🅱Roger Bacon - Collected Quotes

"All science requires mathematics […] the knowledge of mathematical things is almost innate in us […] this is the easiest of sciences. A fact which is obvious in that no one’s brain rejects it. For laymen and people who are utterly illiterate know how to count and reckon.” (Roger Bacon, "Opus Majus”, 1267)

"For the things of this world cannot be made known without a knowledge of mathematics.” (Roger Bacon, "Opus Majus”, 1267)

"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics.” (Roger Bacon, "Opus Majus", 1267)

"Mathematics is the gate and key of the sciences. [...] Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy..” (Roger Bacon, "Opus Majus", 1267)

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

"There are four great sciences, without which the other sciences cannot be known nor a knowledge of things secured […] Of these sciences the gate and key is mathematics […] He who is ignorant of this [mathematics] cannot know the other sciences nor the affairs of this world.” (Roger Bacon, "Opus Majus", 1267)

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

"Without experience nothing can be sufficiently known. For there are two modes of acquiring knowledge, namely, by reasoning and by experience. Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain [...] unless the mind discovers it by the method of experience." (Roger Bacon, "Opus Majus", 1267)

"All sciences are connected; they lend each other material aid as parts of one great whole, each doing its own work, not for itself alone, but for the other parts; as the eye guides the body and the foot sustains it and leads it from place to place.” (Roger Bacon, "Opus Tertium”, [1266–1268])

"Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences of the things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy." (Roger Bacon)

"The strongest arguments prove nothing so long as the conclusions are not verified by experience. Experimental science is the queen of sciences and the goal of all speculation." (Roger Bacon)

🅰Jean le Rond d’Alembert - Collected Quotes

"Newton started out from another principle; and one can say that the metaphysics of this great mathematician on the calculus of fluxions is very exact and illuminating, even though he allowed us only an imperfect glimpse of his thoughts. He never considered the differential calculus as the study of infinitely small quantities, but as the method of first and ultimate ratios, that is to say, the method of finding the limits of ratios. Thus this famous author has never differentiated quantities but only equations; in fact, every equation involves a relation between two variables and the differentiation of equations consists 

merely in finding the limit of the ratio of the finite differences of the two quantitiescontained in the equation." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"What concerns us most here is the metaphysics of the differential calculus. This metaphysics, of which so much has been written, is even more important and perhaps more difficult to explain than the rules of this calculus themselves: various mathematicians, among them Rolle, who were unable to accept the assumption concerning infinitely small quantities, have rejected it entirely, and have held that the principle was false and capable of leading to error. Yet in view of the fact that all results obtained by means of ordinary Geometry can be established similarly and much more easily by means of the differential calculus, one cannot help concluding that, since this calculus yields reliable, simple, and exact methods, the principles on which it depends must also be simple and certain." (Jean LeRond D'Alembert, "Differentiel" ["Differentials", 1754)

"Day by day natural science accumulates new riches […] The true system of the World has been recognized, developed and perfected […] Everything has been discussed and analyzed, or at least mentioned.” (Jean le Rond d’Alembert, "Elements of Philosophy", 1759)

 "No other person can judge better of either [the merits of a writer and the merits of his works] than himself; for none have had access to a closer or more deliberate examination of them. It is for this reason, that in proportion that the value of a work is intrinsic, and independent of opinion, the less eagerness will the author feel to conciliate the suffrages of the public. Hence that inward satisfaction, so pure and so complete, which the study of geometry yields. The progress which an individual makes in this science, the degree of eminence which he attains in it, all this may be measured with the same rigorous accuracy as the methods about which his thoughts are employed. It is only when we entertain some doubts about the justness of our own standard, that we become anxious to relieve ourselves from our uncertainty, by comparing it with the standard of another. Now, in all matters which fall under the cognizance of taste, this standard is necessarily somewhat variable; depending on a sort of gross estimate, always a little arbitrary, either in whole or in part; and liable to continual alteration in its dimensions, from negligence, temper, or caprice. In consequence of these circumstances I have no doubt, that if men lived separate from each other, and could in such a situation occupy themselves about anything but self-preservation, they would prefer the study of the exact sciences to the cultivation of the agreeable arts. It is chiefly on account of others, that a man aims at excellence in the latter, it is on his own account that he devotes himself to the former. In a desert island, accordingly, I should think that a poet could scarcely be vain; whereas a geometrician might still enjoy the pride of discovery." (Jean le Rond D’Alembert, "Essai sur les Gens Lettres", 1764)

