Economics and Intentionality

“The Scientific Revolution” in high school world history textbooks (1949-2014) Yuer-Hsing Chi Heng-An Chen Department of History & College of Liberal Arts SUMMARY This study mainly investigated how the world history textbooks in high school have presented “Scientific Revolution” since the national government moved to Taiwan. That is, we looked into the changes and features of “Scientific Revolution” in high school world history textbooks. Through the development of world history education in Taiwanese high schools, the study first analyzed the curriculum guidelines of the middle school history. We found that since the abolishment of martial laws in 1987, because of the educational reform, the guidelines have gone through several changes. They turned to focus on cultivating the students’ world view and eliminating “European Centrism.” The concept of “Scientific Revolution” has become popular in historical studies since the end of WWII. The related studies nowadays have also started to review and rethink critically on this issue. In the world history textbooks of the Taiwanese high school, the term of “Scientific Revolution” was from nothing to something. In Taiwan, most of the world history textbooks adopted the traditional methods on describing “Scientific Revolution.” Centering on the scientists, the major axis is the revolution of Astronomy and scientific methods. In the future, regarding the introduction on “Scientific Revolution,” in addition to basing on traditional descriptive methods, we suggested to incorporate more reflections, and integrated more political and social backgrounds in the high school world history textbooks. In this way, the students can understand the history from different aspects, holding multiple historical views. Key words: textbooks, history education, high school education, the Scientific Revolution, world history INTRODUCTION Because of the technical improvements brought about by the new technology, the trends globalization were triggered, which forced us to cultivate more profound world view as well as the understanding and tolerance on multi-cultures. Therefore, recent education and learning of world history in high schools have been centered on cultivating macro world view as the primary learning objective. Among the world history textbooks, although the chapter of “Scientific Revolution” does not take up major printed pages, it is one of the very few chapters that lead students to understand the required scientific subjects from a historic perspective. For this reason, it has its value for investigating. The study mainly explored how the world history textbooks in high school have presented “Scientific Revolution” since the national government moved to Taiwan, and how historical studies and perspectives have influenced on the presentations. MATERIALS AND METHODS The present study focused on the “Scientific Revolution” presented in the world history textbooks used by Taiwanese high schools. We investigated the textbooks published from the time that the national government moved to Taiwan to the latest version of textbooks. Because these textbooks were compiled based on the curriculum standards and guidelines set up by MOE, this research also analyzed the changes of the standards and guidelines in this years. By literature review and analysis, we collected related literature on middle school history education. Moreover, we generalized and analyzed based on the main subject of the study “Scientific Revolution” in order to learn the formation, appearance, reflections and rethought on the concept “Scientific Revolution” in the academic field. Afterward, we adopted content analysis method to analyze how “Scientific Revolution” is presented in the textbook chapter. RESULTS AND DISCUSSION After 1987, because of educational reform, the purpose of Taiwanese history education had transformed from enable students to learn the position of “Our Nation” from the learning of “Foreign Countries” to equipped students with “World View.” The content had also changed from political-history-focused to cultural-history-focused, hoping to eliminate “European Centrism” and centering on the present rather than the past. Recently, there have been less political constraints on middle school world history textbooks. However, it is still a big challenge to incorporate historical study results and multiple perspectives properly in the textbooks. “The Scientific Revolution,” from the historical perspective, indicates the period from 16th to 18th century in Europe (Especially 17th century; the year 1543 is viewed as the index of its outset.) There were revolutionary developments in the scientific theories and experiments in these years, which thoroughly changed the scientific approaches. It meant the appearance of modern science. Also, thanks to these scientists, there are tremendous changes in Europeans Universal View. The concept of the term “Scientific Revolution” was originated from Jean le Rond D’Alembert in the 18th century. It was after 1939 that Alexandre Koyre formally brought up the concept. Then, Herbert Butterfield popularized the concept, so the concept became very popular in historical field in the western world. Recently, the academics have had profound reflections and rethought on it. However, “Scientific Revolution” is still a widely-used concept in history. The early versions of curriculum guidelines and textbooks in Taiwanese high school world history did not include the issue of “Scientific Revolution.” The term of “Scientific Revolution” in Taiwanese history education could be said to be from nothing to something. The related content of “Scientific Revolution” in these textbooks that appear the most often in the attached pictures is the revolution-related figures, especially scientists. There is high reappearing and continuing rate of the revolution-related attached pictures. However, the explanations on these pictures have been changing constantly, causing the phenomenon of “one picture, multiple explanations.” Beginning from Nicolau Copernicus through Galileo Galilei,and Johannes Kepler and finally Isaac Newton represented a generalization of views. The presenting approach of traditional “Scientific Revolution”, from astronomy physics, was always included as the center of content. In addition, the inductive method by Francis Bacon and the deductive method by Rene Descartes were the must-mentioned “Scientific methods.” CONCLUSION From the “Scientific Revolution” in the middle school world history textbooks, we can see that the Taiwanese world history teaching material has been renewed with the current academic research. However, the textbooks obviously revealed “fixation.” Once appearing, many fixed terms tend to reappear in the following versions, which are difficult to change, even relive. However, it is apparent that the descriptions in the textbooks still focused too much on the contribution of “Scientific Revolution,” which might be too heroic-oriented. Recently, there is only a few reflection and rethought on “Scientific Revolution” in the academic field. So far, the related content only appeared the Han-Lin Senior High School History based on the latest 2011 curriculum guideline. In the end of the research, we gave some suggestions on the future introduction of “Scientific Revolution” in the middle school world history textbooks. From the junior high school textbooks, we can still focus on introducing traditional concepts of “Scientific Revolution,” but more clear definition, time scope and background information and other related contents should be presented. In the senior high school stage, in addition to the original contents on “Scientific Revolution,” we can discuss the scientific activities at that time through the political perspectives and social background. Also, we should incorporate some reflections and rethought by the academics in the textbook. In this way, students can not only learn the historical knowledge, but also cultivate the ability to think critically at the same time.

