📁On Data (1940-1949)

"Scientific data are not taken for museum purposes; they are taken as a basis for doing something. If nothing is to be done with the data, then there is no use in collecting any. The ultimate purpose of taking data is to provide a basis for action or a recommendation for action. The step intermediate between the collection of data and the action is prediction." (William E Deming, "On a Classification of the Problems of Statistical Inference", Journal of the American Statistical Association Vol. 37 (218), 1942)

"The faith of scientists in the power of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual, empirical results. But the facts [...] accepted by virtue of these tests are not actually observed at all." (Susanne K Langer, "Philosophy in a New Key", 1942)

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

"True, the universe is more than a collection of objective experimental data; more than the complexus of theories, abstractions, and special assumptions devised to hold the data together; more, indeed, than any construct modeled on this cold objectivity. For there is a deeper, more subjective world, a world of sensation and emotion, of aesthetic, moral, and religious values as yet beyond the grasp of objective science. And towering majestically over all, inscrutable and inescapable, is the awful mystery of Existence itself, to confound the mind with an eternal enigma." (Banesh Hoffmann, "The Strange Story of the Quantum", 1947)

"There is only one kind of whiskey, but two broad classes of data, good and bad." (William E Deming, "On the Classification of Statistics", The American Statistician Vol. 2 (2), 1948)

🗼On Philosophy of Science: On Models (1900-1929)

"Confronted with the mystery of the Universe, we are driven to ask if the model our minds have framed at all corresponds with the reality; if, indeed, there be any reality behind the image." (Sir William Cecil Dampier, "The Recent Development of Physical Science", 1904)

"The different sciences are not even parts of a whole; they are but different aspects of a whole, which essentially has nothing in it corresponding to the divisions we make; they are, so to speak, sections of our model of Nature in certain arbitrary planes, cut in directions to suit our convenience." (Sir William Cecil Dampier, "The Recent Development of Physical Science", 1904)

"We can only study Nature through our senses – that is […] we can only study the model of Nature that our senses enable our minds to construct; we cannot decide whether that model, consistent though it be, represents truly the real structure of Nature; whether, indeed, there be any Nature as an ultimate reality behind its phenomena." (Sir William C Dampier, "The Recent Development of Physical Science", 1904)

"A symbolical representation of a method of calculation has the same significance for a mathematician as a model or a visualisable working hypothesis has for a physicist. The symbol, the model, the hypothesis runs parallel with the thing to be represented. But the parallelism may extend farther, or be extended farther, than was originally intended on the adoption of the symbol. Since the thing represented and the device representing are after all different, what would be concealed in the one is apparent in the other." (Ernst Mach, "Space and Geometry: In the Light of physiological, phycological and physical inquiry", 1906) 

“We should always aim toward the economy of thought. It is not enough to give models for imitation. It must be possible to pass beyond these models and, in place of repeating their reasoning at length each time, to sum this in a few words.” (Jules H Poincaré, 1909)

"It seems rather futile, if such be the normal history of hypothetical models, to inflict on us the labor of learning abstruse hypotheses which continually revamp old metaphysical terms and merely dress them up in new transcendental symbols. It is a valuable exercise to strip hypotheses of their technical phraseology; to change those words which deceive our minds into believing that a clear idea has been conveyed, when, in fact, they have merely been wrenched from any real significance." (Louis T More," The Limitations of Science", 1915)

"Our model of Nature […] should be like an engine with movable parts. We need not fix the position of any one lever; that is to be adjusted from time to time as the latest observations indicate. The aim of the theorist is to know the train of wheels which the lever sets in motion - that binding of the parts which is the soul of the engine." (Sir Arthur S Eddington, "The Internal Constitution of Stars", Nature Vol. 106 (2603), 1920)

"[…] while the building of Nature is growing spontaneously from within, the model of it, which we seek to construct in our descriptive science, can only be constructed by means of scaffolding from without, a scaffolding of hypotheses. While in the real building all is continuous, in our model there are detached parts which must be connected with the rest by temporary ladders and passages, or which must be supported till we can see how to fill in the understructure. To give the hypotheses equal validity with facts is to confuse the temporary scaffolding with the building itself." (John H Poynting, "Collected Scientific Papers", 1920)

