SQL Troubles: experiments

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22 August 2023

🔖Book Review: Laurent Bossavit's The Leprechauns of Software Engineering (2015)


	Software Engineering should be the "establishment and use of sound engineering principles to obtain economically software that is reliable and works on real machines efficiently" [2]. Working for more than 20 years in the field I feel sometimes that its foundation is a strange mix of sound and questionable ideas that take the form of methodologies, principles, standards, myths, folklore, statistics and other similar concepts that form its backbone. I tend to look with critical eyes at the important numbers advanced in research and pseudo-scientific papers especially when they’re related to my job, this because I know that statistics are seldom what they appear to be - there are accidental and sometimes even intended errors made to support the facts. Unfortunately, the missing row data and often the information about the methodologies used in collecting and processing the respective data make numbers and/or graphics' understanding more challenging, not to mention the considerable amount of effort and time spent to uncover the evidence trail.
Fortunately, there are other professionals who went further down the path of bibliographical references and shared their findings in blogs, papers, books and other media content. It’s also the case of Laurent Bossavit, who in his book, "The Leprechauns of Software Engineering" (2015), looks behind some of the numbers that over time become part of the leprechaunish folklore of IT professionals, puts them into the historical context and provides in appendix the evidence trails for the reader to validate his findings. Over several chapters the author focuses mainly on the cost of defects, Boehm’s cone of uncertainty, the differences in productivity amount individual programmers (aka 10x claim), respectively the relation between poor requirements and defects. His most important finding is that the references used in most of the researched sources advancing the above numbers were secondary, while the actual sources provide no direct information of empirical data or the methodology for its collection. The way the numbers are advanced and used makes one question the validity of the measurements performed, respectively the character of the mistakes the authors made. Many of the cited papers hardly match the academic requirements of other scientific fields, being a mix of false claims, improperly conducted research and citations. Secondly, he argues that the small sample sizes used as basis for the experiments, the small population formed usually of students, respectively the way numbers were mixed without any reliable scientific character makes him (and the reader as well) question even more how the experiments were performed in the respective papers. With this, it is more likely that a bigger number of research based on these sources should raise further concerns. The reader can thus ask himself/herself how deep the domino effect goes inside of the Software Engineering field. In author’s opinion Software Engineering as social process "needs to be studied with tools that borrow as much from the social and cognitive sciences as they do from the mathematical theories of computation". How much is possible to extend the theories and models of the respective fields is an open topic. The bottom line, the field of Software Engineering needs better and scientific empirical experiments that are based on commonly agreed definitions, data collection and processing techniques, respectively higher standards for research publications. Without this, we’ll continue to compare apples with peaches and mix them in calculations so we can get some stories that support our leprechaunish theories. Overall, the book is a good read for software engineers as well as for other IT professionals. Even if it barely scratched the surface of software myths and folklore, there’s enough material for the readers who want to dive deeper. Previous Post <<\|\|>> Next Post References: [1] Laurent Bossavit (2015) "The Leprechauns of Software Engineering" [2] Friedrich Bauer (1972) "Software Engineering", Information Processing

30 December 2018

🔭Data Science: Testing (Just the Quotes)

"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)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"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)

"The preliminary examination of most data is facilitated by the use of diagrams. Diagrams prove nothing, but bring outstanding features readily to the eye; they are therefore no substitutes for such critical tests as may be applied to the data, but are valuable in suggesting such tests, and in explaining the conclusions founded upon them." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"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 Popper, "The Logic of Scientific Discovery", 1934)

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

"To a scientist a theory is something to be tested. He seeks not to defend his beliefs, but to improve them. He is, above everything else, an expert at ‘changing his mind’." (Wendell Johnson, 1946)

"As usual we may make the errors of I) rejecting the null hypothesis when it is true, II) accepting the null hypothesis when it is false. But there is a third kind of error which is of interest because the present test of significance is tied up closely with the idea of making a correct decision about which distribution function has slipped furthest to the right. We may make the error of III) correctly rejecting the null hypothesis for the wrong reason." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"Errors of the third kind happen in conventional tests of differences of means, but they are usually not considered, although their existence is probably recognized. It seems to the author that there may be several reasons for this among which are 1) a preoccupation on the part of mathematical statisticians with the formal questions of acceptance and rejection of null hypotheses without adequate consideration of the implications of the error of the third kind for the practical experimenter, 2) the rarity with which an error of the third kind arises in the usual tests of significance." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"If significance tests are required for still larger samples, graphical accuracy is insufficient, and arithmetical methods are advised. A word to the wise is in order here, however. Almost never does it make sense to use exact binomial significance tests on such data - for the inevitable small deviations from the mathematical model of independence and constant split have piled up to such an extent that the binomial variability is deeply buried and unnoticeable. Graphical treatment of such large samples may still be worthwhile because it brings the results more vividly to the eye." (Frederick Mosteller & John W Tukey, "The Uses and Usefulness of Binomial Probability Paper?", Journal of the American Statistical Association 44, 1949)

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

"The only relevant test of the validity of a hypothesis is comparison of prediction with experience." (Milton Friedman, "Essays in Positive Economics", 1953)

"The main purpose of a significance test is to inhibit the natural enthusiasm of the investigator." (Frederick Mosteller, "Selected Quantitative Techniques", 1954)

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

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

"Null hypotheses of no difference are usually known to be false before the data are collected [...] when they are, their rejection or acceptance simply reflects the size of the sample and the power of the test, and is not a contribution to science." (I Richard Savage, "Nonparametric statistics", Journal of the American Statistical Association 52, 1957)

"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)

"One feature [...] which requires much more justification than is usually given, is the setting up of unplausible null hypotheses. For example, a statistician may set out a test to see whether two drugs have exactly the same effect, or whether a regression line is exactly straight. These hypotheses can scarcely be taken literally." (Cedric A B Smith, "Book review of Norman T. J. Bailey: Statistical Methods in Biology", Applied Statistics 9, 1960)