The ‘marginalist revolution’: an overview The term ‘marginalist revolution’ is commonly utilised to indicate a sudden change of direction in economic science, with the abandonment of the classical – and, more precisely, Ricardian – approach, and the shift to a new approach based on a subjective theory of value and the analytical notion of marginal utility. The outbreak of the ‘revolution’ is commonly located in the years between 1871 and 1874, when the main writings were published of the leaders of the Austrian marginalist school, Carl Menger (1840–1921), of the British school, William Stanley Jevons (1835–82), and of the French (Lausanne) school, Leon Walras (1834–1910). In fact, 1871 saw the appearance of both the Principles of pure economics by Menger and The theory of political economy by Jevons, while Walras brought out his Elements of pure economics in 1874. Let us, however, once again reiterate that the ‘marginalist revolution’ had had important precursors, as we will see again below. Moreover, the differences between the Austrian imputation approach, the French general economic equilibrium and Marshallian partial equilibriums were quite important, as far as both method and the basic view of the functioning of the economy were concerned.

ITis significant that Joseph Schumpeter entered our field in the year I906 with a study on mathematical methods in theoretical economics.' This, his very first work, contains the points from which his own original research took its departure. Reading it today, one gains not only an impression of its author's comprehensive familiarity with the literature on mathematical economics that had by then been published, but of the influence which the study of these works exerted on young Schumpeter. Reared in the atmosphere of the Vienna School, he was attracted far more by the views of such as Cournot, Jevons, Edgeworth, Marshall, and above all Leon Walras. What Walras meant to him is seen plainly from the obituary for the founder of the Lausanne School which he published four years later in the same journal. When look back today on the life of this scholar, he wrote, we are struck by the simple grandeur that lies in uncompromising devotion to a single task. The impression is as of a natural phenomenon, powerful, self-evident, of foreordained necessity. The study of problems in pure economics -such was the content of that career, to the exclusion of all else. Schumpeter was really describing his own scientific ideal, one to which he clung to the end of his life. Walras was his great model, the man whom he held in higher esteem than any other. He once told me that whoever failed to study and understand Walras was unlikely ever to become a good economist. And, indeed, his first great work, which attracted world-wide attention to him at the age of only twenty-five, came into being against a background of Walrasian thinking. His Das Wesen und Hauptinhalt der theoretischen Nationalokonomie (Nature and Main Content of Theoretical Economics, Leipzig, I908) breathes the spirit of Lausanne rather than Vienna. The book, written in the brilliant style peculiar to Schumpeter, is at once a program and a profession of faith. I hold aloof from practical politics and recognize no purpose other than knowledge. ... We seek to understand rather than to engage in polemics, to learn rather than to criticize, to work out the elements of truth in every theorem rather than simply to accept or reject (Preface, pp. vi, vii). The work is essentially a study in methodology and epistemology. One looks to it in vain for a systematic presentation of theory. It seeks, rather, to set forth the principles that should, in the author's view, govern the pursuit of theoretical economics as such. Solutions of concrete problems are presented only by way of example and in illustration of his methodological reasoning. The book, nevertheless, touches on all the central problems of theory, and foreshadows the approaches toward their solution which Schumpeter elaborated in his later works. Even this first outline contains nearly all the thoughts that only later came to full maturity. The concepts of statics and dynamics, the imputation problem, questions of price theory, the distribution theory, the principles of the theory of money, the method of variations, interest as a phenomenon in economic development -all these are found in this work. To be sure, much of what Schumpeter then had to say on these questions e.g., the definition of static and dynamic economies appears in a different light today and was viewed differently even by him later on. He still held at the time that the phenomenon of economic development was not susceptible to the same kind of exact treatment as the problem of static equilibrium, and in this respect the latest elaboration of dynamic theory has not upheld him. Nor has his thesis of the nonexistence of interest in a stationary economy proved tenable. But that is not what matters. The value of the book must be judged by the message it brought to its contemporaries at the time it was published. In a period that paid little heed to exact theory, 'The editor is indebted to Heinz Norden for translating this essay from the German. 2 Zeitschrift fur Volkswirtschaft, Sozialpolitik und Verwaltung, Volume I5 (I906), pp. 30-49.

The paper is a partly provocative essay edited as a humanitarian study in philosophy of science and social philosophy, reflecting on the practical, “anti-metaphysical” turn taken place since the 20th century and continuing until now. The article advocates that it is about time it to be overcome because it is the main obstacle for the further development of exact and natural sciences including mathematics therefore restoring the unity of philosophy and sciences in the dawn of modern science when the great scientists were philosophers as a necessary condition for their revolutionary achievements, and the physicists were simultaneously mathematicians not less than philosophers and even theologians as Descartes, Newton, Leibnitz were just as their predecessors, Copernicus or Galileo Galilei. The revolution in science accomplished by them needed philosophy since any scientific revolution, then necessarily growing into social, needs philosophy; and if ones wish to prevent social revolutions originating from fundamental scientific discoveries, in turn relying on the close link of sciences and philosophy, they are to cut the link at issue, and just that happened in the 20th centuries therefore implicitly heralding a “brave new world” of eternal normal science without revolutions whether scientific or social. Fukuyama’s “end of history” requires an “end of scientific history” as it is an obligatory premise, and separating sciences from philosophy is sufficient for that, though proclaimed quite otherwise: as overcoming metaphysics preventing sciences and substituting them by quasi-sciences. Particularly, that “anti-metaphysical turn” has established for science to obey society absolutely and thoroughly, obviously a condition contradicting the scientific and social revolutions in Modernity featured by the domination of science over society by the mediation of philosophy able to translate all epochal scientific discoveries as social corollaries. A special attention is paid to quantum mechanics, being the frontier of physics in the 20th century, where that anti-metaphysical turn is discernibly concentrated and may be notated by the famous slogan “Shut up and calculate!” regardless of its authorship. Just the revolutionary discoveries in physics, for example those of “dark mass” and “dark energy” or entanglement force now its rejection therefore restoring the unity of philosophy, mathematics and physics, made ever possible the establishment of modern science by its emancipation from religion, and thus and ind final analysis, from society.

Classical political economy is the earliest stage and school in the evolution of economic science from the late eighteenth century to the second half of the nineteenth century, since Adam Smith the founder. It is the science of the production, distribution, exchange, and consumption of wealth. It has two related branches: pure economics as the theory of a market economy and social economics or economic sociology as an analysis of the institutional structure of economies, including markets. Classical political economy is succeeded by neoclassical economics, the next stage and school in the evolution of economic science from the 1870s to the 1930s and later. It begins with the “marginalist revolution” in economics during the 1870s–1890s, such as the marginal utility theory of value and prices, in adverse reaction to classical political economy's labor version. The founders of “marginalism” are William Jevons, Carl Menger, and Leon Walras, “discovering” marginal utility theory in Europe during 1871–1874. Neoclassical economics consists of two main branches or orientations, “pure” economic theory in the form of “market economics” and social economics or economic sociology.

