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Early evidence of Italian Baroque ideas in painting occurred in Bologna, where Annibale Carracci, Agostino Carracci and Ludovico Carracci sought to return the visual arts to the ordered Classicism of the Renaissance. Their art, however, also incorporated ideas central the Counter-Reformation; these included intense emotion and religious imagery that appealed more to the heart than to the intellect. Another influential painter of the Baroque era was Michelangelo Merisi da Caravaggio. His realistic approach to the human figure, painted directly from life and dramatically spotlit against a dark background, shocked his contemporaries and opened a new chapter in the history of painting. Other major painters associated closely with the Baroque style include Artemisia Gentileschi, Elisabetta Sirani, Giovanna Garzoni, Guido Reni, Domenichino, Andrea Pozzo, and Paolo de Matteis in Italy; Francisco de Zurbarán, Bartolomé Esteban Murillo and Diego Velázquez in Spain; Adam Elsheimer in Germany; and Nicolas Poussin and Georges de La Tour in France (though Poussin spent most of his working life in Italy). Poussin and de La Tour adopted a "classical" Baroque style with less focus on emotion and greater attention to the line of the figures in the painting than to colour.
Peter Paul Rubens was the most important painter of the Flemish Baroque style. Rubens' highly charged compositions reference erudite aspects of classical and Christian history. His unique and immensely popular Baroque style emphasised movement, colour, and sensuality, which followed the immediate, dramatic artistic style promoted in the Counter-Reformation. Rubens specialized in making altarpieces, portraits, landscapes, and history paintings of mythological and allegorical subjects. One important domain of Baroque painting was "Quadratura", or paintings in "trompe-l'œil", which literally "fooled the eye". These were usually painted on the stucco of ceilings or upper walls and balustrades, and gave the impression to those on the ground looking up were that they were seeing the heavens populated with crowds of angels, saints and other heavenly figures, set against painted skies and imaginary architecture. In Italy, artists often collaborated with architects on interior decoration; Pietro da Cortona was one of the painters of the 17th century who employed this illusionist way of painting. Among his most important commissions were the frescoes he painted for the Palazzo Barberini (1633–39), to glorify the reign of Pope Urban VIII. Pietro da Cortona's compositions were the largest decorative frescoes executed in Rome since the work of Michelangelo at the Sistine Chapel.
François Boucher was an important figure in the more delicate French Rococo style, which appeared during the late Baroque period. He designed tapestries, carpets and theatre decoration as well as painting. His work was extremely popular with Madame de Pompadour, the Mistress of King Louis XV. His paintings featured mythological romantic, and mildly erotic themes. Hispanic Americas. In the Hispanic Americas, the first influences were from Sevillan Tenebrism, mainly from Zurbarán—some of whose works are still preserved in Mexico and Peru—as can be seen in the work of the Mexicans José Juárez and Sebastián López de Arteaga, and the Bolivian Melchor Pérez de Holguín. The Cusco School of painting arose after the arrival of the Italian painter Bernardo Bitti in 1583, who introduced Mannerism in the Americas. It highlighted the work of Luis de Riaño, disciple of the Italian Angelino Medoro, author of the murals of the Church of San Pedro, Andahuaylillas. It also highlighted the Indian (Quechua) painters Diego Quispe Tito and Basilio Santa Cruz Pumacallao, as well as Marcos Zapata, author of the fifty large canvases that cover the high arches of Cusco Cathedral. In Ecuador, the Quito School was formed, mainly represented by the mestizo Miguel de Santiago and the criollo Nicolás Javier de Goríbar.
In the 18th century sculptural altarpieces began to be replaced by paintings, developing notably the Baroque painting in the Americas. Similarly, the demand for civil works, mainly portraits of the aristocratic classes and the ecclesiastical hierarchy, grew. The main influence was the Murillesque, and in some cases—as in the criollo Cristóbal de Villalpando–that of Juan de Valdés Leal. The painting of this era has a more sentimental tone, with sweet and softer shapes. Its proponents include Gregorio Vasquez de Arce y Ceballos in Colombia, and Juan Rodríguez Juárez and Miguel Cabrera in Mexico. Sculpture. The dominant figure in baroque sculpture was Gian Lorenzo Bernini. Under the patronage of Pope Urban VIII, he made a remarkable series of monumental statues of saints and figures whose faces and gestures vividly expressed their emotions, as well as portrait busts of exceptional realism, and highly decorative works for the Vatican such as the imposing Chair of St. Peter beneath the dome in St. Peter's Basilica. In addition, he designed fountains with monumental groups of sculpture to decorate the major squares of Rome.
Baroque sculpture was inspired by ancient Roman statuary, particularly by the famous first century CE statue of "Laocoön and His Sons", which was unearthed in 1506 and put on display in the gallery of the Vatican. When he visited Paris in 1665, Bernini addressed the students at the academy of painting and sculpture. He advised the students to work from classical models, rather than from nature. He told the students, "When I had trouble with my first statue, I consulted the "Antinous" like an oracle." That "Antinous" statue is known today as the Hermes of the Museo Pio-Clementino. Notable late French baroque sculptors included Étienne Maurice Falconet and Jean Baptiste Pigalle. Pigalle was commissioned by Frederick the Great to make statues for Frederick's own version of Versailles at Sanssouci in Potsdam, Germany. Falconet also received an important foreign commission, creating the famous "Bronze Horseman" statue of Peter the Great found in St. Petersburg. In Spain, the sculptor Francisco Salzillo worked exclusively on religious themes, using polychromed wood. Some of the finest baroque sculptural craftsmanship was found in the gilded stucco altars of churches of the Spanish colonies of the New World, made by local craftsmen; examples include the Chapel del Rosario, Puebla, (Mexico), 1724–1731.
Furniture. The main motifs used are: horns of plenty, festoons, baby angels, lion heads holding a metal ring in their mouths, female faces surrounded by garlands, oval cartouches, acanthus leaves, classical columns, caryatids, pediments, and other elements of Classical architecture sculpted on some parts of pieces of furniture, baskets with fruits or flowers, shells, armour and trophies, heads of Apollo or Bacchus, and C-shaped volutes. During the first period of the reign of Louis XIV, furniture followed the previous Louis XIII style, and was massive, and profusely decorated with sculpture and gilding. After 1680, thanks in large part to the furniture designer André-Charles Boulle, a more original and delicate style appeared, sometimes known as Boulle work. It was based on the inlay of ebony and other rare woods, a technique first used in Florence in the 15th century, which was refined and developed by Boulle and others working for Louis XIV. Furniture was inlaid with plaques of ebony, copper, and exotic woods of different colors.
New and often enduring types of furniture appeared; the commode, with two to four drawers, replaced the old "coffre", or chest. The "canapé", or sofa, appeared, in the form of a combination of two or three armchairs. New kinds of armchairs appeared, including the "fauteuil en confessionale" or "Confessional armchair", which had padded cushions ions on either side of the back of the chair. The console table also made its first appearance; it was designed to be placed against a wall. Another new type of furniture was the "table à gibier", a marble-topped table for holding dishes. Early varieties of the desk appeared; the Mazarin desk had a central section set back, placed between two columns of drawers, with four feet on each column. Music. The term "Baroque" is also used to designate the style of music composed during a period that overlaps with that of Baroque art. The first uses of the term 'baroque' for music were criticisms. In an anonymous, satirical review of the première in October 1733 of Jean-Philippe Rameau's "Hippolyte et Aricie," printed in the "Mercure de France" in May 1734, the critic implied that the novelty of this opera was "du barocque," complaining that the music lacked coherent melody, was filled with unremitting dissonances, constantly changed key and meter, and speedily ran through every compositional device. Jean-Jacques Rousseau, who was a musician and noted composer as well as philosopher, made a very similar observation in 1768 in the famous "Encyclopédie" of Denis Diderot: "Baroque music is that in which the harmony is confused, and loaded with modulations and dissonances. The singing is harsh and unnatural, the intonation difficult, and the movement limited. It appears that term comes from the word 'baroco' used by logicians."
Common use of the term for the music of the period began only in 1919, by Curt Sachs, and it was not until 1940 that it was first used in English in an article published by Manfred Bukofzer. The baroque was a period of musical experimentation and innovation which explains the amount of ornaments and improvisation performed by the musicians. New forms were invented, including the concerto and sinfonia. Opera was born in Italy at the end of the 16th century (with Jacopo Peri's mostly lost "Dafne", produced in Florence in 1598) and soon spread through the rest of Europe: Louis XIV created the first Royal Academy of Music. In 1669 the poet Pierre Perrin opened an academy of opera in Paris, the first opera theatre in France open to the public, and premiered "Pomone", the first grand opera in French, with music by Robert Cambert, with five acts, elaborate stage machinery, and a ballet. Heinrich Schütz in Germany, Jean-Baptiste Lully in France, and Henry Purcell in England all helped to establish their national traditions in the 17th century.
Several new instruments, including the piano, were introduced during this period. The invention of the piano is credited to Bartolomeo Cristofori (1655–1731) of Padua, Italy, who was employed by Ferdinando de' Medici, Grand Prince of Tuscany, as the Keeper of the Instruments. Cristofori named the instrument "un cimbalo di cipresso di piano e forte" ("a keyboard of cypress with soft and loud"), abbreviated over time as "pianoforte", "fortepiano", and later, simply, piano. Dance. The classical ballet also originated in the Baroque era. The style of court dance was brought to France by Marie de' Medici, and in the beginning the members of the court themselves were the dancers. Louis XIV himself performed in public in several ballets. In March 1662, the Académie Royale de Danse, was founded by the King. It was the first professional dance school and company, and set the standards and vocabulary for ballet throughout Europe during the period. Literary theory. Heinrich Wölfflin was the first to transfer the term Baroque to literature. The key concepts of Baroque literary theory, such as "conceit" ("concetto"), "wit" ("acutezza", "ingegno"), and "wonder" ("meraviglia"), were not fully developed in literary theory until the publication of Emanuele Tesauro's "Il Cannocchiale aristotelico" (The Aristotelian Telescope) in 1654. This seminal treatise - inspired by Giambattista Marino's epic "Adone" and the work of the Spanish Jesuit philosopher Baltasar Gracián - developed a theory of metaphor as a universal language of images and as a supreme intellectual act, at once an artifice and an epistemologically privileged mode of access to truth.
Theatre. The Baroque period was a golden age for theatre in France and Spain; playwrights included Corneille, Racine and Molière in France; and Lope de Vega and Pedro Calderón de la Barca in Spain. During the Baroque period, the art and style of the theatre evolved rapidly, alongside the development of opera and of ballet. The design of newer and larger theatres, the invention the use of more elaborate machinery, the wider use of the proscenium arch, which framed the stage and hid the machinery from the audience, encouraged more scenic effects and spectacle. The Baroque had a Catholic and conservative character in Spain, following an Italian literary model during the Renaissance. The Hispanic Baroque theatre aimed for a public content with an ideal reality that manifested fundamental three sentiments: Catholic religion, monarchist and national pride and honour originating from the chivalric, knightly world. Two periods are known in the Baroque Spanish theatre, with the division occurring in 1630. The first period is represented chiefly by Lope de Vega, but also by Tirso de Molina, Gaspar Aguilar, Guillén de Castro, Antonio Mira de Amescua, Luis Vélez de Guevara, Juan Ruiz de Alarcón, Diego Jiménez de Enciso, Luis Belmonte Bermúdez, Felipe Godínez, Luis Quiñones de Benavente or Juan Pérez de Montalbán. Many of these figures attended "academias literarias" (literary academies) including the famous Medrano Academy founded by Sebastián Francisco de Medrano. The second period is represented by Pedro Calderón de la Barca and fellow dramatists Antonio Hurtado de Mendoza, Álvaro Cubillo de Aragón, Jerónimo de Cáncer, Francisco de Rojas Zorrilla, Juan de Matos Fragoso, Antonio Coello y Ochoa, Agustín Moreto, and Francisco Bances Candamo. These classifications are loose because each author had his own way and could occasionally adhere himself to the formula established by Lope. It may even be that Lope's "manner" was more liberal and structured than Calderón's.
Lope de Vega introduced through his "Arte nuevo de hacer comedias en este tiempo" (1609) the "new comedy". He established a new dramatic formula that broke the three Aristotle unities of the Italian school of poetry (action, time, and place) and a fourth unity of Aristotle which is about style, mixing of tragic and comic elements showing different types of verses and stanzas upon what is represented. Although Lope has a great knowledge of the plastic arts, he did not use it during the major part of his career nor in theatre or scenography. The Lope's comedy granted a second role to the visual aspects of the theatrical representation. Tirso de Molina, Lope de Vega, and Calderón were the most important play writers in Golden Era Spain. Their works, known for their subtle intelligence and profound comprehension of a person's humanity, could be considered a bridge between Lope's primitive comedy and the more elaborate comedy of Calderón. Tirso de Molina is best known for two works, "The Convicted Suspicions" and "The Trickster of Seville", one of the first versions of the Don Juan myth.