"As we continue the great adventure of scientific exploration our models must often be recast. New laws and postulates will be required, while those that we already have must be broadened, extended and generalized in ways that we are now hardly able to surmise." (Gilbert Newton Lewis, "The Anatomy of Science", 1926)

🕸️On Graph Theory: On Networks (1980-1989)

"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)

"The traditional boundaries between various fields of science are rapidly disappearing and what is more important science does not know any national borders. The scientists of the world are forming an invisible network with a very free flow of scientific information - a freedom accepted by the countries of the world irrespective of political systems or religions. […] Great care must be taken that the scientific network is utilized only for scientific purposes - if it gets involved in political questions it loses its special status and utility as a nonpolitical force for development." (Sune K. Bergström, [speech] 1982) 

"We define a semantic network as 'the collection of all the relationships that concepts have to other concepts, to percepts, to procedures, and to motor mechanisms' of the knowledge." (John F Sowa, "Conceptual Structures", 1984)

"Cybernetics, although not ignoring formal networks, suggests that an informal communications structure will also be present such that complex conversations at a number of levels between two or more individuals exist." (Robert L Flood, "Dealing with Complexity", 1988) 

"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. [...] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", 1988)

"A culture may be conceived as a network of beliefs and purposes in which any string in the net pulls and is pulled by the others, thus perpetually changing the configuration of the whole. If the cultural element called morals takes on a new shape, we must ask what other strings have pulled it out of line. It cannot be one solitary string, nor even the strings nearby, for the network is three-dimensional at least." (Jacques Barzun, "The Culture We Deserve", 1989)

On Extrema III

"In order to regain in a rigorously defined function those properties that are analogous to those ascribed to an empirical curve with respect to slope and curvature (first and higher difference quotients), we need not only to require that the function is continuous and has a finite number of maxima and minima in a finite interval, but also assume explicitly that it has the first and a series of higher derivatives (as many as one will want to use)." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)

"A variety of natural phenomena exhibit what is called the minimum principle. The principle is displayed where the amount of energy expended in performing a given action is the least required for its execution, where the path of a particle or wave in moving from one point to another is the shortest possible, where a motion is completed in the shortest possible time, and so on." (James R Newman, "The World of Mathematics" Vol. II, 1956)

"In the mathematical theory of the maximum and minimum problems in calculus of variations, different methods are employed. The old classical method consists in finding criteria -as to whether or not for a given curve the corresponding number assumes a maximum or minimum. In order to find such criteria a considered curve is a little varied, and it is from this method that the name 'calculus of variations' for the whole branch of mathematics is derived." (Karl Menger, "What Is Calculus of Variations and What Are Its Applications?" [James R Newman, "The World of Mathematics" Vol. II], 1956)

"We frequently find that nature acts in such a way as to minimize certain magnitudes. The soap film will take the shape of a surface of smallest area. Light always follows the shortest path, that is, the straight line, and, even when reflected or broken, follows a path which takes a minimum of time. In mechanical systems we find that the movements actually take place in a form which requires less effort in a certain sense than any other possible movement would use. There was a period, about 150 years ago, when physicists believed that the whole of physics might be deduced from certain minimizing principles, subject to calculus of variations, and these principles were interpreted as tendencies--so to say, economical tendencies of nature. Nature seems to follow the tendency of economizing certain magnitudes, of obtaining maximum effects with given means, or to spend minimal means for given effects." (Karl Menger, "What Is Calculus of Variations and What Are Its Applications?" [James R Newman, "The World of Mathematics" Vol. II], 1956)

"While the minimum and maximum problems of calculus of variations correspond to the problem in the ordinary calculus of finding peaks and pits of a surface, the minimax problems correspond to the problem of finding the saddle points of the surface (the passes of a mountain)."(Karl Menger, "What Is Calculus of Variations and What Are Its Applications?" [James R Newman, "The World of Mathematics" Vol. II], 1956)

"Extrema is the generic term for the concepts 'maximum' and 'minimum' , like 'parents' is the generic term for 'father' and 'mother'. Extremal problems have to do with finding maxima and minima. We encounter them everywhere. It is hardly an exaggeration to say that all problems solved by living organisms are those involving a search for extrema." (Yakov Khurgin, "Did You Say Mathematics?", 1974)

