🔭Data Science: Experiment (Just the Quotes)

"Those who have not imbibed the prejudices of philosophers, are easily convinced that natural knowledge is to be founded on experiment and observation." (Colin Maclaurin, "An Account of Sir Isaac Newton’s Philosophical Discoveries", 1748)

"We have three principal means: observation of nature, reflection, and experiment. Observation gathers the facts reflection combines them, experiment verifies the result of the combination. It is essential that the observation of nature be assiduous, that reflection be profound, and that experimentation be exact. Rarely does one see these abilities in combination. And so, creative geniuses are not common." (Denis Diderot, "On the Interpretation of Nature", 1753)

"Facts, observations, experiments - these are the materials of a great edifice, but in assembling them we must combine them into classes, distinguish which belongs to which order and to which part of the whole each pertains." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)

"The art of drawing conclusions from experiments and observations consists in evaluating probabilities and in estimating whether they are sufficiently great or numerous enough to constitute proofs. This kind of calculation is more complicated and more difficult than it is commonly thought to be […]" (Antoine-Laurent Lavoisier, cca. 1790)

"We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation." (Antoin-Laurent de Lavoisiere, "Elements of Chemistry", 1790)

"Conjecture may lead you to form opinions, but it cannot produce knowledge. Natural philosophy must be built upon the phenomena of nature discovered by observation and experiment." (George Adams, "Lectures on Natural and Experimental Philosophy" Vol. 1, 1794)

"[Precision] is the very soul of science; and its attainment afford the only criterion, or at least the best, of the truth of theories, and the correctness of experiments." (John F W Herschel, "A Preliminary Discourse on the Study of Natural Philosophy", 1830)

"The hypothesis, by suggesting observations and experiments, puts us upon the road to that independent evidence if it be really attainable; and till it be attained, the hypothesis ought not to count for more than a suspicion." (John S Mill, "A System of Logic, Ratiocinative and Inductive", 1843)

"The framing of hypotheses is, for the enquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth, to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention." (William Whewell, "Philosophy of the Inductive Sciences" Vol. 2, 1847)

"An anticipative idea or an hypothesis is, then, the necessary starting point for all experimental reasoning. Without it, we could not make any investigation at all nor learn anything; we could only pile up sterile observations. If we experiment without a preconceived idea, we should move at random […]" (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"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)

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

"A discoverer is a tester of scientific ideas; he must not only be able to imagine likely hypotheses, and to select suitable ones for investigation, but, as hypotheses may be true or untrue, he must also be competent to invent appropriate experiments for testing them, and to devise the requisite apparatus and arrangements." (George Gore, "The Art of Scientific Discovery", 1878)

"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)

"Every experiment, every observation has, besides its immediate result, effects which, in proportion to its value, spread always on all sides into ever distant parts of knowledge." (Sir Michael Foster, "Annual Report of the Board of Regents of the Smithsonian Institution", 1898)

"If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty: (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals." William S Gosset, "The Probable Error of a Mean", Biometrika, 1908)

"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)

"Theory is the best guide for experiment - that were it not for theory and the problems and hypotheses that come out of it, we would not know the points we wanted to verify, and hence would experiment aimlessly" (Henry Hazlitt,  "Thinking as a Science", 1916)

"A scientist, whether theorist or experimenter, puts forward statements, or systems of statements, and tests them step by step. In the field of the empirical sciences, more particularly, he constructs hypotheses, or systems of theories, and tests them against experience by observation and experiment." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"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)

"In relation to any experiment we may speak of this hypothesis as the null hypothesis, and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis." (Ronald Fisher, "The Design of Experiments", 1935)

"Statistics is a scientific discipline concerned with collection, analysis, and interpretation of data obtained from observation or experiment. The subject has a coherent structure based on the theory of Probability and includes many different procedures which contribute to research and development throughout the whole of Science and Technology." (Egon Pearson, 1936)

"Experiment as compared with mere observation has some of the characteristics of cross-examining nature rather than merely overhearing her." (Alan Gregg, "The Furtherance of Medical Research", 1941)

"The well-known virtue of the experimental method is that it brings situational variables under tight control. It thus permits rigorous tests of hypotheses and confidential statements about causation. The correlational method, for its part, can study what man has not learned to control. Nature has been experimenting since the beginning of time, with a boldness and complexity far beyond the resources of science. The correlator’s mission is to observe and organize the data of nature’s experiments." (Lee J Cronbach, "The Two Disciplines of Scientific Psychology", The American Psychologist Vol. 12, 1957)

"A satisfactory prediction of the sequential properties of learning data from a single experiment is by no means a final test of a model. Numerous other criteria - and some more demanding - can be specified. For example, a model with specific numerical parameter values should be invariant to changes in independent variables that explicitly enter in the model." (Robert R Bush & Frederick Mosteller,"A Comparison of Eight Models?", Studies in Mathematical Learning Theory, 1959)

"Mathematical statistics provides an exceptionally clear example of the relationship between mathematics and the external world. The external world provides the experimentally measured distribution curve; mathematics provides the equation (the mathematical model) that corresponds to the empirical curve. The statistician may be guided by a thought experiment in finding the corresponding equation." (Marshall J Walker, "The Nature of Scientific Thought", 1963)

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

"Science consists simply of the formulation and testing of hypotheses based on observational evidence; experiments are important where applicable, but their function is merely to simplify observation by imposing controlled conditions." (Henry L Batten, "Evolution of the Earth", 1971)

"In moving from conjecture to experimental data, (D), experiments must be designed which make best use of the experimenter's current state of knowledge and which best illuminate his conjecture. In moving from data to modified conjecture, (A), data must be analyzed so as to accurately present information in a manner which is readily understood by the experimenter." (George E P Box & George C Tjao, "Bayesian Inference in Statistical Analysis", 1973)

"Statistical methods are tools of scientific investigation. Scientific investigation is a controlled learning process in which various aspects of a problem are illuminated as the study proceeds. It can be thought of as a major iteration within which secondary iterations occur. The major iteration is that in which a tentative conjecture suggests an experiment, appropriate analysis of the data so generated leads to a modified conjecture, and this in turn leads to a new experiment, and so on." (George E P Box & George C Tjao, "Bayesian Inference in Statistical Analysis", 1973)

"A hypothesis is empirical or scientific only if it can be tested by experience. […] A hypothesis or theory which cannot be, at least in principle, falsified by empirical observations and experiments does not belong to the realm of science." (Francisco J Ayala, "Biological Evolution: Natural Selection or Random Walk", American Scientist, 1974)

"An experiment is a failure only when it also fails adequately to test the hypothesis in question, when the data it produces don't prove anything one way or the other." (Robert M Pirsig, "Zen and the Art of Motorcycle Maintenance", 1974)

"The essential function of a hypothesis consists in the guidance it affords to new observations and experiments, by which our conjecture is either confirmed or refuted." (Ernst Mach, "Knowledge and Error: Sketches on the Psychology of Enquiry", 1976)

"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, "Biophilia", 1984)

"The only touchstone for empirical truth is experiment and observation." (Heinz Pagels, "Perfect Symmetry: The Search for the Beginning of Time", 1985)

"Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory." (Stephen Hawking,  "A Brief History of Time", 1988)

"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)

"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)

"Probability theory is an ideal tool for formalizing uncertainty in situations where class frequencies are known or where evidence is based on outcomes of a sufficiently long series of independent random experiments. Possibility theory, on the other hand, is ideal for formalizing incomplete information expressed in terms of fuzzy propositions." (George Klir, "Fuzzy sets and fuzzy logic", 1995)

