Des Jardins (1976) and Dreher (1990) have suggested that Plato's Line should be thought of as divided in the mean and extreme ('golden') ratio. I examine their arguments, as well as other reasons that could be brought up in support of the 'golden division' of the Line, and show that all of them are wanting.

: This study aims to discuss the basic argument that sociology, as a science, emerged as an intellectual response to the lost sense of community during social and cultural changes. This argument carries the assumption that the dominating metaphors and perspectives of classical sociology are informed by conservatism. In sociology, this claim is supported by well-known and ambivalent theoretical structures that are developed to explain the process of social change. This study aims to make a criticism of nostalgic sociology considering (...) the idea that the fundamental assumptions of the ambivalent theoretical structure in sociology are nostalgic. In addition, this study also aims to critically read the historical development of Islamism, one of the modern ideologies, with nostalgia and utopia. The suggestion of the article is that either classical sociology or Islamism –two subject appear differently in terms of their topics- gave similar intellectual reactions about the subject that they are unable to cope with ‘the present’ and produce a ‘golden age’ discourse as a solution to ‘the present’. The argument of the study is that either the effort of idealizing ‘the past’ in classical sociology or the myth of coming back home in Islamism against cultural alienation and sense of loss which are lived in ‘the present’ are actually determined by sovereign modernity paradigm. Summary: Behind the nostalgic paradigm, there is a rebuilt history that is shaped as a transition from feudalism to capitalism. In this history, the decline of feudalism corresponds to the loss of rural community, the loss of personal expressionism and the loss of unregulated society. In classical sociology, the heritage left by the solution of this historical reconstruction of society has become common. The anomaly of the modern world is precisely where the modern society from traditional society has emerged in the pathological state created by the loss of social ties with the passing. This pathological condition was first seen in Swiss mercenaries serving away from home, diagnosing nostalgia as a diagnosis of discomfort. We know that Johannes Hofer, who has a sense of humor, has not written any prescription for this disease, which gives some common signs with his melancholy. Sociology, shaped by three different intellectual movements as intellectual responses to the French and Industrial revolutions that allow the transformation of the European society, has taken its place as its focal point, and in the pioneering names, this change is "a change in everything at a dizzying pace, everything that has happened has evaporated and the glory of the world has deteriorated.” Modernity, which refers to the ideals of enlightenment, is blessed not to progress by nature, fluid, rational, contingent, lacking certainty. In fact, this blessing has brought with it the enemy of tradition to the 'new' with reference to its etymological origin. This sophisticated and complex structure unique to modernity only, has inspired some thinkers to conceive of an idealized past or future that is now determinative. Both of these ideas are moderators. The nostalgia becomes modern because of the longing for a home that no longer exists or has never existed. Nostalgia is coeval with modernity. The article refers to Stauth-Turner's nostalgic paradigm, which provides the meta-phasic and meta-phase dominance of classical sociology detailed in Nietzsche's Dance. This paradigm consists of four main components. The first is that the history that we can summarize as a departure from the golden age when the world was a nest for man is seen as a decline and a loss. History is a history of sorrow and despair, as this decline will continue to exacerbate in the future. The example of such a feeling of grief in society theory is Weber's fate sociology. Because, according to Weber, whatever is waiting for us in the future is the polar night of the icy darkness, not the sunlight of summer. The second component of the nostalgic paradigm is the sense of secularization, together with the loss of integrity and moral certainty. This nostalgic trajectory is a very powerful secularization that emphasizes that such devastating social processes as urbanization, capitalist industrialization and the rationalization of everyday life, such as the diversity and complexity of social structure, the spread of scientific knowledge, urbanization with increasing population ratio, it brings forward its theory. With the announcement of the death of God, the gate of a competing and conflicting world has been opened, from which we have been transformed into a very godlike world. It is possible to observe a similar point of view in classical sociology in Durkheim, which has a theoretical basis for the transformation of social structures through professional distinction in the form of mechanical and organic solidarity. Durkheim analyzes social change in a deliberate way, and pre-change stake favors moral coherence. Moral coherence is now lost when collective consciousness is generally weakened in the post-change phase. The third trajectory we encounter in the nostalgic paradigm is the loss of individual autonomy and the decline of genuine social relations. With the loss of the moral unity, the individual has been caught under the domination of the bureaucratic state, in macro-social processes and institutions. It is inevitable that the individual who lost his autonomy is subject to the denial. The increasing exposure of the individual to social bureaucratic associations has been conceptualized by the iron cage metaphor in Weberian sociology. The enlightenment is the result of the panoptic collection of prison. So there is a nostalgic stance in this compound of the nostalgic paradigm that autonomy-ben lost because of the fall of the bureaucratic world under the domination of the modern state. In the nostalgic paradigm, the ultimate component is the feeling of laxity, spontaneity and loss of naturalness. Here, the individual is subject to not only macro-social processes but also micro-ethics. That is, it is understood that Adorno's "managed society" or Foucault's notion of closure prevents the individual's true emotions and enthusiasm, and that the consumer culture is preoccupied with certain preconceived ways of doing in a world dominated. To sum up, the metaphor of nostalgia that we are living in a world where we have been seized by administrative rules of a central state in a way that has lost the moral certainty and autonomy of the individual. The return to home, which is found in a significant part of the texts and practices put forward in the name of Islamism, has reached a deterministic attitude just as it was in classical sociology. In the nostalgic imagination where those who cannot cope with it are thought of as a safe harbor, there is a certain attitude towards deterministic ideologists that simplify, sanctify, and therefore falsify. Indeed, the imagination of a supra-historical, supra-community model for a time like the Golden Age discourse and for all time is itself history from the very beginning to the end. Therefore, it is a manifestation of a major historical process and the ideological design of sociality. The rhetoric discourse presented as a remedy in the present is possible with an anachronistic point of view which idealizes the past, and therefore the reality is distorted. The authentic one is extremely informal. This kind of discourse of authenticity, which is produced as opposed to the modernity that all that is solid melts into air, eventually has to make iron cages around it. As a result, the nostalgic rhetoric, which aims to be a modern chivalrous remedy that everything changes at a dizzying pace, has been determined by the paradigm of modernity, thanks to its self-reflexive nature which contains the opposite. (shrink)

