The “unknown heritage” is the name usually given to a problem type in whose archetype a father leaves to his first son 1 monetary unit and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{n}}$$\end{document} (n usually being 7 or 10) of what remains, to the second 2 units and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\frac{1}{n}}$$\end{document} of what remains, and so on. In the end, all sons get the same, and nothing remains. The earliest known (...) occurrence is in Fibonacci’s Liber abbaci, which also contains a number of much more sophisticated versions, together with a partial algebraic solution for one of these and rules for all which do not follow from his algebraic calculation. The next time the problem turns up is in Planudes’s late thirteenth century Calculus according to the Indians, Called the Great. After that the simple problem type turns up regularly in Provençal, Italian and Byzantine sources. It seems never to appear in Arabic or Indian writings, although two Arabic texts (one from c. 1190) contain more regular problems where the number of shares is given; they are clearly derived from the type known from European and Byzantine works, not its source. The sophisticated versions turn up again in Barthélemy de Romans’ Compendy de la praticque des nombres (c. 1467) and, apparently inspired from there, in the appendix to Nicolas Chuquet’s Triparty (1484). Apart from a single trace in Cardano’s Practica arithmetice et mensurandi singularis, the sophisticated versions never surface again, but the simple version spreads for a while to German practical arithmetic and, more persistently, to French polite recreational mathematics. Close examination of the texts shows that Barthélemy cannot have drawn his familiarity with the sophisticated rules from Fibonacci. It also suggests that the simple version is originally either a classical, strictly Greek or Hellenistic, or a medieval Byzantine invention; and that the sophisticated versions must have been developed before Fibonacci within an environment (located in Byzantium, Provence, or possibly in Sicily?) of which all direct traces has been lost, but whose mathematical level must have been quite advanced. (shrink)

One of the ways in which the artificial languages of mathematics are “generous”, that is, in which they assists the advance of thought, is through its establishment of advanced operatory structures that permit an even further advance of intuition. However, this generosity may be delusive, suggest ideas which in the longer run turn out to be untenable. The paper analyses two cases of “honest generosity”, namely a “proof” of the sign rule “less times less makes plus” from the 1340s and (...) a result in partition theory obtained by Euler by means of rash manipulations of infinite series and products, case-Cantor’s introduction of transfinite numbers from 1895-and (in modern terms) a failed attempt to extend the semi-group of algebraic powers into a complete group, also from c. 1340. Gewöhnlich glaubt der Mensch, wenn er nur Worte hört es müsse sich dabei wohl auch was denken lassen Goethe, Faust I, 2565-2566He gives the kids free samples because he knows full well that today’s young innocent faces will be tomorrow’s clientele Tom Lehrer, “The Old Dope Peddler”. (shrink)

Critical types of infrastructure are provided by the state to maintain the people’s livelihood, ensure economic development, and systematic government operations. Given the development of ever more complicated critical infrastructure systems, increasing importance is being attached to the protection of the components of this infrastructure to reduce the risk of failure. Power facilities are one of the most important kinds of critical infrastructure. Developing an effective risk detection system to identify potential failure modes of power supply equipment is crucial. This (...) study seeks to improve upon prior approaches for risk assessment by proposing a hybrid risk-assessment model using the concepts of failure mode and effect analysis and multiple-criteria decision-making. The proposed model includes a cost-based factor for decision-makers. The subjectivity and uncertainty in FM assessment are adjusted through the rough number method. The original risk priority number can be expanded by including the entropy weights in the risk index. Furthermore, to rank the risk priorities in a rational manner, a modified technique for order preference by similarity to ideal solution is adopted. The applicability and effectiveness of the proposed method were demonstrated by considering an example of a turbine steam engine in a nuclear power plant. (shrink)