"One must admit that it is not a simple matter to accurately outline the idea of negative numbers, and that some capable people have added to the confusion by their inexact pronouncements. To say that the negative numbers are below nothing is to assert an unimaginable thing.” (Jean le Rond d'Alembert, "Negatif”, Encyclopédie [1751 – 1772])

"[…] the algebraic rules of operation with negative numbers are generally admitted by everyone and acknowledged as exact, whatever idea we may have about this quantities. " (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])

"Thus, metaphysics and mathematics are, among all the sciences that belong to reason, those in which imagination has the greatest role.” (Jean le Rond d'Alembert, Encyclopédie, [1751 – 1772])

"Geometrical truths are in a way asymptotes to physical truths, that is to say, the latter approach the former indefinitely near without ever reaching them exactly.” (Jean le Rond d’Alembert)

"The imagination in a mathematician who creates makes no less difference than in a poet who invents […]." (Jean le Rond d'Alembert, Encyclopedie, [1751 – 1772])

"To someone who could grasp the universe from one unified viewpoint, the entire creation would appear as a unique fact and a great truth.” (Jean le Rond d'Alembert)

"We shall content ourselves with the remark that if mathematics (as is asserted with sufficient reason) only make straight the minds which are without bias, so they only dry up and chill the minds already prepared for this operation by nature.” (Jean le Rond d'Alembert)

🪷On Mind: Mental Models XX

“We perceive an image of truth, and possess only a lie.” (Blaise Pascal, “Pensées”, 1670)

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

"Wit, you know, is the unexpected copulation of ideas, the discovery of some occult relation between images in appearance remote from each other." (Samuel Johnson, "The Rambler", 1750)

“This schematism of our understanding, in its application to appearances and their mere form, is an art concealed in the depths of the human soul, whose real modes of activity nature is hardly likely ever to allow us to discover, and to have open to our gaze.” (Immanuel Kant, “Critique of Pure Reason”, 1781) 

“Everything possible to be believed is an image of truth.” (William Blake, “The Marriage of Heaven and Hell”, 1790)

"The identifying ourselves with the visual image of ourselves has become an instinct; the habit is already old. The picture of me, the me that is seen, is me." (David H Lawrence, "Art and Morality", 1925)

“We do not know why the imagination has accepted that image before the reason can reject it; or why such correspondences seem really to correspond to something in the soul.” (Gilbert K Chesterton, “The Everlasting Man”, 1925)

“If we hang beautiful pictures on the walls of our souls, mental images that establish us in the habitual companionship of the highest that we know, and live with them long enough, we cannot will evil.” (Harry E Fosdick, “The Hope of the World”, 1933)

“Truth is a totality, the sum of many overlapping partial images. History, on the other hand, sacrifices totality in the interest of continuity.” (Edmund Leach, "Brain-Twister”, 1967)

🆃Edward R Tufte - Collected Quotes

"Almost all efforts at data analysis seek, at some point, to generalize the results and extend the reach of the conclusions beyond a particular set of data. The inferential leap may be from past experiences to future ones, from a sample of a population to the whole population, or from a narrow range of a variable to a wider range. The real difficulty is in deciding when the extrapolation beyond the range of the variables is warranted and when it is merely naive. As usual, it is largely a matter of substantive judgment - or, as it is sometimes more delicately put, a matter of 'a priori nonstatistical considerations'." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"If two or more describing variables in an analysis are highly intercorrelated, it will be difficult and perhaps impossible to assess accurately their independent impacts on the response variable. As the association between two or more describing variables grows stronger, it becomes more and more difficult to tell one variable from the other. This problem, called "multicollinearity" in the statistical jargon, sometimes causes difficulties in the analysis of nonexperimental data. […] No statistical technique can go very far to remedy the problem because the fault lies basically with the data rather than the method of analysis. Multicollinearity weakens inferences based on any statistical method--regression, path analysis, causal modeling, or cross-tabulations (where the difficulty shows up as a lack of deviant cases and as near-empty cells)."  (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

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

"Our inability to measure important factors does not mean either that we should sweep those factors under the rug or that we should give them all the weight in a decision. Some important factors in some problems can be assessed quantitatively. And even though thoughtful and imaginative efforts have sometimes turned the 'unmeasurable' into a useful number, some important factors are simply not measurable. As always, every bit of the investigator's ingenuity and good judgment must be brought into play. And, whatever un- knowns may remain, the analysis of quantitative data nonetheless can help us learn something about the world - even if it is not the whole story." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Random data contain no substantive effects; thus if the analysis of the random data results in some sort of effect, then we know that the analysis is producing that spurious effect, and we must be on the lookout for such artifacts when the genuine data are analyzed." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