"Maximum and minimum always exist together: if our cup-like surface is turned over, we get a cap, in which the highest point (maximum) corresponds to the lowest point of the cup (minimum). By climbing to the uppermost peak of a mountain we can find ourselves (via reflection in a nearby lake) in the lowest point of the valley below. Here, the mathematician calmly reasons to within an accuracy that amounts to the opposite, so to say, for if we find a maximum and then view the situation from another angle, we see a minimum. The answer thus depends solely on how we view the surface. That is why we always speak of seeking an extremum and not, separately, a maximum or a minimum." (Yakov Khurgin, "Did You Say Mathematics?", 1974) 

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution." (Richard A Epstein, "The Theory of Gambling and Statistical Logic" [Revised Edition], 1977)

"So the strategy of mixing the choices with equal likelihood is an equilibrium point for the game, in the same sense that the minimax point is an equilibrium for a game having a saddle point. Thus, using a strategy that randomizes their choices, Max and Min can each announce his or her strategy to the other without the opponent being able to exploit this information to get a larger average payoff for himself or herself." (John L Casti, "Five Golden Rules", 1995)

"What's important about a saddle point is that it represents a decision by the two players that neither can improve upon by unilaterally departing from it. In short, either player can announce such a choice in advance to the other player and suffer no penalty by doing so. Consequently, the best choice for each player is at the saddle point, which is called a 'solution' to the game in pure strategies. This is because regardless of the number of times the game is played, the optimal choice for each player is to always take his or her saddle-point decision. […] the saddle point is at the same time the highest point on the payoff surface in one direction and the lowest in the other direction. Put in algebraic terms using the payoff matrix, the saddle point is where the largest of the row minima coincides with the smallest of the column maxima." (John L Casti, "Five Golden Rules", 1995)

🕸️On Graph Theory: On Networks (1970-1979)

"Nature is a network of happenings that do not unroll like a red carpet into time, but are intertwined between every part of the world; and we are among those parts. In this nexus, we cannot reach certainty because it is not there to be reached; it goes with the wrong model, and the certain answers ironically are the wrong answers. Certainty is a demand that is made by philosophers who contemplate the world from outside; and scientific knowledge is knowledge for action, not contemplation. There is no God’s eye view of nature, in relativity, or in any science: only a man’s eye view." (Jacob Bronowski, "The Identity of Man", 1972)

"In the province of the mind, what one believes to be true is true or becomes true, within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the mind, there are no limit. […] In the province of connected minds, what the network believes to be true, either is true or becomes true within certain limits to be found experientially and experimentally. These limits are further beliefs to be transcended. In the network's mind there are no limits." (John C Lilly, "The Human Biocomputer", 1974)

"As with any graphic, networks are used in order to discover pertinent troups of to inform others of the groups and structures discovered. It is a good means of displaying structures, However, it ceases to be a means of discovery when the elements are numerous. The figure rapidly becomes complex, illegible and untransformable." (Jacques Bertin, "Graphics and graphic information processing", 1977)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 1979)

On Inequalities II

"Although they play a fundamental role in nearly all branches of mathematics, inequalities are usually obtained by ad hoc methods rather than as consequences of some underlying 'theory of inequalities'. For certain kinds of inequalities. the notion of majorization leads to such a theory that is sometimes extremely useful and powerful for deriving inequalities." (Albert W Marshall, "Inequalities: Theory of Majorization and its Applications", 1979)

"Inequalities are useful for bounding quantities that might otherwise be hard to compute." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"The triangle inequality is perhaps the most important property for proving theorems involving distance. The name is appropriate because the triangle inequality is an abstraction of the property that the sum of the lengths of two sides of a triangle must be at least as large as the length of the third side." (Robert Messer & Philip Straffin, "Topology Now!", 2006)

"There are three reasons for the study of inequalities: practical, theoretical and aesthetic. In many practical investigations, it is necessary to bound one quantity by another. The classical inequalities are very useful for this purpose. From the theoretical point of view, very simple questions give rise to entire theories. […] Finally, let us turn to the aesthetic aspects. As has been pointed out, beauty is in the eye of the beholder. However. it is generally agreed that certain pieces of music, art, or mathematics are beautiful. There is an elegance to inequalities that makes them very attractive." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)