"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)

"[…] because observations are all we have, we take them seriously. We choose hard data and the framework of mathematics as our guides, not unrestrained imagination or unrelenting skepticism, and seek the simplest yet most wide-reaching theories capable of explaining and predicting the outcome of today’s and future experiments." (Brian Greene, "The Fabric of the Cosmos", 2004)

"In science, for a theory to be believed, it must make a prediction - different from those made by previous theories - for an experiment not yet done. For the experiment to be meaningful, we must be able to get an answer that disagrees with that prediction. When this is the case, we say that a theory is falsifiable - vulnerable to being shown false. The theory also has to be confirmable, it must be possible to verify a new prediction that only this theory makes. Only when a theory has been tested and the results agree with the theory do we advance the statement to the rank of a true scientific theory." (Lee Smolin, "The Trouble with Physics", 2006)

"Observation and experiment, without a rational hypothesis, is like a man groping at objects at random with his eyes shut." (Henry P Tappan, "Elements of Logic", 2015)

"The dialectical interplay of experiment and theory is a key driving force of modern science. Experimental data do only have meaning in the light of a particular model or at least a theoretical background. Reversely theoretical considerations may be logically consistent as well as intellectually elegant: Without experimental evidence they are a mere exercise of thought no matter how difficult they are. Data analysis is a connector between experiment and theory: Its techniques advise possibilities of model extraction as well as model testing with experimental data." (Achim Zielesny, "From Curve Fitting to Machine Learning" 2^nd Ed., 2016)

"If your experiment needs statistics, you ought to have done a better experiment." (Ernest Rutherford)

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

🕸Systems Engineering: Similarity (Just the Quotes)

"Symmetry is evidently a kind of unity in variety, where a whole is determined by the rhythmic repetition of similar." (George Santayana, "The Sense of Beauty", 1896)

"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)

"By a model we thus mean any physical or chemical system which has a similar relation-structure to that of the process it imitates. By ’relation-structure’ I do not mean some obscure non-physical entity which attends the model, but the fact that it is a physical working model which works in the same way as the process it parallels, in the aspects under consideration at any moment." (Kenneth Craik, "The Nature of Explanation", 1943)

"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12" (4), 1945)

"Industrial production, the flow of resources in the economy, the exertion of military effort in a war theater-all are complexes of numerous interrelated activities. Differences may exist in the goals to be achieved, the particular processes involved, and the magnitude of effort. Nevertheless, it is possible to abstract the underlying essential similarities in the management of these seemingly disparate systems." (George Dantzig, "Linear programming and extensions", 1963) 

"System' is the concept that refers both to a complex of interdependencies between parts, components, and processes, that involves discernible regularities of relationships, and to a similar type of interdependency between such a complex and its surrounding environment." (Talcott Parsons, "Systems Analysis: Social Systems", 1968)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic" (that is fixed) rules" (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order" (a pattern) within disorder" (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"The dimensionality and nonlinearity requirements of chaos do not guarantee its appearance. At best, these conditions allow it to occur, and even then under limited conditions relating to particular parameter values. But this does not imply that chaos is rare in the real world. Indeed, discoveries are being made constantly of either the clearly identifiable or arguably persuasive appearance of chaos. Most of these discoveries are being made with regard to physical systems, but the lack of similar discoveries involving human behavior is almost certainly due to the still developing nature of nonlinear analyses in the social sciences rather than the absence of chaos in the human setting. " (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"From a more general philosophical perspective we can say that we wish to model complex systems because we want to understand them better.  The main requirement for our models accordingly shifts from having to be correct to being rich in information.  This does not mean that the relationship between the model and the system itself becomes less important, but the shift from control and prediction to understanding does have an effect on our approach to complexity: the evaluation of our models in terms of performance can be deferred. Once we have a better understanding of the dynamics of complexity, we can start looking for the similarities and differences between different complex systems and thereby develop a clearer understanding of the strengths and limitations of different models." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder. " (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

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

"Although the detailed moment-to-moment behavior of a chaotic system cannot be predicted, the overall pattern of its 'random' fluctuations may be similar from scale to scale. Likewise, while the fine details of a chaotic system cannot be predicted one can know a little bit about the range of its 'random' fluctuation." (F David Peat, "From Certainty to Uncertainty", 2002)

"Complexity is the characteristic property of complicated systems we don’t understand immediately. It is the amount of difficulties we face while trying to understand it. In this sense, complexity resides largely in the eye of the beholder - someone who is familiar with s.th. often sees less complexity than someone who is less familiar with it. [...] A complex system is created by evolutionary processes. There are multiple pathways by which a system can evolve. Many complex systems are similar, but each instance of a system is unique." (Jochen Fromm, The Emergence of Complexity, 2004)

"Diverse groups of problem solvers outperformed the groups of the best individuals at solving complex problems. The reason: the diverse groups got stuck less often than the smart individuals, who tended to think similarly." (Scott E Page, [interview in The New York Times] 2008)

"A key discovery of network science is that the architecture of networks emerging in various domains of science, nature, and technology are similar to each other, a consequence of being governed by the same organizing principles. Consequently we can use a common set of mathematical tools to explore these systems. " (Albert-László Barabási, "Network Science", 2016)

"The exploding interest in network science during the first decade of the 21st century is rooted in the discovery that despite the obvious diversity of complex systems, the structure and the evolution of the networks behind each system is driven by a common set of fundamental laws and principles. Therefore, notwithstanding the amazing differences in form, size, nature, age, and scope of real networks, most networks are driven by common organizing principles. Once we disregard the nature of the components and the precise nature of the interactions between them, the obtained networks are more similar than different from each other." (Albert-László Barabási, "Network Science", 2016)

See also the quotes on Similarity in Graphical Representation series

🔭Data Science: Uncertainty (Just the Quotes)

"If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty: (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals." (William S Gosset, "The Probable Error of a Mean", Biometrika, 1908)

"The making of decisions, as everyone knows from personal experience, is a burdensome task. Offsetting the exhilaration that may result from correct and successful decision and the relief that follows the termination of a struggle to determine issues is the depression that comes from failure, or error of decision, and the frustration which ensues from uncertainty." (Chester I Barnard, "The Functions of the Executive", 1938)

"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)

"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)

"The most dominant decision type [that will have to be made in an organic organization] will be decisions under uncertainty." (Henry L Tosi & Stephen J Carroll, "Management", 1976)

"The greater the uncertainty, the greater the amount of decision making and information processing. It is hypothesized that organizations have limited capacities to process information and adopt different organizing modes to deal with task uncertainty. Therefore, variations in organizing modes are actually variations in the capacity of organizations to process information and make decisions about events which cannot be anticipated in advance." (John K Galbraith, "Organization Design", 1977)

"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 Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"Models are often used to decide issues in situations marked by uncertainty. However statistical differences from data depend on assumptions about the process which generated these data. If the assumptions do not hold, the inferences may not be reliable either. This limitation is often ignored by applied workers who fail to identify crucial assumptions or subject them to any kind of empirical testing. In such circumstances, using statistical procedures may only compound the uncertainty." (David A Greedman & William C Navidi, "Regression Models for Adjusting the 1980 Census", Statistical Science Vol. 1 (1), 1986)