Takashi Tachibana , widely regarded as one of Japan's most prominent journalists, has written more than 30 books. Trained in French literature and philosophy, in the 1980s he began to cover scientific topics. His most recent book, Ten Billion Years Voyage , addresses scientific research in Japan today. I am a Japanese science writer. For years I have been writing about all aspects of science including neuroscience, molecular biology, evolutionary theory, x-ray astronomy, elementary particles, computer science, artificial intelligence, robotics, and space exploration. In short—to borrow Erwin Schrodinger's expression from What Is Life [*][1]—I am a man of keen longing for unified, all-embracing knowledge. Yet, since ours is an age of knowledge explosion, it is virtually impossible to know it all, or even for a reporter to cover it all. There are so many important fields in science, and their advancement is so rapid, that, like Alice's Queen of Hearts, I must run as fast as possible just to remain in place. Nearly all of my time is spent interviewing scientists in one field or another, watching their experiments, or reading their papers. Somehow I still manage at least to follow the most important scientific advancements. Yet, I have discovered that reporting what I have learned in terms that the general readership can understand is quite a different matter: It is far more difficult. In his classic work Two Cultures and the Scientific Revolution , [**][2] C. P. Snow wrote that the chasm between scientists and literary intellectuals was so vast that they could not communicate with each other. For example in physics, Snow found the mid-20th century literati to be as ignorant about science as had been their Neolithic ancestors. And this situation that Snow lamented nearly four decades ago has only grown worse. The current level of basic scientific knowledge is so low that it is difficult to interest even the brightest layman or nonscience student in what modern science is doing. I border on despair at my inability to keep them interested long enough to correctly understand both a specific research project, and its aims. The chasm between scientist and nonscientist has widened to become a gulf. And it is the task of science and society to narrow that gulf through an intellectual shift of tectonic plates. Modern scientists can no longer expect to live their lives in proud isolation because most significant scientific research requires substantial funding. A fortunate few enjoy private sources—problems with benefactors are another story. But in most cases government support, that is, tax money, is required to get research started and to keep it from grinding to a halt. When especially large sums are involved, taxpayers can be inquisitive, cost-conscious, and prone to finding fault, and in a democracy they must be taken into account. But public support requires a modicum of public understanding. If a project is very expensive, such as the superconducting super collider (SSC), or involves a highly controversial issue such as when human life begins—as in the debate over the use of near-term embryos for research—the final decision will always be political. Yet political decisions are not always rational, since public emotions can easily be influenced by irrational arguments. Vagueness, anxiety, fear, or abhorrence often prevail over rational judgment, and incorrect or even hostile (it is “absurd,” “extravagant,” “useless,” or “diabolical”) commentary about certain kinds of research spreads quickly. C. P. Snow was talking mainly about intellectuals. But today the reactions of ordinary people and the mass media matter more. Since politicians are easily swayed by their perceptions of public opinion, key to promoting wise political decisions about scientific matters is a sound understanding of science among the general population and the media that feed, reinforce, and mobilize its views. Alas, that understanding is presently lacking. The figure shows scientific discoveries, beginning with the 15th century, required by the Ministry of Education of Japan to be covered in Japanese high school science textbooks. This graph makes clear that we are not teaching our children about many of the great scientific achievements of our time. Hence the average high school graduate is unlikely to know, least of all appreciate, the numerous, life-changing discoveries that have taken place in the 20th century. ![Figure][3] This graph only reflects the situation in Japan, but I suspect that there is little difference in this regard with textbooks of other countries. In most industrialized countries high school is the basic educational requirement. In Japan about one-half of high school graduates do not go on to university, so that their scientific knowledge effectively stops there. Half of the university students major in the