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

"The use of statistical methods to analyze data does not make a study any more 'scientific', 'rigorous', or 'objective'. The purpose of quantitative analysis is not to sanctify a set of findings. Unfortunately, some studies, in the words of one critic, 'use statistics as a drunk uses a street lamp, for support rather than illumination'. Quantitative techniques will be more likely to illuminate if the data analyst is guided in methodological choices by a substantive understanding of the problem he or she is trying to learn about. Good procedures in data analysis involve techniques that help to (a) answer the substantive questions at hand, (b) squeeze all the relevant information out of the data, and (c) learn something new about the world." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Inept graphics also flourish because many graphic artists believe that statistics are boring and tedious. It then follows that decorated graphics must pep up, animate, and all too often exaggerate what evidence there is in the data. […] If the statistics are boring, then you've got the wrong numbers." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Of course statistical graphics, just like statistical calculations, are only as good as what goes into them. An ill-specified or preposterous model or a puny data set cannot be rescued by a graphic (or by calculation), no matter how clever or fancy. A silly theory means a silly graphic." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

“The theory of the visual display of quantitative information consists of principles that generate design options and that guide choices among options. The principles should not be applied rigidly or in a peevish spirit; they are not logically or mathematically certain; and it is better to violate any principle than to place graceless or inelegant marks on paper. Most principles of design should be greeted with some skepticism, for word authority can dominate our vision, and we may come to see only though the lenses of word authority rather than with our own eyes.” (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Vigorous writing is concise. A sentence should contain no  unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no  unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all his sentences short, or that he avoid all detail and treat his subjects only in outline,  but that every word tell." (Edward Tufte, "The Visual Display of Quantitative Information", 1983)

"What about confusing clutter? Information overload? Doesn't data have to be ‘boiled down’ and  ‘simplified’? These common questions miss the point, for the quantity of detail is an issue completely separate from the difficulty of reading. Clutter and confusion are failures of design, not attributes of information." (Edward R Tufte, "Envisioning Information", 1990)

"Audience boredom is usually a content failure, not a decoration failure." (Edward R Tufte, "The cognitive style of PowerPoint", 2003)

"If your words or images are not on point, making them dance in color won't make them relevant." (Edward R Tufte, "The cognitive style of PowerPoint", 2003)

🆃John W Tukey - Collected Quotes

"[We] need men who can practice science - not a particular science - in a word, we need scientific generalists." (John W Tukey, "The Education of a Scientific Generalist", 1949)

"[...] the whole of modern statistics, philosophy and methods alike, is based on the principle of interpreting what did happen in terms of what might have happened." (John W Tukey, "Standard Methods of Analyzing Data, 1951)

"Just remember that not all statistics has been mathematized - and that we may not have to wait for its mathematization in order to use it." (John W Tukey, "The Growth of Experimental Design in a Research Laboratory, 1953)

"Difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." (John W Tukey, Unsolved Problems of Experimental Statistics, 1954)

"Just as there is an applied mathematics of games, genetics, and mechanics, so there should be an applied mathematics (at least in terms of concepts, perhaps with techniques and operations) of the applications of mathematics. When there is, mathematicians will be able to teach the applications of mathematics." (John W Tukey, "The Teaching of Concrete Mathematics", The American Mathematical Monthly Vol. 65 (1), 1958)

"The practical power of a statistical test is the product of its’ statistical power and the probability of use." (John W Tukey, A Quick, "Compact, Two Sample Test to Duckworth’s Specifications", 1959)

"Predictions, prophecies, and perhaps even guidance - those who suggested this title to me must have hoped for such-even though occasional indulgences in such actions by statisticians has undoubtedly contributed to the characterization of a statistician as a man who draws straight lines from insufficient data to foregone conclusions!" (John W Tukey, "Where do We Go From Here?", Journal of the American Statistical Association, Vol. 55 (289), 1960)

"Today one of statistics' great needs is a body of able investigators who make it clear to the intellectual world that they are scientific statisticians. and they are proud of that fact that to them mathematics is incidental, though perhaps indispensable." (John W Tukey, "Statistical and Quantitative Methodology, 1961)

"If data analysis is to be well done, much of it must be a matter of judgment, and ‘theory’ whether statistical or non-statistical, will have to guide, not command." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33 (1), 1962)

"If one technique of data analysis were to be exalted above all others for its ability to be revealing to the mind in connection with each of many different models, there is little doubt which one would be chosen. The simple graph has brought more information to the data analyst’s mind than any other device. It specializes in providing indications of unexpected phenomena." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics Vol. 33 (1), 1962)