"The mathematical theories generally called 'mathematical theories of chance' actually ignore chance, uncertainty and probability. The models they consider are purely deterministic, and the quantities they study are, in the final analysis, no more than the mathematical frequencies of particular configurations, among all equally possible configurations, the calculation of which is based on combinatorial analysis. In reality, no axiomatic definition of chance is conceivable." (Maurice Allais, "An Outline of My Main Contributions to Economic Science", [Noble lecture] 1988)

"The worst, i.e., most dangerous, feature of 'accepting the null hypothesis' is the giving up of explicit uncertainty. [...] Mathematics can sometimes be put in such black-and-white terms, but our knowledge or belief about the external world never can." (John Tukey, "The Philosophy of Multiple Comparisons", Statistical Science Vol. 6 (1), 1991)

"In nonlinear systems - and the economy is most certainly nonlinear - chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably. After a while, your predictions are nonsense." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

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

"There is a new science of complexity which says that the link between cause and effect is increasingly difficult to trace; that change (planned or otherwise) unfolds in non-linear ways; that paradoxes and contradictions abound; and that creative solutions arise out of diversity, uncertainty and chaos." (Andy P Hargreaves & Michael Fullan, "What’s Worth Fighting for Out There?", 1998)

"Information entropy has its own special interpretation and is defined as the degree of unexpectedness in a message. The more unexpected words or phrases, the higher the entropy. It may be calculated with the regular binary logarithm on the number of existing alternatives in a given repertoire. A repertoire of 16 alternatives therefore gives a maximum entropy of 4 bits. Maximum entropy presupposes that all probabilities are equal and independent of each other. Minimum entropy exists when only one possibility is expected to be chosen. When uncertainty, variety or entropy decreases it is thus reasonable to speak of a corresponding increase in information." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Any scientific data without (a stated) uncertainty is of no avail. Therefore the analysis and description of uncertainty are almost as important as those of the data value itself . It should be clear that the uncertainty itself also has an uncertainty – due to its nature as a scientific quantity – and so on. The uncertainty of an uncertainty is generally not determined." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"As uncertainties of scientific data values are nearly as important as the data values themselves, it is usually not acceptable that a best estimate is only accompanied by an estimated uncertainty. Therefore, only the size of nondominant uncertainties should be estimated. For estimating the size of a nondominant uncertainty we need to find its upper limit, i.e., we want to be as sure as possible that the uncertainty does not exceed a certain value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before best estimates are extracted from data sets by way of a regression analysis, the uncertainties of the individual data values must be determined.In this case care must be taken to recognize which uncertainty components are common to all the values, i.e., those that are correlated (systematic)." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Due to the theory that underlies uncertainties an infinite number of data values would be necessary to determine the true value of any quantity. In reality the number of available data values will be relatively small and thus this requirement can never be fully met; all one can get is the best estimate of the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"For linear dependences the main information usually lies in the slope. It is obvious that those points that lie far apart have the strongest influence on the slope if all points have the same uncertainty. In this context we speak of the strong leverage of distant points; when determining the parameter 'slope' these distant points carry more effective weight. Naturally, this weight is distinct from the 'statistical' weight usually used in regression analysis." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In error analysis the so-called 'chi-squared' is a measure of the agreement between the uncorrelated internal and the external uncertainties of a measured functional relation. The simplest such relation would be time independence. Theory of the chi-squared requires that the uncertainties be normally distributed. Nevertheless, it was found that the test can be applied to most probability distributions encountered in practice." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In many cases systematic errors are interpreted as the systematic difference between nature (which is being questioned by the experimenter in his experiment) and the model (which is used to describe nature). If the model used is not good enough, but the measurement result is interpreted using this model, the final result (the interpretation) will be wrong because it is biased, i.e., it has a systematic deviation (not uncertainty). If we do not use the best model (the best theory) available for the description of a certain phenomenon this procedure is just wrong. It has nothing to do with an uncertainty." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is also inevitable for any model or theory to have an uncertainty (a difference between model and reality). Such uncertainties apply both to the numerical parameters of the model and to the inadequacy of the model as well. Because it is much harder to get a grip on these types of uncertainties, they are disregarded, usually." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is important that uncertainty components that are independent of each other are added quadratically. This is also true for correlated uncertainty components, provided they are independent of each other, i.e., as long as there is no correlation between the components." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the nature of an uncertainty that it is not known and can never be known, whether the best estimate is greater or less than the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Outliers or flyers are those data points in a set that do not quite fit within the rest of the data, that agree with the model in use. The uncertainty of such an outlier is seemingly too small. The discrepancy between outliers and the model should be subject to thorough examination and should be given much thought. Isolated data points, i.e., data points that are at some distance from the bulk of the data are not outliers if their values are in agreement with the model in use." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"The fact that the same uncertainty (e.g., scale uncertainty) is uncorrelated if we are dealing with only one measurement, but correlated (i.e., systematic) if we look at more than one measurement using the same instrument shows that both types of uncertainties are of the same nature. Of course, an uncertainty keeps its characteristics (e.g., Poisson distributed), independent of the fact whether it occurs only once or more often." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"To fulfill the requirements of the theory underlying uncertainties, variables with random uncertainties must be independent of each other and identically distributed. In the limiting case of an infinite number of such variables, these are called normally distributed. However, one usually speaks of normally distributed variables even if their number is finite." (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)

"Data always vary randomly because the object of our inquiries, nature itself, is also random. We can analyze and predict events in nature with an increasing amount of precision and accuracy, thanks to improvements in our techniques and instruments, but a certain amount of random variation, which gives rise to uncertainty, is inevitable." (Alberto Cairo, "The Functional Art", 2011)

"The storytelling mind is allergic to uncertainty, randomness, and coincidence. It is addicted to meaning. If the storytelling mind cannot find meaningful patterns in the world, it will try to impose them. In short, the storytelling mind is a factory that churns out true stories when it can, but will manufacture lies when it can't." (Jonathan Gottschall, "The Storytelling Animal: How Stories Make Us Human", 2012)

"The data is a simplification - an abstraction - of the real world. So when you visualize data, you visualize an abstraction of the world, or at least some tiny facet of it. Visualization is an abstraction of data, so in the end, you end up with an abstraction of an abstraction, which creates an interesting challenge. […] Just like what it represents, data can be complex with variability and uncertainty, but consider it all in the right context, and it starts to make sense." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos", 2013)

"The greater the uncertainty, the bigger the gap between what you can measure and what matters, the more you should watch out for overfitting - that is, the more you should prefer simplicity." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)

"A notable difference between many fields and data science is that in data science, if a customer has a wish, even an experienced data scientist may not know whether it’s possible. Whereas a software engineer usually knows what tasks software tools are capable of performing, and a biologist knows more or less what the laboratory can do, a data scientist who has not yet seen or worked with the relevant data is faced with a large amount of uncertainty, principally about what specific data is available and about how much evidence it can provide to answer any given question. Uncertainty is, again, a major factor in the data scientific process and should be kept at the forefront of your mind when talking with customers about their wishes."  (Brian Godsey, "Think Like a Data Scientist", 2017)

"The elements of this cloud of uncertainty (the set of all possible errors) can be described in terms of probability. The center of the cloud is the number zero, and elements of the cloud that are close to zero are more probable than elements that are far away from that center. We can be more precise in this definition by defining the cloud of uncertainty in terms of a mathematical function, called the probability distribution." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Uncertainty is an adversary of coldly logical algorithms, and being aware of how those algorithms might break down in unusual circumstances expedites the process of fixing problems when they occur - and they will occur. A data scientist’s main responsibility is to try to imagine all of the possibilities, address the ones that matter, and reevaluate them all as successes and failures happen." (Brian Godsey, "Think Like a Data Scientist", 2017)