Upon his arrival to Madrid, Cosimo Lotti brought to the Spanish court the most advanced theatrical techniques of Europe. His techniques and mechanic knowledge were applied in palace exhibitions called "Fiestas" and in lavish exhibitions of rivers or artificial fountains called "Naumaquias". He was in charge of styling the Gardens of Buen Retiro, of Zarzuela, and of Aranjuez and the construction of the theatrical building of Coliseo del Buen Retiro. Lope's formulas begin with a verse that it unbefitting of the palace theatre foundation and the birth of new concepts that begun the careers of some play writers like Calderón de la Barca. Marking the principal innovations of the New Lopesian Comedy, Calderón's style marked many differences, with a great deal of constructive care and attention to his internal structure. Calderón's work is in formal perfection and a very lyric and symbolic language. Liberty, vitality and openness of Lope gave a step to Calderón's intellectual reflection and formal precision. In his comedy it reflected his ideological and doctrine intentions in above the passion and the action, the work of Autos sacramentales achieved high ranks. The genre of Comedia is political, multi-artistic and in a sense hybrid. The poetic text interweaved with Medias and resources originating from architecture, music and painting freeing the deception that is in the Lopesian comedy was made up from the lack of scenery and engaging the dialogue of action.
The best known German playwright was Andreas Gryphius, who used the Jesuit model of the Dutch Joost van den Vondel and Pierre Corneille. There was also Johannes Velten who combined the traditions of the English comedians and the commedia dell'arte with the classic theatre of Corneille and Molière. His touring company was perhaps the most significant and important of the 17th century. The foremost Italian baroque tragedian was Federico Della Valle. His literary activity is summed up by the four plays that he wrote for the courtly theater: the tragicomedy "Adelonda di Frigia" (1595) and especially his three tragedies, "Judith" (1627), "Esther" (1627) and "La reina di Scotia" (1628). Della Valle had many imitators and followers who combined in their works Baroque taste and the didactic aims of the Jesuits (Francesco Sforza Pallavicino, Girolamo Graziani, etc.) In the Tsardom of Russia, the development of the Russian version of Baroque took shape only in the second half of the 17th century, primarily due to the initiative of tsar Alexis of Russia, who wanted to open a court theatre in 1672. Its director and dramatist was Johann Gottfried Gregorii, a German-Russian Lutheran pastor, who wrote, in particular, a 10-hour play "The Action of Artaxerxes". The dramaturgy of Symeon of Polotsk and Demetrius of Rostov became key contribution to the Russian Baroque.
Spanish colonial Americas. Following the evolution marked from Spain, at the end of the 16th century, the companies of comedians, essentially transhumant, began to professionalize. With professionalization came regulation and censorship: as in Europe, the theatre oscillated between tolerance and even government protection and rejection (with exceptions) or persecution by the Church. The theatre was useful to the authorities as an instrument to disseminate the desired behavior and models, respect for the social order and the monarchy, school of religious dogma. The "corrales" were administered for the benefit of hospitals that shared the benefits of the representations. The itinerant companies (or "of the league"), who carried the theatre in improvised open-air stages by the regions that did not have fixed locals, required a viceregal license to work, whose price or "pinción" was destined to alms and works pious. For companies that worked stably in the capitals and major cities, one of their main sources of income was participation in the festivities of the Corpus Christi, which provided them with not only economic benefits, but also recognition and social prestige. The representations in the viceregal palace and the mansions of the aristocracy, where they represented both the comedies of their repertoire and special productions with great lighting effects, scenery, and stage, were also an important source of well-paid and prestigious work.
Born in the Viceroyalty of New Spain but later settled in Spain, Juan Ruiz de Alarcón is the most prominent figure in the Baroque theatre of New Spain. Despite his accommodation to Lope de Vega's new comedy, his "marked secularism", his discretion and restraint, and a keen capacity for "psychological penetration" as distinctive features of Alarcón against his Spanish contemporaries have been noted. Noteworthy among his works "La verdad sospechosa", a comedy of characters that reflected his constant moralizing purpose. The dramatic production of Sor Juana Inés de la Cruz places her as the second figure of the Spanish-American Baroque theatre. It is worth mentioning among her works the auto sacramental "El divino Narciso" and the comedy "Los empeños de una casa". Gardens. The Baroque garden, also known as the "jardin à la française" or French formal garden, first appeared in Rome in the 16th century, and then most famously in France in the 17th century in the gardens of Vaux le Vicomte and the Palace of Versailles. Baroque gardens were built by Kings and princes in Germany, the Netherlands, Austria, Spain, Poland, Italy and Russia until the mid-18th century, when they began to be remade into by the more natural English landscape garden.
The purpose of the baroque garden was to illustrate the power of man over nature, and the glory of its builder, Baroque gardens were laid out in geometric patterns, like the rooms of a house. They were usually best seen from the outside and looking down, either from a château or terrace. The elements of a baroque garden included parterres of flower beds or low hedges trimmed into ornate Baroque designs, and straight lanes and alleys of gravel which divided and crisscrossed the garden. Terraces, ramps, staircases and cascades were placed where there were differences of elevation, and provided viewing points. Circular or rectangular ponds or basins of water were the settings for fountains and statues. Bosquets or carefully trimmed groves or lines of identical trees, gave the appearance of walls of greenery and were backdrops for statues. On the edges, the gardens usually had pavilions, orangeries and other structures where visitors could take shelter from the sun or rain. Baroque gardens required enormous numbers of gardeners, continual trimming, and abundant water. In the later part of the Baroque period, the formal elements began to be replaced with more natural features, including winding paths, groves of varied trees left to grow untrimmed; rustic architecture and picturesque structures, such as Roman temples or Chinese pagodas, as well as "secret gardens" on the edges of the main garden, filled with greenery, where visitors could read or have quiet conversations. By the mid-18th century most of the Baroque gardens were partially or entirely transformed into variations of the English landscape garden.
Besides Versailles and Vaux-le-Vicomte, celebrated baroque gardens still retaining much of their original appearance include the Royal Palace of Caserta near Naples; Nymphenburg Palace and Augustusburg and Falkenlust Palaces, Brühl in Germany; Het Loo Palace, Netherlands; the Belvedere Palace in Vienna; Royal Palace of La Granja de San Ildefonso, Spain; and Peterhof Palace in St. Petersburg, Russia. Urban planning and design. 16th through 19th century European cities witnessed a large change in urban design and planning principals that reshaped the landscapes and built environment. Rome, Paris, and other major cities were transformed to accommodate growing populations through improvements in housing, transportation, and public services. Throughout this time, the Baroque style was in full swing, and the influences of elaborate, dramatic, and artistic architectural styles extended into the urban fabric through what is known as Baroque urban planning. The experience of living and walking in the cities aims to complement the emotions of the Baroque style. This style of planning often embraced displaying the wealth and strength of the ruling powers, and the important buildings served as the visual and symbolic center of the cities.
The replanning of the city of Rome under the rule of Pope Sixtus V revived and expanded the city in the 16th century. Many grand piazzas and squares were added as public spaces to contribute to the dramatic effect of the Baroque style. The piazzas featured fountains and other decorative features to embody the emotions of the time. An important factor in Baroque style planning was to connect churches, government structures, and piazzas together in a refined network of axis'. This allowed the important landmarks of the Catholic Church to become the focal points of the city. As another example of Baroque urban planning, Paris was in desperate need for an urban revival in the 19th century. The city underwent a dramatic change within its urban fabric through the help of Baron Haussmann. Under the rule of Napoleon III, Haussmann was appointed to reconstruct Paris by adding a new network of streets, parks, trains, and public services. Some of the characteristics of Haussmann's design include straight, wide boulevards lined with trees, and short access to parks and green spaces. The plan highlights some important buildings, such as the Paris Opera House.
More characteristics of Baroque urban planning are embodied in Barcelona. The Eixample district, designed by Ildefons Cerdà, showcases wide avenues in a grid system with a few diagonal boulevards. The intersections are unique with octagonal blocks, which provide the streets with great visibility and light. Many works in this district come from architect Antoni Gaudí, who displays a unique style. Centered in the Eixample district design is the Sagrada Família by Gaudí, which poses great significance to the city. Posterity. Transition to rococo. The Rococo is the final stage of the Baroque, and in many ways took the Baroque's fundamental qualities of illusion and drama to their logical extremes. Beginning in France as a reaction against the heavy Baroque grandeur of Louis XIV's court at the Palace of Versailles, the rococo movement became associated particularly with the powerful (1721–1764), the mistress of the new king, Louis XV (1710–1774). Because of this, the style was also known as "Pompadour". Although it's highly associated with the reign of Louis XV, it didn't appear in this period. Multiple works from the last years of Louis XIV's reign are examples of early Rococo. The name of the movement derives from the French , or pebble, and refers to stones and shells that decorate the interiors of caves, as similar shell forms became a common feature in Rococo design. It began as a design and decorative arts style, and was characterized by elegant flowing shapes. Architecture followed and then painting and sculpture. The French painter with whom the term Rococo is most often associated is Jean-Antoine Watteau, whose pastoral scenes, or , dominate the early part of the 18th century.
There are multiple similarities between Rococo and Baroque. Both styles insist on monumental forms, and so use continuous spaces, double columns or pilasters, and luxurious materials (including gilded elements). There also noticeable differences. Rococo designed freed themselves from the adherence to symmetry that had dominated architecture and design since the Renaissance. Many small objects, like ink pots or porcelain figures, but also some ornaments, are often asymmetrical. This goes hand in hand with the fact that most ornamentation consisted of interpretation of foliage and sea shells, not as many Classical ornaments inherited from the Renaissance like in Baroque. Another key difference is the fact that since the Baroque is the main cultural manifestation of the spirit of the Counter-Reformation, it is most often associated with ecclesiastical architecture. In contrast, the Rococo is mainly associated with palaces and domestic architecture. In Paris, the popularity of the Rococo coincided with the emergence of the salon as a new type of social gathering, the venues for which were often decorated in this style. Rococo rooms were typically smaller than their Baroque counterparts, reflecting a movement towards domestic intimacy. Colours also match this change, from the earthy tones of Caravaggio's paintings, and the interiors of red marble and gilded mounts of the reign of Louis XIV, to the pastel and relaxed pale blue, Pompadour pink, and white of the Louis XV and Madame de Pompadour's France. Similarly to colours, there was also a transition from serious, dramatic and moralistic subjects in painting and sculpture, to lighthearted and joyful themes.
One last difference between Baroque and Rococo is the interest that 18th century aristocrats had for East Asia. Chinoiserie was a style in fine art, architecture and design, popular during the 18th century, that was heavily inspired by Chinese art, but also by Rococo at the same time. Because traveling to China or other Far Eastern countries was hard at that time and so remained mysterious to most Westerners, European imagination were fuelled by perceptions of Asia as a place of wealth and luxury, and consequently patrons from emperors to merchants vied with each other in adorning their living quarters with Asian goods and decorating them in Asian styles. Where Asian objects were hard to obtain, European craftsmen and painters stepped up to fill the demand, creating a blend of Rococo forms and Asian figures, motifs and techniques. Aside from European recreations of objects in East Asian style, Chinese lacquerware was reused in multiple ways. European aristocrats fully decorated a handful of rooms of palaces, with Chinese lacquer panels used as wall panels. Due to its aspect, black lacquer was popular for Western men's studies. Those panels used were usually glossy and black, made in the Henan province of China. They were made of multiple layers of lacquer, then incised with motifs in-filled with colour and gold. Chinese, but also Japanese lacquer panels were also used by some 18th century European carpenters for making furniture. In order to be produced, Asian screens were dismantled and used to veneer European-made furniture.
Condemnation and academic rediscovery. The pioneer German art historian and archeologist Johann Joachim Winckelmann also condemned the baroque style, and praised the superior values of classical art and architecture. By the 19th century, Baroque was a target for ridicule and criticism. The neoclassical critic Francesco Milizia wrote: "Borrominini in architecture, Bernini in sculpture, Pietro da Cortona in painting...are a plague on good taste, which infected a large number of artists." In the 19th century, criticism went even further; the British critic John Ruskin declared that baroque sculpture was not only bad, but also morally corrupt. The Swiss-born art historian Heinrich Wölfflin (1864–1945) started the rehabilitation of the word Baroque in his "Renaissance und Barock" (1888); Wölfflin identified the Baroque as "movement imported into mass", an art antithetic to Renaissance art. He did not make the distinctions between Mannerism and Baroque that modern writers do, and he ignored the later phase, the academic Baroque that lasted into the 18th century. Baroque art and architecture became fashionable in the interwar period, and has largely remained in critical favor. The term "Baroque" may still be used, often pejoratively, describing works of art, craft, or design that are thought to have excessive ornamentation or complexity of line. At the same time "baroque" has become an accepted terms for various trends in Roman art and Roman architecture in the 2nd and 3rd centuries AD, which display some of the same characteristics as the later Baroque.
Revivals and influence through eclecticism. Highly criticized, the Baroque would later be a source of inspiration for artists, architects and designers during the 19th century through Romanticism, a movement that developed in the 18th century and that reached its peak in the 19th. It was characterized by its emphasis on emotion and individualism, as well as glorification of the past and nature, preferring the medieval to the classical. A mix of literary, religious, and political factors prompted late-18th and 19th century British architects and designers to look back to the Middle Ages for inspiration. Romanticism is the reason the 19th century is best known as the century of revivals. In France, Romanticism was not the key factor that led to the revival of Gothic architecture and design. Vandalism of monuments and buildings associated with the Ancien Régime (Old Regime) happened during the French Revolution. Because of this an archaeologist, Alexandre Lenoir, was appointed curator of the Petits-Augustins depot, where sculptures, statues and tombs removed from churches, abbeys and convents had been transported. He organized the Museum of French Monuments (1795–1816), and was the first to bring back the taste for the art of the Middle Ages, which progressed slowly to flourish a quarter of a century later.