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

"The physical sciences are used to ‘praying over’ their data, examining the same data from a variety of points of view. This process has been very rewarding, and has led to many extremely valuable insights. Without this sort of flexibility, progress in physical science would have been much slower. Flexibility in analysis is often to be had honestly at the price of a willingness not to demand that what has already been observed shall establish, or prove, what analysis suggests. In physical science generally, the results of praying over the data are thought of as something to be put to further test in another experiment, as indications rather than conclusions." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics Vol. 33 (1), 1962)

"The histogram, with its columns of area proportional to number, like the bar graph, is one of the most classical of statistical graphs. Its combination with a fitted bell-shaped curve has been common since the days when the Gaussian curve entered statistics. Yet as a graphical technique it really performs quite poorly. Who is there among us who can look at a histogram-fitted Gaussian combination and tell us, reliably, whether the fit is excellent, neutral, or poor? Who can tell us, when the fit is poor, of what the poorness consists? Yet these are just the sort of questions that a good graphical technique should answer at least approximately." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"The first step in data analysis is often an omnibus step. We dare not expect otherwise, but we equally dare not forget that this step, and that step, and other step, are all omnibus steps and that we owe the users of such techniques a deep and important obligation to develop ways, often varied and competitive, of replacing omnibus procedures by ones that are more sharply focused." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"The basic general intent of data analysis is simply stated: to seek through a body of data for interesting relationships and information and to exhibit the results in such a way as to make them recognizable to the data analyzer and recordable for posterity. Its creative task is to be productively descriptive, with as much attention as possible to previous knowledge, and thus to contribute to the mysterious process called insight." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Comparable objectives in data analysis are (l) to achieve more specific description of what is loosely known or suspected; (2) to find unanticipated aspects in the data, and to suggest unthought-of-models for the data's summarization and exposure; (3) to employ the data to assess the (always incomplete) adequacy of a contemplated model; (4) to provide both incentives and guidance for further analysis of the data; and (5) to keep the investigator usefully stimulated while he absorbs the feeling of his data and considers what to do next." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"The science and art of data analysis concerns the process of learning from quantitative records of experience. By its very nature it exists in relation to people. Thus, the techniques and the technology of data analysis must be harnessed to suit human requirements and talents. Some implications for effective data analysis are: (1) that it is essential to have convenience of interaction of people and intermediate results and (2) that at all stages of data analysis the nature and detail of output, both actual and potential, need to be matched to the capabilities of the people who use it and want it." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"In many instances, a picture is indeed worth a thousand words. To make this true in more diverse circumstances, much more creative effort is needed to pictorialize the output from data analysis. Naive pictures are often extremely helpful, but more sophisticated pictures can be both simple and even more informative." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Data analysis must be iterative to be effective. [...] The iterative and interactive interplay of summarizing by fit and exposing by residuals is vital to effective data analysis. Summarizing and exposing are complementary and pervasive." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Summarizing data is a process of constrained and partial a process that essentially and inevitably corresponds to description - some sort of fitting, though it need not necessarily involve formal criteria or well-defined computations." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"The typical statistician has learned from bitter experience that negative results are just as important as positive ones, sometimes more so." (John W Tukey, "A Statistician's Comment", 1967)

"It is fair to say that statistics has made its greatest progress by having to move away from certainty [...] If we really want to make progress, we need to identify our next step away from certainty." (John W Tukey, "What Have Statisticians Been Forgetting", 1967)

"Every student of the art of data analysis repeatedly needs to build upon his previous statistical knowledge and to reform that foundation through fresh insights and emphasis." (John W Tukey, "Data Analysis, Including Statistics", 1968)

"Every graph is at least an indication, by contrast with some common instances of numbers." (John W Tukey, "Data Analysis, Including Statistics", 1968)

"Nothing can substitute for relatively direct assessment of variability." (John W Tukey, "Data Analysis, Including Statistics", 1968)

"No one knows how to appraise a procedure safely except by using different bodies of data from those that determined it."  (John W Tukey, "Data Analysis, Including Statistics", 1968)

"The problems of different fields are much more alike than their practitioners think, much more alike than different." (John W Tukey, "Analyzing Data: Sanctification or Detective Work?", 1969)

"[...] bending the question to fit the analysis is to be shunned at all costs." (John W Tukey, "Analyzing Data: Sanctification or Detective Work?", 1969)

"Data analysis is in important ways an antithesis of pure mathematics." (John W Tukey, "Data Analysis, Computation and Mathematics", 1972)

"Undoubtedly, the swing to exploratory data analysis will go somewhat too far. However : It is better to ride a damped pendulum than to be stuck in the mud." (John W Tukey, "Exploratory Data Analysis as Part of a Larger Whole", 1973)