"Bootstrapping provides an intuitive, computer-intensive way of assessing the uncertainty in our estimates, without making strong assumptions and without using probability theory. But the technique is not feasible when it comes to, say, working out the margins of error on unemployment surveys of 100,000 people. Although bootstrapping is a simple, brilliant and extraordinarily effective idea, it is just too clumsy to bootstrap such large quantities of data, especially when a convenient theory exists that can generate formulae for the width of uncertainty intervals." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"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)

"Estimates based on data are often uncertain. If the data were intended to tell us something about a wider population (like a poll of voting intentions before an election), or about the future, then we need to acknowledge that uncertainty. This is a double challenge for data visualization: it has to be calculated in some meaningful way and then shown on top of the data or statistics without making it all too cluttered." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Uncertainty confuses many people because they have the unreasonable expectation that science and statistics will unearth precise truths, when all they can yield is imperfect estimates that can always be subject to changes and updates." (Alberto Cairo, "How Charts Lie", 2019)

"We over-fit when we go too far in adapting to local circumstances, in a worthy but misguided effort to be ‘unbiased’ and take into account all the available information. Usually we would applaud the aim of being unbiased, but this refinement means we have less data to work on, and so the reliability goes down. Over-fitting therefore leads to less bias but at a cost of more uncertainty or variation in the estimates, which is why protection against over-fitting is sometimes known as the bias/variance trade-off." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

🔭Data Science: Causality (Just the Quotes)

"All human actions have one or more of these seven causes: chance, nature, compulsions, habit, reason, passion, desire." (Aristotle, 4th century BC)

"In all disciplines in which there is systematic knowledge of things with principles, causes, or elements, it arises from a grasp of those: we think we have knowledge of a thing when we have found its primary causes and principles, and followed it back to its elements." (Aristotle, "Physics", cca. 350 BC)

"Constantly regard the universe as one living being, having one substance and one soul; and observe how all things have reference to one perception, the perception of this one living being; and how all things act with one movement; and how all things are the cooperating causes of all things which exist; observe too the continuous spinning of the thread and the contexture of the web." (Marcus Aurelius, "Meditations". cca. 121–180 AD)

"The universal cause is one thing, a particular cause another. An effect can be haphazard with respect to the plan of the second, but not of the first. For an effect is not taken out of the scope of one particular cause save by another particular cause which prevents it, as when wood dowsed with water, will not catch fire. The first cause, however, cannot have a random effect in its own order, since all particular causes are comprehended in its causality. When an effect does escape from a system of particular causality, we speak of it as fortuitous or a chance happening […]" (Thomas Aquinas, “Summa Theologica”, cca. 1266-1273)

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

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

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

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

"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)

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

"'Causation' has been popularly used to express the condition of association, when applied to natural phenomena. There is no philosophical basis for giving it a wider meaning than partial or absolute association. In no case has it been proved that there is an inherent necessity in the laws of nature. Causation is correlation. [...] perfect correlation, when based upon sufficient experience, is causation in the scientific sense." (Henry E. Niles, "Correlation, Causation and Wright's Theory of 'Path Coefficients'", Genetics, 1922)

"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)

"[...] the conception of chance enters in the very first steps of scientific activity in virtue of the fact that no observation is absolutely correct. I think chance is a more fundamental conception that causality; for whether in a concrete case, a cause-effect relation holds or not can only be judged by applying the laws of chance to the observation." (Max Born, 1949)

"There is no correlation between the cause and the effect. The events reveal only an aleatory determination, connected not so much with the imperfection of our knowledge as with the structure of the human world." (Raymond Aron, "The Opium of the Intellectuals", 1955)

"Nature is pleased with simplicity, and affects not the pomp of superfluous causes." (Morris Kline, "Mathematics and the Physical World", 1959) 

"Every part of the system is so related to every other part that a change in a particular part causes a changes in all other parts and in the total system." (Arthur D Hall, "A methodology for systems engineering", 1962)

"In complex systems cause and effect are often not closely related in either time or space. The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by nonlinear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive-feedback loops describing growth processes as well as negative, goal-seeking loops. In the complex system the cause of a difficulty may lie far back in time from the symptoms, or in a completely different and remote part of the system. In fact, causes are usually found, not in prior events, but in the structure and policies of the system." (Jay W Forrester, "Urban dynamics", 1969)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world."  (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"The complexities of cause and effect defy analysis." (Douglas Adams, "Dirk Gently's Holistic Detective Agency", 1987)

"Until we can distinguish between an event that is truly random and an event that is the result of cause and effect, we will never know whether what we see is what we'll get, nor how we got what we got. When we take a risk, we are betting on an outcome that will result from a decision we have made, though we do not know for certain what the outcome will be. The essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"Statistical models in the social sciences rely on correlations, generally not causes, of our behavior. It is inevitable that such models of reality do not capture reality well. This explains the excess of false positives and false negatives." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)

"Statisticians set a high bar when they assign a cause to an effect. [...] A model that ignores cause–effect relationships cannot attain the status of a model in the physical sciences. This is a structural limitation that no amount of data - not even Big Data - can surmount." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)

"Effects without an understanding of the causes behind them, on the other hand, are just bunches of data points floating in the ether, offering nothing useful by themselves. Big Data is information, equivalent to the patterns of light that fall onto the eye. Big Data is like the history of stimuli that our eyes have responded to. And as we discussed earlier, stimuli are themselves meaningless because they could mean anything. The same is true for Big Data, unless something transformative is brought to all those data sets… understanding." (Beau Lotto, "Deviate: The Science of Seeing Differently", 2017)

"Any time you run regression analysis on arbitrary real-world observational data, there’s a significant risk that there’s hidden confounding in your dataset and so causal conclusions from such analysis are likely to be (causally) biased." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Expert knowledge is a term covering various types of knowledge that can help define or disambiguate causal relations between two or more variables. Depending on the context, expert knowledge might refer to knowledge from randomized controlled trials, laws of physics, a broad scope of experiences in a given area, and more." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"In summary, the relationship between different branches of contemporary machine learning and causality is nuanced. That said, most broadly adopted machine learning models operate on rung one, not having a causal world model." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The basic goal of causal inference is to estimate the causal effect of one set of variables on another. In most cases, to do it accurately, we need to know which variables we should control for. [...] to accurately control for confounders, we need to go beyond the realm of pure statistics and use the information about the data-generating process, which can be encoded as a (causal) graph. In this sense, the ability to translate between graphical and statistical properties is central to causal inference." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The causal interpretation of linear regression only holds when there are no spurious relationships in your data. This is the case in two scenarios: when you control for a set of all necessary variables (sometimes this set can be empty) or when your data comes from a properly designed randomized experiment." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The first level of creativity [for evaluating causal models] is to use the refutation tests [...] The second level of creativity is available when you have access to historical data coming from randomized experiments. You can compare your observational model with the experimental results and try to adjust your model accordingly. The third level of creativity is to evaluate your modeling approach on simulated data with known outcomes. [...] The fourth level of creativity is sensitivity analysis." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Although to penetrate into the intimate mysteries of nature and hence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena." (Leonhard Euler)

