem to be characterized by a peculiar kind of incalculability which makes one disposed to believe - after many unsuccessful attempts - that all known rational methods of prediction must fail in their case. We have, as it were, the feeling that not a scientist but only a prophet could predict them. And yet, it is just this incalculability that makes us conclude that the calculus of probability can be applied to these events." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"Equiprobability in the physical world is purely a hypothesis. We may exercise the greatest care and the most accurate of scientific instruments to determine whether or not a penny is symmetrical. Even if we are satisfied that it is, and that our evidence on that point is conclusive, our knowledge, or rather our ignorance, about the vast number of other causes which affect the fall of the penny is so abysmal that the fact of the penny’s symmetry is a mere detail. Thus, the statement 'head and tail are equiprobable' is at best an assumption." (Edward Kasner & James R Newman, "Mathematics and the Imagination", 1940)

"Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation." (Emile Borel, "Probabilities and Life", 1943)

"Just as entropy is a measure of disorganization, the information carried by a set of messages is a measure of organization. In fact, it is possible to interpret the information carried by a message as essentially the negative of its entropy, and the negative logarithm of its probability. That is, the more probable the message, the less information it gives. Clichés, for example, are less illuminating than great poems." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"To say that observations of the past are certain, whereas predictions are merely probable, is not the ultimate answer to the question of induction; it is only a sort of intermediate answer, which is incomplete unless a theory of probability is developed that explains what we should mean by ‘probable’ and on what ground we can assert probabilities." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)

"Uncertainty is introduced, however, by the impossibility of making generalizations, most of the time, which happens to all members of a class. Even scientific truth is a matter of probability and the degree of probability stops somewhere short of certainty." (Wayne C Minnick, "The Art of Persuasion", 1957)

"Everybody has some idea of the meaning of the term 'probability' but there is no agreement among scientists on a precise definition of the term for the purpose of scientific methodology. It is sufficient for our purpose, however, if the concept is interpreted in terms of relative frequency, or more simply, how many times a particular event is likely to occur in a large population." (Alfred R Ilersic, "Statistics", 1959)

"Incomplete knowledge must be considered as perfectly normal in probability theory; we might even say that, if we knew all the circumstances of a phenomenon, there would be no place for probability, and we would know the outcome with certainty." (Félix E Borel, Probability and Certainty", 1963)

"Probability is the mathematics of uncertainty. Not only do we constantly face situations in which there is neither adequate data nor an adequate theory, but many modem theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential. Statistics is the reverse of probability (glibly speaking). In probability you go from the model of the situation to what you expect to see; in statistics you have the observations and you wish to estimate features of the underlying model." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985) 

"Probability plays a central role in many fields, from quantum mechanics to information theory, and even older fields use probability now that the presence of 'noise' is officially admitted. The newer aspects of many fields start with the admission of uncertainty." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"Probabilities are summaries of knowledge that is left behind when information is transferred to a higher level of abstraction." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Network of Plausible, Inference", 1988)

"[In statistics] you have the fact that the concepts are not very clean. The idea of probability, of randomness, is not a clean mathematical idea. You cannot produce random numbers mathematically. They can only be produced by things like tossing dice or spinning a roulette wheel. With a formula, any formula, the number you get would be predictable and therefore not random. So as a statistician you have to rely on some conception of a world where things happen in some way at random, a conception which mathematicians don’t have." (Lucien LeCam, [interview] 1988)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996) 

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"In the laws of probability theory, likelihood distributions are fixed properties of a hypothesis. In the art of rationality, to explain is to anticipate. To anticipate is to explain." (Eliezer S. Yudkowsky, "A Technical Explanation of Technical Explanation", 2005)

"For some scientific data the true value cannot be given by a constant or some straightforward mathematical function but by a probability distribution or an expectation value. Such data are called probabilistic. Even so, their true value does not change with time or place, making them distinctly different from  most statistical data of everyday life." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In fact, H [entropy] measures the amount of uncertainty that exists in the phenomenon. If there were only one event, its probability would be equal to 1, and H would be equal to 0 - that is, there is no uncertainty about what will happen in a phenomenon with a single event because we always know what is going to occur. The more events that a phenomenon possesses, the more uncertainty there is about the state of the phenomenon. In other words, the more entropy, the more information." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"The four questions of data analysis are the questions of description, probability, inference, and homogeneity. [...] 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.  [...] 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)

"Entropy is a measure of amount of uncertainty or disorder present in the system within the possible probability distribution. The entropy and amount of unpredictability are directly proportional to each other." (G Suseela & Y Asnath V Phamila, "Security Framework for Smart Visual Sensor Networks", 2019)

🔭Data Science: Coincidence (Just the Quotes)

"It is no great wonder if in long process of time, while fortune takes her course hither and thither, numerous coincidences should spontaneously occur. If the number and variety of subjects to be wrought upon be infinite, it is all the more easy for fortune, with such an abundance of material, to effect this similarity of results." (Plutarch, Life of Sertorius, 1st century BC)

"Coincidences, in general, are great stumbling blocks in the way of that class of thinkers who have been educated to know nothing of the theory of probabilities - that theory to which the most glorious objects of human research are indebted for the most glorious of illustrations." (Edgar A Poe, "The Murders in the Rue Morgue", 1841)