"The null-hypothesis significance test treats ‘acceptance’ or ‘rejection’ of a hypothesis as though these were decisions one makes. But a hypothesis is not something, like a piece of pie offered for dessert, which can be accepted or rejected by a voluntary physical action. Acceptance or rejection of a hypothesis is a cognitive process, a degree of believing or disbelieving which, if rational, is not a matter of choice but determined solely by how likely it is, given the evidence, that the hypothesis is true." (William W Rozeboom, "The fallacy of the null–hypothesis significance test", Psychological Bulletin 57, 1960)

"It is easy to obtain confirmations, or verifications, for nearly every theory - if we look for confirmations. Confirmations should count only if they are the result of risky predictions. […] A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)

"The final test of a theory is its capacity to solve the problems which originated it." (George Dantzig, "Linear Programming and Extensions", 1963)

"The mediation of theory and praxis can only be clarified if to begin with we distinguish three functions, which are measured in terms of different criteria: the formation and extension of critical theorems, which can stand up to scientific discourse; the organization of processes of enlightenment, in which such theorems are applied and can be tested in a unique manner by the initiation of processes of reflection carried on within certain groups toward which these processes have been directed; and the selection of appropriate strategies, the solution of tactical questions, and the conduct of the political struggle. On the first level, the aim is true statements, on the second, authentic insights, and on the third, prudent decisions." (Jürgen Habermas, "Introduction to Theory and Practice", 1963)

"The null hypothesis of no difference has been judged to be no longer a sound or fruitful basis for statistical investigation. […] Significance tests do not provide the information that scientists need, and, furthermore, they are not the most effective method for analyzing and summarizing data." (Cherry A Clark, "Hypothesis Testing in Relation to Statistical Methodology", Review of Educational Research Vol. 33, 1963)

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results" (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)

"The validation of a model is not that it is 'true' but that it generates good testable hypotheses relevant to important problems.” (Richard Levins, "The Strategy of Model Building in Population Biology”, 1966)

"Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. […] Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge." (Richard J. Blackwell, "Discovery in the Physical Sciences", 1969)

"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)

"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)

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

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

"Tests appear to many users to be a simple way to discharge the obligation to provide some statistical treatment of the data." (H V Roberts, "For what use are tests of hypotheses and tests of significance", Communications in Statistics [Series A], 1976)

"Prediction can never be absolutely valid and therefore science can never prove some generalization or even test a single descriptive statement and in that way arrive at final truth." (Gregory Bateson, "Mind and Nature, A necessary unity", 1979)

"The fact must be expressed as data, but there is a problem in that the correct data is difficult to catch. So that I always say 'When you see the data, doubt it!' 'When you see the measurement instrument, doubt it!' [...]For example, if the methods such as sampling, measurement, testing and chemical analysis methods were incorrect, data. […] to measure true characteristics and in an unavoidable case, using statistical sensory test and express them as data." (Kaoru Ishikawa, Annual Quality Congress Transactions, 1981)

"All interpretations made by a scientist are hypotheses, and all hypotheses are tentative. They must forever be tested and they must be revised if found to be unsatisfactory. Hence, a change of mind in a scientist, and particularly in a great scientist, is not only not a sign of weakness but rather evidence for continuing attention to the respective problem and an ability to test the hypothesis again and again." (Ernst Mayr, "The Growth of Biological Thought: Diversity, Evolution and Inheritance", 1982)

"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)

"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)

"Science has become a social method of inquiring into natural phenomena, making intuitive and systematic explorations of laws which are formulated by observing nature, and then rigorously testing their accuracy in the form of predictions. The results are then stored as written or mathematical records which are copied and disseminated to others, both within and beyond any given generation. As a sort of synergetic, rigorously regulated group perception, the collective enterprise of science far transcends the activity within an individual brain." (Lynn Margulis & Dorion Sagan, "Microcosmos", 1986)

"Beware of the problem of testing too many hypotheses; the more you torture the data, the more likely they are to confess, but confessions obtained under duress may not be admissible in the court of scientific opinion." (Stephen M. Stigler, "Neutral Models in Biology", 1987)

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

"The heart of the scientific method is the problem-hypothesis-test process. And, necessarily, the scientific method involves predictions. And predictions, to be useful in scientific methodology, must be subject to test empirically." (Paul Davies, "The Cosmic Blueprint: New Discoveries in Nature's Creative Ability to, Order the Universe", 1988)

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

"A little thought reveals a fact widely understood among statisticians: The null hypothesis, taken literally (and that’s the only way you can take it in formal hypothesis testing), is always false in the real world. [...] If it is false, even to a tiny degree, it must be the case that a large enough sample will produce a significant result and lead to its rejection. So if the null hypothesis is always false, what’s the big deal about rejecting it?" (Jacob Cohen, "Things I Have Learned (So Far)", American Psychologist, 1990)

"How has the virtually barren technique of hypothesis testing come to assume such importance in the process by which we arrive at our conclusions from our data?" (Geoffrey R Loftus, "On the tyranny of hypothesis testing in the social sciences", Contemporary Psychology 36, 1991)

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

"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)

"The amount of understanding produced by a theory is determined by how well it meets the criteria of adequacy - testability, fruitfulness, scope, simplicity, conservatism - because these criteria indicate the extent to which a theory systematizes and unifies our knowledge." (Theodore Schick Jr., "How to Think about Weird Things: Critical Thinking for a New Age", 1995)

"The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions." (Fergus Daly et al, "Elements of Statistics", 1995)

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

"There are two kinds of mistakes. There are fatal mistakes that destroy a theory; but there are also contingent ones, which are useful in testing the stability of a theory." (Gian-Carlo Rota, [lecture] 1996)

"Validation is the process of testing how good the solutions produced by a system are. The results produced by a system are usually compared with the results obtained either by experts or by other systems. Validation is an extremely important part of the process of developing every knowledge-based system. Without comparing the results produced by the system with reality, there is little point in using it." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

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

"Let us regard a proof of an assertion as a purely mechanical procedure using precise rules of inference starting with a few unassailable axioms. This means that an algorithm can be devised for testing the validity of an alleged proof simply by checking the successive steps of the argument; the rules of inference constitute an algorithm for generating all the statements that can be deduced in a finite number of steps from the axioms." (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"The greatest plus of data modeling is that it produces a simple and understandable picture of the relationship between the input variables and responses [...] different models, all of them equally good, may give different pictures of the relation between the predictor and response variables [...] One reason for this multiplicity is that goodness-of-fit tests and other methods for checking fit give a yes–no answer. With the lack of power of these tests with data having more than a small number of dimensions, there will be a large number of models whose fit is acceptable. There is no way, among the yes–no methods for gauging fit, of determining which is the better model." (Leo Breiman, "Statistical Modeling: The two cultures", Statistical Science 16(3), 2001)