"Nature is pleased with simplicity, and affects not the pomp of superfluous causes." (Sir Issac Newton)

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

🔭Data Science: Precision (Just the Quotes)

"Simplicity and precision ought to be the characteristics of a scientific nomenclature: words should signify things, or the analogies of things, and not opinions." (Sir Humphry Davy, Elements of Chemical Philosophy", 1812)

"[Precision] is the very soul of science; and its attainment afford the only criterion, or at least the best, of the truth of theories, and the correctness of experiments." (John F W Herschel, "A Preliminary Discourse on the Study of Natural Philosophy", 1830)

"Numerical facts, like other facts, are but the raw materials of knowledge, upon which our reasoning faculties must be exerted in order to draw forth the principles of nature. [...] Numerical precision is the soul of science [...]" (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"One is almost tempted to assert that quite apart from its intellectual mission, theory is the most practical thing conceivable, the quintessence of practice as it were, since the precision of its conclusions cannot be reached by any routine of estimating or trial and error; although given the hidden ways of theory, this will hold only for those who walk them with complete confidence." (Ludwig E Boltzmann, "On the Significance of Theories", 1890)

"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)

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

"It is difficult to find an intelligible account of the meaning of ‘probability’, or of how we are ever to determine the probability of any particular proposition; and yet treatises on the subject profess to arrive at complicated results of the greatest precision and the most profound practical importance." (John M Keynes, "A Treatise on Probability", 1921)

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "A Scientific Autobiography", 1949)

"Precision is expressed by an international standard, viz., the standard error. It measures the average of the difference between a complete coverage and a long series of estimates formed from samples drawn from this complete coverage by a particular procedure or drawing, and processed by a particular estimating formula." (W Edwards Deming, "On the Presentation of the Results of Sample Surveys as Legal Evidence", Journal of the American Statistical Association Vol 49 (268), 1954)

"Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment." (C West Churchman, "Costs, Utilities, and Values", 1956)

"The precision of a number is the degree of exactness with which it is stated, while the accuracy of a number is the degree of exactness with which it is known or observed. The precision of a quantity is reported by the number of significant figures in it." (Edmund C Berkeley & Lawrence Wainwright, Computers: Their Operation and Applications", 1956)

"The two most important characteristics of the language of statistics are first, that it describes things in quantitative terms, and second, that it gives this description an air of accuracy and precision." (Ely Devons, "Essays in Economics", 1961)

"We all know that in economic statistics particularly, true precision, comparability and accuracy is extremely difficult to achieve, and it is for this reason that the language of economic statistics is so difficult to handle." (Ely Devons, "Essays in Economics", 1961)

"It is of course desirable to work with manageable models which maximize generality, realism, and precision toward the overlapping but not identical goals of understanding, predicting, and modifying nature. But this cannot be done." (Richard Levins, "The strategy of model building in population biology", American Scientist Vol. 54 (4), 1966) 

"In general, complexity and precision bear an inverse relation to one another in the sense that, as the complexity of a problem increases, the possibility of analysing it in precise terms diminishes. Thus 'fuzzy thinking' may not be deplorable, after all, if it makes possible the solution of problems which are much too complex for precise analysis." (Lotfi A Zadeh, "Fuzzy languages and their relation to human intelligence", 1972)

"As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics." (Lotfi A Zadeh, 1973)

"Simplicity is worth buying if we do not have to pay too great a loss of precision for it." (George Pólya, "Mathematical Methods in Science", 1977)

"Computational reducibility may well be the exception rather than the rule: Most physical questions may be answerable only through irreducible amounts of computation. Those that concern idealized limits of infinite time, volume, or numerical precision can require arbitrarily long computations, and so be formally undecidable." (Stephen Wolfram, Undecidability and intractability in theoretical physics", Physical Review Letters 54 (8), 1985)

"Negative feedback only improves the precision of goal-seeking, but does not determine it. Feedback devices are only executive mechanisms that operate during the translation of a program." (Ernst Mayr, "Toward a New Philosophy of Biology: Observations of an Evolutionist", 1988)

"A mathematical model uses mathematical symbols to describe and explain the represented system. Normally used to predict and control, these models provide a high degree of abstraction but also of precision in their application." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Precision does not vary linearly with increasing sample size. As is well known, the width of a confidence interval is a function of the square root of the number of observations. But it is more complicate than that. The basic elements determining a confidence interval are the sample size, an estimate of variability, and a pivotal variable associated with the estimate of variability." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Statistics can certainly pronounce a fact, but they cannot explain it without an underlying context, or theory. Numbers have an unfortunate tendency to supersede other types of knowing. […] Numbers give the illusion of presenting more truth and precision than they are capable of providing." (Ronald J Baker, "Measure what Matters to Customers: Using Key Predictive Indicators", 2006)

"[myth:] Accuracy is more important than precision. For single best estimates, be it a mean value or a single data value, this question does not arise because in that case there is no difference between accuracy and precision. (Think of a single shot aimed at a target.) Generally, it is good practice to balance precision and accuracy. The actual requirements will differ from case to case." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Popular accounts of mathematics often stress the discipline’s obsession with certainty, with proof. And mathematicians often tell jokes poking fun at their own insistence on precision. However, the quest for precision is far more than an end in itself. Precision allows one to reason sensibly about objects outside of ordinary experience. It is a tool for exploring possibility: about what might be, as well as what is." (Donal O’Shea, “The Poincaré Conjecture”, 2007)

"Precision and recall are ways of monitoring the power of the machine learning implementation. Precision is a metric that monitors the percentage of true positives. […] Recall is the ratio of true positives to true positive plus false negatives." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"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)

🔭Data Science: Weights (Just the Quotes)

"In many cases general probability samples can be thought of in terms of (1) a subdivision of the population into strata, (2) a self-weighting probability sample in each stratum, and (3) combination of the stratum sample means weighted by the size of the stratum." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"Averaging results, whether weighted or not, needs to be done with due caution and commonsense. Even though a measurement has a small quoted error it can still be, not to put too fine a point on it, wrong. If two results are in blatant and obvious disagreement, any average is meaningless and there is no point in performing it. Other cases may be less outrageous, and it may not be clear whether the difference is due to incompatibility or just unlucky chance." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"An artificial neural network is an information-processing system that has certain performance characteristics in common with biological neural networks. Artificial neural networks have been developed as generalizations of mathematical models of human cognition or neural biology, based on the assumptions that: (1) Information processing occurs at many simple elements called neurons. (2) Signals are passed between neurons over connection links. (3) Each connection link has an associated weight, which, in a typical neural net, multiplies the signal transmitted. (4) Each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals) to determine its output signal." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"A neural network is characterized by (1) its pattern of connections between the neurons (called its architecture), (2) its method of determining the weights on the connections (called its training, or learning, algorithm), and (3) its activation function." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"A neural network training method based on presenting input vector x and looking at the output vector calculated by the network. If it is considered 'good', then a 'reward' is given to the network in the sense that the existing connection weights get increased, otherwise the network is "punished"; the connection weights, being considered as 'not appropriately set,' decrease." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"More than just a new computing architecture, neural networks offer a completely different paradigm for solving problems with computers. […] The process of learning in neural networks is to use feedback to adjust internal connections, which in turn affect the output or answer produced. The neural processing element combines all of the inputs to it and produces an output, which is essentially a measure of the match between the input pattern and its connection weights. When hundreds of these neural processors are combined, we have the ability to solve difficult problems such as credit scoring." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"When training a neural network, it is important to understand when to stop. […] If the same training patterns or examples are given to the neural network over and over, and the weights are adjusted to match the desired outputs, we are essentially telling the network to memorize the patterns, rather than to extract the essence of the relationships. What happens is that the neural network performs extremely well on the training data. However, when it is presented with patterns it hasn't seen before, it cannot generalize and does not perform well. What is the problem? It is called overtraining." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"For linear dependences the main information usually lies in the slope. It is obvious that those points that lie far apart have the strongest influence on the slope if all points have the same uncertainty. In this context we speak of the strong leverage of distant points; when determining the parameter 'slope' these distant points carry more effective weight. Naturally, this weight is distinct from the 'statistical' weight usually used in regression analysis." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Generally, these programs fall within the techniques of reinforcement learning and the majority use an algorithm of temporal difference learning. In essence, this computer learning paradigm approximates the future state of the system as a function of the present state. To reach that future state, it uses a neural network that changes the weight of its parameters as it learns." (Diego Rasskin-Gutman, "Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Neural networks can model very complex patterns and decision boundaries in the data and, as such, are very powerful. In fact, they are so powerful that they can even model the noise in the training data, which is something that definitely should be avoided. One way to avoid this overfitting is by using a validation set in a similar way as with decision trees.[...] Another scheme to prevent a neural network from overfitting is weight regularization, whereby the idea is to keep the weights small in absolute sense because otherwise they may be fitting the noise in the data. This is then implemented by adding a weight size term (e.g., Euclidean norm) to the objective function of the neural network." (Bart Baesens, "Analytics in a Big Data World: The Essential Guide to Data Science and Its Applications", 2014)