"Nothing is more certain in scientific method than that approximate coincidence alone can be expected. In the measurement of continuous quantity perfect correspondence must be accidental, and should give rise to suspicion rather than to satisfaction." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"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)

"As science progress, it becomes more and more difficult to fit in the new facts when they will not fit in spontaneously. The older theories depend upon the coincidences of so many numerical results which can not be attributed to chance. We should not separate what has been joined together." (Henri Poincaré, "The Ether and Matter", 1912)

"By the laws of statistics we could probably approximate just how unlikely it is that it would happen. But people forget - especially those who ought to know better, such as yourself - that while the laws of statistics tell you how unlikely a particular coincidence is, they state just as firmly that coincidences do happen." (Robert A Heinlein, "The Door Into Summer", 1957)

"There is no coherent knowledge, i.e. no uniform comprehensive account of the world and the events in it. There is no comprehensive truth that goes beyond an enumeration of details, but there are many pieces of information, obtained in different ways from different sources and collected for the benefit of the curious. The best way of presenting such knowledge is the list - and the oldest scientific works were indeed lists of facts, parts, coincidences, problems in several specialized domains." (Paul K Feyerabend, "Farewell to Reason", 1987)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"The law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen." (Frederick Mosteller, "Methods for Studying Coincidences", Journal of the American Statistical Association Vol. 84, 1989)

"Most coincidences are simply chance events that turn out to be far more probable than many people imagine." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Coincidence surprises us because our intuition about the likelihood of an event is often wildly inaccurate." (Michael Starbird, "Coincidences, Chaos, and All That Math Jazz", 2005)

"With our heads spinning in the world of coincidence and chaos, we nevertheless must make decisions and take steps into the minefield of our future. To avoid explosive missteps, we rely on data and statistical reasoning to inform our thinking." (Michael Starbird, "Coincidences, Chaos, and All That Math Jazz", 2005)

"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)

More quotes on "Coincidence" at the-web-of-knowledge.blogspot.com.

🔭Data Science: Approximation (Just the Quotes)

"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)

"[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature." (Pierre-Simon Laplace, "Mémoire sur les Inégalites Séculaires des Planètes et des Satellites", 1787)

"Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man." (Bertrand Russell, "The Scientific Outlook", 1931)

"We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere. We are encamped in nature, not domesticated." (Ralph W Emerson, "Essays", 1865)

"It is well to notice in this connection [the mutual relations between the results of counting and measuring] that a natural law, in the statement of which measurable magnitudes occur, can only be understood to hold in nature with a certain degree of approximation; indeed natural laws as a rule are not proof against sufficient refinement of the measuring tools." (Luitzen E J Brouwer, "Intuitionism and Formalism", Bulletin of the American Mathematical Society, Vol. 20, 1913)

"[…] as the sciences have developed further, the notion has gained ground that most, perhaps all, of our laws are only approximations." (William James, "Pragmatism: A New Name for Some Old Ways of Thinking", 1914)

"Science does not aim at establishing immutable truths and eternal dogmas; its aim is to approach the truth by successive approximations, without claiming that at any stage final and complete accuracy has been achieved." (Bertrand Russell, "The ABC of Relativity", 1925)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939) 

"The most important maxim for data analysis to heed, and one which many statisticians seem to have shunned is this: ‘Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.’ Data analysis must progress by approximate answers, at best, since its knowledge of what the problem really is will at best be approximate." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33, No. 1, 1962)

"Because engineering is science in action - the practice of decision making at the earliest moment - it has been defined as the art of skillful approximation. No situation in engineering is simple enough to be solved precisely, and none worth evaluating is solved exactly. Never are there sufficient facts, sufficient time, or sufficient money for an exact solution, for if by chance there were, the answer would be of academic and not economic interest to society. These are the circumstances that make engineering so vital and so creative." (Ronald B Smith, "Engineering Is…", Mechanical Engineering Vol. 86 (5), 1964)

"Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected." (Richard Feynman, "The Feynman Lectures on Physics" Vol. 1, 1964)

"Engineering is the art of skillful approximation; the practice of gamesmanship in the highest form. In the end it is a method broad enough to tame the unknown, a means of combing disciplined judgment with intuition, courage with responsibility, and scientific competence within the practical aspects of time, of cost, and of talent." (Ronald B Smith, "Professional Responsibility of Engineering", Mechanical Engineering Vol. 86 (1), 1964)

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"One grievous error in interpreting approximations is to allow only good approximations." (Preston C Hammer, "Mind Pollution", Cybernetics, Vol. 14, 1971)

"The fact that [the model] is an approximation does not necessarily detract from its usefulness because models are approximations. All models are wrong, but some are useful." (George Box, 1987)

"Science is more than a mere attempt to describe nature as accurately as possible. Frequently the real message is well hidden, and a law that gives a poor approximation to nature has more significance than one which works fairly well but is poisoned at the root." (Robert H March, "Physics for Poets", 1996)

"Most physical systems, particularly those complex ones, are extremely difficult to model by an accurate and precise mathematical formula or equation due to the complexity of the system structure, nonlinearity, uncertainty, randomness, etc. Therefore, approximate modeling is often necessary and practical in real-world applications. Intuitively, approximate modeling is always possible. However, the key questions are what kind of approximation is good, where the sense of 'goodness' has to be first defined, of course, and how to formulate such a good approximation in modeling a system such that it is mathematically rigorous and can produce satisfactory results in both theory and applications." (Guanrong Chen & Trung Tat Pham, "Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems", 2001)