This taste and revival of medieval art led to the revival of other periods, including the Baroque and Rococo. Revivalism started with themes first from the Middle Ages, then, towards the end of the reign of Louis Philippe I (1830–1848), from the Renaissance. Baroque and Rococo inspiration was more popular during the reign of Napoleon III (1852–1870), and continued later, after the fall of the Second French Empire. Compared to how in England architects and designers saw the Gothic as a national style, Rococo was seen as one of the most representative movements for France. The French felt much more connected to the styles of the Ancien Régime and Napoleon's Empire, than to the medieval or Renaissance past, although Gothic architecture appeared in France, not in England. The revivalism of the 19th century led in time to eclecticism (mix of elements of different styles). Because architects often revived Classical styles, most Eclectic buildings and designs have a distinctive look. Besides pure revivals, the Baroque was also one of the main sources of inspiration for eclecticism. The coupled column and the giant order, two elements widely used in Baroque, are often present in this kind of 19th and early 20th century buildings. Eclecticism was not limited only to architecture. Many designs from the Second Empire style (1848–1870) have elements taken from different styles. Little furniture from the period escaped its three most prevalent historicist influences, which are sometimes kept distinct and sometimes combined: the Renaissance, Louis XV (Rococo), and Louis XVI styles. Revivals and inspiration also came sometimes from Baroque, like in the case of remakes and arabesques that imitate Boulle marquetry, and from other styles, like Gothic, Renaissance, or English Regency.
The Belle Époque was a period that begun around 1871–1880 and that ended with the outbreak of World War I in 1914. It was characterized by optimism, regional peace, economic prosperity, colonial expansion, and technological, scientific, and cultural innovations. Eclecticism reached its peak in this period, with Beaux Arts architecture. The style takes its name from the École des Beaux-Arts in Paris, where it developed and where many of the main exponents of the style studied. Buildings in this style often feature Ionic columns with their volues on the corner (like those found in French Baroque), a rusticated basement level, overall simplicity but with some really detailed parts, arched doors, and an arch above the entrance like the one of the Petit Palais in Paris. The style aimed for a Baroque opulence through lavishly decorated monumental structures that evoked Louis XIV's Versailles. When it comes to the design of the Belle Époque, all furniture from the past was admired, including, perhaps, contrary to expectations, the Second Empire style (the style of the proceeding period), which remained popular until 1900. In the years around 1900, there was a gigantic recapitulation of styles of all countries in all preceding periods. Everything from Chinese to Spanish models, from Boulle to Gothic, found its way into furniture production, but some styles were more appreciated than others. The High Middle Ages and the early Renaissance were especially prized. Exoticism of every stripe and exuberant Rococo designs were also favoured.
Revivals and influence of the Baroque faded away and disappeared with Art Deco, a style created as a collective effort of multiple French designers to make a new modern style around 1910. It was obscure before WW1, but became very popular during the interwar period, being heavily associated with the 1920s and the 1930s. The movement was a blend of multiple characteristics taken from Modernist currents from the 1900s and the 1910s, like the Vienna Secession, Cubism, Fauvism, Primitivism, Suprematism, Constructivism, Futurism, De Stijl, and Expressionism. Besides Modernism, elements taken from styles popular during the Belle Époque, like Rococo Revival, Neoclassicism, or the neo-Louis XVI style, are also present in Art Deco. The proportions, volumes and structure of Beaux Arts architecture before WW1 is present in early Art Deco buildings of the 1910s and 1920s. Elements taken from Baroque are quite rare, architects and designers preferring the Louis XVI style. At the end of the interwar period, with the rise in popularity of the International Style, characterized by the complete lack of any ornamentation led to the complete abandonment of influence and revivals of the Baroque. Multiple International Style architects and designers, but also Modernist artists criticized Baroque for its extravagance and what they saw as "excess". Ironically this was just at the same time as the critical appreciation of the original Baroque was reviving strongly.
Postmodern appreciation and reinterpretations. Appreciation for the Baroque reappeared with the rise of Postmodernism, a movement that questioned Modernism (the status quo after WW2), and which promoted the inclusion of elements of historic styles in new designs, and appreciation for the pre-Modernist past. Specific references to Baroque are rare, since Postmodernism often included highly simplified elements that were 'quotations' of Classicism in general, like pediments or columns. More references to Baroque are found in Versace ceramic ware and fashion, decorated with maximalist acanthus rinceaux, very similar to the ones found in Italian Baroque ornament plates and in Boulle work, but also similar to the ones found on Empire objects, especially textiles, from the reign of Napoleon I.
Boolean algebra (structure) In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution). Every Boolean algebra gives rise to a Boolean ring, and vice versa, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨). However, the theory of Boolean rings has an inherent asymmetry between the two operators, while the axioms and theorems of Boolean algebra express the symmetry of the theory described by the duality principle. History.
Definition. A Boolean algebra is a set , equipped with two binary operations (called "meet" or "and"), (called "join" or "or"), a unary operation (called "complement" or "not") and two elements and in (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols and , respectively), such that for all elements , and of , the following axioms hold: Note, however, that the absorption law and even the associativity law can be excluded from the set of axioms as they can be derived from the other axioms (see Proven properties). A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra. (In older works, some authors required and to be "distinct" elements in order to exclude this case.) It follows from the last three pairs of axioms above (identity, distributivity and complements), or from the absorption axiom, that The relation defined by if these equivalent conditions hold, is a partial order with least element 0 and greatest element 1. The meet and the join of two elements coincide with their infimum and supremum, respectively, with respect to ≤.
The first four pairs of axioms constitute a definition of a bounded lattice. It follows from the first five pairs of axioms that any complement is unique. The set of axioms is self-dual in the sense that if one exchanges with and with in an axiom, the result is again an axiom. Therefore, by applying this operation to a Boolean algebra (or Boolean lattice), one obtains another Boolean algebra with the same elements; it is called its dual. Examples. formula_1 becomes a Boolean algebra when its operations are defined by and . Homomorphisms and isomorphisms. A "homomorphism" between two Boolean algebras and is a function such that for all , in : It then follows that for all in . The class of all Boolean algebras, together with this notion of morphism, forms a full subcategory of the category of lattices. An "isomorphism" between two Boolean algebras and is a homomorphism with an inverse homomorphism, that is, a homomorphism such that the composition is the identity function on , and the composition is the identity function on . A homomorphism of Boolean algebras is an isomorphism if and only if it is bijective.
Boolean rings. Every Boolean algebra gives rise to a ring by defining (this operation is called symmetric difference in the case of sets and XOR in the case of logic) and . The zero element of this ring coincides with the 0 of the Boolean algebra; the multiplicative identity element of the ring is the of the Boolean algebra. This ring has the property that for all in ; rings with this property are called Boolean rings. Conversely, if a Boolean ring is given, we can turn it into a Boolean algebra by defining and . Since these two constructions are inverses of each other, we can say that every Boolean ring arises from a Boolean algebra, and vice versa. Furthermore, a map is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings. The categories of Boolean rings and Boolean algebras are equivalent; in fact the categories are isomorphic. Hsiang (1985) gave a rule-based algorithm to check whether two arbitrary expressions denote the same value in every Boolean ring. More generally, Boudet, Jouannaud, and Schmidt-Schauß (1989) gave an algorithm to solve equations between arbitrary Boolean-ring expressions.
Employing the similarity of Boolean rings and Boolean algebras, both algorithms have applications in automated theorem proving. Ideals and filters. An "ideal" of the Boolean algebra is a nonempty subset such that for all , in we have in and for all in we have in . This notion of ideal coincides with the notion of ring ideal in the Boolean ring . An ideal of is called "prime" if and if in always implies in or in . Furthermore, for every we have that , and then if is prime we have or for every . An ideal of is called "maximal" if and if the only ideal properly containing is itself. For an ideal , if and , then or is contained in another proper ideal . Hence, such an is not maximal, and therefore the notions of prime ideal and maximal ideal are equivalent in Boolean algebras. Moreover, these notions coincide with ring theoretic ones of prime ideal and maximal ideal in the Boolean ring . The dual of an "ideal" is a "filter". A "filter" of the Boolean algebra is a nonempty subset such that for all , in we have in and for all in we have in . The dual of a "maximal" (or "prime") "ideal" in a Boolean algebra is "ultrafilter". Ultrafilters can alternatively be described as 2-valued morphisms from to the two-element Boolean algebra. The statement "every filter in a Boolean algebra can be extended to an ultrafilter" is called the "ultrafilter lemma" and cannot be proven in Zermelo–Fraenkel set theory (ZF), if ZF is consistent. Within ZF, the ultrafilter lemma is strictly weaker than the axiom of choice.
The ultrafilter lemma has many equivalent formulations: "every Boolean algebra has an ultrafilter", "every ideal in a Boolean algebra can be extended to a prime ideal", etc. Representations. It can be shown that every "finite" Boolean algebra is isomorphic to the Boolean algebra of all subsets of a finite set. Therefore, the number of elements of every finite Boolean algebra is a power of two. Stone's celebrated "representation theorem for Boolean algebras" states that "every" Boolean algebra is isomorphic to the Boolean algebra of all clopen sets in some (compact totally disconnected Hausdorff) topological space. Axiomatics. The first axiomatization of Boolean lattices/algebras in general was given by the English philosopher and mathematician Alfred North Whitehead in 1898. It included the above axioms and additionally and . In 1904, the American mathematician Edward V. Huntington (1874–1952) gave probably the most parsimonious axiomatization based on , , , even proving the associativity laws (see box). He also proved that these axioms are independent of each other.
In 1933, Huntington set out the following elegant axiomatization for Boolean algebra. It requires just one binary operation and a unary functional symbol , to be read as 'complement', which satisfy the following laws: Herbert Robbins immediately asked: If the Huntington equation is replaced with its dual, to wit: do (1), (2), and (4) form a basis for Boolean algebra? Calling (1), (2), and (4) a "Robbins algebra", the question then becomes: Is every Robbins algebra a Boolean algebra? This question (which came to be known as the Robbins conjecture) remained open for decades, and became a favorite question of Alfred Tarski and his students. In 1996, William McCune at Argonne National Laboratory, building on earlier work by Larry Wos, Steve Winker, and Bob Veroff, answered Robbins's question in the affirmative: Every Robbins algebra is a Boolean algebra. Crucial to McCune's proof was the computer program EQP he designed. For a simplification of McCune's proof, see Dahn (1998). Further work has been done for reducing the number of axioms; see Minimal axioms for Boolean algebra.
Generalizations. Removing the requirement of existence of a unit from the axioms of Boolean algebra yields "generalized Boolean algebras". Formally, a distributive lattice is a generalized Boolean lattice, if it has a smallest element and for any elements and in such that , there exists an element such that and . Defining as the unique such that and , we say that the structure is a "generalized Boolean algebra", while is a "generalized Boolean semilattice". Generalized Boolean lattices are exactly the ideals of Boolean lattices. A structure that satisfies all axioms for Boolean algebras except the two distributivity axioms is called an orthocomplemented lattice. Orthocomplemented lattices arise naturally in quantum logic as lattices of closed linear subspaces for separable Hilbert spaces.
Bank of Italy The Bank of Italy (Italian: "Banca d'Italia", , informally referred to as "Bankitalia") is the Italian member of the Eurosystem and has been the monetary authority for Italy from 1893 to 1998, issuing the Italian lira. Since 2014, it has also been Italy's national competent authority within European Banking Supervision. It is located in Palazzo Koch, via Nazionale, Rome. History. The institution was established in 1893 from the combination of three major banks in Italy (after the Banca Romana scandal). The new central bank first issued banknotes during 1926. Until 1928, it was directed by a general manager, after this time instead by a governor elected by an internal commission of managers, with a decree from the President of the Italian Republic, for a term of seven years. In 1863 the crisis of the world money market created panic and the rush to the counters to collect the metallic currency in exchange for the banknotes. The Italian government responded in 1866 by introducing the fiat and legal tender of paper money. The government was accused in this way of favouring the issuing banks, and a long debate called the "banking question" arose about the advisability of having one or more issuers.
The Minghetti-Finali law of 1873 established the mandatory consortium of issuing institutions among the six existing issuing institutions, the National Bank of the Kingdom of Italy, Banca Nazionale Toscana, Banca Toscana di Credito, Banca Romana, Banco di Napoli, and Banco di Sicilia; but the measure proved insufficient. Following the Banca Romana scandal, the reorganization of the issuing institutions became necessary. Establishment. Law no. 449 of 10 August 1893 of the Giolitti I government established the Bank of Italy through the merger of four banks: the National Bank in the Kingdom of Italy (formerly Banca Nazionale in the Sardinian States), the Banca Nazionale Toscana, the Banca Toscana di Credito for the Industries and Commerce of Italy and with the liquidation management of Banca Romana. With a complex series of mergers between these banks, the current Bank of Italy was formed. Some families of bankers, historical partners: Bombrini, Bastogi, Balduino, were the supporters of the operation. The institute enjoyed (together with the Banks of Naples and Sicily) the issuing privilege, it also acted as a "bank of banks" through the rediscount of bills, but did not have supervisory powers over other banks. The bank remains a private limited company and was headed by a director.