"The twin assumptions of normality of distribution and homogeneity of variance are not ever exactly fulfilled in practice, and often they do not even hold to a good approximation." (John W Tukey, "The problem of multiple comparisons", [unpublished manuscript] 1973)

"Exploratory data analysis can never be the whole story, but nothing else can serve as the foundation stone - as the first step." (John W. Tukey, "Exploratory Data Analysis", 1977)

"In data analysis, a plot of y against x may help us when we know nothing about the logical connection from x to y–even when we do not know whether or not there is one–even when we know that such a connection is impossible." (John W Tukey, "Exploratory Data Analysis", 1977)

"It is a rare thing that a specific body of data tells us as clearly as we would wish how it itself should be analyzed." (John W Tukey, "Exploratory Data Analysis", 1977)

"One thing the data analyst has to learn is how to expose himself to what his data are willing - or even anxious - to tell him. Finding clues requires looking in the right places and with the right magnifying glass." (John W. Tukey, "Exploratory Data Analysis", 1977)

"The greatest value of a picture is when it forces us to notice what we never expected to see." (John W Tukey, "Exploratory Data Analysis", 1977)

"There is no excuse for failing to plot and look." (John W Tukey, "Exploratory Data Analysis", 1977)

"There is no more reason to expect one graph to ‘tell all’ than to expect one number to do the same." (John W Tukey, "Exploratory Data Analysis", 1977)

"Unless exploratory data analysis uncovers indications, usually quantitative ones, there is likely to nothing for confirmatory data analysis to consider." (John W Tukey, "Exploratory Data Analysis", 1977)

"Whatever the data, we can try to gain understanding by straightening or by flattening. When we succeed in doing one or both, we almost always see more clearly what is going on." (John W Tukey, "Exploratory Data Analysis", 1977)

"[...] exploratory data analysis is an attitude, a state of flexibility, a willingness to look for those things that we believe are not there, as well as for those we believe might be there. Except for its emphasis on graphs, its tools are secondary to its purpose." (John W Tukey, [comment] 1979)

"There is NO question of teaching confirmatory OR exploratory - we need to teach both." (John W Tukey, "We Need Both Exploratory and Confirmatory", 1980)

"Finding the question is often more important than finding the answer." (John W Tukey, "We Need Both Exploratory and Confirmatory", 1980)

"[...] any hope that we are smart enough to find even transiently optimum solutions to our data analysis problems is doomed to failure, and, indeed, if taken seriously, will mislead us in the allocation of effort, thus wasting both intellectual and computational effort." (John W Tukey, "Choosing Techniques for the Analysis of Data", 1981)

"Detailed study of the quality of data sources is an essential part of applied work. [...] Data analysts need to understand more about the measurement processes through which their data come. To know the name by which a column of figures is headed is far from being enough." (John W Tukey, "An Overview of Techniques of Data Analysis, Emphasizing Its Exploratory Aspects", 1982)

"Exploratory data analysis, EDA, calls for a relatively free hand in exploring the data, together with dual obligations: (•) to look for all plausible alternatives and oddities - and a few implausible ones, (graphic techniques can be most helpful here) and (•) to remove each appearance that seems large enough to be meaningful - ordinarily by some form of fitting, adjustment, or standardization [...] so that what remains, the residuals, can be examined for further appearances." (John W Tukey, "Introduction to Styles of Data Analysis Techniques", 1982)

"A competent data analysis of an even moderately complex set of data is a thing of trials and retreats, of dead ends and branches." (John W Tukey, Computer Science and Statistics: Proceedings of the 14th Symposium on the Interface, 1983)

"If we need a short suggestion of what exploratory data analysis is, I would suggest that: (1) it is an attitude, AND (2) a flexibility, AND (3) some graph paper (or transparencies, or both)." (John W Tukey [in "The collected works of John W. Tukey: Philosophy and principles of data analysis 1949-1964" Vols. III & IV, 1986])

"The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data." (John W Tukey, "Sunset Salvo", The American Statistician Vol. 40 (1), 1986)

"Three of the main strategies of data analysis are: (1) graphical presentation, (2) provision of flexibility in viewpoint and in facilities, (3) intensive search for parsimony and simplicity."  (John W Tukey [in "The collected works of John W. Tukey: Philosophy and principles of data analysis 1949-1964" Vols. III & IV, 1986])

"The greatest possibilities of visual display lie in vividness and inescapability of the intended message. A visual display can stop your mental flow in its tracks and make you think. A visual display can force you to notice what you never expected to see. One should see the intended at once; one should not even have to wait for it to appear." (John W Tukey, "Data-based graphics: Visual display in the decades to come", Statistical Science 5, 1990)