"Mathematical modeling is as much ‘art’ as ‘science’: it requires the practitioner to (i) identify a so-called ‘real world’ problem (whatever the context may be); (ii) formulate it in mathematical terms (the ‘word problem’ so beloved of undergraduates); (iii) solve the problem thus formulated (if possible; perhaps approximate solutions will suffice, especially if the complete problem is intractable); and (iv) interpret the solution in the context of the original problem." (John A Adam, "Mathematics in Nature", 2003)

"All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind." (George E P Box & Norman R Draper, "Response Surfaces, Mixtures, and Ridge Analyses", 2007)

"Science, at its core, is simply a method of practical logic that tests hypotheses against experience. Scientism, by contrast, is the worldview and value system that insists that the questions the scientific method can answer are the most important questions human beings can ask, and that the picture of the world yielded by science is a better approximation to reality than any other." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

"Science is about finding ever better approximations rather than pretending you have already found ultimate truth." (Friedrich Nietzsche)

More quotes on "Approximation" at the-web-of-knowledge.blogspot.com. 

🔭Data Science: Measurement (Just the Quotes)

"Accurate and minute measurement seems to the nonscientific imagination a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been but the rewards of accurate measurement and patient long contained labor in the minute sifting of numerical results." (William T Kelvin, "Report of the British Association For the Advancement of Science" Vol. 41, 1871)

"It is clear that one who attempts to study precisely things that are changing must have a great deal to do with measures of change." (Charles Cooley, "Observations on the Measure of Change", Journal of the American Statistical Association (21), 1893)

"Nothing is more certain in scientific method than that approximate coincidence alone can be expected. In the measurement of continuous quantity perfect correspondence must be accidental, and should give rise to suspicion rather than to satisfaction." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"Physical research by experimental methods is both a broadening and a narrowing field. There are many gaps yet to be filled, data to be accumulated, measurements to be made with great precision, but the limits within which we must work are becoming, at the same time, more and more defined." (Elihu Thomson, "Annual Report of the Board of Regents of the Smithsonian Institution", 1899)

"[…] statistics is the science of the measurement of the social organism, regarded as a whole, in all its manifestations." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may rightly be called the science of averages. […] Great numbers and the averages resulting from them, such as we always obtain in measuring social phenomena, have great inertia. […] It is this constancy of great numbers that makes statistical measurement possible. It is to great numbers that statistical measurement chiefly applies." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Just as data gathered by an incompetent observer are worthless - or by a biased observer, unless the bias can be measured and eliminated from the result - so also conclusions obtained from even the best data by one unacquainted with the principles of statistics must be of doubtful value." (William F White, "A Scrap-Book of Elementary Mathematics: Notes, Recreations, Essays", 1908)

"Science begins with measurement and there are some people who cannot be measurers; and just as we distinguish carpenters who can work to this or that traction of an inch of accuracy, so we must distinguish ourselves and our acquaintances as able to observe and record to this or that degree of truthfulness." (John A Thomson, "Introduction to Science", 1911)

"Science depends upon measurement, and things not measurable are therefore excluded, or tend to be excluded, from its attention." (Arthur J Balfour, "Address", 1917)

"Make more measurements than necessary to obtain the result and see to what extent these measurements, which in a certain sense control one another, agree with one another. By looking at how the measures fit to one another one can gain a sort of indication of probability of how precise the single measurements are and within which margins the result reasonably has to be maintained." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)

"Search for measurable elements among your phenomena, and then search for relations between these measures of physical quantities." (Alfred N Whitehead, "Science and the Modern World", 1929)

"While it is true that theory often sets difficult, if not impossible tasks for the experiment, it does, on the other hand, often lighten the work of the experimenter by disclosing cogent relationships which make possible the indirect determination of inaccessible quantities and thus render difficult measurements unnecessary." (Georg Joos, "Theoretical Physics", 1934)

"It is important to realize that it is not the one measurement, alone, but its relation to the rest of the sequence that is of interest." (William E Deming, "Statistical Adjustment of Data", 1938)

"Probabilities must be regarded as analogous to the measurement of physical magnitudes; that is to say, they can never be known exactly, but only within certain approximation." (Emile Borel, "Probabilities and Life", 1943)

"A model, like a novel, may resonate with nature, but it is not a ‘real’ thing. Like a novel, a model may be convincing - it may ‘ring true’ if it is consistent with our experience of the natural world. But just as we may wonder how much the characters in a novel are drawn from real life and how much is artifice, we might ask the same of a model: How much is based on observation and measurement of accessible phenomena, how much is convenience? Fundamentally, the reason for modeling is a lack of full access, either in time or space, to the phenomena of interest." (Kenneth Belitz, Science, Vol. 263, 1944)