From 1900 to 1928 Bonaldo Stringher was the director, who gave the Bank the role of manager of Italian monetary policy and lender of last resort, bringing it closer to a modern central bank. In particular, he understood that a central bank cannot aim at maximizing profit (which is achieved by printing as much paper money) but must instead aim at price stability. In 1907, the Bank of Italy coordinated the rescue of the Italian Banking Company, a major lender of FIAT, an operation that ended with the absorption of the bank in crisis into the Italian Discount Bank. In 1911 the central bank organized a consortium to rescue the steel companies (Acciaierie di Terni, Ilva and others) of which the Bank of Italy was directly creditor, financing the operation also through the issue of banknotes. In 1912 the credit institute for cooperation, with social purposes, was established, led by the Bank of Italy and also participated by public bodies, savings banks, Monte dei Paschi di Siena, the Cassa di Previdenza, and the Credit Institution for the Cooperatives of Milan. The institute in 1929 was transformed by its director Arturo Osio into the Banca Nazionale del Lavoro.
In 1913 the Subsidy Consortium was established, led by the Bank of Italy and also participated by the Banks of Naples and Sicily, some savings banks, Monte dei Paschi di Siena and by the San Paolo Bank of Turin. In 1922 the Consortium saved Ansaldo and took control of it, and in 1923 it did the same with Banco di Roma. In the same 1913 Francesco Saverio Nitti drew up a bill that entrusted the Bank of Italy with the supervision of other banks, but the private banks managed to avoid its approval. In 1914 the Bank of Italy assisted the Banco di Roma, which had to devalue its capital due to losses reported in the activities in the eastern Mediterranean. After the First World War, in 1921, it was always the Bank of Italy that led the consortium that managed the liquidation of the Italian Discount Bank and saved the Banco di Roma once again from crisis. The Banking Law of 1926. Even with these strong regulatory and intervention powers, the fascist state allowed the crisis of the banks that were headed by the National Credit, the Popular Party bank, to worsen.
In this way, fascism, which equally aimed at the political control of monetary issuance, intended to strike one of the electoral strengths and of the business system that orbited around the industrial policy of the Catholic world, supported by credit institutions. With R.D.L. 812 of 6 May 1926, the Bank of Italy obtained the exclusive right to issue the currency (the royal decree of 28 April 1910, no. 204 was thus repealed, which had confirmed the prerogative also to the Bank of Naples and the Bank of Sicily). The subsequent R.D.L. 6 November 1926 n. 1830 entrusted the Bank of Italy with the task of supervising savings banks. In 1928 the Bank was reorganized. The general manager was joined by a governor with greater powers. Meanwhile, in 1926 the Subsidy Consortium had been transformed into a Liquidation Institute, still under the control of the central bank. In 1933 it was absorbed by the new Institute for Industrial Reconstruction, autonomous from the Bank of Italy. While all the banks were in very bad conditions, the Banca Nazionale del Lavoro of the self-styled socialist Arturo Osio, in 1929 confiscated eleven Catholic banks, and in 1932 the Banca Agricola Italiana which had financed SNIA Viscosa di Gualino.
Banks and the economy of the 1930s. Italy in the 1930s had an agricultural economy, a small number of industrial families who relied on the subcontracting of local suppliers, formed by a myriad of small family-run businesses, not international and whose survival depended on large groups of industrialists, in turn, linked to commercial banks. The savings from agriculture flowed into the rural coffers, the popular banks and the cooperative credit which financed the life of the provincial crafts, small businesses and construction. The job of the banks was to match the customers' short-term investment horizon with the long-term investments of large groups (Rediscount). National banks turned to local banks that had large deposits of deposits for smaller, low-risk loans. The Cassa Depositi e Prestiti channelled postal savings in favour of local authorities, public institutions and infrastructures, which were a way of absorbing mass unemployment, through a vast program of public works. The ideological basis of the law was that savings are a matter of national interest and must be protected by the State, a principle also enshrined in the Republican Constitution and concretized in the first place in the law establishing the interbank guarantee fund and in the policy of public bailouts. The banking legislation of 1936-1938 established a banking supervisory agency, the (IDREC), chaired by the Bank of Italy's governor. The bank no longer had the right to give credit to individuals but only to other banks as a lender of last resort. public bailout policy. Finally, it had the power to require other banks to deposit a portion of the available funds with the same central bank; by varying the share, the Bank of Italy could operate credit tightening or enlargements.
The law established certain minimum capital and management requirements necessary to guarantee risk management, stability and operational continuity: minimum capital, minimum ratio between loans and deposits, credit limits, provisions for compulsory reserve. IRI and the war. After the "defenestration" of Bonaldo Stringher, Alberto Beneduce took over and was forced to retire in 1936 after a "heart attack" during a meeting at the Bank for International Settlements in Basel. They conceived the duty of the banks towards the public interest of the country, as the subject who had to collect savings to lend them to entrepreneurs, as a tool for development and growth. The process was to be led by a "circulation bank", which would increase the speed of circulation of money in the real economy. The Central Bank supported the fascist monetary policy of defending the stability of the Italian lira (known as the "Quota 90"), through the reduction of discounts and advances, and financing the enormous expenses of wars in the 1930s and 1940s through the unlimited issuing of money (and the "inflation tax", not progressive with income), as Hjalmar Schacht did in Germany under Hitler.
Operationally, the government issued and sold debt securities to finance military spending, and the military industry reinvested its government profits in the purchase of such bonds as a "de facto" advance on future orders, fueling a closed financial circuit. In simple terms, this was something like the ECB issuing money and lending it to private banks who keep it in their current accounts with the ECB. This mechanism was called "capital circuit". The printing of tickets and the scarcity of consumer goods created an overabundance of money that poured into bank deposits, allowing a new expansion of credit, which was directed in favour of the economic sectors themselves. given that the state paid the banks a higher interest on the BOTs than the savers. The absorption of savings into investments in fixed capital had already taken place in the First World War and industries were working with existing production capacities. Without consumption and investments, public spending by the state remained. The war could start with a modest tax levy and inflation within the normal limits in the first months, before the black market and ration cards.
The situation followed the conflict of interest between the state entrepreneur and the state bank, albeit in the name of a higher ideological purpose. In 1938, the government decreed the power to directly appoint presidents and vice-presidents of the board of directors of banks. Beneduce planned to have a public bank take over the long-term credit of large companies, financed with bonds of equal duration for public works, energy, and industry. After them, the Central Bank maintained a low-profile monetary policy, consistent with the directives of fascism. IRI operated differently, in agreement with the Italian banks and industries that supported fascism. The banks renounced exercising an option by "converting" the debts into shares (or a law in this regard), preferring not to enter directly into the ownership of the industrial groups. The groups transferred the bank debts to IRI, which became the new owner in exchange for shares (at the book value, not always the same as the market value), until they held control of the property and therefore of management.
The debt of the IRI rose to nine and a half billion lire at the time, two-thirds of which were paid within the war, because they were drastically diluted by inflation which has the effect of lowering the real weight of debts until the accounting entries are cancelled. of issuance, but also to halve the purchasing power of small savers. The remaining debt was paid by 1953. The IRI in turn had debts towards the Bank of Italy for five billion lire: the State issued bonds for IRI for one and a half billion, "sterilizing" the debt that should have been repaid with "annuity" interest. accrued until 1971. The change of constitutional order and currency (exchange rate for conversion), and inflation meant that IRI (and industries) paid the Bank of Italy less than a third of the sum. After the armistice of 8 September, the German authorities demanded the delivery of the gold reserve. 173 tons of gold were first transferred to the Milan office, and then to Fortezza. Traces of it were subsequently lost. In the 1960s, the public debt increased and so did inflation. Governor Guido Carli made a policy of credit crunch to stop inflation, particularly in 1964. In general, the Bank of Italy played an important political role under this governorship. Other credit crunches were implemented between 1969 and 1970 due to the flight of capital abroad and in 1974 as a result of the oil crisis.
In March 1979 the governor of the Bank of Italy, Paolo Baffi, and the deputy director in charge of supervision, Mario Sarcinelli, were accused by the Rome public prosecutor of private interest in official acts and personal aiding and abetting. Sarcinelli was arrested, and released from prison only after being suspended from duties relating to surveillance, while Baffi avoided prison due to his age. In 1981 the two will be completely acquitted. Subsequently, the suspicion will emerge that the indictment was wanted by P2 to prevent the Bank of Italy from supervising Roberto Cavali Banco Ambrosiano. The postwar period. The post-war inflation, also due to the Am-lire, was fought with the credit crunch desired by the governor Luigi Einaudi, which was obtained through the compulsory reserve on deposits. In particular, the instrument of compulsory reserves of banks at the central bank was used, introduced in 1926 but never really applied. In 1948 the governor was given the task of regulating the money supply and deciding the discount rate.
The universal banks were the ones that had gained the most from war and inflation (under the Authorization Regime of the Interministerial Credit Committee), with the greatest growth in deposits. Along with the recovery, speculative stocks and capital flight abroad appeared. Credit limits were no longer tied to equity, as equity figures were completely distorted by inflation. The squeeze on lending, the liquidity crisis and the Eenaudian deflation pushed operators to finance themselves by placing stocks on the market and returning capital, thus blocking the rise in prices; and by resorting to self-financing (even without distributing profits), aided by the fact that inflation had made it possible to quickly amortize fixed assets whose book value was now nominal. During the years of the Reconstruction, governor Donato Menichella governed the issue in a gradual and balanced way: he did not implement expansionary manoeuvres to encourage growth but was careful to avoid the creation of credit crunches. In this, he was helped by the low public debt. Its monetary policy program was stability for development.
A part of the available bank savings was channelled annually to the Treasury to cover the budget deficit (in the current year), while during his tenure the public debt of the state never rose above 1% of GDP, until 1964. In July 1981, a "divorce" between the State (Ministry of the Treasury) and its central bank was initiated by the decision of the then Treasury Minister Beniamino Andreatta. From that moment on, the institute was no longer required to purchase the bonds that the government was unable to place on the market, thus ceasing the monetization of the Italian public debt that it had carried out since the Second World War up to that moment. This decision was opposed by the Minister of Finance Rino Formica, who would have liked the Bank of Italy to be required to repay at least a portion of these securities, and from the summer of 1982 a series of intra-government verbal clashes between the two ministers known as the wives' quarrel, which was followed by the fall of the second Spadolini government a few months later.
The divorce between the Ministry of the Treasury and the Bank of Italy is still considered by economic doctrine as a factor of great stabilization of inflation (which went from over 20% in 1980 to less than 5% in the following years) and a central prerequisite for guarantee the full independence of the technical monetary policy body (central bank) from the choices related to fiscal policy (under the responsibility of the government), but also a factor of considerable incidence of growth of the Italian public debt. The law of 7 February 1992 n. 82, proposed by the then Minister of the Treasury Guido Carli, clarifies that the decision on the discount rate is the exclusive competence of the governor and must no longer be agreed in concert with the Minister of the Treasury (the previous decree of the President of the Republic is modified in relation to the new law with the Presidential Decree of 18 July). The euro and the 2006 reform. The Legislative Decree 10 March 1998 n. 43 removes the Bank of Italy from management by the Italian government, sanctioning its belonging to the European system of central banks. From this date, therefore, the quantity of currency in circulation is decided autonomously by the Central Bank. With the introduction of the Euro on 1 January 1999, the Bank thus loses the function of presiding over national monetary policy. This function has since been exercised collectively by the Governing Council of the European Central Bank, which also includes the Governor of the Bank of Italy.
On 13 June 1999 the Senate of the Republic, during the XIII Legislature, discussed bill no. 4083 "Rules on the ownership of the Bank of Italy and on the criteria for appointing the Board of Governors of the Bank of Italy". This bill would like the state to acquire all the shares of the institute, but it is never approved. On 4 January 2004, the weekly "Famiglia Cristiana" reports, for the first time in history, the list of participants in the capital of the Bank of Italy with the relative shares. The source is a Mediobanca Research & Studies dossier, directed by the researcher Fulvio Coltorti, who, by investigating backwards on the balance sheets of banks, insurance companies and institutions, and gradually noting the shares that indicated a shareholding in the capital of the Bank of Italia managed to reconstruct a large part of the list of participants of the highest Italian financial institution. On 20 September 2005, the list of shareholders was officially made available by the Bank of Italy; until now it was considered confidential. On 19 December 2005, after intense press campaigns and criticism of his actions in the context of the Bancopoli scandal, Governor Antonio Fazio resigned. A few days later, Mario Draghi, who took office on 16 January 2006, was appointed in his place.
The law of 28 December 2005, n. 262, as part of various measures to protect savings, introduces for the first time a term to the mandate of the governor and the members of the directorate. It also dealt with (article 19, paragraph 10) the issue of ownership of the capital of the Bank of Italy, providing for the redefinition of the Bank's shareholding structure by means of a government regulation to be issued within three years of the law's entry into force. This regulation should have governed the methods of transferring shares held by "subjects other than the State or other public bodies". The delegation made by law 262/2005, therefore, expired without the regulation being issued, but the right to ownership of the shares of the current participants is in any case safeguarded by a provision of the Bank's Statute. On the basis of law 262/2005, Mario Draghi becomes the first governor to have a term of six years, renewable once for a further six years. Missions and organization. Missions. After the charge of monetary and exchange rate policies was shifted in 1998 to the European Central Bank, within the European institutional framework, the bank implements the decisions, issues euro banknotes and withdraws and destroys worn pieces.