"Keep in mind that a weighted average may be different than a simple (non- weighted) average because a weighted average - by definition - counts certain data points more heavily. When you’re thinking about an average, try to determine if it’s a simple average or a weighted average. If it’s weighted, ask yourself how it’s being weighted, and see which data points count more than others." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

"Boosting is a non-linear flexible regression technique that helps increase the accuracy of trees by assigning more weights to wrong predictions. The reason for inducing more weight is so the model can emphasize more on these wrongly predicted samples and tune itself to increase accuracy. The gradient boosting method solves the inherent problem in boosting trees (i.e., low speed and human interpretability). The algorithm supports parallelism by specifying the number of threads." (Danish Haroon, "Python Machine Learning Case Studies", 2017)

"Early stopping and regularization can ensure network generalization when you apply them properly. [...] With early stopping, the choice of the validation set is also important. The validation set should be representative of all points in the training set. When you use Bayesian regularization, it is important to train the network until it reaches convergence. The sum-squared error, the sum-squared weights, and the effective number of parameters should reach constant values when the network has converged. With both early stopping and regularization, it is a good idea to train the network starting from several different initial conditions. It is possible for either method to fail in certain circumstances. By testing several different initial conditions, you can verify robust network performance." (Mark H Beale et al, "Neural Network Toolbox™ User's Guide", 2017)

"In Boosting, the selection of samples is done by giving more and more weight to hard-to-classify observations. Gradient boosting classification produces a prediction model in the form of an ensemble of weak predictive models, usually decision trees. It generalizes the model by optimizing for the arbitrary differentiable loss function. At each stage, regression trees fit on the negative gradient of binomial or multinomial deviance loss function." (Danish Haroon, "Python Machine Learning Case Studies", 2017)

"Deep neural networks have an input layer and an output layer. In between, are “hidden layers” that process the input data by adjusting various weights in order to make the output correspond closely to what is being predicted. [...] The mysterious part is not the fancy words, but that no one truly understands how the pattern recognition inside those hidden layers works. That’s why they’re called 'hidden'. They are an inscrutable black box - which is okay if you believe that computers are smarter than humans, but troubling otherwise." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

🔭Data Science: Data Scientists (Just the quotes)

"[...] be wary of analysts that try to quantify the unquantifiable." (Ralph Keeney & Raiffa Howard, "Decisions with Multiple Objectives: Preferences and Value Trade-offs", 1976)

"Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance." (Richard W Hamming, "You and Your Research", 1986) 

"Many new data scientists tend to rush past it to get their data into a minimally acceptable state, only to discover that the data has major quality issues after they apply their (potentially computationally intensive) algorithm and get a nonsense answer as output. (Sandy Ryza, "Advanced Analytics with Spark: Patterns for Learning from Data at Scale", 2009)

"Data scientists combine entrepreneurship with patience, the willingness to build data products incrementally, the ability to explore, and the ability to iterate over a solution. They are inherently interdisciplinary. They can tackle all aspects of a problem, from initial data collection and data conditioning to drawing conclusions. They can think outside the box to come up with new ways to view the problem, or to work with very broadly defined problems: 'there’s a lot of data, what can you make from it?'" (Mike Loukides, "What Is Data Science?", 2011)

"As data scientists, we prefer to interact with the raw data. We know how to import it, transform it, mash it up with other data sources, and visualize it. Most of your customers can’t do that. One of the biggest challenges of developing a data product is figuring out how to give data back to the user. Giving back too much data in a way that’s overwhelming and paralyzing is 'data vomit'. It’s natural to build the product that you would want, but it’s very easy to overestimate the abilities of your users. The product you want may not be the product they want." (Dhanurjay Patil, "Data Jujitsu: The Art of Turning Data into Product", 2012)

"In an emergency, a data product that just produces more data is of little use. Data scientists now have the predictive tools to build products that increase the common good, but they need to be aware that building the models is not enough if they do not also produce optimized, implementable outcomes." (Jeremy Howard et al, "Designing Great Data Products", 2012)

"Smart data scientists don’t just solve big, hard problems; they also have an instinct for making big problems small." (Dhanurjay Patil, "Data Jujitsu: The Art of Turning Data into Product", 2012)

"More generally, a data scientist is someone who knows how to extract meaning from and interpret data, which requires both tools and methods from statistics and machine learning, as well as being human. She spends a lot of time in the process of collecting, cleaning, and munging data, because data is never clean. This process requires persistence, statistics, and software engineering skills - skills that are also necessary for understanding biases in the data, and for debugging logging output from code. Once she gets the data into shape, a crucial part is exploratory data analysis, which combines visualization and data sense. She’ll find patterns, build models, and algorithms - some with the intention of understanding product usage and the overall health of the product, and others to serve as prototypes that ultimately get baked back into the product. She may design experiments, and she is a critical part of data-driven decision making. She’ll communicate with team members, engineers, and leadership in clear language and with data visualizations so that even if her colleagues are not immersed in the data themselves, they will understand the implications." (Rachel Schutt, "Doing Data Science: Straight Talk from the Frontline", 2013)

"Unfortunately, creating an objective function that matches the true goal of the data mining is usually impossible, so data scientists often choose based on faith and experience." (Foster Provost, "Data Science for Business", 2013)

"[...] a data scientist role goes beyond the collection and reporting on data; it must involve looking at a business The role of a data scientist goes beyond the collection and reporting on data. application or process from multiple vantage points and determining what the main questions and follow-ups are, as well as recommending the most appropriate ways to employ the data at hand." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"In terms of characteristics, a data scientist has an inquisitive mind and is prepared to explore and ask questions, examine assumptions and analyse processes, test hypotheses and try out solutions and, based on evidence, communicate informed conclusions, recommendations and caveats to stakeholders and decision makers." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 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)