"Every bit of knowledge we gain and every conclusion we draw about the universe or about any part or feature of it depends finally upon some observation or measurement. Mankind has had again and again the humiliating experience of trusting to intuitive, apparently logical conclusions without observations, and has seen Nature sail by in her radiant chariot of gold in an entirely different direction." (Oliver J Lee, "Measuring Our Universe: From the Inner Atom to Outer Space", 1950)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"We are committed to the scientific method, and measurement is the foundation of that method; hence we are prone to assume that whatever is measurable must be significant and that whatever cannot be measured may as well be disregarded." (Joseph W Krutch, "Human Nature and the Human Condition", 1959)

"No observations are absolutely trustworthy. In no field of observation can we entirely rule out the possibility that an observation is vitiated by a large measurement or execution error. If a reading is found to lie a very long way from its fellows in a series of replicate observations, there must be a suspicion that the deviation is caused by a blunder or gross error of some kind. [...] One sufficiently erroneous reading can wreck the whole of a statistical analysis, however many observations there are." (Francis J Anscombe, "Rejection of Outliers", Technometrics Vol. 2 (2), 1960)

"Statistics provides a quantitative example of the scientific process usually described qualitatively by saying that scientists observe nature, study the measurements, postulate models to predict new measurements, and validate the model by the success of prediction." (Marshall J Walker, "The Nature of Scientific Thought", 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)

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"Measurement is the link between mathematics and science." (Brian Ellis, "Basic Concepts of Measurement", 1966)

"The aim of science is not so much to search for truth, or even truths, as to classify our knowledge and to establish relations between observable phenomena in order to be able to predict the future in a certain measure and to explain the sequence of phenomena in relation to ourselves." (Pierre L du Noüy, "Between Knowing and Believing", 1967)

"[…] it is not enough to say: 'There's error in the data and therefore the study must be terribly dubious'. A good critic and data analyst must do more: he or she must also show how the error in the measurement or the analysis affects the inferences made on the basis of that data and analysis." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Typically, data analysis is messy, and little details clutter it. Not only confounding factors, but also deviant cases, minor problems in measurement, and ambiguous results lead to frustration and discouragement, so that more data are collected than analyzed. Neglecting or hiding the messy details of the data reduces the researcher's chances of discovering something new." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"A mature science, with respect to the matter of errors in variables, is not one that measures its variables without error, for this is impossible. It is, rather, a science which properly manages its errors, controlling their magnitudes and correctly calculating their implications for substantive conclusions." (Otis D Duncan, "Introduction to Structural Equation Models", 1975)

"Crude measurement usually yields misleading, even erroneous conclusions no matter how sophisticated a technique is used." (Henry T Reynolds, "Analysis of Nominal Data", 1977)

"But real-life situations often require us to measure probability in precisely this fashion - from sample to universe. In only rare cases does life replicate games of chance, for which we can determine the probability of an outcome before an event even occurs - a priori […] . In most instances, we have to estimate probabilities from what happened after the fact - a posteriori. The very notion of a posteriori implies experimentation and changing degrees of belief." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Measurement has meaning only if we can transmit the information without ambiguity to others." (Russell Fox & Max Gorbuny, "The Science of Science", 1997)

"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)

"First, good statistics are based on more than guessing. [...] Second, good statistics are based on clear, reasonable definitions. Remember, every statistic has to define its subject. Those definitions ought to be clear and made public. [...] Third, good statistics are based on clear, reasonable measures. Again, every statistic involves some sort of measurement; while all measures are imperfect, not all flaws are equally serious. [...] Finally, good statistics are based on good samples." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"There are several key issues in the field of statistics that impact our analyses once data have been imported into a software program. These data issues are commonly referred to as the measurement scale of variables, restriction in the range of data, missing data values, outliers, linearity, and nonnormality." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"There are three possible reasons for [the] absence of predictive power. First, it is possible that the models are misspecified. Second, it is possible that the model’s explanatory factors are measured at too high a level of aggregation [...] Third, [...] the search for statistically significant relationships may not be the strategy best suited for evaluating our model’s ability to explain real world events [...] the lack of predictive power is the result of too much emphasis having been placed on finding statistically significant variables, which may be overdetermined. Statistical significance is generally a flawed way to prune variables in regression models [...] Statistically significant variables may actually degrade the predictive accuracy of a model [...] [By using] models that are constructed on the basis of pruning undertaken with the shears of statistical significance, it is quite possible that we are winnowing our models away from predictive accuracy." (Michael D Ward et al, "The perils of policy by p-value: predicting civil conflicts" Journal of Peace Research 47, 2010)

"GIGO is a famous saying coined by early computer scientists: garbage in, garbage out. At the time, people would blindly put their trust into anything a computer output indicated because the output had the illusion of precision and certainty. If a statistic is composed of a series of poorly defined measures, guesses, misunderstandings, oversimplifications, mismeasurements, or flawed estimates, the resulting conclusion will be flawed." (Daniel J Levitin, "Weaponized Lies", 2017)

"Repeated observations of the same phenomenon do not always produce the same results, due to random noise or error. Sampling errors result when our observations capture unrepresentative circumstances, like measuring rush hour traffic on weekends as well as during the work week. Measurement errors reflect the limits of precision inherent in any sensing device. The notion of signal to noise ratio captures the degree to which a series of observations reflects a quantity of interest as opposed to data variance. As data scientists, we care about changes in the signal instead of the noise, and such variance often makes this problem surprisingly difficult." (Steven S Skiena, "The Data Science Design Manual", 2017)