Monetary intelligence theory asserts that individuals apply their money attitude to frame critical concerns in the context and strategically select certain options to achieve financial goals and ultimate happiness. This study explores the dark side of monetary Intelligence and behavioral economics—dishonesty. Dishonesty, a risky prospect, involves cost–benefit analysis of self-interest. We frame good or bad barrels in the environmental context as a proxy of high or low probability of getting caught for dishonesty, respectively. We theorize: The magnitude and intensity of (...) the relationship between love of money and dishonest prospect may reveal how individuals frame dishonesty in the context of two levels of subjective norm—perceived corporate ethical values at the micro-level and Corruption Perceptions Index at the macro-level, collected from multiple sources. Based on 6382 managers in 31 geopolitical entities across six continents, our cross-level three-way interaction effect illustrates: As expected, managers in good barrels, mixed barrels, and bad barrels display low, medium, and high magnitude of dishonesty, respectively. With high CEV, the intensity is the same across cultures. With low CEV, the intensity of dishonesty is the highest in high CPI entities —the Enron Effect, but the lowest in low CPI entities. CPI has a strong impact on the magnitude of dishonesty, whereas CEV has a strong impact on the intensity of dishonesty. We demonstrate dishonesty in light of monetary values and two frames of social norm, revealing critical implications to the field of behavioral economics and business ethics. (shrink)

Since Barry Stroud's classic paper in 1968, the general discussion on transcendental arguments tends to focus on examples from theoretical philosophy. It also tends to be pessimistic, or at least extremely reluctant, about the potential of this kind of arguments. Nevertheless, transcendental reasoning continues to play a prominent role in some recent approaches to moral philosophy. Moreover, some authors argue that transcendental arguments may be more promising in moral philosophy than they are in theoretical contexts. Against this background, the current (...) volume focuses on transcendental arguments in practical philosophy. Experts from different countries and branches of philosophy share their views about whether there are actually differences between "theoretical" and "practical" uses of transcendental arguments. They examine and compare different versions of transcendental arguments in moral philosophy, explain their structure, and assess their respective problems and promises. This book offers all those interested in ethics, meta-ethics, or epistemology a more comprehensive understanding of transcendental arguments. It also provides them with new insights into uses of transcendental reasoning in moral philosophy. (shrink)

This article examines a neglected ancient source for desire between women that nonetheless has a rich reception history in the context of female homoeroticism: the Callisto episode in Ovid’s Metamorphoses. The article argues that the relationship between Diana and her hunting companion Callisto can be read as homoerotic and that, unlike many ancient accounts of female-female eroticism, neither character is represented as a tribas (a gender-deviant “woman” with a masculinized body, who seeks to penetrate other women). The Callisto episode is (...) therefore an invaluable piece of evidence for ancient discourses on sexuality exceeding the bounds of the active/passive model. (shrink)

Corruption involves greed, money, and risky decision-making. We explore the love of money, pay satisfaction, probability of risk, and dishonesty across cultures. Avaricious monetary aspiration breeds unethicality. Prospect theory frames decisions in the gains-losses domain and high-low probability. Pay dissatisfaction (in the losses domain) incites dishonesty in the name of justice at the individual level. The Corruption Perceptions Index, CPI, signals a high-low probability of getting caught for dishonesty at the country level. We theorize that decision-makers adopt avaricious love-of-money aspiration (...) as a lens and frame dishonesty in the gains-losses domain (pay satisfaction-dissatisfaction, Level 1) and high-low probability (CPI, Level 2) to maximize expected utility and ultimate serenity. We challenge the myth: Pay satisfaction mitigates dishonesty across nations consistently. Based on 6500 managers in 32 countries, our cross-level three-dimensional visualization offers the following discoveries. Under high aspiration conditions, pay dissatisfaction excites the highest- (third-highest) avaricious justice-seeking dishonesty in high (medium) CPI nations, supporting the certainty effect. However, pay satisfaction provokes the second-highest avaricious opportunity-seizing dishonesty in low CPI entities, sustaining the possibility effect—maximizing expected utility. Under low aspiration conditions, high pay satisfaction consistently leads to low dishonesty, demonstrating risk aversion—achieving ultimate serenity. We expand prospect theory from a micro and individual-level theory to a cross-level theory of monetary wisdom across 32 nations. We enhance the S-shaped Curve to three 3-D corruption surfaces across three levels of the global economic pyramid, providing novel insights into behavioral economics, business ethics, the environment, and responsibility. (shrink)