"When significance tests are used and a null hypothesis is not rejected, a major problem often arises - namely, the result may be interpreted, without a logical basis, as providing evidence for the null hypothesis." (David F Parkhurst, "Statistical Significance Tests: Equivalence and Reverse Tests Should Reduce Misinterpretation", BioScience Vol. 51 (12), 2001)

"Visualizations can be used to explore data, to confirm a hypothesis, or to manipulate a viewer. [...] In exploratory visualization the user does not necessarily know what he is looking for. This creates a dynamic scenario in which interaction is critical. [...] In a confirmatory visualization, the user has a hypothesis that needs to be tested. This scenario is more stable and predictable. System parameters are often predetermined." (Usama Fayyad et al, "Information Visualization in Data Mining and Knowledge Discovery", 2002)

"There is a tendency to use hypothesis testing methods even when they are not appropriate. Often, estimation and confidence intervals are better tools. Use hypothesis testing only when you want to test a well-defined hypothesis." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 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)

"A type of error used in hypothesis testing that arises when incorrectly rejecting the null hypothesis, although it is actually true. Thus, based on the test statistic, the final conclusion rejects the Null hypothesis, but in truth it should be accepted. Type I error equates to the alpha (α) or significance level, whereby the generally accepted default is 5%." (Lynne Hambleton, "Treasure Chest of Six Sigma Growth Methods, Tools, and Best Practices", 2007)

"Each systems archetype embodies a particular theory about dynamic behavior that can serve as a starting point for selecting and formulating raw data into a coherent set of interrelationships. Once those relationships are made explicit and precise, the 'theory' of the archetype can then further guide us in our data-gathering process to test the causal relationships through direct observation, data analysis, or group deliberation." (Daniel H Kim, "Systems Archetypes as Dynamic Theories", The Systems Thinker Vol. 24 (1), 2013)

"In common usage, prediction means to forecast a future event. In data science, prediction more generally means to estimate an unknown value. This value could be something in the future (in common usage, true prediction), but it could also be something in the present or in the past. Indeed, since data mining usually deals with historical data, models very often are built and tested using events from the past." (Foster Provost & Tom Fawcett, "Data Science for Business", 2013)

"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern." (Gary Smith, "Standard Deviations", 2014)

"Data clusters are everywhere, even in random data. Someone who looks for an explanation will inevitably find one, but a theory that fits a data cluster is not persuasive evidence. The found explanation needs to make sense and it needs to be tested with uncontaminated data." (Gary Smith, "Standard Deviations", 2014)

"Machine learning is a science and requires an objective approach to problems. Just like the scientific method, test-driven development can aid in solving a problem. The reason that TDD and the scientific method are so similar is because of these three shared characteristics: Both propose that the solution is logical and valid. Both share results through documentation and work over time. Both work in feedback loops." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

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

"The 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" 2nd Ed., 2016)

"Bias is error from incorrect assumptions built into the model, such as restricting an interpolating function to be linear instead of a higher-order curve. [...] Errors of bias produce underfit models. They do not fit the training data as tightly as possible, were they allowed the freedom to do so. In popular discourse, I associate the word 'bias' with prejudice, and the correspondence is fairly apt: an apriori assumption that one group is inferior to another will result in less accurate predictions than an unbiased one. Models that perform lousy on both training and testing data are underfit." (Steven S Skiena, "The Data Science Design Manual", 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)

"Scientists generally agree that no theory is 100 percent correct. Thus, the real test of knowledge is not truth, but utility." (Yuval N Harari, "Sapiens: A brief history of humankind", 2017)

"Variance is error from sensitivity to fluctuations in the training set. If our training set contains sampling or measurement error, this noise introduces variance into the resulting model. [...] Errors of variance result in overfit models: their quest for accuracy causes them to mistake noise for signal, and they adjust so well to the training data that noise leads them astray. Models that do much better on testing data than training data are overfit." (Steven S Skiena, "The Data Science Design Manual", 2017)

"[...] a hypothesis test tells us whether the observed data are consistent with the null hypothesis, and a confidence interval tells us which hypotheses are consistent with the data." (William C Blackwelder)

27 December 2018

🔭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)

"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)

"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)

"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)

"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)

"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)

"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)

"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)

"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)

"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)

"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.

26 December 2018

🔭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)

"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)

20 December 2018

🔭Data Science: Accuracy (Just the Quotes)

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

"The test of the accuracy and completeness of a description is, not that it may assist, but that it cannot mislead." (Burt G Wilder, "A Partial Revision of Anatomical Nomenclature", Science, 1881)

"Accuracy of statement is one of the first elements of truth; inaccuracy is a near kin to falsehood." (Tyron Edwards, "A Dictionary of Thoughts", 1891)

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

"Great numbers are not counted correctly to a unit, they are estimated; and we might perhaps point to this as a division between arithmetic and statistics, that whereas arithmetic attains exactness, statistics deals with estimates, sometimes very accurate, and very often sufficiently so for their purpose, but never mathematically exact." (Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may, for instance, be called the science of counting. Counting appears at first sight to be a very simple operation, which any one can perform or which can be done automatically; but, as a matter of fact, when we come to large numbers, e.g., the population of the United Kingdom, counting is by no means easy, or within the power of an individual; limits of time and place alone prevent it being so carried out, and in no way can absolute accuracy be obtained when the numbers surpass certain limits." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Accuracy is the foundation of everything else." (Thomas H Huxley, "Method and Results", 1893)