"Data scientists should have some domain expertise. Most data science projects begin with a real-world, domain-specific problem and the need to design a data-driven solution to this problem. As a result, it is important for a data scientist to have enough domain expertise that they understand the problem, why it is important, an dhow a data science solution to the problem might fit into an organization’s processes. This domain expertise guides the data scientist as she works toward identifying an optimized solution." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"A data scientist should be able to wrangle, mung, manipulate, and consolidate datasets before performing calculations on that data that help us to understand it. Analysis is a broad term, but it's clear that the end result is knowledge of your dataset that you didn't have before you started, no matter how basic or complex. [...] A data scientist usually has to be able to apply statistical, mathematical, and machine learning models to data in order to explain it or perform some sort of prediction." (Andrew P McMahon, "Machine Learning Engineering with Python", 2021)

"Data scientists are advanced in their technical skills. They like to do coding, statistics, and so forth. In its purest form, data science is where an individual uses the scientific method on data." (Jordan Morrow, "Be Data Literate: The data literacy skills everyone needs to succeed", 2021)

"The ideal data scientist is a multi-disciplinary person, persistent in pursuing the solution." (Anil Maheshwari, "Data Analytics Made Accessible", 2021)

"Overall [...] everyone also has a need to analyze data. The ability to analyze data is vital in its understanding of product launch success. Everyone needs the ability to find trends and patterns in the data and information. Everyone has a need to ‘discover or reveal (something) through detailed examination’, as our definition says. Not everyone needs to be a data scientist, but everyone needs to drive questions and analysis. Everyone needs to dig into the information to be successful with diagnostic analytics. This is one of the biggest keys of data literacy: analyzing data." (Jordan Morrow, "Be Data Literate: The data literacy skills everyone needs to succeed", 2021)

"A data scientist is someone who can obtain, scrub, explore, model and interpret data, blending hacking, statistics and machine learning. Data scientists not only are adept at working with data, but appreciate data itself as a first-class product." (Hillary Mason)

"A data scientist is someone who knows more statistics than a computer scientist and more computer science than a statistician." (Josh Blumenstock) [attributed]

"All businesses could use a garden where Data Scientists plant seeds of possibility and water them with collaboration." (Damian Mingle)

"Data scientist (noun): Person who is better at statistics than any software engineer and better at software engineering than any statistician." (Josh Wills)

"Data Scientists should recall innovation often times is not providing fancy algorithms, but rather value to the customer." (Damian Mingle)

"Data Scientists should refuse to be defined by someone else's vision of what's possible." (Damian Mingle)

🔭Data Science: Statistics' Usage (Just the Quotes)

"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)

"To a very striking degree our culture has become a Statistical culture. Even a person who may never have heard of an index number is affected [...] by [...] of those index numbers which describe the cost of living. It is impossible to understand Psychology, Sociology, Economics, Finance or a Physical Science without some general idea of the meaning of an average, of variation, of concomitance, of sampling, of how to interpret charts and tables." (Carrol D Wright, 1887)

"[…] the new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and to write." (Herbert G Wells, "Mankind In the Making", 1906)

"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)

"Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. " (Richard von Mises, "Probability, Statistics, and Truth", 1939)

"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)

"While the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what anyone man will be up to, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician." (Sir Arthur C Doyle)

🔭Data Science: Variation (Just the Quotes)

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

"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)

"The conception of statistics as the study of variation is the natural outcome of viewing the subject as the study of populations; for a population of individuals in all respects identical is completely described by a description of anyone individual, together with the number in the group. The populations which are the object of statistical study always display variations in one or more respects. To speak of statistics as the study of variation also serves to emphasise the contrast between the aims of modern statisticians and those of their predecessors." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"Postulate 1. All chance systems of causes are not alike in the sense that they enable us to predict the future in terms of the past. Postulate 2. Constant systems of chance causes do exist in nature. Postulate 3. Assignable causes of variation may be found and eliminated."(Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)

"In our definition of system we noted that all systems have interrelationships between objects and between their attributes. If every part of the system is so related to every other part that any change in one aspect results in dynamic changes in all other parts of the total system, the system is said to behave as a whole or coherently. At the other extreme is a set of parts that are completely unrelated: that is, a change in each part depends only on that part alone. The variation in the set is the physical sum of the variations of the parts. Such behavior is called independent or physical summativity." (Arthur D Hall & Robert E Fagen, "Definition of System", General Systems Vol. 1, 1956)

"The statistics themselves prove nothing; nor are they at any time a substitute for logical thinking. There are […] many simple but not always obvious snags in the data to contend with. Variations in even the simplest of figures may conceal a compound of influences which have to be taken into account before any conclusions are drawn from the data." (Alfred R Ilersic, "Statistics", 1959)

"Adaptive system - whether on the biological, psychological, or sociocultural level - must manifest (1) some degree of 'plasticity' and 'irritability' vis-a-vis its environment such that it carries on a constant interchange with acting on and reacting to it; (2) some source or mechanism for variety, to act as a potential pool of adaptive variability to meet the problem of mapping new or more detailed variety and constraints in a changeable environment; (3) a set of selective criteria or mechanisms against which the 'variety pool' may be sifted into those variations in the organization or system that more closely map the environment and those that do not; and (4) an arrangement for preserving and/or propagating these 'successful' mappings." (Walter F Buckley," Sociology and modern systems theory", 1967)

"To adapt to a changing environment, the system needs a variety of stable states that is large enough to react to all perturbations but not so large as to make its evolution uncontrollably chaotic. The most adequate states are selected according to their fitness, either directly by the environment, or by subsystems that have adapted to the environment at an earlier stage. Formally, the basic mechanism underlying self-organization is the (often noise-driven) variation which explores different regions in the system’s state space until it enters an attractor. This precludes further variation outside the attractor, and thus restricts the freedom of the system’s components to behave independently. This is equivalent to the increase of coherence, or decrease of statistical entropy, that defines self-organization." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Thus, the construction of a mathematical model consisting of certain basic equations of a process is not yet sufficient for effecting optimal control. The mathematical model must also provide for the effects of random factors, the ability to react to unforeseen variations and ensure good control despite errors and inaccuracies." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"The greater the uncertainty, the greater the amount of decision making and information processing. It is hypothesized that organizations have limited capacities to process information and adopt different organizing modes to deal with task uncertainty. Therefore, variations in organizing modes are actually variations in the capacity of organizations to process information and make decisions about events which cannot be anticipated in advance." (John K Galbraith, "Organization Design", 1977)

"Uncontrolled variation is the enemy of quality." (W Edwards Deming, 1980)

"A good description of the data summarizes the systematic variation and leaves residuals that look structureless. That is, the residuals exhibit no patterns and have no exceptionally large values, or outliers. Any structure present in the residuals indicates an inadequate fit. Looking at the residuals laid out in an overlay helps to spot patterns and outliers and to associate them with their source in the data." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)

"A useful description relates the systematic variation to one or more factors; if the residuals dwarf the effects for a factor, we may not be able to relate variation in the data to changes in the factor. Furthermore, changes in the factor may bring no important change in the response. Such comparisons of residuals and effects require a measure of the variation of overlays relative to each other." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"Fitting data means finding mathematical descriptions of structure in the data. An additive shift is a structural property of univariate data in which distributions differ only in location and not in spread or shape. […] The process of identifying a structure in data and then fitting the structure to produce residuals that have the same distribution lies at the heart of statistical analysis. Such homogeneous residuals can be pooled, which increases the power of the description of the variation in the data." (William S Cleveland, "Visualizing Data", 1993)