The tsunami effect of the COVID-19 pandemic is affecting many aspects of scientific activities. Multidisciplinary experimental studies with international collaborators are hindered by the closing of the national borders, logistic issues due to lockdown, quarantine restrictions, and social distancing requirements. The full impact of this crisis on science is not clear yet, but the above-mentioned issues have most certainly restrained academic research activities. Sharing innovative solutions between researchers is in high demand in this situation. The aim of this paper is (...) to share our successful practice of using web-based communication and remote control software for real-time long-distance control of brain stimulation. This solution may guide and encourage researchers to cope with restrictions and has the potential to help expanding international collaborations by lowering travel time and costs. (shrink)

The engineering profession has experienced some ethical cases that were rarely reported, scrutinized, or discussed because: they did not necessarily represent violations of existing codes even if they breached ethical principles; those within the organization were not prepared to take steps to address the issues or impose sanction; an/or some of the personnel associated with these cases resorted to silence to avoid being labeled as trouble-makers in their organizations and, perhaps, more broadly, in society. The goal of this paper is (...) to heighten managerial awareness of ethical issues, interrelated ethical lapses, and appropriate responsive actions within professional engineering communities. As such, the authors reviewed recent well-known professional and organizational ethical cases including impact of leadership role and existing standards, and critically analyzed interrelated literature. The paper’s case studies exemplify that because ethical issues are complex, intricate, and nuanced; bylaws are insufficient for establishing the inclusive culture for handling potential ethical situations. In fact, through what is known as the codification of ethics, it is possible that someone’s conduct can totally fulfill all professional responsibilities but still be unethical. As such, ethical leadership is needed to provide the means for establishing appropriate norms so as to set the proper structures for addressing the diverse ethical matters. Perceptions about the responses of leaders to potential ethical lapses are a critical factor in formulating, changing, and maintaining ethical values at the individual and organizational levels. A leader’s passive attitude toward ethical issues can be the signal for the ignored lapses to become the norm at not only the organizational level but also the society. Guided by the new Code of Ethics by the American Society of Civil Engineers, this paper aims to trigger the proper ethical behavior and expectations for the welfare of the engineering profession both in the present and future. (shrink)

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. (...) The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank. (shrink)

Over the past several decades, a group of scholars at the Berkeley campus of the University of California have frequently challenged many of the dominant themes of contemporary agricultural research. In their work, they have organized curricula questioning the assumptions of conventional agriculture and its sciences while encouraging the development of alternative agricultural practices based on principles of ecology. Their collective critique has stimulated an intellectual climate calling forth a scrutiny of the university's role in the production of knowledge and (...) the social consequences of its works. The result of this intellectual project has been a group that has also largely challenged the dominant themes of the modern university. In place of a setting where ideas are a passive currency, the modern university is a place where knowledge and power are manifest in a dialectic that is revealed not simply by the production of knowledge, but its destruction as well. It is in this context that the recent history of a group of scholars at the University of California provides a striking testimony concerning the disturbing character of science in the modern university. The ecological and social dimensions of “killing fields” that captures the contemporary hazards of food and fiber production in California is also reflected in the gradual demise of a group of researchers at Berkeley who have endeavored to provide an alternative vision of agriculture. (shrink)