Numbers. Natural numbers -- Integers -- Real numbers -- Irrational and transcendental numbers -- Funny numbers. Zero -- e : the unnatural natural number -- [Phi] : the golden ratio -- i : the imaginary number -- Writing numbers. Roman numerals -- Egyptian fractions -- Continued fractions -- Logic. Mr. Spock is not logical -- Proofs, truth, and trees : oh my! -- Programming with logic -- Temporal reasoning -- Sets. Cantor's diagonalization : infinity isn't just infinity -- (...) Axiomatic set theory : keep the good, dump the bad -- Models : using sets as the LEGOs of the math world -- Transfinite numbers : counting and ordering infinite sets -- Group theory : finding symmetries with sets -- Mechanical math. Finite state machines : simplicity goes far -- The turing machine -- Pathology and the heart of computing -- Calculus : no, not that calculus- [lambda] calculus -- Numbers, booleans, and recursion -- Types, types, types : modeling [lambda] calculus -- The halting problem. (shrink)

Between 1942 and 1943 the editor of the journal «Domus» invited the most important Italian architects to design their ideal houses: fifteen projects designed by seventeen architects were published. They are most instructive to try to understand, firstly, what the philosophical notion of ideal means and, secondly, why mathematical and geometric tools are extensively used to work on ideality, namely, to design ideal houses. The first part of the article focuses on the philosophical foundations of ideality and, after an overview (...) of the fifteen projects, on the use of the golden ratio in two particularly meaningful cases. The second part of the article focuses on the cases in which there is a hidden use of the golden ratio, on the use of the modulus and on the use of the number 2. (shrink)