"Empirical knowledge is always fuzzy! And theoretical knowledge, like all the laws of physics, as of today’s date, is always wrong-in detail, though possibly providing some very good approximations indeed." (John W Tukey, "The philosophy of multiple comparisons", Statistical Science 6, 1991)

"Statisticians classically asked the wrong question–and were willing to answer with a lie, one that was often a downright lie. They asked 'Are the effects of A and B different?' and they were willing to answer 'no'. All we know about the world teaches us that the effects of A and B are always different–in some decimal place–for every A and B. Thus asking 'Are the effects different?' is foolish. What we should be answering first is 'Can we tell the direction in which the effects of A differ from the effects of B?' In other words, can we be confident about the direction from A to B? Is it 'up', 'down' or 'uncertain'?" (John W Tukey, "The Philosophy of Multiple Comparisons", Statistical Science 6, 1991)

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

"No one has ever shown that he or she had a free lunch. Here, of course, 'free lunch' means 'usefulness of a model that is locally easy to make inferences from'. (John Tukey, "Issues relevant to an honest account of data-based inference, partially in the light of Laurie Davies’ paper", 1993)

"The purpose of plotting is to convey phenomena to the viewer’s cortex, not to provide a place to lookup observed numbers." (Kaye Basford & John W Tukey, "Graphical Analysis of Multi-Response Data", 1998)

"I believe that there are many classes of problems where Bayesian analyses are reasonable, mainly classes with which I have little acquaintance." (John Tukey, "The life and professional contributions of John W. Tukey, The Annals of Statistics", Vol 30, 2001)

"Since the aim of exploratory data analysis is to learn what seems to be, it should be no surprise that pictures play a vital role in doing it well." (John W Tukey, "John W Tukey’s Works on Interactive Graphics", The Annals of Statistics Vol. 30 (6), 2002)

"Just which robust/resistant methods you use is not important–what is important is that you use some. It is perfectly proper to use both classical and robust/resistant methods routinely, and only worry when they differ enough to matter. But, when they differ, you should think hard." (John W Tukey)

"Statistics is the science, the art, the philosophy, and the technique of making inferences from the particular to the general." (John W Tukey)

"The greatest possibilities of visual display lie in vividness and inescapability of the intended message. A visual display can stop your mental flow in its tracks and make you think. A visual display can force you to notice what you never expected to see." (John W Tukey)

"The purpose of [data] display is comparison (recognition of phenomena), not numbers [...] The phenomena are the main actors, numbers are the supporting cast." (John W Tukey)

🪷On Mind: Mental Models XIX

"'Schema' refers to an active organisation of past reactions, or of past experiences, which must always be supposed to be operating in any well-adapted organic response. That is, whenever there is any order or regularity of behavior, a particular response is possible only because it is related to other similar responses which have been serially organised, yet which operate, not simply as individual members coming one after another, but as a unitary mass. Determination by schemata is the most fundamental of all the ways in which we can be influenced by reactions and experiences which occurred some time in the past. All incoming impulses of a certain kind, or mode, go together to build up an active, organised setting: visual, auditory, various types of cutaneous impulses and the like, at a relatively low level; all the experiences connected by a common interest: in sport, in literature, history, art, science, philosophy, and so on, on a higher level." (Frederic C Bartlett, "Remembering: A study in experimental and social psychology", 1932)

"[T]he sudden inventions characteristic of the sixth stage [of infant development] are in reality the product of a long evolution of schemata and not only of an internal maturation of perceptive structures. [..] This is revealed by the existence of a fifth stage, characterized by experimental groping. […] What does this mean if not that the practice of actual experience is necessary in order to acquire the practice of mental experience and that invention does not arise entirely preformed despite appearances? (Jean Piaget, "The origin of intelligence in children" 1936)

"My hypothesis then is that thought models, or parallels, reality - that its essential feature is not ‘the mind’, ‘the self’, ‘sense-data’, nor propositions but symbolism, and that this symbolism is largely of the same kind as that which is familiar to us in mechanical devices which aid thought and calculation." (Kenneth Craik, "The Nature of Explanation", 1943)

"A person is changed by the contingencies of reinforcement under which he behaves; he does not store the contingencies. In particular, he does not store copies of the stimuli which have played a part in the contingencies. There are no 'iconic representations' in his mind; there are no 'data structures stored in his memory'; he has no 'cognitive map' of the world in which he has lived. He has simply been changed in such a way that stimuli now control particular kinds of perceptual behavior." (Burrhus F Skinner, "About behaviorism", 1974)