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

"The ordinary mathematical treatment of any applied science substitutes exact axioms for the approximate results of experience, and deduces from these axioms the rigid mathematical conclusions. In applying this method it must not be forgotten that the mathematical developments transcending the limits of exactness of the science are of no practical value. It follows that a large portion of abstract mathematics remains without finding any practical application, the amount of mathematics that can be usefully employed in any science being in proportion to the degree of accuracy attained in the science. Thus, while the astronomer can put to use a wide range of mathematical theory, the chemist is only just beginning to apply the first derivative, i. e. the rate of change at which certain processes are going on; for second derivatives he does not seem to have found any use as yet." (Felix Klein, "Lectures on Mathematics", 1911)

"It [science] involves an intelligent and persistent endeavor to revise current beliefs so as to weed out what is erroneous, to add to their accuracy, and, above all, to give them such shape that the dependencies of the various facts upon one another may be as obvious as possible." (John Dewey, "Democracy and Education", 1916)

"The man of science, by virtue of his training, is alone capable of realising the difficulties - often enormous - of obtaining accurate data upon which just judgment may be based." (Sir Richard Gregory, "Discovery; or, The Spirit and Service of Science", 1918)

"The complexity of a system is no guarantee of its accuracy." (John P Jordan, "Cost accounting; principles and practice", 1920)

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

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

"The structure of a theoretical system tells us what alternatives are open in the possible answers to a given question. If observed facts of undoubted accuracy will not fit any of the alternatives it leaves open, the system itself is in need of reconstruction." (Talcott Parsons, "The structure of social action", 1937)

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

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

"The art of using the language of figures correctly is not to be over-impressed by the apparent air of accuracy, and yet to be able to take account of error and inaccuracy in such a way as to know when, and when not, to use the figures. This is a matter of skill, judgment, and experience, and there are no rules and short cuts in acquiring this expertness." (Ely Devons, "Essays in Economics", 1961)

"Relativity is inherently convergent, though convergent toward a plurality of centers of abstract truths. Degrees of accuracy are only degrees of refinement and magnitude in no way affects the fundamental reliability, which refers, as directional or angular sense, toward centralized truths. Truth is a relationship." (R Buckminster Fuller, "The Designers and the Politicians", 1962)

"Theories are usually introduced when previous study of a class of phenomena has revealed a system of uniformities. […] Theories then seek to explain those regularities and, generally, to afford a deeper and more accurate understanding of the phenomena in question. To this end, a theory construes those phenomena as manifestations of entities and processes that lie behind or beneath them, as it were." (Carl G Hempel, "Philosophy of Natural Science", 1966)

"Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity there is no such jump, and because jump is missing in the world of quantity it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate." (Gregory Bateson, "Number is Different from Quantity", CoEvolution Quarterly, 1978)

"A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations." (Stephen Hawking, "A Brief History of Time: From Big Bang To Black Holes", 1988)

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

"There is no sharp dividing line between scientific theories and models, and mathematics is used similarly in both. The important thing is to possess a delicate judgement of the accuracy of your model or theory. An apparently crude model can often be surprisingly effective, in which case its plain dress should not mislead. In contrast, some apparently very good models can be hiding dangerous weaknesses." (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)

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

"Accuracy of observation is the equivalent of accuracy of thinking." (Wallace Stevens, "Collected Poetry and Prose", 1997)

“Accurate estimates depend at least as much upon the mental model used in forming the picture as upon the number of pieces of the puzzle that have been collected.” (Richards J. Heuer Jr, “Psychology of Intelligence Analysis”, 1999)

"To be numerate means to be competent, confident, and comfortable with one’s judgements on whether to use mathematics in a particular situation and if so, what mathematics to use, how to do it, what degree of accuracy is appropriate, and what the answer means in relation to the context." (Diana Coben, "Numeracy, mathematics and adult learning", 2000)

"Innumeracy - widespread confusion about basic mathematical ideas - means that many statistical claims about social problems don't get the critical attention they deserve. This is not simply because an innumerate public is being manipulated by advocates who cynically promote inaccurate statistics. Often, statistics about social problems originate with sincere, well-meaning people who are themselves innumerate; they may not grasp the full implications of what they are saying. Similarly, the media are not immune to innumeracy; reporters commonly repeat the figures their sources give them without bothering to think critically about them." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"There are two problems with sampling - one obvious, and the other more subtle. The obvious problem is sample size. Samples tend to be much smaller than their populations. [...] Obviously, it is possible to question results based on small samples. The smaller the sample, the less confidence we have that the sample accurately reflects the population. However, large samples aren't necessarily good samples. This leads to the second issue: the representativeness of a sample is actually far more important than sample size. A good sample accurately reflects (or 'represents') the population." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"[…] most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial. No matter how puzzled we are by the behavior of an electron or an atom, we rarely call it complex, as quantum mechanics offers us the tools to describe them with remarkable accuracy. The demystification of crystals-highly regular networks of atoms and molecules-is one of the major success stories of twentieth-century physics, resulting in the development of the transistor and the discovery of superconductivity. Yet, we continue to struggle with systems for which the interaction map between the components is less ordered and rigid, hoping to give self-organization a chance." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"Blissful data consist of information that is accurate, meaningful, useful, and easily accessible to many people in an organization. These data are used by the organization’s employees to analyze information and support their decision-making processes to strategic action. It is easy to see that organizations that have reached their goal of maximum productivity with blissful data can triumph over their competition. Thus, blissful data provide a competitive advantage.". (Margaret Y Chu, "Blissful Data", 2004)

"[…] we would like to observe that the butterfly effect lies at the root of many events which we call random. The final result of throwing a dice depends on the position of the hand throwing it, on the air resistance, on the base that the die falls on, and on many other factors. The result appears random because we are not able to take into account all of these factors with sufficient accuracy. Even the tiniest bump on the table and the most imperceptible move of the wrist affect the position in which the die finally lands. It would be reasonable to assume that chaos lies at the root of all random phenomena." (Iwo Bialynicki-Birula & Iwona Bialynicka-Birula, "Modeling Reality: How Computers Mirror Life", 2004)

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

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

"Humans have difficulty perceiving variables accurately […]. However, in general, they tend to have inaccurate perceptions of system states, including past, current, and future states. This is due, in part, to limited ‘mental models’ of the phenomena of interest in terms of both how things work and how to influence things. Consequently, people have difficulty determining the full implications of what is known, as well as considering future contingencies for potential systems states and the long-term value of addressing these contingencies. " (William B. Rouse, "People and Organizations: Explorations of Human-Centered Design", 2007)

"Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. [...] We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that out picture is clear and accurate. But is it?" (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Prior to the discovery of the butterfly effect it was generally believed that small differences averaged out and were of no real significance. The butterfly effect showed that small things do matter. This has major implications for our notions of predictability, as over time these small differences can lead to quite unpredictable outcomes. For example, first of all, can we be sure that we are aware of all the small things that affect any given system or situation? Second, how do we know how these will affect the long-term outcome of the system or situation under study? The butterfly effect demonstrates the near impossibility of determining with any real degree of accuracy the long term outcomes of a series of events." (Elizabeth McMillan, Complexity, "Management and the Dynamics of Change: Challenges for practice", 2008)

"In the predictive modeling disciplines an ensemble is a group of algorithms that is used to solve a common problem [...] Each modeling algorithm has specific strengths and weaknesses and each provides a different mathematical perspective on the relationships modeled, just like each instrument in a musical ensemble provides a different voice in the composition. Predictive modeling ensembles use several algorithms to contribute their perspectives on the prediction problem and then combine them together in some way. Usually ensembles will provide more accurate models than individual algorithms which are also more general in their ability to work well on different data sets [...] the approach has proven to yield the best results in many situations." (Gary Miner et al, "Practical Text Mining and Statistical Analysis for Non-Structured Text Data Applications", 2012)

"The problem of complexity is at the heart of mankind’s inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", 2014)

“A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, “Calculus: Early Transcedentals” 8th Ed., 2016)

"Validity of a theory is also known as construct validity. Most theories in science present broad conceptual explanations of relationship between variables and make many different predictions about the relationships between particular variables in certain situations. Construct validity is established by verifying the accuracy of each possible prediction that might be made from the theory. Because the number of predictions is usually infinite, construct validity can never be fully established. However, the more independent predictions for the theory verified as accurate, the stronger the construct validity of the theory." (K N Krishnaswamy et al, "Management Research Methodology: Integration of Principles, Methods and Techniques", 2016)

"The margin of error is how accurate the results are, and the confidence interval is how confident you are that your estimate falls within the margin of error." (Daniel J Levitin, "Weaponized Lies", 2017)

"Are your insights based on data that is accurate and reliable? Trustworthy data is correct or valid, free from significant defects and gaps. The trustworthiness of your data begins with the proper collection, processing, and maintenance of the data at its source. However, the reliability of your numbers can also be influenced by how they are handled during the analysis process. Clean data can inadvertently lose its integrity and true meaning depending on how it is analyzed and interpreted." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"The only way to achieve any accuracy is to ignore most of the information available." (Preston C Hammer)

12 December 2018

🔭Data Science: Theory (Just the Quotes)

"The moment a person forms a theory, his imagination sees, in every object, only the traits which favor that theory." (Thomas Jefferson, [letter to Charles Thompson] 1787)

"It is not possible to feel satisfied at having said the last word about some theory as long as it cannot be explained in a few words to any passerby encountered in the street." (Joseph D Gergonne, [letter] 1825)

"[…] in order to observe, our mind has need of some theory or other. If in contemplating phenomena we did not immediately connect them with principles, not only would it be impossible for us to combine these isolated observations, and therefore to derive profit from them, but we should even be entirely incapable of remembering facts, which would for the most remain unnoted by us." (Auguste Comte, "Cours de Philosophie Positive", 1830-1842)

"The function of theory is to put all this in systematic order, clearly and comprehensively, and to trace each action to an adequate, compelling cause. […] Theory should cast a steady light on all phenomena so that we can more easily recognize and eliminate the weeds that always spring from ignorance; it should show how one thing is related to another, and keep the important and the unimportant separate. If concepts combine of their own accord to form that nucleus of truth we call a principle, if they spontaneously compose a pattern that becomes a rule, it is the task of the theorist to make this clear." (Carl von Clausewitz, "On War", 1832)

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"Theories usually result from the precipitate reasoning of an impatient mind which would like to be rid of phenomena and replace them with images, concepts, indeed often with mere words." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error. Not only so; but scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of error is without some latent charm derived from truth." (William Whewell, "Lectures on the History of Moral Philosophy in England", 1852)

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

"[…] ideas may be both novel and important, and yet, if they are incorrect – if they lack the very essential support of incontrovertible fact, they are unworthy of credence. Without this, a theory may be both beautiful and grand, but must be as evanescent as it is beautiful, and as unsubstantial as it is grand." (George Brewster, "A New Philosophy of Matter", 1858)

"If an idea presents itself to us, we must not reject it simply because it does not agree with the logical deductions of a reigning theory." (Claude Bernard, "An Introduction to the Study of Experimental Medicine", 1865)

"Science asks no questions about the ontological pedigree or a priori character of a theory, but is content to judge it by its performance; and it is thus that a knowledge of nature, having all the certainty which the senses are competent to inspire, has been attained - a knowledge which maintains a strict neutrality toward all philosophical systems and concerns itself not with the genesis or a priori grounds of ideas." (Chauncey Wright, "The Philosophy of Herbert Spencer", North American Review, 1865)

"The triumph of a theory is to embrace the greatest number and the greatest variety of facts." (Charles A Wurtz, "A History of Chemical Theory from the Age of Lavoisier to the Present Time", 1869)

"Mathematics is not the discoverer of laws, for it is not induction; neither is it the framer of theories, for it is not hypothesis; but it is the judge over both, and it is the arbiter to which each must refer its claims; and neither law can rule nor theory explain without the sanction of mathematics." (Benjamin Peirce, "Linear Associative Algebra", American Journal of Mathematics, Vol. 4, 1881)

"As for everything else, so for a mathematical theory: beauty can be perceived but not explained." (Arthur Cayley, [president's address] 1883)

"It would be an error to suppose that the great discoverer seizes at once upon the truth, or has any unerring method of divining it. In all probability the errors of the great mind exceed in number those of the less vigorous one. Fertility of imagination and abundance of guesses at truth are among the first requisites of discovery; but the erroneous guesses must be many times as numerous as those that prove well founded. The weakest analogies, the most whimsical notions, the most apparently absurd theories, may pass through the teeming brain, and no record remain of more than the hundredth part. […] The truest theories involve suppositions which are inconceivable, and no limit can really be placed to the freedom of hypotheses." (W Stanley Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1877)