"It’d be nice to fondly imagine that high-quality statistics simply appear in a spreadsheet somewhere, divine providence from the numerical heavens. Yet any dataset begins with somebody deciding to collect the numbers. What numbers are and aren’t collected, what is and isn’t measured, and who is included or excluded are the result of all-too-human assumptions, preconceptions, and oversights." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"People do care about how they are measured. What can we do about this? If you are in the position to measure something, think about whether measuring it will change people’s behaviors in ways that undermine the value of your results. If you are looking at quantitative indicators that others have compiled, ask yourself: Are these numbers measuring what they are intended to measure? Or are people gaming the system and rendering this measure useless?" (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"Premature enumeration is an equal-opportunity blunder: the most numerate among us may be just as much at risk as those who find their heads spinning at the first mention of a fraction. Indeed, if you’re confident with numbers you may be more prone than most to slicing and dicing, correlating and regressing, normalizing and rebasing, effortlessly manipulating the numbers on the spreadsheet or in the statistical package - without ever realizing that you don’t fully understand what these abstract quantities refer to. Arguably this temptation lay at the root of the last financial crisis: the sophistication of mathematical risk models obscured the question of how, exactly, risks were being measured, and whether those measurements were something you’d really want to bet your global banking system on." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"The whole discipline of statistics is built on measuring or counting things. […] it is important to understand what is being measured or counted, and how. It is surprising how rarely we do this. Over the years, as I found myself trying to lead people out of statistical mazes week after week, I came to realize that many of the problems I encountered were because people had taken a wrong turn right at the start. They had dived into the mathematics of a statistical claim - asking about sampling errors and margins of error, debating if the number is rising or falling, believing, doubting, analyzing, dissecting - without taking the ti- me to understand the first and most obvious fact: What is being measured, or counted? What definition is being used?" (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

🔭Data Science: The Science in Data Science (Just the Quotes)

"The aim of every science is foresight. For the laws of established observation of phenomena are generally employed to foresee their succession. All men, however little advanced make true predictions, which are always based on the same principle, the knowledge of the future from the past." (Auguste Compte, "Plan des travaux scientifiques nécessaires pour réorganiser la société", 1822)

"Science is nothing but the finding of analogy, identity, in the most remote parts." (Ralph W Emerson, 1837)

"Therefore science always goes abreast with the just elevation of the man, keeping step with religion and metaphysics; or, the state of science is an index of our self-knowledge." (Ralph W Emerson, "The Poet", 1844)

"It may sound quite strange, but for me, as for other scientists on whom these kinds of imaginative images have a greater effect than other poems do, no science is at its very heart more closely related to poetry, perhaps, than is chemistry." (Just Liebig, 1854)

"Science is the systematic classification of experience." (George H Lewes, "The Physical Basis of Mind", 1877)

"Science is the observation of things possible, whether present or past; prescience is the knowledge of things which may come to pass, though but slowly." (Leonardo da Vinci, "The Notebooks of Leonardo da Vinci", 1883)

"While science is pursuing a steady onward movement, it is convenient from time to time to cast a glance back on the route already traversed, and especially to consider the new conceptions which aim at discovering the general meaning of the stock of facts accumulated from day to day in our laboratories." (Dmitry Mendeleyev, "The Periodic Law of the Chemical Elements", Journal of the Chemical Society Vol. 55, 1889)

"The aim of science is always to reduce complexity to simplicity." (William James, "The Principles of Psychology", 1890)

"Science is not the monopoly of the naturalist or the scholar, nor is it anything mysterious or esoteric. Science is the search for truth, and truth is the adequacy of a description of facts." (Paul Carus, "Philosophy as a Science", 1909)

"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized. The universe, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)

"Abstract as it is, science is but an outgrowth of life. That is what the teacher must continually keep in mind. […] Let him explain […] science is not a dead system - the excretion of a monstrous pedantism - but really one of the most vigorous and exuberant phases of human life." (George A L Sarton, "The Teaching of the History of Science", The Scientific Monthly, 1918)

"The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, ‘Seek simplicity and distrust it’." (Alfred N Whitehead, "The Concept of Nature", 1919)

"Science is simply setting out on a fishing expedition to see whether it cannot find some procedure which it can call measurement of space and some procedure which it can call the measurement of time, and something which it can call a system of forces, and something which it can call masses." (Alfred N Whitehead, "The Concept of Nature", 1920)

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

"Science is but a method. Whatever its material, an observation accurately made and free of compromise to bias and desire, and undeterred by consequence, is science." (Hans Zinsser, "Untheological Reflections", The Atlantic Monthly, 1929)

"Although this may seem a paradox, all exact science is dominated by the idea of approximation. When a man tells you that he knows the exact truth about anything, you are safe in inferring that he is an inexact man." (Bertrand Russell, "The Scientific Outlook", 1931)

"The common view of science is that it is a sort of machine for increasing the race’s store of dependable facts. It is that only in part; in even larger part it is a machine for upsetting undependable facts." (Will Durant, 1931)

"One has to recognize that science is not metaphysics, and certainly not mysticism; it can never bring us the illumination and the satisfaction experienced by one enraptured in ecstasy. Science is sobriety and clarity of conception, not intoxicated vision."(Ludwig Von Mises, "Epistemological Problems of Economics", 1933)