"Probabilistic inference is the classical paradigm for data analysis in science and technology. It rests on a foundation of randomness; variation in data is ascribed to a random process in which nature generates data according to a probability distribution. This leads to a codification of uncertainly by confidence intervals and hypothesis tests." (William S Cleveland, "Visualizing Data", 1993)

"Swarm systems generate novelty for three reasons: (1) They are 'sensitive to initial conditions' - a scientific shorthand for saying that the size of the effect is not proportional to the size of the cause - so they can make a surprising mountain out of a molehill. (2) They hide countless novel possibilities in the exponential combinations of many interlinked individuals. (3) They don’t reckon individuals, so therefore individual variation and imperfection can be allowed. In swarm systems with heritability, individual variation and imperfection will lead to perpetual novelty, or what we call evolution." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Unlike classical mathematics, net math exhibits nonintuitive traits. In general, small variations in input in an interacting swarm can produce huge variations in output. Effects are disproportional to causes - the butterfly effect." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"When visualization tools act as a catalyst to early visual thinking about a relatively unexplored problem, neither the semantics nor the pragmatics of map signs is a dominant factor. On the other hand, syntactics (or how the sign-vehicles, through variation in the visual variables used to construct them, relate logically to one another) are of critical importance." (Alan M MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"Statistics is a general intellectual method that applies wherever data, variation, and chance appear. It is a fundamental method because data, variation and chance are omnipresent in modern life. It is an independent discipline with its own core ideas rather than, for example, a branch of mathematics. […] Statistics offers general, fundamental, and independent ways of thinking." (David S Moore, "Statistics among the Liberal Arts", Journal of the American Statistical Association, 1998)

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

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

"Statistics is the analysis of variation. There are many sources and kinds of variation. In environmental studies it is particularly important to understand the kinds of variation and the implications of the difference. Two important categories are variability and uncertainty. Variability refers to variation in environmental quantities (which may have special regulatory interest), uncertainty refers to the degree of precision with which these quantities are estimated." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"When there is more than one source of variation it is important to identify those sources." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Thus, nonlinearity can be understood as the effect of a causal loop, where effects or outputs are fed back into the causes or inputs of the process. Complex systems are characterized by networks of such causal loops. In a complex, the interdependencies are such that a component A will affect a component B, but B will in general also affect A, directly or indirectly.  A single feedback loop can be positive or negative. A positive feedback will amplify any variation in A, making it grow exponentially. The result is that the tiniest, microscopic difference between initial states can grow into macroscopically observable distinctions." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 2010)

"Statistics is the scientific discipline that provides methods to help us make sense of data. […] The field of statistics teaches us how to make intelligent judgments and informed decisions in the presence of uncertainty and variation." (Roxy Peck & Jay L Devore, "Statistics: The Exploration and Analysis of Data" 7th Ed, 2012)

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

"One of the most common problems that you will encounter when training deep neural networks will be overfitting. What can happen is that your network may, owing to its flexibility, learn patterns that are due to noise, errors, or simply wrong data. [...] The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented the underlying model structure. The opposite is called underfitting - when the model cannot capture the structure of the data." (Umberto Michelucci, "Applied Deep Learning: A Case-Based Approach to Understanding Deep Neural Networks", 2018)

"We over-fit when we go too far in adapting to local circumstances, in a worthy but misguided effort to be ‘unbiased’ and take into account all the available information. Usually we would applaud the aim of being unbiased, but this refinement means we have less data to work on, and so the reliability goes down. Over-fitting therefore leads to less bias but at a cost of more uncertainty or variation in the estimates, which is why protection against over-fitting is sometimes known as the bias/variance trade-off." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

🔭Data Science: Trial and Error (Just the Quotes)

"One is almost tempted to assert that quite apart from its intellectual mission, theory is the most practical thing conceivable, the quintessence of practice as it were, since the precision of its conclusions cannot be reached by any routine of estimating or trial and error; although given the hidden ways of theory, this will hold only for those who walk them with complete confidence." (Ludwig E Boltzmann, "On the Significance of Theories", 1890)

"The discoveries in physical science, the triumphs in invention, attest the value of the process of trial and error. In large measure, these advances have been due to experimentation." (Louis Brandeis, "Judicial opinions", 1932)

"We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, [Nobel Prize Lecture], 1974)

"The natural as well as the social sciences always start from problems, from the fact that something inspires amazement in us, as the Greek philosophers used to say. To solve these problems, the sciences use fundamentally the same method that common sense employs, the method of trial and error. To be more precise, it is the method of trying out solutions to our problem and then discarding the false ones as erroneous. This method assumes that we work with a large number of experimental solutions. One solution after another is put to the test and eliminated." (Karl R Popper, "All Life is Problem Solving", 1999) 

"Heuristics are rules of thumb that help constrain the problem in certain ways (in other words they help you to avoid falling back on blind trial and error), but they don't guarantee that you will find a solution. Heuristics are often contrasted with algorithms that will guarantee that you find a solution - it may take forever, but if the problem is algorithmic you will get there. However, heuristics are also algorithms." (S Ian Robertson, "Problem Solving", 2001)

"Technology is the result of antifragility, exploited by risk-takers in the form of tinkering and trial and error, with nerd-driven design confined to the backstage." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"We can simplify the relationships between fragility, errors, and antifragility as follows. When you are fragile, you depend on things following the exact planned course, with as little deviation as possible - for deviations are more harmful than helpful. This is why the fragile needs to be very predictive in its approach, and, conversely, predictive systems cause fragility. When you want deviations, and you don’t care about the possible dispersion of outcomes that the future can bring, since most will be helpful, you are antifragile. Further, the random element in trial and error is not quite random, if it is carried out rationally, using error as a source of information. If every trial provides you with information about what does not work, you start zooming in on a solution - so every attempt becomes more valuable, more like an expense than an error. And of course you make discoveries along the way." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"Another crowning achievement of deep learning is its extension to the domain of reinforcement learning. In the context of reinforcement learning, an autonomous agent must learn to perform a task by trial and error, without any guidance from the human operator." (Ian Goodfellow et al, "Deep Learning", 2015)

"A learning algorithm for a robot or a software agent to take actions in an environment so as to maximize the sum of rewards through trial and error." (Tomohiro Yamaguchi et al, "Analyzing the Goal-Finding Process of Human Learning With the Reflection Subtask", 2018)

"Reinforcement learning is also a subset of AI algorithms which creates independent, self-learning systems through trial and error. Any positive action is assigned a reward and any negative action would result in a punishment. Reinforcement learning can be used in training autonomous vehicles where the goal would be obtaining the maximum rewards." (Vijayaraghavan Varadharajan & Akanksha Rajendra Singh, "Building Intelligent Cities: Concepts, Principles, and Technologies", 2021)

"Methodologically, much of modern machine learning practice rests on a variant of trial and error, which we call the train-test paradigm. Practitioners repeatedly build models using any number of heuristics and test their performance to see what works. Anything goes as far as training is concerned, subject only to computational constraints, so long as the performance looks good in testing. Trial and error is sound so long as the testing protocol is robust enough to absorb the pressure placed on it." (Moritz Hardt & Benjamin Recht, "Patterns, Predictions, and Actions: Foundations of Machine Learning", 2022)