The main function has thus become banking and financial supervision. The objective is to ensure the stability and efficiency of the system and compliance with rules and regulations; the bank pursues it through secondary legislation, controls and cooperation with governmental authorities. Following a reform in 2005, which was prompted by takeover scandals, the bank has lost exclusive antitrust authority in the credit sector, which is now shared with the Italian Competition Authority (). Other functions include market supervision, oversight of the payment system and provision of settlement services, State treasury service, Central Credit Register, economic analysis and institutional consultancy. As of 2021, the Bank of Italy owned 2,451.8 tonnes of gold, the third-largest gold reserve in the world. Governing bodies. The bank's governing bodies are the General Meeting of Shareholders, the board of directors, the governor, the director general and three deputy directors-general; the last five constitute the directorate.
The general meeting takes place yearly and with the purpose of approving accounts and appointing the auditors. The board of directors has administrative powers and is chaired by the governor (or by the director-general in his absence). Following a reform in 2005, the governor lost exclusive responsibility regarding decisions of external relevance (i.e. banking and financial supervision), which has been transferred to the directorate (by majority vote). The director-general is responsible for the day-to-day administration of the bank and acts as governor when absent. The board of auditors assesses the bank's administration and compliance with the law, regulations and statute. Appointment. The directorate's term of office lasts six years and is renewable once. The appointment of the governor is the responsibility of the government, head of the board of directors, with the approval of the president (formally a decree of the president). The board of directors is elected by the shareholders according to the bank statute.
On 25 October 2011, Silvio Berlusconi nominated Ignazio Visco to be the bank's new governor to replace Mario Draghi when he left to become president of the European Central Bank in November. Currency and coinage. Italy has a long history of different coinage types, which spans thousands of years. Since Italy has been for centuries divided into many historic states, they all had different coinage systems, but when the country became unified in 1861, the Italian lira came into place, and was used until 2002. The term originates from "libra", the largest unit of the Carolingian monetary system used in Western Europe and elsewhere from the 8th to the 20th century. Italian lira was introduced by the Napoleonic Kingdom of Italy in 1807 at par with the French franc, and was subsequently adopted by the different states that would eventually form the Kingdom of Italy in 1861. It was subdivided into 100 "centesimi" (singular: "centesimo"), which means "hundredths" or "cents". The lira was also the currency of the Albanian Kingdom from 1941 to 1943.
There was no standard sign or abbreviation for the Italian lira. The abbreviations "Lit." (standing for "Lira italiana") and L. (standing for "Lira") and the signs ₤ or £ were all accepted representations of the currency. Banks and financial institutions, including the Bank of Italy, often used "Lit." and this was regarded internationally as the abbreviation for the Italian lira. Handwritten documents and signs at market stalls would often use "£" or "₤", while coins used "L." Italian postage stamps mostly used the word in full but some (such as the 1975 monuments series) used "L." The name of the currency could also be written in full as a prefix or a suffix (e.g. Lire 100,000 or 100,000 lire). The ISO 4217 currency code for the lira was "ITL". The Italian lira was the official unit of currency in Italy until 1 January 1999, when it was replaced by the euro (euro coins and notes were not introduced until 2002). Old lira denominated currency ceased to be legal tender on 28 February 2002. The conversion rate is 1,936.27 lire to the euro.
All lira banknotes in use immediately before the introduction of the euro, as all post WW2 coins, were still exchangeable for euros in all branches of the Bank of Italy until 29 February 2012. Shareholders. Banca d'Italia had 300,000 shares with a nominal value of €25,000. Originally scattered around the banks of Italy, the shares now accumulated due to the merger of the banks since the 1990s and also a number of pension and social security institutions. The status of the bank states that a minimum of 54% of profits would go to the Italian government, and only a maximum of 6% of profits would be distributed as dividends according to share ratios. Even so, the Bank of Italy stands out among central banks in the Eurosystem as having no state ownership (the National Bank of Belgium and Bank of Greece have mixed ownership). As of early 2024, the 15 largest shareholders represented slightly over half of the bank's equity, namely UniCredit (5.0 percent), (4.9 percent), (4.9 percent), (4.9 percent), Intesa Sanpaolo (4.9 percent), (3.7 percent), BPER Banca (3.3 percent), ICCREA Banca (3.1 percent), Generali Italia (3.0 percent), the National Institute for Social Security (3.0 percent), Istituto nazionale per l'assicurazione contro gli infortuni sul lavoro (3.0 percent), (3.0 percent), Cassa di Risparmio di Asti (3.0 percent), Banca Nazionale del Lavoro (2.8 percent), and Crédit Agricole Italia (2.8 percent). The remaining 49 percent were dispersed among 157 shareholders, mainly banks and banking foundations.
Beachcomber (pen name) Beachcomber is a "nom de plume" that has been used by several journalists writing a long-running humorous column in the "Daily Express". It was originated in 1917 by Major John Bernard Arbuthnot MVO as his signature on the column, titled 'By the Way'. The name Beachcomber was then passed to D. B. Wyndham Lewis in 1919 and, in turn, to J. B. Morton, who wrote the column till 1975. It was later revived by William Hartston, current author of the column. "By the Way" column. "By the Way" was originally a column in "The Globe", consisting of unsigned humorous pieces; P. G. Wodehouse was assistant editor of the column from August 1903 and editor from August 1904 to May 1909, during which time he was assisted by Herbert Westbrook. After the "Globe"'s closure, it was re-established as a society news column in the "Daily Express" from 1917, initially written by social correspondent Major John Arbuthnot, who invented the name "Beachcomber". After Arbuthnot was promoted to deputy editor, it was taken over sometime in 1919 by Wyndham-Lewis, who reinvented it as an outlet for his wit and humour. It was then passed to Morton during 1924, though it is likely there was a period when they overlapped. Morton wrote the column until 1975; it was revived in January 1996 and continues today, written by William Hartston. The column is unsigned except by "Beachcomber" and it was not publicly known that Morton or Wyndham-Lewis wrote it until the 1930s. The name is mainly associated with Morton, who has been credited as an influence by Spike Milligan amongst others. Morton introduced the recurring characters and serial stories that were a major feature of the column during his 51-year run.
The format of the column was a random assortment of small paragraphs which were otherwise unconnected. These could be anything, such as: Morton's other interest, France, was occasionally represented by epic tales of his rambling walks through the French countryside. These were not intended as humour. "By the Way" was popular with the readership, and of course, this is one of the reasons it lasted so long. Its style and randomness could be off-putting and it is safe to say the humour could be something of an acquired taste. Oddly, one of the column's greatest opponents was the "Express" newspaper's owner, Lord Beaverbrook, who had to keep being assured the column was indeed funny. A prominent critic was George Orwell, who frequently referred to him in his essays and diaries as "A Catholic Apologist" and accused him of being "silly-clever", in line with his criticisms of G. K. Chesterton, Hilaire Belloc, Ronald Knox and Wyndham-Lewis. "By the Way" was one of the few features kept continuously running in the often seriously reduced "Daily Express" throughout World War II, when Morton's lampooning of Hitler, including the British invention of bracerot to make the Nazis' trousers fall down at inopportune moments, was regarded as valuable for morale. The column appeared daily until 1965 when it was changed to weekly. It was cancelled in 1975 and revived as a daily piece in January 1996. It continues to the present day in much the same format but is now entitled "Beachcomber", not "By the Way".
Other media. The Will Hay film "Boys Will Be Boys" (1935) was set at Morton's Narkover school. According to Spike Milligan, the columns were an influence on the comedic style of his radio series, "The Goon Show". In 1969, Milligan based a BBC television series named "The World of Beachcomber" on the columns. A small selection was issued on a 1971 LP and a 2-cassette set of the series' soundtrack was made available in the late 1990s. In 1989, BBC Radio 4 broadcast the first of three series based on Morton's work. This featured Richard Ingrams as Beachcomber, John Wells as Prodnose, Patricia Routledge and John Sessions. The compilations prepared by Mike Barfield. Series 1 was also made available as a 2-cassette set.
Bill Joy William Nelson Joy (born November 8, 1954) is an American computer engineer and venture capitalist. He co-founded Sun Microsystems in 1982 along with Scott McNealy, Vinod Khosla, and Andy Bechtolsheim, and served as Chief Scientist and CTO at the company until 2003. He played an integral role in the early development of BSD UNIX while being a graduate student at Berkeley, and he is the original author of the vi text editor. He also wrote the 2000 essay "Why The Future Doesn't Need Us", in which he expressed deep concerns over the development of modern technologies. Joy was elected a member of the National Academy of Engineering (1999) for contributions to operating systems and networking software. Early career. Joy was born in the Detroit suburb of Farmington Hills, Michigan, to William Joy, a school vice-principal and counselor, and Ruth Joy. He earned a Bachelor of Science in electrical engineering from the University of Michigan and a Master of Science in electrical engineering and computer science from the University of California, Berkeley, in 1979.
While a graduate student at Berkeley, he worked for Fabry's Computer Systems Research Group (CSRG) on the Berkeley Software Distribution (BSD) version of the Unix operating system. He initially worked on a Pascal compiler left at Berkeley by Ken Thompson, who had been visiting the university when Joy had just started his graduate work. He later moved on to improving the Unix kernel, and also handled BSD distributions. Some of his most notable contributions were the ex and vi editors and the C shell. Joy's prowess as a computer programmer is legendary, with an oft-told anecdote that he wrote the vi editor in a weekend. Joy denies this assertion. A few of his other accomplishments have also been sometimes exaggerated; Eric Schmidt, CEO of Novell at the time, inaccurately reported during an interview in PBS's documentary "Nerds 2.0.1" that Joy had personally rewritten the BSD kernel in a weekend. In 1980, he also wrote codice_1, about which Rob Pike and Brian W. Kernighan wrote that it went against Unix philosophy.
According to a "Salon" article, during the early 1980s, DARPA had contracted the company Bolt, Beranek and Newman (BBN) to add TCP/IP to Berkeley UNIX. Joy had been instructed to plug BBN's stack into Berkeley Unix, but he refused to do so, as he had a low opinion of BBN's TCP/IP. So, Joy wrote his own high-performance TCP/IP stack. According to John Gage: Rob Gurwitz, who was working at BBN at the time, disputes this version of events. Sun Microsystems. In 1982, after the firm had been going for six months, Joy, Sun's sixteenth employee, was brought in with full co-founder status at Sun Microsystems. At Sun, Joy was an inspiration for the development of NFS, the SPARC microprocessors, the Java programming language, Jini/JavaSpaces, and JXTA. In 1986, Joy was awarded a Grace Murray Hopper Award by the ACM for his work on the Berkeley UNIX Operating System. On September 9, 2003, Sun announced Joy was leaving the company and that he "is taking time to consider his next move and has no definite plans". Post-Sun activities.
In 1999, Joy co-founded a venture capital firm, HighBAR Ventures, with two Sun colleagues, Andy Bechtolsheim and Roy Thiele-Sardiña. In January 2005 he was named a partner in venture capital firm Kleiner Perkins. There, Joy has made several investments in green energy industries, even though he does not have any credentials in the field. He once said, "My method is to look at something that seems like a good idea and assume it's true". In 2011, he was inducted as a Fellow of the Computer History Museum for his work on the Berkeley Software Distribution (BSD) Unix system and the co-founding of Sun Microsystems. Technology concerns. In 2000, Joy gained notoriety with the publication of his article in "Wired" magazine, "Why The Future Doesn't Need Us", in which he declared, in what some have described as a "neo-Luddite" position, that he was convinced that growing advances in genetic engineering and nanotechnology would bring risks to humanity. He argued that intelligent robots would replace humanity, at the very least in intellectual and social dominance, in the relatively near future. He supports and promotes the idea of abandonment of GNR (genetics, nanotechnology, and robotics) technologies, instead of going into an arms race between negative uses of the technology and defense against those negative uses (good nano-machines patrolling and defending against Grey goo "bad" nano-machines). This stance of broad relinquishment was criticized by technologists such as technological-singularity thinker Ray Kurzweil, who instead advocates fine-grained relinquishment and ethical guidelines. Joy was also criticized by "The American Spectator", which characterized Joy's essay as a (possibly unwitting) rationale for statism.
A bar-room discussion of these technologies with Ray Kurzweil started to set Joy's thinking along this path. He states in his essay that during the conversation, he became surprised that other serious scientists were considering such possibilities likely, and even more astounded at what he felt was a lack of consideration of the contingencies. After bringing the subject up with a few more acquaintances, he states that he was further alarmed by what he felt was that although many people considered these futures possible or probable, that very few of them shared as serious a concern for the dangers as he seemed to. This concern led to his in-depth examination of the issue and the positions of others in the scientific community on it, and eventually, to his current activities regarding it. Despite this, he is a venture capitalist, investing in technology companies. He has also raised a specialty venture fund to address the dangers of pandemic diseases, such as the H5N1 avian influenza and biological weapons. Joy's law.
Of management. In his 2013 book "Makers", author Chris Anderson credited Joy with establishing "Joy's law" based on a quip: "No matter who you are, most of the smartest people work for someone else [other than you]." His argument was that companies use an inefficient process by not hiring the best employees, only those they are able to hire. His "law" was a continuation of Friedrich Hayek's "The Use of Knowledge in Society" and warned that the competition outside of a company would always have the potential to be greater than the company itself. Of computing. Joy devised a formula in 1983, also called "Joy's law", stating that the peak computer speed doubles each year and thus is given by a simple function of time. Specifically, in which is the peak computer speed attained during year , expressed in MIPS.