"Modern positivists are apt to see more clearly that science is not a system of concepts but rather a system of statements." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements." (Rudolf Carnap, "The Unity of Science", 1934)

"Science is the attempt to discover, by means of observation, and reasoning based upon it, first, particular facts about the world, and then laws connecting facts with one another and (in fortunate cases) making it possible to predict future occurrences." (Bertrand Russell, "Religion and Science, Grounds of Conflict", 1935)

"[…] that all science is merely a game can be easily discarded as a piece of wisdom too easily come by. But it is legitimate to enquire whether science is not liable to indulge in play within the closed precincts of its own method. Thus, for instance, the scientist’s continuous penchant for systems tends in the direction of play." (Johan Huizinga, "Homo Ludens", 1938)

"Science makes no pretension to eternal truth or absolute truth; some of its rivals do. That science is in some respects inhuman may be the secret of its success in alleviating human misery and mitigating human stupidity." (Eric T Bell, "Mathematics: Queen and Servant of Science", 1938)

"Science is the attempt to make the chaotic diversity of our sense experience correspond to a logically uniform system of thought." (Albert Einstein, "Considerations Concerning the Fundaments of Theoretical Physics", Science Vol. 91 (2369), 1940)

"Science is the organised attempt of mankind to discover how things work as causal systems. The scientific attitude of mind is an interest in such questions. It can be contrasted with other attitudes, which have different interests; for instance the magical, which attempts to make things work not as material systems but as immaterial forces which can be controlled by spells; or the religious, which is interested in the world as revealing the nature of God." (Conrad H Waddington, "The Scientific Attitude", 1941)

"Science, in the broadest sense, is the entire body of the most accurately tested, critically established, systematized knowledge available about that part of the universe which has come under human observation. For the most part this knowledge concerns the forces impinging upon human beings in the serious business of living and thus affecting man’s adjustment to and of the physical and the social world. […] Pure science is more interested in understanding, and applied science is more interested in control […]" (Austin L Porterfield, "Creative Factors in Scientific Research", 1941)

"Science is an interconnected series of concepts and schemes that have developed as a result of experimentation and observation and are fruitful of further experimentation and observation."(James B Conant, "Science and Common Sense", 1951)

"[…] theoretical science is essentially disciplined exploitation of metaphor." (Anatol Rapoport, "Operational Philosophy", 1953)

"Prediction is all very well; but we must make sense of what we predict. The mainspring of science is the conviction that by honest, imaginative enquiry we can build up a system of ideas about Nature which has some legitimate claim to ‘reality’." (Stephen Toulmin, "The Philosophy of Science: An Introduction", 1953)

"An engineering science aims to organize the design principles used in engineering practice into a discipline and thus to exhibit the similarities between different areas of engineering practice and to emphasize the power of fundamental concepts. In short, an engineering science is predominated by theoretical analysis and very often uses the tool of advanced mathematics." (Qian Xuesen, "Engineering cybernetics", 1954))

"The true aim of science is to discover a simple theory which is necessary and sufficient to cover the facts, when they have been purified of traditional prejudices." (Lancelot L Whyte, "Accent on Form", 1954)

"Science is the creation of concepts and their exploration in the facts. It has no other test of the concept than its empirical truth to fact." (Jacob Bronowski, "Science and Human Values", 1956)

"The progress of science is the discovery at each step of a new order which gives unity to what had seemed unlike." (Jacob Bronowski, "Science and Human Values", 1956)

"[…] any serious examination of the basic concepts of any science is far more difficult than the elaboration of their ultimate consequences." (George F J Temple, "Turning Points in Physics", 1959)

"Science is usually understood to depict a universe of strict order and lawfulness, of rigorous economy - one whose currency is energy, convertible against a service charge into a growing common pool called entropy." (Paul A Weiss,"Organic Form: Scientific and Aesthetic Aspects", 1960)

"[…] the progress of science is a little like making a jig-saw puzzle. One makes collections of pieces which certainly fit together, though at first it is not clear where each group should come in the picture as a whole, and if at first one makes a mistake in placing it, this can be corrected later without dismantling the whole group." (Sir George Thomson, "The Inspiration of Science", 1961)

"Science is the reduction of the bewildering diversity of unique events to manageable uniformity within one of a number of symbol systems, and technology is the art of using these symbol systems so as to control and organize unique events. Scientific observation is always a viewing of things through the refracting medium of a symbol system, and technological praxis is always handling of things in ways that some symbol system has dictated. Education in science and technology is essentially education on the symbol level." (Aldous L Huxley, "Essay", Daedalus, 1962)

"The important distinction between science and those other systematizations [i.e., art, philosophy, and theology] is that science is self-testing and self-correcting. Here the essential point of science is respect for objective fact. What is correctly observed must be believed [...] the competent scientist does quite the opposite of the popular stereotype of setting out to prove a theory; he seeks to disprove it." (George G Simpson, "Notes on the Nature of Science", 1962)

"What, then, is science according to common opinion? Science is what scientists do. Science is knowledge, a body of information about the external world. Science is the ability to predict. Science is power, it is engineering. Science explains, or gives causes and reasons." (John Bremer "What Is Science?" [in "Notes on the Nature of Science"], 1962)