"[...] we may also look for representations which make inequalities obvious. Often, these representations are maxima or minima of certain quantities. […] we know that many inequalities are associated with geometric properties. Hence. we can go in either direction. We can find the geometric equivalent of an analytic result, or the analytic consequence of a geometric fact such as convexity or duality." (Claudi Alsina & Roger B Nelsen, "When Less is More: Visualizing Basic Inequalities", 2009)

"Second Law of thermodynamics is not an equality, but an inequality, asserting merely that a certain quantity referred to as the entropy of an isolated system - which is a measure of the system’s disorder, or ‘randomness’ - is greater (or at least not smaller) at later times than it was at earlier times." (Roger Penrose, "Cycles of Time: An Extraordinary New View of the Universe", 2010)

On Intelligence (Unsourced)

"Education appears to be the thing that enables a man to get along without using his intelligence." (A E Wiggan)

"Education is one of the chief obstacles to intelligence and freedom of thought." (Bertrand Russel)

"Much learning does not teach a man to have intelligence." (Heraclitus)

"Music is architecture translated or transposed from space into time; for in music, besides the deepest feeling, there reigns also a rigorous mathematical intelligence." (Georg W F Hegel)

"Science is intelligence in action with no holds barred." (Percy W Bridgman)

"The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education." (Martin L King, Jr.)

"The learning of many things does not teach intelligence […]." (Pythagoras of Samos)

"The present state of the system of nature is evidently a consequence of what is in the preceding moment, and if we conceive of an intelligence which at a given instant knew all the forces acting in nature and the position of every object in the universe - if endowed with a brain sufficiently vast to make all necessary calculations - could describe with a single formula the motions of the largest astronomical bodies and those of the smallest atoms. To such an intelligence, nothing would be uncertain; the future, like the past, would be an open book." (Pierre-Simon Laplace)

"The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living. Of course I do not here speak of that beauty that strikes the senses, the beauty of qualities and appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmonious order of the parts, and which a pure intelligence can grasp." (Henri Poincaré)

🦋On Chaos Theory II

"Fractal geometry and chaos theory can convey a new level of understanding to systems engineering and make it more effective." (Arthur D Hall, "The fractal architecture of the systems engineering method", 1989)

"At the large scale where many processes and structures appear continuous and stable much of the time, important changes may occur discontinuously. When only a few variables are involved, as well as an optimizing process, the event may be analyzed using catastrophe theory. As the number of variables in- creases the bifurcations can become more complex to the point where chaos theory becomes the relevant approach. That chaos theory as well as the fundamentally discontinuous quantum processes may be viewed through fractal eyeglasses can also be admitted. We can even argue that a cascade of bifurcations to chaos contains two essentially structural catastrophe points, namely the initial bifurcation point at which the cascade commences and the accumulation point at which the transition to chaos is finally achieved." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"There is no question but that the chains of events through which chaos can develop out of regularity, or regularity out of chaos, are essential aspects of families of dynamical systems [...]  Sometimes [...] a nearly imperceptible change in a constant will produce a qualitative change in the system’s behaviour: from steady to periodic, from steady or periodic to almost periodic, or from steady, periodic, or almost periodic to chaotic. Even chaos can change abruptly to more complicated chaos, and, of course, each of these changes can proceed in the opposite direction. Such changes are called bifurcations." (Edward Lorenz, "The Essence of Chaos", 1993)

"Chaos theory explains the ways in which natural and social systems organize themselves into stable entities that have the ability to resist small disturbances and perturbations. It also shows that when you push such a system too far it becomes balanced on a metaphoric knife-edge. Step back and it remains stable; give it the slightest nudge and it will move into a radically new form of behavior such as chaos." (F David Peat, "From Certainty to Uncertainty", 2002)

"In chaos theory this 'butterfly effect' highlights the extreme sensitivity of nonlinear systems at their bifurcation points. There the slightest perturbation can push them into chaos, or into some quite different form of ordered behavior. Because we can never have total information or work to an infinite number of decimal places, there will always be a tiny level of uncertainty that can magnify to the point where it begins to dominate the system. It is for this reason that chaos theory reminds us that uncertainty can always subvert our attempts to encompass the cosmos with our schemes and mathematical reasoning." (F David Peat, "From Certainty to Uncertainty", 2002)