"Perfect readiness to reject a theory inconsistent with fact is a primary requisite of the philosophic mind. But it, would be a mistake to suppose that this candour has anything akin to fickleness; on the contrary, readiness to reject a false theory may be combined with a peculiar pertinacity and courage in maintaining an hypothesis as long as its falsity is not actually apparent." (William S Jevons, "The Principles of Science", 1887)

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

"Facts are not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter. Theory is of the essence of facts. Without theory scientific knowledge would be only worthy of the mad house." (Oliver Heaviside, "Electromagnetic Theory", 1893)

"Scientific facts accumulate rapidly, and give rise to theories with almost equal rapidity. These theories are often wonderfully enticing, and one is apt to pass from one to another, from theory to theory, without taking care to establish each before passing on to the next, without assuring oneself that the foundation on which one is building is secure. Then comes the crash; the last theory breaks down utterly, and on attempting to retrace our steps to firm ground and start anew, we may find too late that one of the cards, possibly at the very foundation of the pagoda, is either faultily placed or in itself defective, and that this blemish easily remedied if detected in time has, neglected, caused the collapse of the whole structure on whose erection so much skill and perseverance have been spent." (Arthur M Marshall, 1894)

"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." (David Hilbert [paraphrasing Joseph D Gergonne], "Mathematical Problems", 1900)

"One does not ask whether a scientific theory is true, but only whether it is convenient." (Henri Poincaré, "La Science et l'Hypothèse", 1902)

"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, "On the Foundations of Geometry and Formal Theories of Arithmetic" , cca. 1903-1909)

"It [a theory] ought to furnish a compass which, if followed, will lead the observer further and further into previously unexplored regions. Whether these regions will be barren or fertile experience alone will decide; but, at any rate, one who is guided in this way will travel onward in a definite direction, and will not wander aimlessly to and fro." (Sir Joseph J Thomson, "The Corpuscular Theory of Matter", 1907)

"Things and events explain themselves, and the business of thought is to brush aside the verbal and conceptual impediments which prevent them from doing so. Start with the notion that it is you who explain the Object, and not the Object that explains itself, and you are bound to end in explaining it away. It ceases to exist, its place being taken by a parcel of concepts, a string of symbols, a form of words, and you find yourself contemplating, not the thing, but your theory of the thing." (Lawrence P Jacks, "The Usurpation Of Language", 1910)

"The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features." (Eliakim H Moore, "Introduction to a Form of General Analysis", 1910)

"The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science." (Sir Oliver J Lodge, [Becquerel Memorial Lecture] Journal of the Chemical Society, Transactions 101 (2), 1912)

"There is no great harm in the theorist who makes up a new theory to fit a new event. But the theorist who starts with a false theory and then sees everything as making it come true is the most dangerous enemy of human reason." (Gilbert K Chesterton, "The Flying Inn", 1914)

"As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies." (Albert Einstein: "Relativity: The Special and General Theory", 1916)

"No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case." (Albert Einstein: "Relativity, The Special and General Theory", 1916)

"To come very near to a true theory, and to grasp its precise application, are two very different things, as the history of a science teaches us. Everything of importance has been said before by somebody who did not discover it." (Alfred N Whitehead, "The Organization of Thought", 1917)

"Facts are carpet-tacks under the pneumatic tires of theory." (Austin O’Malley, "Keystones of Thought", 1918)

"Philosophy, like science, consists of theories or insights arrived at as a result of systemic reflection or reasoning in regard to the data of experience. It involves, therefore, the analysis of experience and the synthesis of the results of analysis into a comprehensive or unitary conception. Philosophy seeks a totality and harmony of reasoned insight into the nature and meaning of all the principal aspects of reality." (Joseph A Leighton, "The Field of Philosophy: An outline of lectures on introduction to philosophy", 1919)

"[…] analogies are not ‘aids’ to the establishment of theories; they are an utterly essential part of theories, without which theories would be completely valueless and unworthy of the name. It is often suggested that the analogy leads to the formulation of the theory, but that once the theory is formulated the analogy has served its purpose and may be removed or forgotten. Such a suggestion is absolutely false and perniciously misleading." (Norman R Campbell, "Physics, the Elements", 1920)

"Nothing is more interesting to the true theorist than a fact which directly contradicts a theory generally accepted up to that time, for this is his particular work." (Max Planck, "A Survey of Physics", 1925)

"[…] the mere collection of facts, without some basis of theory for guidance and elucidation, is foolish and profitless." (Gamaliel Bradford, "Darwin", 1926)

"[…] facts are too bulky to be lugged about conveniently except on the wheels of theory." (Julian Huxley, "Essays of a Biologist", 1929)

"We can invent as many theories we like, and any one of them can be made to fit the facts. But that theory is always preferred which makes the fewest number of assumptions." (Albert Einstein [interview] 1929)

"Every theory of the course of events in nature is necessarily based on some process of simplification and is to some extent, therefore, a fairy tale." (Sir Napier Shaw, "Manual of Meteorology", 1932)

"[…] the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well-constructed theory is in some respects undoubtedly an artistic production." (Ernest Rutherford, 1932)

"It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience." (Albert Einstein, [lecture] 1933)

"All the theories and hypotheses of empirical science share this provisional character of being established and accepted ‘until further notice’ [...]" (Carl G Hempel, "Geometry and Empirical Science", 1935)

"[while] the traditional way is to regard the facts of science as something like the parts of a jig-saw puzzle, which can be fitted together in one and only one way, I regard them rather as the tiny pieces of a mosaic, which can be fitted together in many ways. A new theory in an old subject is, for me, a new mosaic pattern made with the pieces taken from an older pattern. [...] Theories come into fashion and theories go out of fashion, but the facts connected with them stay." (William H George, "The Scientist in Action", 1936)

"Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer." (Percy W Bridgman, "The Nature of Physical Theory", 1936)