Bandwidth (signal processing) Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in unit of hertz (symbol Hz). It may refer more specifically to two subcategories: "Passband bandwidth" is the difference between the upper and lower cutoff frequencies of, for example, a band-pass filter, a communication channel, or a signal spectrum. "Baseband bandwidth" is equal to the upper cutoff frequency of a low-pass filter or baseband signal, which includes a zero frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, digital communications, radio communications, signal processing, and spectroscopy and is one of the determinants of the capacity of a given communication channel. A key characteristic of bandwidth is that any band of a given width can carry the same amount of information, regardless of where that band is located in the frequency spectrum. For example, a 3 kHz band can carry a telephone conversation whether that band is at baseband (as in a POTS telephone line) or modulated to some higher frequency. However, wide bandwidths are easier to obtain and process at higher frequencies because the is smaller.
Overview. Bandwidth is a key concept in many telecommunications applications. In radio communications, for example, bandwidth is the frequency range occupied by a modulated carrier signal. An FM radio receiver's tuner spans a limited range of frequencies. A government agency (such as the Federal Communications Commission in the United States) may apportion the regionally available bandwidth to broadcast license holders so that their signals do not mutually interfere. In this context, bandwidth is also known as channel spacing. For other applications, there are other definitions. One definition of bandwidth, for a system, could be the range of frequencies over which the system produces a specified level of performance. A less strict and more practically useful definition will refer to the frequencies beyond which performance is degraded. In the case of frequency response, degradation could, for example, mean more than 3 dB below the maximum value or it could mean below a certain absolute value. As with any definition of the "width" of a function, many definitions are suitable for different purposes.
In the context of, for example, the sampling theorem and Nyquist sampling rate, bandwidth typically refers to baseband bandwidth. In the context of Nyquist symbol rate or Shannon-Hartley channel capacity for communication systems it refers to passband bandwidth. The of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a Rayleigh bandwidth of one megahertz. The is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal. "x" dB bandwidth. In some contexts, the signal bandwidth in hertz refers to the frequency range in which the signal's spectral density (in W/Hz or V2/Hz) is nonzero or above a small threshold value. The threshold value is often defined relative to the maximum value, and is most commonly the , that is the point where the spectral density is half its maximum value (or the spectral amplitude, in formula_1 or formula_2, is 70.7% of its maximum). This figure, with a lower threshold value, can be used in calculations of the lowest sampling rate that will satisfy the sampling theorem.
The bandwidth is also used to denote system bandwidth, for example in filter or communication channel systems. To say that a system has a certain bandwidth means that the system can process signals with that range of frequencies, or that the system reduces the bandwidth of a white noise input to that bandwidth. The 3 dB bandwidth of an electronic filter or communication channel is the part of the system's frequency response that lies within 3 dB of the response at its peak, which, in the passband filter case, is typically at or near its center frequency, and in the low-pass filter is at or near its cutoff frequency. If the maximum gain is 0 dB, the 3 dB bandwidth is the frequency range where attenuation is less than 3 dB. 3 dB attenuation is also where power is half its maximum. This same "half-power gain" convention is also used in spectral width, and more generally for the extent of functions as full width at half maximum (FWHM). In electronic filter design, a filter specification may require that within the filter passband, the gain is nominally 0 dB with a small variation, for example within the ±1 dB interval. In the stopband(s), the required attenuation in decibels is above a certain level, for example >100 dB. In a transition band the gain is not specified. In this case, the filter bandwidth corresponds to the passband width, which in this example is the 1 dB-bandwidth. If the filter shows amplitude ripple within the passband, the "x" dB point refers to the point where the gain is "x" dB below the nominal passband gain rather than "x" dB below the maximum gain.
In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak. In communication systems, in calculations of the Shannon–Hartley channel capacity, bandwidth refers to the 3 dB-bandwidth. In calculations of the maximum symbol rate, the Nyquist sampling rate, and maximum bit rate according to the Hartley's law, the bandwidth refers to the frequency range within which the gain is non-zero. The fact that in equivalent baseband models of communication systems, the signal spectrum consists of both negative and positive frequencies, can lead to confusion about bandwidth since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as formula_3, where formula_4 is the total bandwidth (i.e. the maximum passband bandwidth of the carrier-modulated RF signal and the minimum passband bandwidth of the physical passband channel), and formula_5 is the positive bandwidth (the baseband bandwidth of the equivalent channel model). For instance, the baseband model of the signal would require a low-pass filter with cutoff frequency of at least formula_5 to stay intact, and the physical passband channel would require a passband filter of at least formula_4 to stay intact.
Relative bandwidth. The absolute bandwidth is not always the most appropriate or useful measure of bandwidth. For instance, in the field of antennas the difficulty of constructing an antenna to meet a specified absolute bandwidth is easier at a higher frequency than at a lower frequency. For this reason, bandwidth is often quoted relative to the frequency of operation which gives a better indication of the structure and sophistication needed for the circuit or device under consideration. There are two different measures of relative bandwidth in common use: "fractional bandwidth" (formula_8) and "ratio bandwidth" (formula_9). In the following, the absolute bandwidth is defined as follows, formula_10 where formula_11 and formula_12 are the upper and lower frequency limits respectively of the band in question. Fractional bandwidth. Fractional bandwidth is defined as the absolute bandwidth divided by the center frequency (formula_13), formula_14 The center frequency is usually defined as the arithmetic mean of the upper and lower frequencies so that,
formula_15 and formula_16 However, the center frequency is sometimes defined as the geometric mean of the upper and lower frequencies, formula_17 and formula_18 While the geometric mean is more rarely used than the arithmetic mean (and the latter can be assumed if not stated explicitly) the former is considered more mathematically rigorous. It more properly reflects the logarithmic relationship of fractional bandwidth with increasing frequency. For narrowband applications, there is only marginal difference between the two definitions. The geometric mean version is inconsequentially larger. For wideband applications they diverge substantially with the arithmetic mean version approaching 2 in the limit and the geometric mean version approaching infinity. Fractional bandwidth is sometimes expressed as a percentage of the center frequency (percent bandwidth, formula_19), formula_20 Ratio bandwidth. Ratio bandwidth is defined as the ratio of the upper and lower limits of the band, formula_21 Ratio bandwidth may be notated as formula_22. The relationship between ratio bandwidth and fractional bandwidth is given by,
formula_23 and formula_24 Percent bandwidth is a less meaningful measure in wideband applications. A percent bandwidth of 100% corresponds to a ratio bandwidth of 3:1. All higher ratios up to infinity are compressed into the range 100–200%. Ratio bandwidth is often expressed in octaves (i.e., as a frequency level) for wideband applications. An octave is a frequency ratio of 2:1 leading to this expression for the number of octaves, formula_25 Noise equivalent bandwidth. The noise equivalent bandwidth (or equivalent noise bandwidth (enbw)) of a system of frequency response formula_26 is the bandwidth of an ideal filter with rectangular frequency response centered on the system's central frequency that produces the same average power outgoing formula_26 when both systems are excited with a white noise source. The value of the noise equivalent bandwidth depends on the ideal filter reference gain used. Typically, this gain equals formula_28 at its center frequency, but it can also equal the peak value of formula_28.
The noise equivalent bandwidth formula_30 can be calculated in the frequency domain using formula_26 or in the time domain by exploiting the Parseval's theorem with the system impulse response formula_32. If formula_26 is a lowpass system with zero central frequency and the filter reference gain is referred to this frequency, then: formula_34 The same expression can be applied to bandpass systems by substituting the equivalent baseband frequency response for formula_26. The noise equivalent bandwidth is widely used to simplify the analysis of telecommunication systems in the presence of noise. Photonics. In photonics, the term "bandwidth" carries a variety of meanings: A related concept is the spectral linewidth of the radiation emitted by excited atoms.
Bodhisattva In Buddhism, a bodhisattva ( ; ; ) or bodhisatva is a person who is on the path towards bodhi ('awakening') or Buddhahood. In the Early Buddhist schools, as well as modern Theravāda Buddhism, bodhisattva (or bodhisatta) refers to someone who has made a resolution to become a Buddha and has also received a confirmation or prediction from a living Buddha that this will come to pass. In Mahāyāna Buddhism, a bodhisattva refers to anyone who has generated "bodhicitta", a spontaneous wish and compassionate mind to attain Buddhahood for the benefit of all sentient beings. Mahayana bodhisattvas are spiritually heroic persons that work to attain awakening and are driven by a great compassion ("mahākaruṇā"). These beings are exemplified by important spiritual qualities such as the "four divine abodes" ("brahmavihāras") of loving-kindness ("maitrī"), compassion ("karuṇā"), empathetic joy ("muditā") and equanimity ("upekṣā"), as well as the various bodhisattva "perfections" ("pāramitās") which include "prajñāpāramitā" ("transcendent knowledge" or "perfection of wisdom") and skillful means ("upāya").
In Theravāda Buddhism, the bodhisattva is mainly seen as an exceptional and rare individual. Only a few select individuals are ultimately able to become bodhisattvas, such as Maitreya. Mahāyāna Buddhism generally understands the bodhisattva path as being open to everyone, and Mahāyāna Buddhists encourage all individuals to become bodhisattvas. Spiritually advanced bodhisattvas such as Avalokiteshvara, Maitreya, and Manjushri are also widely venerated across the Mahāyāna Buddhist world and are believed to possess great magical power, which they employ to help all living beings. Early Buddhism. In pre-sectarian Buddhism, the term "bodhisatta" is used in the early texts to refer to Gautama Buddha in his previous lives and as a young man in his last life, when he was working towards liberation. In the early Buddhist discourses, the Buddha regularly uses the phrase "when I was an unawakened Bodhisatta" to describe his experiences before his attainment of awakening. The early texts which discuss the period before the Buddha's awakening mainly focus on his spiritual development. According to Bhikkhu Analayo, most of these passages focus on three main themes: "the bodhisattva's overcoming of unwholesome states of mind, his development of mental tranquillity, and the growth of his insight."
Other early sources like the "Acchariyabbhutadhamma-sutta" (MN 123, and its Chinese parallel in Madhyama-āgama 32) discuss the marvelous qualities of the bodhisattva Gautama in his previous life in Tuṣita heaven. The Pali text focuses on how the bodhisattva was endowed with mindfulness and clear comprehension while living in Tuṣita, while the Chinese source states that his lifespan, appearance, and glory was greater than all the devas (gods). These sources also discuss various miracles which accompanied the bodhisattva's conception and birth, most famously, his taking seven steps and proclaiming that this was his last life. The Chinese source (titled "Discourse on Marvellous Qualities") also states that while living as a monk under the Buddha Kāśyapa he "made his initial vow to [realize] Buddhahood [while] practicing the holy life." Another early source that discusses the qualities of bodhisattvas is the "Mahāpadāna sutta." This text discusses bodhisattva qualities in the context of six previous Buddhas who lived long ago, such as Buddha Vipaśyī. Yet another important element of the bodhisattva doctrine, the prediction of someone's future Buddhahood, is found in another Chinese early Buddhist text, the "Discourse on an Explanation about the Past" (MĀ 66). In this discourse, a monk named Maitreya aspires to become a Buddha in the future and the Buddha then predicts that Maitreya will become a Buddha in the future Other discourses found in the " Ekottarika-āgama" present the "bodhisattva Maitreya" as an example figure (EĀ 20.6 and EĀ 42.6) and one sutra in this collection also discuss how the Buddha taught the bodhisattva path of the six perfections to Maitreya (EĀ 27.5).
'Bodhisatta' may also connote a being who is "bound for enlightenment", in other words, a person whose aim is to become fully enlightened. In the Pāli canon, the Bodhisatta (bodhisattva) is also described as someone who is still subject to birth, illness, death, sorrow, defilement, and delusion. According to the Theravāda monk Bhikkhu Bodhi, while all the Buddhist traditions agree that to attain Buddhahood, one must "make a deliberate resolution" and fulfill the spiritual perfections (pāramīs or pāramitās) as a bodhisattva, the actual bodhisattva path is not taught in the earliest strata of Buddhist texts such as the Pali Nikayas (and their counterparts such as the Chinese Āgamas) which instead focus on the ideal of the arahant. The oldest known story about how Gautama Buddha becomes a bodhisattva is the story of his encounter with the previous Buddha, Dīpankara. During this encounter, a previous incarnation of Gautama, variously named Sumedha, Megha, or Sumati offers five blue lotuses and spreads out his hair or entire body for Dīpankara to walk on, resolving to one day become a Buddha. Dīpankara then confirms that they will attain Buddhahood. Early Buddhist authors saw this story as indicating that the making of a resolution ("abhinīhāra") in the presence of a living Buddha and his prediction/confirmation ("vyākaraṇa") of one's future Buddhahood was necessary to become a bodhisattva. According to Drewes, "all known models of the path to Buddhahood developed from this basic understanding."