"Imagining is not perceiving, but images are indeed derivatives of perceptual activity. In particular, they are the anticipatory phases of that activity, schemata that the perceiver has detached from the perceptual cycle for other purposes. […] The experience of having an image is just the inner aspect of a readiness to perceive the imagined object. (Ulrich Neisser, "Cognition and Reality" 1976)

"[I]t seems (to many) that we cannot account for perception unless we suppose it provides us with an internal image (or model or map) of the external world, and yet what good would that image do us unless we have an inner eye to perceive it, and how are we to explain its capacity for perception? It also seems (to many) that understanding a heard sentence must be somehow translating it into some internal message, but how will this message be understood: by translating it into something else? The problem is an old one, and let’s call it Hume’s Problem, for while he did not state it explicitly, he appreciated its force and strove mightily to escape its clutches. (Daniel Dennett, "Brainstorms: Philosophical essays on mind and psychology", 1978)

"A schema, then is a data structure for representing the generic concepts stored in memory. There are schemata representing our knowledge about all concepts; those underlying objects, situations, events, sequences of events, actions and sequences of actions. A schema contains, as part of its specification, the network of interrelations that is believed to normally hold among the constituents of the concept in question. A schema theory embodies a prototype theory of meaning. That is, inasmuch as a schema underlying a concept stored in memory corresponds to the meaning of that concept, meanings are encoded in terms of the typical or normal situations or events that instantiate that concept." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)

"Once we have accepted a configuration of schemata, the schemata themselves provide a richness that goes far beyond our observations. […] In fact, once we have determined that a particular schema accounts for some event, we may not be able to determine which aspects of our beliefs are based on direct sensory information and which are merely consequences of our interpretation." (David E Rumelhart, "Schemata: The building blocks of cognition", 1980)

"Since mental models can take many forms and serve many purposes, their contents are very varied. They can contain nothing but tokens that represent individuals and identities between them, as in the sorts of models that are required for syllogistic reasoning. They can represent spatial relations between entities, and the temporal or causal relations between events. A rich imaginary model of the world can be used to compute the projective relations required for an image. Models have a content and form that fits them to their purpose, whether it be to explain, to predict, or to control." (Philip Johnson-Laird, "Mental models: Toward a cognitive science of language, inference, and consciousness", 1983)

"The basic idea is that schemata are data structures for representing the generic concepts stored in memory. There are schemata for generalized concepts underlying objects, situations, events, sequences of events, actions, and sequences of actions. Roughly, schemata are like models of the outside world. To process information with the use of a schema is to determine which model best fits the incoming information. Ultimately, consistent configurations of schemata are discovered which, in concert, offer the best account for the input. This configuration of schemata together constitutes the interpretation of the input. (David E Rumelhart, Paul Smolensky, James L McClelland & Geoffrey E Hinton, "Schemata and sequential thought processes in PDP models", 1986)

🆃Gheorghe Ţiţeica - Collected Quotes

"At difficult times like this, the only salvation is an enthusiasm for science and elevated thinking, and from all sciences, mathematics, through its precise problems, through its rigorous proofs, gives the most important and immediate rewarding and serves then as a solid foundation for any other theoretical or applied profession." (Gheorghe Ţiţeica, "Gazeta Matematica", ["Mathematical Gazette"] XXXVI, 1916)

"Born at the same time with the Greek art, the mathematics kept in its canvas, in its intimate structure, a certain affinity with art. It comes to the same harmony in Euclid’s geometry as in the ancient temples. It is the same silence, the same balance in demonstrating a theorem as in the admirable columns of the Acropolis." (Gheorghe Ţiţeica)

"Mathematics is a way to express the natural laws, it is the simplest and the most appropriate mode to describe a general law or the flow of a phenomenon, it is the most perfect language for narrating a natural phenomenon." (Gheorghe Ţiţeica)

"The slyness, cunning, lie and how many other abilities that are employed, sometimes successfully, unfortunately even with very high success, in the everyday life, have no place in the mathematical proof." (Gheorghe Ţiţeica, "Mathematics and Art")

"The world of mathematics is an ideal world, governed by a crystal-like order and beauty."  (Gheorghe Ţiţeica, "Mathematics and Art")

"There exists, among mathematicians, a deep-seated and strong belief which sustains them in their abstract studies, namely that none of their problems can remain without any answer." (Gheorghe Ţiţeica)

🅱Dan Barbilian - Collected Quotes

"As in geometry, I understand through poetry a particular symbolism for representing the possible forms of existence. [...] For me poetry is a prolongation of geometry, so that, while remaining a poet, I have never abandoned the divine domain of geometry." (Dan Barbilian, 1927)  