humanities or social sciences, and the majority of those students do not take natural science courses, with the consequence that even for college graduates scientific knowledge has also effectively stopped with high school graduation. They will, of course, pick up fragmentary scientific knowledge through the mass media, but this is usually superficial in nature. Downplaying or inadequately teaching about the great innovations in science has created a situation where today's world is composed of people who might be classified according to their level of scientific knowledge on a scale ranging from Neolithic man through late-20th century man. ![Figure][3] Y. MIDORIKAWA ET AL. The 20th century has been an age of revolution in science. Quantum physics began the process by revolutionizing first physics and then all aspects of science and technology. Relativity theory followed, changing cosmology. Molecular biology fundamentally altered life science. The 20th-century revolution in science has given us a whole new way of looking at the world, vastly different from the way people in the 19th or earlier centuries saw it. Mother Nature looks different. The universe looks different. Life is different. But the changes have not been as thorough as they might have been because, while those with a more comprehensive scientific education can recognize that something important has occurred, the great majority of people do not even realize that a revolution has taken place. Understanding comes through knowledge. Only with knowledge and understanding can we, using the latest image-enhancing techniques, create novel and exciting images from both new and established data. When we look at a beautiful night sky, we may feel the same wonder and awe that our ancient ancestors felt. But with our knowledge of modern astronomy we can add things that our eyes cannot see: Imagining dark matter, gamma-ray bursts, black holes, neutron stars, or quasars as we look at the sky adds to our sense of wonder and mystery. With the development of new observatory techniques in the latter half of the 20th century, our information about the universe has exploded to an extent even greater than the information explosion brought on by Galileo. With the enormous expansion of scientific knowledge has come an increasing tendency toward specialization into ever more minute areas and an understandable, if lamentable, corresponding tendency to use time “efficiently” by shutting out up-to-date information that appears to have no direct application to one's chosen field. This has led to an often counterproductive fragmentation of scientific knowledge: A biologist may know little about physics, and an expert in the physics of condensed matter may be totally ignorant of modern astronomy. Exacerbating this are the scientific turf wars and empire building that have resulted, in the main, from keen competition for funding sources. Most nonscientists who like to think of themselves as knowledgeable about modern science really know only about technologies—and specifically those technologies considered likely to bring economic profits in the short term (“This research can strengthen our economy.” “Our future lives can be made more convenient thanks to this technology.”). This is also the mind-set of most government officials and lawmakers who consider themselves sympathetic to science and technology budget requests. Thus in countries that pride themselves on having substantial budgets for research in science and technology, most of the money is given to industry-connected technologies. Even when major funding is channeled to pure science, it usually targets an area of clear benefit to industry such as condensed-matter physics, useful for the semiconductor industry. Thus science for homo economicus and homo faber is flourishing, while science for Homo sapiens is diminishing. Given this scenario, it seems that the ascent of man has been left in the care of homo ignorantis. Within this fortress, the “Better Living Through Science” crowd is busy trying to monopolize science and technology funding and is, in the process, choking off what remains of funding for pure research. As we struggle to counter their court intrigues, we may one day wake up to find barbarians at the gate, in the form of an upsurge in “new” science—that is, not science at all—promoted by one or another fundamentalist religious or occultist group ready to lead us into a new Dark Age. How can we respond to these threats? We who understand real science need to court more allies, and this can be done by ensuring that far more people join us in that knowledge. What we must urgently do is renovate education and significantly raise the basic level of scientific knowledge, for, as C. P. Snow warned four decades ago, we must “educate ourselves or perish.” [1]: #fn-1 [2]: #fn-2 [3]: pending:yes