Stories and teachings on the bodhisattva ideal are found in the various Jataka tale sources, which mainly focus on stories of the past lives of the Sakyamuni. Among the non-Mahayana Nikaya schools, the Jataka literature was likely the main genre that contained bodhisattva teachings. These stories had certainly become an important part of popular Buddhism by the time of the carving of the Bharhut Stupa railings (c. 125–100 BCE), which contain depictions of around thirty Jataka tales. Thus, it is possible that the bodhisattva ideal was popularized through the telling of Jatakas. Jataka tales contain numerous stories which focus on the past life deeds of Sakyamuni when he was a bodhisattva. These deeds generally express bodhisattva qualities and practices (such as compassion, the six perfections, and supernatural power) in dramatic ways, and include numerous acts of self-sacrifice. Apart from Jataka stories related to Sakyamuni, the idea that Metteya (Maitreya), who currently resides in Tuṣita, would become the future Buddha and that this had been predicted by the Buddha Sakyamuni was also an early doctrine related to the bodhisattva ideal. It first appears in the "Cakkavattisihanadasutta". According to A. L. Basham, it is also possible that some of the Ashokan edicts reveal knowledge of the bodhisattva ideal. Basham even argues that Ashoka may have considered himself a bodhisattva, as one edict states that he "set out for sambodhi."
Nikāya schools. By the time that the Buddhist tradition had developed into various competing sects, the idea of the bodhisattva vehicle (Sanskrit: "bodhisattvayana") as a distinct (and superior) path from that of the arhat and solitary buddha was widespread among all the major non-Mahayana Buddhist traditions or Nikaya schools, including Theravāda, Sarvāstivāda and Mahāsāṃghika. The doctrine is found, for example, in 2nd century CE sources like the "Avadānaśataka" and the "Divyāvadāna." The bodhisattvayana was referred by other names such as "vehicle of the perfections" ("pāramitāyāna"), "bodhisatva dharma", "bodhisatva training", and "vehicle of perfect Buddhahood". According to various sources, some of the Nikaya schools (such as the Dharmaguptaka and some of the Mahasamghika sects) transmitted a collection of texts on bodhisattvas alongside the Tripitaka, which they termed "Bodhisattva Piṭaka" or "Vaipulya (Extensive) Piṭaka". None of these have survived. Dar Hayal attributes the historical development of the bodhisattva ideal to "the growth of bhakti (devotion, faith, love) and the idealisation and spiritualisation of the Buddha."
The North Indian Sarvāstivāda school held it took Gautama three "incalculable aeons" ("asaṃkhyeyas") and ninety one aeons ("kalpas") to become a Buddha after his resolution ("praṇidhāna") in front of a past Buddha. During the first incalculable aeon he is said to have encountered and served 75,000 Buddhas, and 76,000 in the second, after which he received his first prediction ("vyākaraṇa") of future Buddhahood from Dīpankara, meaning that he could no longer fall back from the path to Buddhahood. For Sarvāstivāda, the first two incalculable aeons is a period of time in which a bodhisattva may still fall away and regress from the path. At the end of the second incalculable aeon, they encounter a buddha and receive their prediction, at which point they are certain to achieve Buddhahood. Thus, the presence of a living Buddha is also necessary for Sarvāstivāda. The "Mahāvibhāṣā" explains that its discussion of the bodhisattva path is partly meant "to stop those who are in fact not bodhisattvas from giving rise to the self-conceit that they are." However, for Sarvāstivāda, one is not technically a bodhisattva until the end of the third incalculable aeon, after which one begins to perform the actions which lead to the manifestation of the marks of a great person.
The "Mahāvastu" of the Mahāsāṃghika-Lokottaravādins presents various ideas regarding the school's conception of the bodhisattva ideal. According to this text, bodhisattva Gautama had already reached a level of dispassion at the time of Buddha Dīpaṃkara many aeons ago and he is also said to have attained the perfection of wisdom countless aeons ago. The "Mahāvastu" also presents four stages or courses ("caryās)" of the bodhisattva path without giving specific time frames (though it's said to take various incalculable aeons). This set of four phases of the path is also found in other sources, including the Gandhari “"Many-Buddhas Sūtra"” (*"Bahubudha gasutra") and the Chinese "Fó běnxíng jí jīng" (佛本行 集經, Taisho vol. 3, no. 190, pp. 669a1–672a11). The four "caryās" (Gandhari: "caria") are the following: Theravāda. The bodhisattva ideal is also found in southern Buddhist sources, like the Theravāda school's "Buddhavaṃsa" (1st-2nd century BCE), which explains how Gautama, after making a resolution ("abhinīhāra") and receiving his prediction ("vyākaraṇa") of future Buddhahood from past Buddha Dīpaṃkara, he became certain ("dhuva") to attain Buddhahood. Gautama then took four incalculable aeons and a hundred thousand, shorter "kalpas" (aeons) to reach Buddhahood. Several sources in the Pali Canon depict the idea that there are multiple Buddhas and that there will be many future Buddhas, all of which must train as bodhisattas. Non-canonical Theravada Jataka literature also teaches about bodhisattvas and the bodhisattva path. The worship of bodhisattvas like Metteya, Saman and Natha (Avalokiteśvara) can also be found in Theravada Buddhism.
By the time of the great scholar Buddhaghosa (5th-century CE), orthodox Theravāda held the standard Indian Buddhist view that there were three main spiritual paths within Buddhism: the way of the Buddhas ("buddhayāna") i.e. the bodhisatta path; the way of the individual Buddhas ("paccekabuddhayāna"); and the way of the disciples ("sāvakayāna"). The Sri Lankan commentator Dhammapāla (6th century CE) wrote a commentary on the "Cariyāpiṭaka", a text which focuses on the bodhisattva path and on the ten perfections of a bodhisatta. Dhammapāla's commentary notes that to become a bodhisattva one must make a valid resolution in front of a living Buddha. The Buddha then must provide a prediction ("vyākaraṇa") which confirms that one is irreversible ("anivattana") from the attainment of Buddhahood. The "Nidānakathā", as well as the "Buddhavaṃsa" and "Cariyāpiṭaka" commentaries makes this explicit by stating that one cannot use a substitute (such as a Bodhi tree, Buddha statue or Stupa) for the presence of a living Buddha, since only a Buddha has the knowledge for making a reliable prediction. This is the generally accepted view maintained in orthodox Theravada today.
According to Theravāda commentators like Dhammapāla as well as the "Suttanipāta" commentary, there are three types of bodhisattvas: According to modern Theravada authors, meeting a Buddha is needed to truly make someone a bodhisattva because any other resolution to attain Buddhahood may easily be forgotten or abandoned during the aeons ahead. The Burmese monk Ledi Sayadaw (1846–1923) explains that though it is easy to make vows for future Buddhahood by oneself, it is very difficult to maintain the necessary conduct and views during periods when the Dharma has disappeared from the world. One will easily fall back during such periods and this is why one is not truly a full bodhisattva until one receives recognition from a living Buddha. Because of this, it was and remains a common practice in Theravada to attempt to establish the necessary conditions to meet the future Buddha Maitreya and thus receive a prediction from him. Medieval Theravada literature and inscriptions report the aspirations of monks, kings and ministers to meet Maitreya for this purpose. Modern figures such as Anagarika Dharmapala (1864–1933), and U Nu (1907–1995) both sought to receive a prediction from a Buddha in the future and believed meritorious actions done for the good of Buddhism would help in their endeavor to become bodhisattvas in the future.
Over time the term came to be applied to other figures besides Gautama Buddha in Theravada lands, possibly due to the influence of Mahayana. The Theravada Abhayagiri tradition of Sri Lanka practiced Mahayana Buddhism and was very influential until the 12th century. Kings of Sri Lanka were often described as bodhisattvas, starting at least as early as Sirisanghabodhi (r. 247–249), who was renowned for his compassion, took vows for the welfare of the citizens, and was regarded as a mahāsatta (Sanskrit: "mahāsattva"), an epithet used almost exclusively in Mahayana Buddhism. Many other Sri Lankan kings from the 3rd until the 15th century were also described as bodhisattas and their royal duties were sometimes clearly associated with the practice of the ten pāramitās. In some cases, they explicitly claimed to have received predictions of Buddhahood in past lives. Popular Buddhist figures have also been seen as bodhisattvas in Theravada Buddhist lands. Shanta Ratnayaka notes that Anagarika Dharmapala, Asarapasarana Saranarikara Sangharaja, and Hikkaduwe Sri Sumamgala "are often called bodhisattvas". Buddhaghosa was also traditionally considered to be a reincarnation of Maitreya. Paul Williams writes that some modern Theravada meditation masters in Thailand are popularly regarded as bodhisattvas. Various modern figures of esoteric Theravada traditions (such as the weizzās of Burma) have also claimed to be bodhisattvas.
Theravada bhikkhu and scholar Walpola Rahula writes that the bodhisattva ideal has traditionally been held to be higher than the state of a "śrāvaka" not only in Mahayana but also in Theravada. Rahula writes "the fact is that both the Theravada and the Mahayana unanimously accept the Bodhisattva ideal as the highest...Although the Theravada holds that anybody can be a Bodhisattva, it does not stipulate or insist that all must be Bodhisattva which is considered not practical." He also quotes the 10th century king of Sri Lanka, Mahinda IV (956–972 CE), who had the words inscribed "none but the bodhisattvas will become kings of a prosperous Lanka," among other examples. Jeffrey Samuels echoes this perspective, noting that while in Mahayana Buddhism the bodhisattva path is held to be universal and for everyone, in Theravada it is "reserved for and appropriated by certain exceptional people." Mahāyāna. Early Mahāyāna. Mahāyāna Buddhism (often also called "Bodhisattvayāna", "Bodhisattva Vehicle") is based principally upon the path of a bodhisattva. This path was seen as higher and nobler than becoming an arhat or a solitary Buddha. Hayal notes that Sanskrit sources generally depict the bodhisattva path as reaching a higher goal (i.e. "anuttara-samyak-sambodhi") than the goal of the path of the "disciples" (śrāvakas), which is the nirvana attained by arhats. For example, the "Lotus Sutra" states:
To the sravakas, he preached the doctrine which is associated with the four Noble Truths and leads to Dependent Origination. It aims at transcending birth, old age, disease, death, sorrow, lamentation, pain, distress of mind and weariness; and it ends in nirvana. But, to the great being, the bodhisattva, he preached the doctrine, which is associated with the six perfections and which ends in the Knowledge of the Omniscient One after the attainment of the supreme and perfect bodhi. According to Peter Skilling, the Mahayana movement began when "at an uncertain point, let us say in the first century BCE, groups of monks, nuns, and lay-followers began to devote themselves exclusively to the Bodhisatva vehicle." These Mahayanists universalized the bodhisattvayana as a path which was open to everyone and which was taught for all beings to follow. This was in contrast to the Nikaya schools, which held that the bodhisattva path was only for a rare set of individuals. Indian Mahayanists preserved and promoted a set of texts called Vaipulya ("Extensive") sutras (later called Mahayana sutras).
Mahayana sources like the "Lotus Sutra" also claim that arhats that have reached nirvana have not truly finished their spiritual quest, for they still have not attained the superior goal of sambodhi (Buddhahood) and thus must continue to strive until they reach this goal. The "", one of the earliest known Mahayana texts, contains a simple and brief definition for the term "bodhisattva", which is also the earliest known Mahāyāna definition. This definition is given as the following: "Because he has bodhi as his aim, a bodhisattva-mahāsattva is so called." Mahayana sutras also depict the bodhisattva as a being which, because they want to reach Buddhahood for the sake of all beings, is more loving and compassionate than the sravaka (who only wishes to end their own suffering). Thus, another major difference between the bodhisattva and the arhat is that the bodhisattva practices the path for the good of others ("par-ārtha"), due to their bodhicitta, while the sravakas do so for their own good ("sv-ārtha") and thus, do not have bodhicitta (which is compassionately focused on others).
Mahayana bodhisattvas were not just abstract models for Buddhist practice, but also developed as distinct figures which were venerated by Indian Buddhists. These included figures like Manjushri and Avalokiteshvara, which are personifications of the basic virtues of wisdom and compassion respectively and are the two most important bodhisattvas in Mahayana. The development of bodhisattva devotion parallels the development of the Hindu bhakti movement. Indeed, Dayal sees the development of Indian bodhisattva cults as a Buddhist reaction to the growth of bhakti centered religion in India which helped to popularize and reinvigorate Indian Buddhism. Some Mahayana sutras promoted another revolutionary doctrinal turn, claiming that the three vehicles of the "Śrāvakayāna, Pratyekabuddhayāna" and the "Bodhisattvayāna" were really just one vehicle ("ekayana"). This is most famously promoted in the "Lotus Sūtra" which claims that the very idea of three separate vehicles is just an "upaya", a skillful device invented by the Buddha to get beings of various abilities on the path. But ultimately, it will be revealed to them that there is only one vehicle, the "ekayana", which ends in Buddhahood.
Mature scholastic Mahāyāna. Classical Indian mahayanists held that the only sutras which teach the bodhisattva vehicle are the Mahayana sutras. Thus, Nagarjuna writes "the subjects based on the deeds of Bodhisattvas were not mentioned in [non-Mahāyāna] sūtras." They also held that the bodhisattva path was superior to the śrāvaka vehicle and so the bodhisattva vehicle is the "great vehicle" (mahayana) due to its greater aspiration to save others, while the śrāvaka vehicle is the "small" or "inferior" vehicle (hinayana). Thus, Asanga argues in his "Mahāyānasūtrālaṃkāra" that the two vehicles differ in numerous ways, such as intention, teaching, employment (i.e., means), support, and the time that it takes to reach the goal. Over time, Mahayana Buddhists developed mature systematized doctrines about the bodhisattva. The authors of the various Madhyamaka treatises often presented the view of the "ekayana", and thus held that all beings can become bodhisattvas. The texts and sutras associated with the Yogacara school developed a different theory of three separate "gotras" (families, lineages), that inherently predisposed a person to either the vehicle of the "arhat", "pratyekabuddha" or "samyak-saṃbuddha" (fully self-awakened one). For the yogacarins then, only some beings (those who have the "bodhisattva lineage") can enter the bodhisattva path. In East Asian Buddhism, the view of the one vehicle ("ekayana") which holds that all Buddhist teachings are really part of a single path, is the standard view.