The Mongol in Our Midst F G Crookshank Originally published in 1925. "A brilliant piece of speculative induction" Saturday Review Combining anthropology, psychology, geography, science and medicine, this volume was a ground-breaking study in the area of race, ethnicity and eugenics, when first published and has to be read in the appropriate historical, social and scientific context of the early twentieth century. 120 pp, 24 b&w plates Prometheus or Biology and the Advancement of Man H S Jennings Originally published (...) in 1925 "This volume is one of the most remarkable that has yet appeared in this series." Times Literary Supplement "An exceedingly brilliant book." New Leader This volume provides a lucid summary of the striking advances of the early 20 th century in biological knowledge, genetics, and the theory of evolution. 88pp Metanthropos or the Body of the Future Ronald Campbell Macfie Originally published in 1928 "An exceptionally stimulating book…" Saturday Review "Should certainly be read by a large public." The Lancet Drawing on the history of evolution and geology, this volume examines the role of society on physical, emotional and psychological changes in the population of Western Europe during the early twentieth century, whilst attempting to predict genetic developments of the future. 88pp. Pygmalion or the Doctor of the Future R M Wilson Originally published in 1925 "No doctor worth his salt would venture to say that Dr.Wilson was wrong." Daily Herald "Dr Wilson has added a brilliant essay to this series." Times Literary Supplement The author foresees an evolution in the personality of the doctor, who will become less of a scientist, more of a humanist, and use every spiritual agency, as well as every practical measure, to restore the human body and soul to health. 66pp. The Conquest of Cancer H W S Wright Originally published in 1925 "Eminently suitable for general reading. The problem is fairly and lucidly presented." F G Crookshank Whilst affirming that the causes and treatment of cancer will never be solved by the efforts of the medical profession alone, this volume provides an accessible source of information on cancer and proposes routine examination for those people aged 40 and over as the best means of defence against cancer. 82pp. (shrink)

Regular musical activity as a complex multimodal lifestyle activity is proposed to be protective against age-related cognitive decline and Alzheimer’s disease. This cross-sectional study investigated the association and interplay between musical instrument playing during life, multi-domain cognitive abilities and brain morphology in older adults from the DZNE-Longitudinal Cognitive Impairment and Dementia Study study. Participants reporting having played a musical instrument across three life periods were compared to controls without a history of musical instrument playing, well-matched for reserve proxies of education, (...) intelligence, socioeconomic status and physical activity. Participants with musical activity outperformed controls in global cognition, working memory, executive functions, language, and visuospatial abilities, with no effects seen for learning and memory. The musically active group had greater gray matter volume in the somatosensory area, but did not differ from controls in higher-order frontal, temporal, or hippocampal volumes. However, the association between gray matter volume in distributed frontal-to-temporal regions and cognitive abilities was enhanced in participants with musical activity compared to controls. We show that playing a musical instrument during life relates to better late-life cognitive abilities and greater brain capacities in OA. Musical activity may serve as a multimodal enrichment strategy that could help preserve cognitive and brain health in late life. Longitudinal and interventional studies are needed to support this notion. (shrink)

Indledning -- Baggrund: Guldalderperioden, 1800-1850 ;Romantikken, den historiske kristendom -- Kierkegaards udvikling ; Lidelsen som kristendommens grundlag -- Konfrontationen: N.F.S. Grundtvig ; H.L. Martensen ; J.P. Mynster -- Den bestående kirke under forandring ; Opgøret i de sidste år, 1848-1855 -- Afslutning.

I argue that if we read E. H. Gombrich's Art and Illusion with the charity that it deserves, we will find a much subtler theory of depiction than the illusion theory that is usually attributed to Gombrich. Instead of suggesting that pictures are illusory because they cause us to have experiences as of seeing the depicted objects face to face, I argue that Art and Illusion is better read as making the point that naturalistic pictures are illusory because they cause (...) us to see qualities and properties that the pictures themselves do not possess. Once we appreciate this point, we will be in a better position to appraise the value and limits of naturalistic art. (shrink)

Studies on American poetry by ten contributors. Notes at the end of each chapter.