The paper reconstructs the teaching and research activities of scholars in statistics and related subjects at the University of Padua from the Restoration to the Second World War. The history of statistics in Padua is an interesting case study, as it allows to shed light on the evolution of the discipline at the national level as well as on its relationships with the international development of statistical methods. Some fascinating antecedents go back to the 16th Century, with contributions by Gerolamo Cardano, student at the School of Medicine from 1524 to 1526, and later by Galileo Galilei, professor of mathematics at the University of Padua from 1592 to 1610. The 150 years from the Restoration to the 1960s are marked by a sequence of phases of renewal and conservatism. At the beginning, the old Statistik took the place of political arithmetic. Statistics experienced telling improvements only with Angelo Messedaglia, who drew from Quetelet and outlined a new role for the discipline within the rethinking of the “science of administration”. After a grey period when statistics was considered as a social science supporting State intervention – without any peculiar methodological apparatus, a new phase of dramatic innovation followed, led by Corrado Gini, professor of Statistics in Padua from 1913 to 1925. His pupils and successors exacerbated the neo-descriptive approach of the «Italian school of Statistcs», the confrontation with modern statistical inference, and the support to the corporatist programme of the Fascism. This motivated a decline immediately after the Second World War. A new revival had to wait up to the mid 1950s, with the appointment of Albino Uggé at the chair of Statistics, the crucial cooperation of Bernardo Colombo – who moved from the University of Venice to Padua in 1967, around whom a group of young scholars assembled. The establishment of a Faculty of Statistics, in 1968, was the prominent result of that process. \nStatistics at the University of Padua: An Emblematic Journey from the Restoration to the Republican Age\nGiovanni Favero and Ugo Trivellato\n\nThe paper reconstructs the teaching and research activities of scholars in statistics and related subjects at the University of Padua from the Restoration to the Second World War. The history of statistics in Padua is an interesting case study, as it allows to shed light on the evolution of the discipline at the national level as well as on its relationships with the international development of statistical methods. Some fascinating antecedents go back to the 16th Century, with contributions by Gerolamo Cardano and by Galileo Galilei. The 150 years from the Restoration to the 1960s are marked by a sequence of phases of renewal and conservatism. At the beginning, the old Statistik took the place of political arithmetic. Statistics experienced telling improvements only with Angelo Messedaglia, who drew from Quetelet and outlined a new political role for the discipline. This led his pupils to view statistics as a social science supporting State intervention, without any methodological peculiarity. A new phase of dramatic innovation was led by Corrado Gini from 1913 to 1925. Again, his pupils and successors exacerbated the neo-descriptive approach of the «Italian school of Statistcs», the confrontation with modern statistical inference, and the support to the corporatist programme of the Fascism, motivating the post-war decline of the discipline. A new revival had to wait the mid 1950s, when Albino Uggé and then Bernardo Colombo started assembling a group of young scholars and planning the establishment of a Faculty of Statistics, finally realized in 1968.

