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Magic was part of life in ancient Greece and Rome, Egypt and Palestine, indeed throughout the ancient world; and certain forms of magic – protective amulets, curse tablets, spells for love, and many other types – were so widely used that it is tempting to say that magic does not really have a history, but is everywhere and always the same. But magic does have a history. Changes in the forms of magic may often be hard to trace, but it is easier to see shifts in attitudes toward magic, ranging from broad tolerance to fierce condemnation and repression. It is possible also to detect some differences over time in the sorts of people most likely to use magic or be suspected of using it. And as commerce, conquest, missionary campaigns, and translation projects brought different cultures into contact, magic was one form of tradition often appropriated across cultural boundaries.
This book will approach magic as a kind of crossroads where different pathways in medieval culture converge. First of all, it is a point of intersection between religion and science. Demonic magic invokes evil spirits and rests upon a network of religious beliefs and practices, while natural magic exploits “occult” powers within nature and is essentially a branch of medieval science. Yet demonic and natural magic are not always as distinct in fact as they seem in principle. Even when magic is clearly nondemonic it sometimes mingles elements of religion and science: a magical cure, for example, may embody both herbal lore from folk medicine and phrases of prayer from Christian ritual. Secondly, magic is an area where popular culture meets with learned culture. Popular notions of magic were taken up and interpreted by “intellectuals” – a term used here for those with philosophical or theological education – and their ideas about magic, demons, and kindred topics were in turn spread throughout the land by preachers. One of the most important tasks in cultural history is working out these lines of transmission. Thirdly, magic represents a particularly interesting crossroads between fiction and reality. The fictional literature of medieval Europe sometimes reflected the realities of medieval life, sometimes distorted them, sometimes provided escapist release from them, and sometimes held up ideals for reality to imitate. When this literature featured sorcerers, fairies, and other workers of magic, it may not have been meant or taken as totally realistic. Even so, the magic of medieval literature did resemble the magical practices of medieval life in ways that are difficult but interesting to disentangle.
A healing charm found as early as the ninth century begins with a story about three angels who encounter a band of personified diseases. They ask where the diseases are going. One disease says he is going to dry out the bones, empty the marrow, and otherwise torment some servant of God. The others all have their evil designs. The angels adjure the diseases by the Trinity, the orders of angels, and various categories of saints not to harm their victim, but rather to depart and not return.1 In this formula, the angels themselves are not adjured or conjured; they are the one who do the adjuring. Still, this is an example of how angels might function in healings, as they did in liturgy and other contexts. Prominent already in parts of the Bible and in early Christianity, they richly populated European folklore.
John of Salisbury, in his Policraticus, tells of an experience from his own youth. He was studying Latin from a priest, using the Psalms as the texts for study. As it happened, however, his teacher was an adept in the divinatory art of crystal-gazing, and abused his position of trust by making John and a somewhat older pupil participate in these activities. The idea was to anoint the boys’ fingernails with some sacred chrism so that images would appear reflected in the nails and would impart information. Alternatively, a polished basin might be used as the reflecting surface. After certain “preliminary magical rites” and the requisite anointing, the priest uttered names “which by the horror they inspired, seemed to me, child though I was, to belong to demons.” The other pupil declared that he saw “certain misty figures,” but John himself saw nothing of the sort and was thus ruled unqualified for this art. John goes on to say that almost all the people he knew who engaged in such practices were punished later in life with blindness and other afflictions. He knew only two exceptions, including the priest who had taught him Latin; both of these men repented and entered into religious life as monks or canons, and even they were punished somewhat for their offenses.1
Norse tradition tells of a conflict between two earls of tenth-century Norway in which both the parties, named Hakon and Thorleif, resorted to magic. Thorleif disguised himself as a beggar, went to the court of Hakon, and under the pretense of singing a poem in his honor, recited a curse that caused Hakon to lose his beard and much of his hair, to itch uncontrollably between his legs, and to suffer a lingering illness. In revenge, Hakon invoked the goddesses Thorgerd and Irpa, who aided him with their “trollish and prophetic powers.” They made a human figure out of driftwood, placed a heart inside it, and sent it to Thorleif, who promptly died.1
There were many reasons for opposing magic. Those who practiced it were in danger of physical and spiritual assault from the wily demons they sought to master. Even in its apparently innocent and entertaining forms it was, at best, frivolous and vain. It could involve presumptuous encroachment on the mysteries and creative powers of God. It involved erroneous assumptions about the demons, their power, and their dignity. All these arguments occur in medieval discussion of magic. In legislation, the central concern was fairly simple: magic can do grievous harm to other people. In moral and theological condemnations there were two further grounds for opposing magic: it may rely on demons even when it seems to use natural forces, and it makes sacrilegious use of holy objects or blasphemously mingles holy with unholy words. These anxieties may seem difficult to share in an age that widely professes disbelief in both religion and magic, but simply to understand the historical record we must be able to grasp what a threat magic represented in an age when its power was almost universally taken for granted.