"[…] while chaos theory deals in regions of randomness and chance, its equations are entirely deterministic. Plug in the relevant numbers and out comes the answer. In principle at least, dealing with a chaotic system is no different from predicting the fall of an apple or sending a rocket to the moon. In each case deterministic laws govern the system. This is where the chance of chaos differs from the chance that is inherent in quantum theory." (F David Peat, "From Certainty to Uncertainty", 2002)

"Chaos theory is a branch of mathematics focusing on the study of chaos - dynamical systems whose random states of disorder and irregularities are governed by underlying patterns and deterministic laws that are highly sensitive to initial conditions. Chaos theory is an interdisciplinary theory stating that, within the apparent randomness of complex, chaotic systems, there are underlying patterns, interconnectedness, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is a sensitive dependence on initial conditions)." (Nima Norouzi, "Criminal Policy, Security, and Justice in the Time of COVID-19", 2022)

📁 On DIKW: On Knowledge (1740-1749)

"Mathematical knowledge adds vigor to the mind, frees it from prejudice, credulity, and superstition." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)

"It is your opinion, the ideas we perceive by our senses are not real things, but images, or copies of them. Our knowledge therefore is no farther real, than as our ideas are the true representations of those originals. But as these supposed originals are in themselves unknown, it is impossible to know how far our ideas resemble them; or whether they resemble them at all. We cannot therefore be sure we have any real knowledge." (George Berkeley, "Three Dialogues", 1713)

"There is nothing more pleasant for man than the certainty of knowledge; whoever has once tasted of it is repelled by everything in which he perceives nothing but uncertainty. This is why the mathematicians who always deal with certain knowledge have been repelled by philosophy and other things, and have found nothing more pleasant than to spend their time with lines and letters." (Christian Wolff, 1741)

"He that would make a real progress in knowledge must dedicate his age as well as first fruits - the latter growth as well as the first-fruits - at the altar of truth." (Bishop George Berkeley, "Siris", 1744)

"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)

📁 On DIKW: On Knowledge (1900-1929)

"A system is not so important as a method. A system is of significance because it brings order and clearness into our knowledge, but he who hopes by its help to reach something more, he who thinks to extend his knowledge by means of a system is self-deceived." (Harald Høffding, "A history of modern philosophy", 1900)

"Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments." (David Hilbert, "Mathematical Problems", Bulletin American Mathematical Society Vol. 8, 1901-1902)

"Man's determination not to be deceived is precisely the origin of the problem of knowledge. The question is always and only this: to learn to know and to grasp reality in the midst of a thousand causes of error which tend to vitiate our observation." (Federigo Enriques, "Problems of Science", 1906)

"If the fresh facts which come to our knowledge all fit themselves into the scheme, then our hypothesis may gradually become a solution." (Arthur C Doyle, "The Adventure of Wisteria Lodge", 1908)

"Knowledge is the distilled essence of our intuitions, corroborated by experience." (Elbert Hubbard, "A Thousand & One Epigrams, 1911)

"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)

"The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another." (Henri Poincaré, 1913)

"By intuition is frequently understood perception, or the knowledge of actual reality, the apprehension of something as real. […] Intuition is the undifferentiated unity of the perception of the real and of the simple image of the possible. " (Benedetto Croce, "The Essence of Æsthetic", 1921)

"Observed facts must be built up, woven together, ordered, arranged, systematized into conclusions and theories by reflection and reason, if they are to have full bearing on life and the universe. Knowledge is the accumulation of facts. Wisdom is the establishment of relations. And just because the latter process is delicate and perilous, it is all the more delightful." (Gamaliel Bradford, "Darwin", 1926)

"Hypothesis, however, is an inference based on knowledge which is insufficient to prove its high probability." (Frederick L Barry, "The Scientific Habit of Thought", 1927)

"In mathematics as in the other sciences, the same processes can be observed again and again. First, new questions arise, for internal or external reasons, and draw researchers away from the old questions. And the old questions, just because they have been worked on so much, need ever more comprehensive study for their mastery. This is unpleasant, and so one is glad to turn to problems that have been less developed and therefore require less foreknowledge - even if it is only a matter of axiomatics, or set theory, or some such thing." (Felix Klein,"Development of Mathematics in the 19th Century", 1928)

"With fuller knowledge we should sweep away the references to probability and substitute the exact facts." (Sir Arthur S Eddington, "The Nature of the Physical World", 1928)