"Science is a matter of disinterested observation, patient ratiocination within some system of logically correlated concepts. In real-life conflicts between reason and passion the issue is uncertain. Passion and prejudice are always able to mobilize their forces more rapidly and press the attack with greater fury; but in the long run (and often, of course, too late) enlightened self-interest may rouse itself, launch a counterattack and win the day for reason." (Aldous L Huxley, "Literature and Science", 1963)

"Science is a way to teach how something gets to be known, what is not known, to what extent things are known (for nothing is known absolutely), how to handle doubt and uncertainty, what the rules of evidence are, how to think about things so that judgments can be made, how to distinguish truth from fraud, and from show." (Richard P Feynman, "The Problem of Teaching Physics in Latin America", Engineering and Science, 1963)

"The aim of science is to apprehend this purely intelligible world as a thing in itself, an object which is what it is independently of all thinking, and thus antithetical to the sensible world. [...] The world of thought is the universal, the timeless and spaceless, the absolutely necessary, whereas the world of sense is the contingent, the changing and moving appearance which somehow indicates or symbolizes it." (Robin G Collingwood, "Essays in the Philosophy of Art", 1964)

"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos." (Herbert A Simon, "The Sciences of the Artificial", 1969)

"The central task of a natural science is to make the wonderful commonplace: to show that complexity, correctly viewed, is only a mask for simplicity; to find pattern hidden in apparent chaos." (Herbert A Simon, "The Sciences of the Artificial", 1969)

"Science is a product of man, of his mind; and science creates the real world in its own image." (Frank E Egler, "The Way of Science", 1970)

"To do science is to search for repeated patterns, not simply to accumulate facts [...]" (Robert H. MacArthur, "Geographical Ecology", 1972)

"Science is systematic organisation of knowledge about the universe on the basis of explanatory hypotheses which are genuinely testable. Science advances by developing gradually more comprehensive theories; that is, by formulating theories of greater generality which can account for observational statements and hypotheses which appear as prima facie unrelated." (Francisco J Ayala, "Studies in the Philosophy of Biology: Reduction and Related Problems", 1974)

"A mature science, with respect to the matter of errors in variables, is not one that measures its variables without error, for this is impossible. It is, rather, a science which properly manages its errors, controlling their magnitudes and correctly calculating their implications for substantive conclusions." (Otis D Duncan, "Introduction to Structural Equation Models", 1975)

"The very nature of science is such that scientists need the metaphor as a bridge between old and new theories." (Earl R MacCormac, "Metaphor and Myth in Science and Religion", 1976)

"Facts do not ‘speak for themselves’; they are read in the light of theory. Creative thought, in science as much as in the arts, is the motor of changing opinion. Science is a quintessentially human activity, not a mechanized, robot-like accumulation of objective information, leading by laws of logic to inescapable interpretation." (Stephen J Gould, "Ever Since Darwin", 1977)

"Science is not a heartless pursuit of objective information. It is a creative human activity, its geniuses acting more as artists than information processors. Changes in theory are not simply the derivative results of the new discoveries but the work of creative imagination influenced by contemporary social and political forces." (Stephen J Gould, "Ever Since Darwin: Reflections in Natural History", 1977)

"Engineering or Technology is the making of things that did not previously exist, whereas science is the discovering of things that have long existed." (David Billington, "The Tower and the Bridge: The New Art of Structural Engineering", 1983)

"Science is a process. It is a way of thinking, a manner of approaching and of possibly resolving problems, a route by which one can produce order and sense out of disorganized and chaotic observations. Through it we achieve useful conclusions and results that are compelling and upon which there is a tendency to agree." (Isaac Asimov, "‘X’ Stands for Unknown", 1984)

"If doing mathematics or science is looked upon as a game, then one might say that in mathematics you compete against yourself or other mathematicians; in physics your adversary is nature and the stakes are higher." (Mark Kac, "Enigmas Of Chance", 1985)

"Science is defined as a set of observations and theories about observations." (F Albert Matsen, "The Role of Theory in Chemistry", Journal of Chemical Education Vol. 62 (5), 1985)

"We expect to learn new tricks because one of our science based abilities is being able to predict. That after all is what science is about. Learning enough about how a thing works so you'll know what comes next. Because as we all know everything obeys the universal laws, all you need is to understand the laws." (James Burke, "The Day the Universe Changed", 1985)

"Science is human experience systematically extended (by intent, methodology and instrumentation) for the purpose of learning more about the natural world and for the critical empirical testing and possible falsification of all ideas about the natural world. Scientific hypotheses may incorporate only elements of the natural empirical world, and thus may contain no element of the supernatural." (Robert E Kofahl, Correctly Redefining Distorted Science: A Most Essential Task", Creation Research Society Quarterly Vol. 23, 1986)

"Science is not a given set of answers but a system for obtaining answers. The method by which the search is conducted is more important than the nature of the solution. Questions need not be answered at all, or answers may be provided and then changed. It does not matter how often or how profoundly our view of the universe alters, as long as these changes take place in a way appropriate to science. For the practice of science, like the game of baseball, is covered by definite rules." (Robert Shapiro, "Origins: A Skeptic’s Guide to the Creation of Life on Earth", 1986)