"When an active individual of sound common sense perceives the sordid state of the world, desire to change it becomes the guiding principle by which he organizes given facts and shapes them into a theory. The methods and categories as well as the transformation of the theory can be understood only in connection with his taking of sides. This, in turn, discloses both his sound common sense and the character of the world. Right thinking depends as much on right willing as right willing on right thinking." (Max Horkheimer, "The Latest Attack on Metaphysics", 1937)

"Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up." (Albert Einstein & Leopold Infeld, "The Evolution of Physics", 1938)

"With the help of physical theories we try to find our way through the maze of observed facts, to order and understand the world of our sense impressions." (Albert Einstein & Leopold Infeld, "The Evolution of Physics", 1938)

"There is nothing as practical as a good theory" (Kurt Z Lewin, "Psychology and the process of group living", Journal of Social Psychology 17, 1943)

"One expects a mathematical theorem or a mathematical theory not only to describe and to classify in a simple and elegant way numerous and a priori disparate special cases. One also expects ‘elegance’ in its ‘architectural’ structural makeup." (John von Neumann, "The Mathematician" [in "Works of the Mind" Vol. I (1), 1947])

"We can put it down as one of the principles learned from the history of science that a theory is only overthrown by a better theory, never merely by contradictory facts." (James B Conant, "On Understanding Science", 1947)

"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability." (Albert Einstein, "Autobiographical Notes", 1949)

"When a scientific theory is firmly established and confirmed, it changes its character and becomes a part of the metaphysical background of the age: a doctrine is transformed into a dogma." (Max Born, "Natural Philosophy of Cause and Chance", 1949)

"As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, these furtive caresses, these inexplicable disagreements; also nothing gives the researcher greater pleasure." (André Weil, "De la Métaphysique aux Mathématiques", 1960)

"A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. " (Paul A M Dirac, Scientific American, 1963)

"The final test of a theory is its capacity to solve the problems which originated it." (George Dantzig, "Linear Programming and Extensions", 1963)

"One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories." (Philip J Davis, "Number", Scientific American, No 211 (3), 1964)

"Another thing I must point out is that you cannot prove a vague theory wrong. If the guess that you make is poorly expressed and rather vague, and the method that you use for figuring out the consequences is a little vague - you are not sure, and you say, 'I think everything's right because it's all due to so and so, and such and such do this and that more or less, and I can sort of explain how this works' […] then you see that this theory is good, because it cannot be proved wrong! Also if the process of computing the consequences is indefinite, then with a little skill any experimental results can be made to look like the expected consequences." (Richard P Feynman, "The Character of Physical Law", 1965)

"This is the key of modern science and it was the beginning of the true understanding of Nature - this idea to look at the thing, to record the details, and to hope that in the information thus obtained might lie a clue to one or another theoretical interpretation." (Richard P Feynman, "The Character of Physical Law", 1965)

"A theory is scientific only if it can be disproved. But the moment you try to cover absolutely everything the chances are that you cover nothing. " (Sir Hermann Bondi, "Assumption and Myth in Physical Theory", 1967)

"As soon as we inquire into the reasons for the phenomena, we enter the domain of theory, which connects the observed phenomena and traces them back to a single ‘pure’ phenomena, thus bringing about a logical arrangement of an enormous amount of observational material." (Georg Joos, "Theoretical Physics", 1968)

"It makes no sense to say what the objects of a theory are, beyond saying how to interpret or reinterpret that theory in another." (Willard v O Quine, "Ontological Relativity and Other Essays", 1969)

"One often hears that successive theories grow ever closer to, or approximate more and more closely to, the truth. Apparently, generalizations like that refer not to the puzzle-solutions and the concrete predictions derived from a theory but rather to its ontology, to the match, that is, between the entities with which the theory populates nature and what is ‘really there’." (Thomas S Kuhn, "The Structure of Scientific Revolutions", 1970)

"Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime." (Imre Lakatos, [radio Lecture] 1973)

"No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempt to find the principles implicit in familiar observational notions." (Paul K Feyerabend, "Against Method: Outline of an Anarchistic Theory of Knowledge", 1975)

"A physical theory remains an empty shell until we have found a reasonable physical interpretation." (Peter Bergmann, [conference] 1976)

"Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things […] are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge." (Alan R Beals, "Strategies of Resort to Curers in South India" [contributed in Charles M. Leslie (ed.), "Asian Medical Systems: A Comparative Study", 1976])

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

"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world." (Steven Weinberg, "The First Three Minutes", 1977)

"The theory of our modern technic shows that nothing is as practical as the theory." (J Robert Oppenheimer, "Reflex", 1977)

"Science has so accustomed us to devising and accepting theories to account for the facts we observe, however fantastic, that our minds must begin their manufacture before we are aware of it." (Gene Wolfe, "Seven American Nights", 1978)

"For mathematicians, only one test was necessary: once the elements of any mathematical theory were seen to be consistent, then they were mathematically acceptable. Nothing more was required." (Joseph W Dauben, "Georg Cantor: His Mathematics and Philosophy of the Infinite", 1979)

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

"Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them." (Stephen J Gould "Evolution as Fact and Theory", 1981)

"A real change of theory is not a change of equations - it is a change of mathematical structure, and only fragments of competing theories, often not very important ones conceptually, admit comparison with each other within a limited range of phenomena." (Yuri I Manin, "Mathematics and Physics", 1981)

"The principal aim of physical theories is understanding. A theory's ability to find a number is merely a useful criterion for a correct understanding." (Yuri I Manin, "Mathematics and Physics", 1981)

"Data in isolation are meaningless, a collection of numbers. Only in context of a theory do they assume significance […]" (George Greenstein, "Frozen Star", 1983)

"In all scientific fields, theory is frequently more important than experimental data. Scientists are generally reluctant to accept the existence of a phenomenon when they do not know how to explain it. On the other hand, they will often accept a theory that is especially plausible before there exists any data to support it." (Richard Morris, 1983)