The term bodhisattva was also used in a broader sense by later authors. According to the eighth-century Mahāyāna philosopher Haribhadra, the term "bodhisattva" can refer to those who follow any of the three vehicles, since all are working towards "bodhi". Therefore, the specific term for a Mahāyāna bodhisattva is a "mahāsattva" (great being) "bodhisattva". According to Atiśa's 11th century "Bodhipathapradīpa," the central defining feature of a Mahāyāna bodhisattva is the universal aspiration to end suffering for all sentient beings, which is termed "bodhicitta" (the mind set on awakening). The bodhisattva doctrine went through a significant transformation during the development of Buddhist tantra, also known as Vajrayana. This movement developed new ideas and texts which introduced new bodhisattvas and re-interpreted old ones in new forms, developed in elaborate mandalas for them and introduced new practices which made use of mantras, mudras and other tantric elements. Entering the bodhisattva path. According to David Drewes, "Mahayana sutras unanimously depict the path beginning with the first arising of the thought of becoming a Buddha ("prathamacittotpāda"), or the initial arising of "bodhicitta", typically aeons before one first receives a Buddha's prediction, and apply the term bodhisattva from this point." The "Ten Stages Sutra", for example, explains that the arising of bodhicitta is the first step in the bodhisattva's career. Thus, the arising of bodhicitta, the compassionate mind aimed at awakening for the sake of all beings, is a central defining element of the bodhisattva path.
Another key element of the bodhisattva path is the concept of a bodhisattva's "praṇidhāna" - which can mean a resolution, resolve, vow, prayer, wish, aspiration and determination. This more general idea of an earnest wish or solemn resolve which is closely connected with bodhicitta (and is the cause and result of bodhicitta) eventually developed into the idea that bodhisattvas take certain formulaic "bodhisattva vows." One of the earliest of these formulas is found in the "" and states: We having crossed (the stream of samsara), may we help living beings to cross! We being liberated, may we liberate others! We being comforted, may we comfort others! We being finally released, may we release others! Other sutras contain longer and more complex formulas, such as the ten vows found in the "Ten Stages Sutra". Mahayana sources also discuss the importance of a Buddha's prediction ("vyākaraṇa") of a bodhisattva's future Buddhahood. This is seen as an important step along the bodhisattva path. Later Mahayana Buddhists also developed specific rituals and devotional acts for which helped to develop various preliminary qualities, such as faith, worship, prayer, and confession, that lead to the arising of "bodhicitta". These elements, which constitute a kind of preliminary preparation for bodhicitta, are found in the "seven part worship" ("saptāṅgavidhi, saptāṇgapūjā" or "saptavidhā anuttarapūjā"). This ritual form is visible in the works of Shantideva (8th century) and includes:
After these preliminaries have been accomplished, then the aspirant is seen as being ready to give rise to bodhicitta, often through the recitation of a bodhisattva vow. Contemporary Mahāyāna Buddhism encourages everyone to give rise to bodhicitta and ceremonially take bodhisattva vows. With these vows and precepts, one makes the promise to work for the complete enlightenment of all sentient beings by practicing the transcendent virtues or paramitas. In Mahāyāna, bodhisattvas are often not Buddhist monks and are former lay practitioners. Bodhisattva conduct (caryā). After a being has entered the path by giving rise to bodhicitta, they must make effort in the practice or conduct ("caryā") of the bodhisattvas, which includes all the duties, virtues and practices that bodhisattvas must accomplish to attain Buddhahood. An important early Mahayana source for the practice of the bodhisattva is the "Bodhisattvapiṭaka sūtra," a major sutra found in the "Mahāratnakūṭa" collection which was widely cited by various sources. According to Ulrich Pagel, this text is "one of the longest works on the bodhisattva in Mahayana literature" and thus provides extensive information on the topic bodhisattva training, especially the perfections ("pāramitā"). Pagel also argues that this text was quite influential on later Mahayana writings which discuss the bodhisattva and thus was "of fundamental importance to the evolution of the bodhisattva doctrine." Other sutras in the "Mahāratnakūṭa" collection are also important sources for the bodhisattva path.
According to Pagel, the basic outline of the bodhisattva practice in the "Bodhisattvapiṭaka" is outlined in a passage which states "the path to enlightenment comprises benevolence towards all sentient beings, striving after the perfections and compliance with the means of conversion." This path begins with contemplating the failures of samsara, developing faith in the Buddha, giving rise to bodhicitta and practicing the four immesurables. It then proceeds through all six perfections and finally discusses the four means of converting sentient beings ("saṃgrahavastu"). The path is presented through prose exposition, mnemonic lists ("matrka") and also through Jataka narratives. Using this general framework, the "Bodhisattvapiṭaka" incorporates discussions related to other practices including super knowledge ("abhijñā"), learning, 'skill' ("kauśalya"), accumulation of merit ("puṇyasaṃbhāra"), the thirty-seven factors of awakening ("bodhipakṣadharmas"), perfect mental quietude ("śamatha") and insight ("vipaśyanā").
Later Mahayana treatises ("śāstras") like the "Bodhisattvabhumi" and the "Mahāyānasūtrālamkāra" provide the following schema of bodhisattva practices: The first six perfections ("pāramitās") are the most significant and popular set of bodhisattva virtues and thus they serve as a central framework for bodhisattva practice. They are the most widely taught and commented upon virtues throughout the history of Mahayana Buddhist literature and feature prominently in major Sanskrit sources such as the "Bodhisattvabhumi", the "Mahāyānasūtrālamkāra," the "King of Samadhis Sutra" and the "Ten Stages Sutra". They are extolled and praised by these sources as "the great oceans of all the bright virtues and auspicious principles" ("Bodhisattvabhumi") and "the Teacher, the Way and the Light...the Refuge and the Shelter, the Support and the Sanctuary" ("Aṣṭasāhasrikā"). While many Mahayana sources discuss the bodhisattva's training in ethical discipline ("śīla") in classic Buddhist terms, over time, there also developed specific sets of ethical precepts for bodhisattvas (Skt. "bodhisattva-śīla"). These various sets of precepts are usually taken by bodhisattva aspirants (lay and ordained monastics) along with classic Buddhist pratimoksha precepts. However, in some Japanese Buddhist traditions, monastics rely solely on the bodhisattva precepts.
The perfection of wisdom ("prajñāpāramitā") is generally seen as the most important and primary of the perfections, without which all the others fall short. Thus, the "Madhyamakavatara" (6:2) states that wisdom leads the other perfections as a man with eyes leads the blind. This perfect or transcendent wisdom has various qualities, such as being non-attached ("asakti"), non-conceptual and non-dual ("advaya") and signless ("animitta"). It is generally understood as a kind of insight into the true nature of all phenomena ("dharmas") which in Mahayana sutras is widely described as emptiness ("shunyatā"). Another key virtue which the bodhisattva must develop is great compassion ("mahā-karuṇā"), a vast sense of care aimed at ending the suffering of all sentient beings. This great compassion is the ethical foundation of the bodhisattva, and it is also an applied aspect of their bodhicitta. Great compassion must also be closely joined with the perfection of wisdom, which reveals that all the beings that the bodhisattva strives to save are ultimately empty of self ("anātman") and lack inherent existence ("niḥsvabhāva"). Due to the bodhisattva's compassionate wish to save all beings, they develop innumerable skillful means or strategies ("upaya") with which to teach and guide different kinds of beings with all sorts of different inclinations and tendencies.
Another key virtue for the bodhisattva is mindfulness ("smṛti"), which Dayal calls "the sine qua non of moral progress for a bodhisattva." Mindfulness is widely emphasized by Buddhist authors and Sanskrit sources and it appears four times in the list of 37 "bodhipakṣadharmas". According to the "Aṣṭasāhasrikā", a bodhisattva must never lose mindfulness so as not to be confused or distracted. The "Mahāyānasūtrālamkāra" states that mindfulness is the principal asset of a bodhisattva, while both Asvaghosa and Shantideva state that without mindfulness, a bodhisattva will be helpless and uncontrolled (like a mad elephant) and will not succeed in conquering the mental afflictions. Length and nature of the path. Just as with non-Mahayana sources, Mahayana sutras generally depict the bodhisattva path as a long path that takes many lifetimes across many aeons. Some sutras state that a beginner bodhisattva could take anywhere from 3 to 22 countless eons ("mahāsaṃkhyeya kalpas") to become a Buddha. The "Mahāyānasaṃgraha" of Asanga states that the bodhisattva must cultivate the six paramitas for three incalculable aeons ("kalpāsaṃkhyeya"). Shantideva meanwhile states that bodhisattvas must practice each perfection for sixty aeons or kalpas and also declares that a bodhisattva must practice the path for an "inconceivable" ("acintya") number of kalpas. Thus, the bodhisattva path could take many billions upon billions of years to complete.
Later developments in Indian and Asian Mahayana Buddhism (especially in Vajrayana or tantric Buddhism) lead to the idea that certain methods and practices could substantially shorten the path (and even lead to Buddhahood in a single lifetime). In Pure Land Buddhism, an aspirant might go to a Buddha's pure land or buddha-field ("buddhakṣetra"), like Sukhavati, where they can study the path directly with a Buddha. This could significantly shorten the length of the path, or at least make it more bearable. East Asian Pure Land Buddhist traditions, such as Jōdo-shū and Jōdo Shinshū, hold the view that realizing Buddhahood through the long bodhisattva path of the perfections is no longer practical in the current age (which is understood as a degenerate age called "mappo"). Thus, they rely on the salvific power of Amitabha to bring Buddhist practitioners to the pure land of Sukhavati, where they will better be able to practice the path. This view is rejected by other schools such as Tendai, Shingon and Zen. The founders of Tendai and Shingon, Saicho and Kukai, held that anyone who practiced the path properly could reach awakening in this very lifetime. Buddhist schools like Tiantai, Huayan, Chan and the various Vajrayāna traditions maintain that they teach ways to attain Buddhahood within one lifetime.
Some of early depictions of the Bodhisattva path in texts such as the "Ugraparipṛcchā Sūtra" describe it as an arduous, difficult monastic path suited only for the few which is nevertheless the most glorious path one can take. Three kinds of bodhisattvas are mentioned: the forest, city, and monastery bodhisattvas—with forest dwelling being promoted a superior, even necessary path in sutras such as the "Ugraparipṛcchā" and the "Samadhiraja" sutras. The early "Rastrapalapariprccha sutra" also promotes a solitary life of meditation in the forests, far away from the distractions of the householder life. The "Rastrapala" is also highly critical of monks living in monasteries and in cities who are seen as not practicing meditation and morality. The "Ratnagunasamcayagatha" also says the bodhisattva should undertake ascetic practices ("dhūtaguṇa"), "wander freely without a home", practice the paramitas and train under a guru in order to perfect his meditation practice and realization of "prajñaparamita". The twelve "dhūtaguṇas" are also promoted by the "King of Samadhis Sutra", the "Ten Stages Sutra" and Shantideva. Some scholars have used these texts to argue for "the forest hypothesis", the theory that the initial Bodhisattva ideal was associated with a strict forest asceticism. But other scholars point out that many other Mahayana sutras do not promote this ideal, and instead teach "easy" practices like memorizing, reciting, teaching and copying Mahayana sutras, as well as meditating on Buddhas and bodhisattvas (and reciting or chanting their names). Ulrich Pagel also notes that in numerous sutras found in the "Mahāratnakūṭa" collection, the bodhisattva ideal is placed "firmly within the reach of non-celibate layfolk."
Nirvana. Related to the different views on the different types of "yanas" or vehicles is the question of a bodhisattva's relationship to nirvāṇa. In the various Mahāyāna texts, two theories can be discerned. One view is the idea that a bodhisattva must postpone their awakening until full Buddhahood is attained (at which point one ceases to be reborn, which is the classical view of nirvāṇa). This view is promoted in some sutras like the "Pañcavimsatisahasrika-prajñaparamita-sutra". The idea is also found in the "Laṅkāvatāra Sūtra", which mentions that bodhisattvas take the following vow: "I shall not enter into final nirvana before all beings have been liberated." Likewise, the "Śikṣāsamuccaya" states "I must lead all beings to Liberation. I will stay here till the end, even for the sake of one living soul." The second theory is the idea that there are two kinds of nirvāṇa, the nirvāṇa of an arhat and a superior type of nirvāṇa called "apratiṣṭhita ("non-abiding) that allows a Buddha to remain engaged in the samsaric realms without being affected by them. This attainment was understood as a kind of non-dual state in which one is neither limited to samsara nor nirvana. A being who has reached this kind of nirvana is not restricted from manifesting in the samsaric realms, and yet they remain fully detached from the defilements found in these realms (and thus they can help others).