In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable finding (...) is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods. (shrink)

With In Focus Sacred Geometry, learn the fascinating history behind this ancient tradition as well as how to decipher the geometrical symbols, formulas, and patterns based on mathematical patterns. People have searched for the meaning behind mathematical patterns for thousands of years. At its core, sacred geometry seeks to find the universal patterns that are found and applied to the objects surrounding us, such as the designs found in temples, churches, mosques, monuments, art, architecture, and nature. Learn the fundamental principles (...) behind: Interpreting the sacred symbolism and principles behind shapes Calculating numbers used in sacred geometry Applying the golden ratio and Fibonacci’s Sequence to objects Translating symbolic and geometrical letters and alphabets This accessible and beautifully designed guide to sacred geometry includes a frameable poster of the main sacred geometrical shapes and their unique, innate arrangements. The In Focus series applies a modern approach to teaching the classic body, mind, and spirit subjects. Authored by experts in their respective fields, these beginner's guides feature smartly designed visual material that clearly illustrates key topics within each subject. As a bonus, each book includes reference cards or a poster, held in an envelope inside the back cover, that give you a quick, go-to guide containing the most important information on the subject. (shrink)

Any living system possesses internal embedded description and exists as a superposition of different potential realisations, which are reduced in interaction with the environment. This reduction cannot be recursively deduced from the state in time present, it includes unpredictable choice and needs to be modelled also from the state in time future. Such non-recursive establishment of emerging configuration, after its memorisation via formation of reflective loop (sign-creating activity), becomes the inherited recursive action. It leads to increase of complexity of the (...) embedded description, which constitutes the rules of generative grammar defining possible directions of open evolutionary process. The states in time future can be estimated from the point of their perfection, which represents the final cause in the Aristotelian sense and may possess a selective advantage. The limits of unfolding of the reflective process, such as the golden ratio and the golden wurf are considered as the canons of perfection established in the evolutionary process. (shrink)

We have provided a model-theoretic proof for the decidability of the additive structure of integers together with the function f mapping x to $$\lfloor \varphi x\rfloor $$ where $$\varphi $$ is the golden ratio.

Simple extrapolation is the orthodox approach to extrapolating from clinical trials in evidence-based medicine: extrapolate the relative effect size from the trial unless there is a compelling reason not to do so. I argue that this method relies on a myth and a fallacy. The myth of simple extrapolation is the idea that the relative risk is a ‘golden ratio’ that is usually transportable due to some special mathematical or theoretical property. The fallacy of simple extrapolation is an (...) unjustified argument from ignorance: we conclude that the relative effect size is transportable in the absence of evidence to the contrary. In short, simple extrapolation is a deeply problematic solution to the problem of extrapolation. (shrink)

Plato believed that behind everything in the universe lie mathematical principles. Plato was inspired by Pythagoras (571 BCE), who developed a school of mathematics at Crotona that studied sacred geometry as a form of religion. The school’s motto was “God is number,” or “All is Number”. Pythagoras believed that numbers represented God in pattern, symmetry, and infinity. When one of its students, Hippasus told the world the secret of the existence of irrational numbers, Greek geometry was born and Pythagoras’ idea (...) of divinity in numbers died because how could God not be perfect and symmetrical? In Plato’s Republic he discusses something called The Divided Line, which is a map, of sorts, for reaching what he calls the highest Good, which is the ultimate truth where one realizes the true state of the universe and can see the world for what it really is. Many mathematicians have attempted to plot Plato’s Divided Line only to come across a litany of problems and conundrums. Some have said that it the Divided Line cannot be plotted and is merely an allegory not meant to be plotted. This paper discusses some of the conundrums preventing the plotting of Plato’s Divided Line (not an exhaustive list), including Whole ‘vs’ Separate, Equality ‘vs’ Ontological Dissimilarity, Linear ‘vs’ Non-linear, and Infinity ‘vs’ Finite. This paper also explores a new understanding of the Allegory of the Cave in light of ‘the problem of the irrational.’ In exploring the link between the Divided Line and the ‘the problem of the irrational,’ I was able to plot it. It was found that the Divided Line is not a line in the linear sense, but a spiral, the Golden Ratio! This paper is an example of a new category of scholarly inquiry I call “Math Theory” based on scholarly mathematical axioms in theory, rather than including actual maths. In my papers I use existing mathematical equations and place them in an encompassing theory, rather than finding new formulae to fit an existing theory. Keywords: Pythagoras, divided line, math theory, highest good, all is number. (shrink)