The common tradition of magic was by no means uniform, but varied its themes from time to time and from place to place. One turning-point in the history of magic came in the twelfth century, with the rise of a new kind of learning that included scientific astrology, astral magic, and alchemy. The common tradition itself had incorporated elements of classical lore: remedies from Pliny or from Marcellus Empiricus, for example, were included in medieval leechbooks. But the new learning claimed to be more deeply rooted in ancient philosophy and science, and presented itself in a more rigorous and sophisticated guise. Like most forms of scholarship it lent itself to popularization, and thus the boundaries between the common tradition and the new magical learning did not remain rigid. Yet the fact remains that in the twelfth century something new was introduced, however complex its relationship with the older tradition became.
Part of the inheritance passed down from classical antiquity to medieval and modern Western culture is the notion of magic as something performed by special individuals. It is the magi, or magicians, who perform magic. Whatever similarities their operations may have to the work of others around them, “magic” remains a negative term associated with a suspicious class of practitioners.
The word “magic,” like many related words, began as a term of abuse, but has taken on more positive connotations. Particularly the adjectival forms of these words, “magical,” “enchanting,” “charming,” “fascinating,” and even “bewitching,” now stand for objects and experiences that are out of the ordinary, but alluring and attractive.1 This shift in usage came after the Middle Ages, but for background to it we must turn to the portrayal of magic in medieval courtly culture, and especially in the literary romances written for that culture. People at court clearly recognized that certain magical practices could be sinister and destructive; there is ample evidence that kings and courtiers feared sorcery at least as much as commoners did. In their imaginative literature, however, they were willing to accord it a different status and to consider, without horror, the symbolic uses of magical motifs. Sorcerers in courtly literature were figures in an enchanted realm. On one level this literature offered escape from the humdrum realities of life, but on a deeper level it reflected the social and psychological complexities of courtly society, and made possible for medieval and for modern readers a richer understanding of that life.
Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.
How was magic practiced in medieval times? How did it relate to the diverse beliefs and practices that characterized this fascinating period? This much revised and expanded new edition of Magic in the Middle Ages surveys the growth and development of magic in medieval Europe. It takes into account the extensive new developments in the history of medieval magic in recent years, featuring new material on angel magic, the archaeology of magic, and the magical efficacy of words and imagination. Richard Kieckhefer shows how magic represents a crossroads in medieval life and culture, examining its relationship and relevance to religion, science, philosophy, art, literature, and politics. In surveying the different types of magic that were used, the kinds of people who practiced magic, and the reasoning behind their beliefs, Kieckhefer shows how magic served as a point of contact between the popular and elite classes, how the reality of magical beliefs is reflected in the fiction of medieval literature, and how the persecution of magic and witchcraft led to changes in the law.
Now reissued by Cambridge University Press, this sixth edition covers the fundamentals of aerodynamics using clear explanations and real-world examples. Aerodynamics concept boxes throughout showcase real-world applications, chapter objectives provide readers with a better understanding of the goal of each chapter and highlight the key 'take-home' concepts, and example problems aid understanding of how to apply core concepts. Coverage also includes the importance of aerodynamics to aircraft performance, applications of potential flow theory to aerodynamics, high-lift military airfoils, subsonic compressible transformations, and the distinguishing characteristics of hypersonic flow. Supported online by a solutions manual for instructors, MATLAB® files for example problems, and lecture slides for most chapters, this is an ideal textbook for undergraduates taking introductory courses in aerodynamics, and for graduates taking preparatory courses in aerodynamics before progressing to more advanced study.
Quantum Field Theory provides a theoretical framework for understanding fields and the particles associated with them, and is the basis of particle physics and condensed matter research. This graduate level textbook provides a comprehensive introduction to quantum field theory, giving equal emphasis to operator and path integral formalisms. It covers modern research such as helicity spinors, BCFW construction and generalized unitarity cuts; as well as treating advanced topics including BRST quantization, loop equations, and finite temperature field theory. Various quantum fields are described, including scalar and fermionic fields, Abelian vector fields and Quantum ElectroDynamics (QED), and finally non-Abelian vector fields and Quantum ChromoDynamics (QCD). Applications to scattering cross sections in QED and QCD are also described. Each chapter ends with exercises and an important concepts section, allowing students to identify the key aspects of the chapter and test their understanding.