The article is devoted to the topical subject of the dynamics of the transformation of worldview and methodological paradigm of man and society understanding, stemming from the marginalist revolution of the late 19th century. This revolution determined a methodological turn to searching for subjective fundamentals of economic behavior and the focus shift from cost to economic performance. The novelty of this study lies in establishing the theoretical significance of such a transition for modern philosophical anthropology. Accordingly, the purpose of the study is to determine the specifics of the changes that the marginalist revolution in economic science brought to the doctrine of man, associated with the characteristics of their social behavior and a new vision of the foundations of social psychology. To do this, it was necessary to solve such problems as, 1) the reconstruction of evolution and the identification of the fundamental principles of the classical (the so-called Marxist) economic-centric model of man; 2) establishing the main directions for revising these principles within the framework of the new paradigm; 3) explication and conceptual analysis of ideological and methodological innovations that the marginalist revolution entailed; 4) a conceptual justification for the prospects of the ideological and methodological paradigm, the core of which is the modernized model of economic man. The study used the method of categorical analysis with elements of discourse analysis. A critical examination of the classical Marxist ideological and methodological paradigm in understanding man and society made it possible to identify the main features that have been revised in the new model. As a result of the study, it was established that the marginalist revolution led to a conceptual rejection of methodological holism, the substantial approach, and the concept of equivalent exchange, substantiating the heuristic value of the principles of individualism, anti-substantialism and unequal exchange. In fact, in this way an understanding of man and society was finally formed, considering the concept of the formation of individual wills on a new scientific basis. The logically impeccable justification for this concept belongs to K. Menger, who was able to resolve the paradox of methodological individualism by showing why this concept does not necessarily lead to an understanding of economic exchange as deception. As a result, the limited understanding of modern domestic Marxism as a purely economic theory is revised, the costs of the classical Marxist understanding of man are shown, and the need to include ideas of a new understanding of economic man, transformed as a result of the marginalist revolution, into the philosophical and anthropological theory is justified.