This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called "Chargaff's grammar of biology" by providing the conceptual theoretical framework necessary to generalize Chargaff's rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides (...) induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.1 (2004) 78-88 [Access article in PDF] Remembering Beauty:Reflections on Kant and Cartier-Bresson for Aspiring Photographers Stuart Richmond In the past few decades beauty has become something of an endangered species in the Western art world. Indeed, beauty has never been a central aim of contemporary art, which has tended to focus on meaning and politics rather than formal values, conceptual art being a (...) case in point. Feminist artists and critics, reacting to the objectification of women in society have rendered attention to women's beauty, especially the nude, impolitic. This is perhaps understandable given the persuasive emphasis on beauty in marketing, that many argue socializes an unhealthy self-image in young people and distracts attention from important social issues. As well, techno-global-business practices increasingly invade our lives and private spaces with a virtual culture of information and efficiency. We do not know how this retreat from the sensual, concrete present will affect human sensibilities and values in the long run, although there are some disturbing signs. Seen as un-cerebral and allied with pleasure, beauty and its alter ego, appreciation, have acquired a decided regressive air. Having said that, for many people at the level of ordinary life — in human relationships, arts activities, and love of nature, for example — beauty never really went away because beauty is a source of pleasure and well-being that we cannot help wanting. As Plato pointed out, beauty is the only visible quality that inspires love. 1 A life of beauty in a free and ethical environment is an invitation to a life worth living. Though I cannot pursue the matter here, it is noteworthy that we often call a person of courage, goodness, and humility, a beautiful human being. Around the world people find many paths to beauty and of late in the Western artistic and academic worlds, beauty seems to be making a comeback. But beauty is a difficult thing to talk about, partly due to its being an experiential concept, partly because it has a long and complex philosophical history, and also because there is the risk in analysis of reducing it to something small and formulaic. Words in the end cannot replace the experience [End Page 78] of beauty. Despite these concerns, however, I believe that now, more thanever in the arts and education, we need to develop capacities for creating and appreciating beauty, if only to bring us back into contact with what is sensual and intrinsically worthwhile after so much arid theorizing, conflict in the world, and technocratic obsession. Through beauty we might be able to regain a stronger sense of human values and pleasure in living. Therefore, my aim here is to re-examine beauty in order to strengthen its role in aesthetic education. I do not expect to develop any precise definitions but I shall aim for a few signposts. Background to the Concept of Beauty "Beauty," "beautiful," or "the beautiful" refer primarily to a quality found pleasing to the senses. Here I shall restrict discussion to the visual domain, and later principally to art. As noted, beauty has a long philosophical history but the concept remains vague. From classical times on, beauty has been defined or associated with such properties as symmetry, balance, variety, harmony, proportion, order, unity, and perfection. And indeed, these features have long provided normative guidelines for the creation and appreciation of beauty. Over time we have learned the shape and proportions of a beautiful pot or supporting column. The golden section, a ratio of 1:1.6, has been used to good effect in design for millennia, the Parthenon being a prime example, the 35 mm negative another. However, as is well known, differences in beauty in individual cases tend to elude definition on account of this or that property or collection of properties. Exceptions can always be found. A painting may be well balanced but lacking in a certain élan vital, or unbalanced but beautiful. The variability of beautiful things seems to rule out a... (shrink)

"Annual dinner and act golden gavel competition." Ethos: Official Publication of the Law Society of the Australian Capital Territory, (194), pp. 18.