"I consider myself more of a practitioner of mathematics and less of a poet, and that only insofar as poetry recalls geometry. No matter how contradictory these two terms might seem at first sight, there is somewhere in the high realm of geometry a bright spot where it meets poetry." (Dan Barbilian, 1927) 

"Mathematical research can lend its organisational characteristics to poetry, whereby disjointed metaphors take on a universal sense. Similarly, the axiomatic foundations of group theory can be assimilated into a larger moral concept of a unified universe. Without this, mathematics would be a laborious Barbary." (Dan Barbilian, “The Autobiography of the Scientist”, 1940) 

“[…] the major mathematical research acquires an organization and orientation similar to the poetical function which, adjusting by means of metaphor disjunctive elements, displays a structure identical to the sensitive universe. Similarly, by means of its axiomatic or theoretical foundation, mathematics assimilates various doctrines and serves the instructive purpose, the one set up by the unifying moral universe of concepts. ” (Dan Barbilian, “The Autobiography of the Scientist”, 1940) 

"The domain of poetry is not the entire soul, but only that privileged part where echoes the playing of lyres. It is the place of all intelligible beauty: pure understanding, the honour of geometries." (Dan Barbilian, 1947)

"After all, Greek thought is expressed not only mythically, in fiction, but also directly, in theorems. The gate through which the Greek world may be discussed – and without the knowledge of which, in my opinion, one’s culture can not be deemed complete – is not necessarily Homer. Greek geometry is a wider gate, through which the eye might grasp an austere, yet essential landscape." (Dan Barbilian, 1967) 

" [if a poem] admits an explanation, rationally it admits an infinity. An exegesis can in no way be absolute. A poet provided certain mathematics can give not one, not two, but a great number of explanations of a hidden poem." (Dan Barbilian, 1968) 

"The mathematical works thrall and delight, just like the works of passion and imagination." (Dan Barbilian)

"The Mathematics bring into play spiritual powers which are not much different from those required by poetry and art." (Dan Barbilian)

🅼Grigore C Moisil - Collected Quotes

“Throwing a small stone may have some influence on the movement of the sun"(Grigore C Moisil, “Determinism si inlantuire”, 1940)

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

"All that is correct thinking is either Mathematics or likely to be reduced to Mathematics." (Grigore C Moisil)

"A mathematician does Mathematics because he sees in it something beautiful, something interesting, something he likes, something to be fond of, something that affects him, something that makes him think, meditate, dream." (Grigore C Moisil)

"A theorem is a love letter to an unknown person, to that person who catches not only its explicit meaning, but all the implicit meanings." (Grigore C Moisil)

"Learning Mathematics, one learns to think." (Grigore C Moisil)

“Logic today is not only an opportunity for philosophy, but an important instrument which people must learn to use.” (Grigore C Moisil)

"No problem has borders. Any answer has many borders." (Grigore C Moisil)

"Science is formed only from affirmations and negations, though the experiencing of science is formed from questions and answers, from hunches and doubts." (Grigore C Moisil)

"The Mathematics will be the Latin language of the future, compulsory for all scientists. Just because the Mathematics allows maximum acceleration of the movement of the scientific ideas." (Grigore C Moisil)

“The spirit of modern mathematics is based on mathematical logic, mathematical linguistics, the study of formal systems and on abstract algebra.” (Grigore C Moisil)

Romanians on Mathematics

"All that is correct thinking is either Mathematics or likely to be reduced to Mathematics." (Grigore Moisil)

"Geometry is the science which restores the situation that existed before the creation of the world and tries to fill the 'gap', relinquishing the help of matter." (Lucian Blaga)

"Learning Mathematics, one learns to think." (Grigore Moisil)

"Equality exists only in Mathematics." (Mihai Eminescu)

"Mathematics is a way of expressing the natural laws, it is the easiest and best way to describe a general law or the flow of a phenomenon, it is the most perfect language in which one can narrate a natural phenomenon." (Gheorghe Ţiţeica) 

"The mathematical works thrall and delight, just like the works of passion and imagination." (Dan Barbilian)

"The mathematician is the tamer who tamed infinity." (Lucian Blaga)

"The Mathematics bring into play spiritual powers which are not much different from those required by poetry and art." (Dan Barbilian)

"The Mathematics will be the Latin language of the future, compulsory for all scientists. Just because the Mathematics allows maximum acceleration of the movement of the scientific ideas." (Grigore Moisil)

"There is an intimate and powerful conviction among mathematicians, that supports them in their abstract researches, namely that none of their problems cannot remain without an answer." (Gheorghe Ţiţeica)