"Physics is like that. It is important that the models we construct allow us to draw the right conclusions about the behaviour of the phenomena and their causes. But it is not essential that the models accurately describe everything that actually happens; and in general it will not be possible for them to do so, and for much the same reasons. The requirements of the theory constrain what can be literally represented. This does not mean that the right lessons cannot be drawn. Adjustments are made where literal correctness does not matter very much in order to get the correct effects where we want them; and very often, as in the staging example, one distortion is put right by another. That is why it often seems misleading to say that a particular aspect of a model is false to reality: given the other constraints that is just the way to restore the representation." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Scientific theories must tell us both what is true in nature, and how we are to explain it. […] Scientific theories are thought to explain by dint of the descriptions they give of reality." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases." (Paul Halmos, "Selecta: Expository writing", 1983)

"A final goal of any scientific theory must be the derivation of numbers. Theories stand or fall, ultimately, upon numbers." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

"Until now, physical theories have been regarded as merely models with approximately describe the reality of nature. As the models improve, so the fit between theory and reality gets closer. Some physicists are now claiming that supergravity is the reality, that the model and the real world are in mathematically perfect accord." (Paul C W Davies, "Superforce", 1984)

"Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does." (James Burke, "The Day the Universe Changed", 1985)

"Experience without theory teaches nothing." (William E Deming, "Out of the Crisis", 1986)

"All great theories are expansive, and all notions so rich in scope and implication are underpinned by visions about the nature of things. You may call these visions ‘philosophy’, or ‘metaphor’, or ‘organizing principle’, but one thing they are surely not - they are not simple inductions from observed facts of the natural world." (Stephen J Gould, "Time’s Arrow, Time’s Cycle", 1987)

"Facts do not 'speak for themselves'. They speak for or against competing theories. Facts divorced from theory or visions are mere isolated curiosities." (Thomas Sowell, "A Conflict of Visions: Ideological Origins of Political Struggles", 1987)

"[…] no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been ‘carpentered’ to do this and would thus be open to suspicion." (Francis H C Crick, "What Mad Pursuit: A Personal View of Scientific Discovery", 1988)

"Theories are not so much wrong as incomplete." (Isaac Asimov, "The Relativity of Wrong", 1988)

"A discovery in science, or a new theory, even where it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalyzed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow: it takes a vast world unchallenged and for granted." (James R Oppenheimer, "Atom and Void", 1989)

"Model is used as a theory. It becomes theory when the purpose of building a model is to understand the mechanisms involved in the developmental process. Hence as theory, model does not carve up or change the world, but it explains how change takes place and in what way or manner. This leads to build change in the structures." (Laxmi K Patnaik, "Model Building in Political Science", The Indian Journal of Political Science Vol. 50 (2), 1989)

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

"It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only ‘true’ for as long as the majority of the scientific community maintain the view that the theory is the one best able to explain the observations." (Jim Baggott, "The Meaning of Quantum Theory", 1992)

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

"Scientists, being as a rule more or less human beings, passionately stick up for their ideas, their pet theories. It's up to someone else to show you are wrong." (Niles Eldredge, "Reinventing Darwin", 1995)

"Paradigms are the most general-rather like a philosophical or ideological framework. Theories are more specific, based on the paradigm and designed to describe what happens in one of the many realms of events encompassed by the paradigm. Models are even more specific providing the mechanisms by which events occur in a particular part of the theory's realm. Of all three, models are most affected by empirical data - models come and go, theories only give way when evidence is overwhelmingly against them and paradigms stay put until a radically better idea comes along." (Lee R Beach, "The Psychology of Decision Making: People in Organizations", 1997)

"Ideas about organization are always based on implicit images or metaphors that persuade us to see, understand, and manage situations in a particular way. Metaphors create insight. But they also distort. They have strengths. But they also have limitations. In creating ways of seeing, they create ways of not seeing. There can be no single theory or metaphor that gives an all-purpose point of view, and there can be no simple 'correct theory' for structuring everything we do." (Gareth Morgan, "Imaginization", 1997)

"An individual understands a concept, skill, theory, or domain of knowledge to the extent that he or she can apply it appropriately in a new situation." (Howard Gardner, "The Disciplined Mind", 1999)

"[…] philosophical theories are structured by conceptual metaphors that constrain which inferences can be drawn within that philosophical theory. The (typically unconscious) conceptual metaphors that are constitutive of a philosophical theory have the causal effect of constraining how you can reason within that philosophical framework." (George Lakoff, "Philosophy in the Flesh: The Embodied Mind and its Challenge to Western Thought", 1999)

"All scientific theories, even those in the physical sciences, are developed in a particular cultural context. Although the context may help to explain the persistence of a theory in the face of apparently falsifying evidence, the fact that a theory arises from a particular context is not sufficient to condemn it. Theories and paradigms must be accepted, modified or rejected on the basis of evidence." (Richard P Bentall, "Madness Explained: Psychosis and Human Nature", 2003)

"A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have." (Murray Gell-Mann, "Beauty and Truth in Physics", 2007)

"In science we try to explain reality by using models (theories). This is necessary because reality itself is too complex. So we need to come up with a model for that aspect of reality we want to understand – usually with the help of mathematics. Of course, these models or theories can only be simplifications of that part of reality we are looking at. A model can never be a perfect description of reality, and there can never be a part of reality perfectly mirroring a model." (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)

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

"All scientific theories, even those in the physical sciences, are developed in a particular cultural context. Although the context may help to explain the persistence of a theory in the face of apparently falsifying evidence, the fact that a theory arises from a particular context is not sufficient to condemn it. Theories and paradigms must be accepted, modified or rejected on the basis of evidence." (Richard P Bentall, "Madness Explained: Psychosis and Human Nature", 2003)

"With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)

"A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized." (Jay Odenbaugh, "True Lies: Realism, Robustness, and Models", Philosophy of Science, Vol. 78, No. 5, 2011)

"Science would be better understood if we called theories ‘misconceptions’ from the outset, instead of only after we have discovered their successors." (David Deutsch, "Beginning of Infinity", 2011)

"Complexity has the propensity to overload systems, making the relevance of a particular piece of information not statistically significant. And when an array of mind-numbing factors is added into the equation, theory and models rarely conform to reality." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"[…] if one has a theory, one needs to be willing to try to prove it wrong as much as one tries to provide that it is right […]" (Lawrence M Krauss et al, A Universe from Nothing, 2013)

"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh,"Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)