This paper provides a systematic exposition of what Wittgenstein took to be the fundamental error committed by James George Frazer, author of the classic anthropological work The Golden Bough, in his account of ritual practices. By construing those rituals in scientific or rationalistic terms, as aimed at the production of certain effects, Frazer ignores, according to Wittgenstein, their expressive and symbolic dimension. It is, moreover, an error to try to explain the powerful emotions evoked even today by traditions such (...) as fire festivals (which may once have involved human sacrifice) by searching for their causal origins in history or prehistory; the disquieting nature of such practices needs to be understood by attending to the inner meaning they already have in our human lives. Certain important general lessons are drawn about the necessarily limited power of scientific and causal explanations when it comes to alleviating many of our fundamental perplexities not just in the area of anthropology but in philosophy as well.1. (shrink)

Timothy J. Golden presents an existential, phenomenological, and political interpretation of Douglass's use of narrative. Reading Douglass with Kierkegaard, Kafka, Kant, and Levinas, Golden argues that analytic theism is an inauthentic preoccupation with knowledge at the expense of a concrete moral sensibility that Douglass's narrative provides.

The aim of this essay is to provide a philosophical discussion of Frederick Douglass's thought in relation to Christianity. I expand upon the work of Bill E. Lawson and Frank M. Kirkland—who both argue that there are Kantian features present in Douglass as it relates to his conception of the individual—by arguing that there are similarities between Douglass and Kant not only concerning the relationship between morality and Christianity, but also concerning the nature of the soul. Specifically, I try to (...) show that the moral weakness of slaveholding Christianity that Douglass attacked is found in the ecclesial formation of the slaveholding Christian church; it is a formation that begins with epistemology, but ignores ethics. I conclude, in part, that both Douglass and Kant reject a Cartesian psychological dualism in favor of a conception of the soul that is more attentive to one's moral development. (shrink)

While society debates whether and how to use public funds to support work on human embryonic stem cells, many scientific groups and businesses debate a different question — the extent to which patents that cover such stem cells should be permitted to limit or to tax their research. The Wisconsin Alumni Research Foundation, a non-profit foundation that manages intellectual property generated by researchers at the University of Wisconsin at Madison, owns three patents that have been at the heart of the (...) latter controversy. The story of WARF’s patents and the controversy they have fostered highlights not only continuing tensions between proprietary and nonproprietary approaches to developing science and technology, but also an at least partly reassuring capacity of public and private sectors to deal with those tensions in a way that can render them substantially manageable, and frequently more manageable as a technology matures. (shrink)

James Baldwin writes that "I underwent, during the summer that I became fourteen, a prolonged religious crisis."1 Baldwin dealt with this crisis in his literary works through the strategic use of Christian theological themes and imagery to make compelling critiques of bourgeois cultural and Christian values. So "prolonged" was his "religious crisis" that Christian theological themes permeate Baldwin's immense literary corpus.2 Baldwin thus both was influenced by Christianity and critiqued it in his works. Considering these two points, I think it (...) appropriate to begin this essay with a biblical reference to the Christian narrative of the "fall" of humanity. I choose this biblical starting point not only because of .. (shrink)

Several widely publicized incidents of academic research misconduct, combined with the politicization of the role of science in public health and policy discourse (e.g., COVID, immunizations) threaten to undermine faith in the integrity of empirical research. Researchers often maintain that peer-review and study replication allow the field to self-police and self-correct; however, stark disparities between official reports of academic research misconduct and self-reports of academic researchers, specifically with regard to data fabrication, belie this argument. Further, systemic imperatives in academic settings (...) often incentivize institutional responses that focus on minimizing reputational harm rather than the impact of fabricated data on the integrity of extant and future research. (shrink)

This study advances the claim that Hume's Dialogues Concerning Natural Religion, which drew its inspiration and guidelines from Cicero's De Natura Deorum, fulfills four basic elements of Michel Meyer's theory of problematology. In doing so, it is argued, the Dialogues contribute importantly to our understanding of the question-answer pair, and to the notion of rhetoric as a way of knowing.