"Science doesn't purvey absolute truth. Science is a mechanism. It's a way of trying to improve your knowledge of nature. It's a system for testing your thoughts against the universe and seeing whether they match. And this works, not just for the ordinary aspects of science, but for all of life. I should think people would want to know that what they know is truly what the universe is like, or at least as close as they can get to it." (Isaac Asimov, [Interview by Bill Moyers] 1988)

"Science doesn’t purvey absolute truth. Science is a mechanism, a way of trying to improve your knowledge of nature. It’s a system for testing your thoughts against the universe, and seeing whether they match." (Isaac Asimov, [interview with Bill Moyers in The Humanist] 1989)

"The view of science is that all processes ultimately run down, but entropy is maximized only in some far, far away future. The idea of entropy makes an assumption that the laws of the space-time continuum are infinitely and linearly extendable into the future. In the spiral time scheme of the timewave this assumption is not made. Rather, final time means passing out of one set of laws that are conditioning existence and into another radically different set of laws. The universe is seen as a series of compartmentalized eras or epochs whose laws are quite different from one another, with transitions from one epoch to another occurring with unexpected suddenness." (Terence McKenna, "True Hallucinations", 1989)

"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)

"In science if you know what you are doing you should not be doing it. In engineering if you do not know what you are doing you should not be doing it. Of course, you seldom, if ever, see either pure state." (Richard W Hamming, "The Art of Probability for Scientists and Engineers", 1991)

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

"The goal of science is to make sense of the diversity of Nature." (John D Barrow, "Theories of Everything: The Quest for Ultimate Explanation", 1991)

"Science is not about control. It is about cultivating a perpetual condition of wonder in the face of something that forever grows one step richer and subtler than our latest theory about it. It is about  reverence, not mastery." (Richard Power, "Gold Bug Variations", 1993)

"Statistics as a science is to quantify uncertainty, not unknown." (Chamont Wang, "Sense and Nonsense of Statistical Inference: Controversy, Misuse, and Subtlety", 1993)

"Clearly, science is not simply a matter of observing facts. Every scientific theory also expresses a worldview. Philosophical preconceptions determine where facts are sought, how experiments are designed, and which conclusions are drawn from them." (Nancy R Pearcey & Charles B. Thaxton, "The Soul of Science: Christian Faith and Natural Philosophy", 1994)

"Science is distinguished not for asserting that nature is rational, but for constantly testing claims to that or any other affect by observation and experiment." (Timothy Ferris, "The Whole Shebang: A State-of-the Universe’s Report", 1996)

"Science is more than a mere attempt to describe nature as accurately as possible. Frequently the real message is well hidden, and a law that gives a poor approximation to nature has more significance than one which works fairly well but is poisoned at the root." (Robert H March, "Physics for Poets", 1996)

"The art of science is knowing which observations to ignore and which are the key to the puzzle." (Edward W Kolb, "Blind Watchers of the Sky", 1996)

"Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding." (Gian-Carlo Rota, "Indiscrete Thoughts", 1997)

"Religion is the antithesis of science; science is competent to illuminate all the deep questions of existence, and does so in a manner that makes full use of, and respects the human intellect. I see neither need nor sign of any future reconciliation." (Peter W Atkins, "Religion - The Antithesis to Science", 1997)

"[…] the pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before." (John A Wheeler, "Geons, Black Holes, and Quantum Foam: A Life in Physics", 1998)

"The rate of the development of science is not the rate at which you make observations alone but, much more important, the rate at which you create new things to test." (Richard Feynman, "The Meaning of It All", 1998)

"The passion and beauty and joy of science is that we humans have invented a process to understand the universe in a way that is true for everyone. We are finding universal truths." (Bill Nye, 2000)

"The poetry of science is in some sense embodied in its great equations, and these equations can also be peeled. But their layers represent their attributes and consequences, not their meanings." (Graham Farmelo, 2002)

"Science is the art of the appropriate approximation. While the flat earth model is usually spoken of with derision it is still widely used. Flat maps, either in atlases or road maps, use the flat earth model as an approximation to the more complicated shape." (Byron K. Jennings, "On the Nature of Science", Physics in Canada Vol. 63 (1), 2007)

"It is ironic but true: the one reality science cannot reduce is the only reality we will ever know. This is why we need art. By expressing our actual experience, the artist reminds us that our science is incomplete, that no map of matter will ever explain the immateriality of our consciousness." (Jonah Lehrer, "Proust Was a Neuroscientist", 2011)

"Science isn’t about being right. It is about convincing others of the correctness of an idea through a methodology all will accept using data everyone can trust. New ideas take time to be accepted because they compete with others that have already passed the test." (Tom Koch, "Commentary: Nobody loves a critic: Edmund A Parkes and John Snow’s cholera", International Journal of Epidemiology Vol. 42 (6), 2013)

"Science, at its core, is simply a method of practical logic that tests hypotheses against experience. Scientism, by contrast, is the worldview and value system that insists that the questions the scientific method can answer are the most important questions human beings can ask, and that the picture of the world yielded by science is a better approximation to reality than any other." (John M Greer, "After Progress: Reason and Religion at the End of the Industrial Age", 2015)

More quotes on "Science" at quotablemath.blogspot.com.