The ArgumentThe development of autonomous theoretical science is often considered a “Greek miracle.” It is argued in the present paper that another “miracle,” necessary for the creation of modern science, took place for the first time in the Islamic Middle Ages, viz. the integration of theory and practice.The discussion focuses on the mathematical disciplines. It starts by investigating the plurality of traditions which were integrated into Islamic mathematics during its formation, emphasizing practitioners' “sub-scientific” traditions, and shows how these were synthesized (...) in a way virtually unknown in earlier cultures. A discussion of the sociocultural roots of this specific synthesis concludes that a major role was played in the earlier period by the combination of fundamentalist convictions characteristic of Islam – that the most humble daily activity is directly responsible to the highest ontological level, while conversely this highest level is concerned with the humblest ranks of daily existence – with the absence of an institutionalized “Church” able to monopolize the interpretation of the mutual bond of the divine and the everyday levels.As the institutions of learning crystallized around the turn of the millennium, the integrative attitude to theory and practice was fixated institutionally; the latter process is discussed, first with the example of the madrasah institution as the carrier of an arithmetical textbook tradition, and second with that of the bond between astronomy and theoretical geometry. (shrink)

For more than a century, there has been some discussion about whether medieval Arabic al-jabr has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later (...) the geometry of Elements II. The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles. (shrink)

Eine Reihe von mittelalterlichen Schriften zur Landmessung (vom 9. islamischen Jahrhundert bis zu Fibonacci und Pacioli) enthält eine besondere Art von „algebraischen” Aufgaben. Darin werden z.B. die Summe der Fläche und einer oder alle vier Seiten eines Quadrates beschrieben und nach der Seite gefragt. Es zeigt sich erstens, daß dieser Aufgabentyp mindestens seit dem frühesten 2. vorchristlichen Jahrtausend von geometrischen Praktikern tradiert wurde, und zweitens, daß er die Entwicklung einer „Algebra” in der altbabylonischen Schreiberschule inspirierte. Der Aufsatz untersucht, in welcher (...) Weise die Überführung der „sub-wissenschaftlichen” Praktikertradition in einen systematischen Schulunterricht den mathematischen Inhalt und den Denkstil künftiger Praktiker präge. Im letzten Kapitel wird diskutiert, inwieweit es sinnvoll ist, innerhalb dieser Schulalgebra von „Schulen” zu sprechen. (shrink)

In French, haute vulgarisation is a recognized genre. Not so in English, but even without the term A New History of Greek Mathematics is still an excellent representative. Regularly—and especially...

pt. I. Institutions, professions and ideas -- pt. II. Human science and human nature -- pt. III. The art of knowing.

A theme like “town and science” invites to comparative analysis, and suggests questions like these: Is the urban context a particularly fertile soil for the development of scientific thinking? Or rather the contrary? Is it fertile or barren under specific circumstances? Or does it favour a particular kind of scientific activity?General answers to such questions can hardly be found; still, they may provide case studies with a guiding perspective. Case studies, on the other hand, may lead to better understanding of (...) the implications of the general questions if not to answers. In the following I therefore try to read the emergence of Mesopotamian mathematics into the context of the “urban revolution” and the rise of states (c. 3300 to c. 2300 B.C.).Mesopotamian city states appeared in the late fourth millennium B.C., and were eventually absorbed in larger territorial states a thousand years later. Contemporary with the incipient state formation was the creation of a script and of genuine, coherent mathematics. Both were based on earlier accounting techniques, both were used by Temple officials for administrative purposes, and both were marked decisively by this application. At the same time, both presuppose modes of thought which are not produced directly by their application but only as mediated by a school system.In the mid‐third millennium, an autonomous scribal profession appears for the first time. At the same time emerge the first literary texts and the first “pure” mathematical problems (i.e., problems not directed at or following the pattern of genuine application). It seems as if the scribes, as soon as they were emancipated as a craft, tried out the range of their professional tools.Neither the use of writing for literary purposes nor the possibility to use numbers for “higher” computation were forgotten when the city states were absorbed in larger social systems. Both, however, were subsumed by the interest of the new territorial state, the former as a means to propagate royal ideology, the latter in the royal administration.The final section of the article compares this early Mesopotamian development with other instances of the “urban revolution” and with the development of scientific thought in the Ancient Greek city state and in the context of Medieval city communes. (shrink)