Who protects individual liberties and human dignity from domination by the State, by Civil Society or by individuals is a question under debate in China as well as the West, not from the point of view of Liberalism, but from the point of view of ‘Relationality’. Liberalism posits the individual as the measure of these matters but the ‘individual’ in question is an abstraction. Relationality posits social relations as the measure of these matters. Persons are not abstractions. They combine several (...) different social ‘roles’, and each role includes obligations as well as rights. These roles limit the individual’s freedom of action. There are no unipersonal societies. Liberalism also posits rights as an abstraction: ‘All men are created equal’. Relationality posits rights in a context of mutual recognition of rights and responsibilities. Rights only exist if they can in fact be exercised. From the point of view of Relationality, therefore, a person’s ability to exercise her or his rights must be seen in the light of a concept of Justice and there must be an agency that can guarantee this Justice, the exercise of these rights, while it guarantees the fulfilment of social obligations. Is this the role of the State? of Civil Society? of the Market? To truly discuss these matters in a transcultural context, we would need to look for common ground, not take as ‘self-evident’ the classical Liberal perception of the individual. Understanding the underlying political philosophy of China’s concept of ‘responsive authoritarianism’ does not mean endorsing it. But understanding this idea and its ramifications does provide room for amplifying the basic question of who protects individual liberties and human dignity. (shrink)

"At its core, Yoga invites practitioners to live fully in the midst of hardship while staying open to the possibility of being transformed by life experiences of all kinds. A seasoned Yoga teacher and writer, the author confronts the ways in which modern Yoga has strayed from its original purposes, challenging current perspectives of practice, balance and peace. Drawing on the foundations of Yoga philosophy, this book provides guideposts for living a resilient life through deepening the understanding and experience of (...) Yoga. To redefine the popular understanding of Yoga, chapters provide practical and applicable tools to reclaim practice as a way to be fully alive and aware, thereby unpacking the resistance, judgment and impatience that stand in the way of living a resilient life."-Provided by publisher. (shrink)

The 21st-century construction of a new Chinese political discourse faces the same dilemma that Chinese intellectuals first identified in the 19th century – how to make currently pre-eminent Eurocen...

In the Introduction to her recent translation of the Poetics, Miss Hubbard astutely recognizes the intellectual orientation of Aristotle's aesthetic theory. She observes that for Aristotle the concept of mimesis is intimately connected with that of mathesis and thus that the basic pleasure of art is the intellectual pleasure involved in learning. She then correctly identifies two levels of the learning process involved in mimesis: on a lower level it signifies the way in which children learn their first lessons but (...) on a much more sophisticated plane it denotes a process by which our understanding of ‘moral facts and moral possibilities’ is deepened. She perceptively concludes that if art is to achieve the goal set for it by Aristotle, it must have a significant relationship to ultimate truth. (shrink)

Examines the significance of Nietzsche’s writings for contemporary debates about embodiment.

What are some of the key historical trends in hours of work per worker in US? What economic, social-psychological, organizational and institutional forces determine the length of individuals' working hours? How much of the trend toward longer working hours among so many workers may be attributable to workers' preferences, workplace incentives or employers' constraints? When can work become overwork or workaholism – an unforced addiction to incessant work activity which risk harm to workers, families or even economies? The first part (...) of this article traces the history of the length of working hours and its recent polarization. The second part develops a multi-disciplinary model to identify motivations behind working longer hours. Individuals' desired work hours will stem from the weighted contribution of five sources: (1) current real wage rates; (2) forward-looking, wage trajectories; (3) relative status associated with hours of labor; (4) intrinsic rewards, process benefits or amenities acquired through work; (5) hours demanded by the employer and other structural constraints, to which workers may adapt. Employers and their established conditions of work have influenced the course of long run trends labor supply and in work time structures. The final section suggests policies that might address the persistence of long hours. (shrink)