The scientific revolution, which developed in Western Europe during the 16th-18th centuries, was one of the most significant fruits of the activity of European universities. The cultural movement of Renaissance, born in Italy a century earlier, which moved the center of attention of scholars on man, ‘blacksmith of his destiny’ and on his dignity, with a marked curiosity for the laws of nature, greatly contributed to it. Another propulsive factor were the maritime expeditions across the Atlantic, the Pacific and the Indian Oceans, promoted by the kingdoms of Portugal and Spain at the end of the ‘Reconquista’, between the 15th and the 16th centuries. Their vessels crossed the Equator Line, discovering new lands and new skies. Celestial Mechanics was at the center of that peaceful revolution, owing to the initiative of scholars as Nicolaus Copernicus, Galileo Galilei, Tycho Brahe, Johannes Kepler, Isaac Newton. The Jesuit missionaries, sent to China by the Roman Catholic Church with evangelizing purposes, propagated among the scholars of the imperial court the use of the astronomical telescope and the adoption of the experimental method in science. Unfortunately, the Roman Catholic Church condemned in the same years the propagation of the heliocentric theory, because it contradicted the Bible, of which the Church considered to be its exclusive interpreter. This was a hindrance to the advancement of modern Celestial Mechanics in the Far East, until the Church ceased to obstruct the heliocentric theory toward the middle of the 18th century. It took another century for that theory to be fully accepted by Chinese scholars.

Neoclassical economics is the stage and branch of economic science since the 1870s through the 1930s and beyond. It was mostly the product or sequel of what economists (Schumpeter 1954) call the Copernican marginalist revolution in economic theory during the 1870–90s. Specifically, the crux of marginalism was a marginal‐utility theory of exchange value and its extensions (e.g., marginal‐productivity principle of income distribution) in reaction and contrast to the labor‐cost conception in classical political economy. The founders or pioneers of marginalism are commonly considered to be William Jevons (England), Carl Menger (Austria), and Leon Walras (Switzerland/France), who almost simultaneously in 1871–4 “discovered” marginal‐utility value theory as a putative revolutionary alternative to its labor‐based versions in Smith, Ricardo, Mill, Marx, and others. (For instance, Jevons specifically attacked Ricardo and Mill's theories, prompting neoclassical economists like Alfred Marshall to rise in their partial defense.) The term neoclassical economics was invented by (Thorstein Veblen Groenewegen 1995), a heterodox institutional economist, in the early 1900s to indicate that marginalism (e.g., marginal‐utility theory) was, in virtue of utilitarianism and hedonism, essentially continuous with and so “scarcely distinguishable” from classical political economy (which apparently overlooks the opposition of the marginalist revolution to Ricardo et al.'s labor theories of value). In this sense, the terms marginalism and neoclassical economics become interchangeable, though the first term is probably more accurate and precise for describing this stage and type of economic theory. Moreover, historians of economics such as Schumpeter (1954: 919) object that “there is no more sense in calling the Jevons‐Menger‐Walras theory neoclassic than there would be in calling the Einstein theory neo‐Newtonian.” This suggests that neoclassical economics is essentially marginalism (with partial exceptions like Marshall), but not conversely: the marginalist revolution is not newly, but counter‐classical (that is what makes it presumably “Copernican”).

Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.

Unified Mathematical Theory Linking Productivity to Risk and Completing Input/Output Substitution

Modern economic analysis was founded by the Scottish philosophers of the 18th century in their general analysis of the determination of observed facts in society. At the center of their analysis was a desire to understand the interaction of human beings. The ingenious invention of the idea of a spontaneous order, mechanisms through which a good result was achieved without an authority giving central commands, is one of the greatest insights in human intellectual history. Adam Smith's invisible hand turned out to be so successful in economic analysis that 100 years later, the whole profession almost unconsciously neglected other methods of coordinating human interaction. With the construction of the general equilibrium model by Leon Walras, the price mechanism moved to center stage in economic analysis and became ever more refined through the analyses of Hicks, Samuelson, and Arrow-Debreu. Other forms of human relations than the price system, such as rules and principles, political decisions and collective group actions, were crowded out by disciplines such as law, political science and sociology. The classical authors, Smith, Mill, and Marshall, in their broad analysis, made some allowance for these factors, but they have since been purged from pure economics. One exceptional man, Joseph Schumpeter, in his monumental work History of Economic Analysis (1954)1 argued for the role of economic history and sociology, but in vain. Schumpeter writes: What distinguishes the 'scientific' economist from all the other people who think, talk, and write about economic topics is a command of techniques that we class under three heads: history, statistics, and 'theory'.

Violence, Morality, and Religion

Not applicable.