text:
Benoit Mandelbrot

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.

Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the Mandelbrot set in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order". His math- and geometry-centered research included contributions to such fields as statistical physics, meteorology, hydrology, geomorphology, anatomy, taxonomy, neurology, linguistics, information technology, computer graphics, economics, geology, medicine, physical cosmology, engineering, chaos theory, econophysics, metallurgy, and the social sciences.

Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot also held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012.

Early years
Benedykt Mandelbrot was born in a Lithuanian Jewish family, in Warsaw during the Second Polish Republic. His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." In 1936, when he was 11, the family emigrated from Poland to France. The move, World War II, and the influence of his father's brother, the mathematician Szolem Mandelbrojt (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.

Mandelbrot attended the Lycée Rollin (now the Collège-lycée Jacques-Decour) in Paris until the start of World War II, when his family moved to Tulle, France. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period: "Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?"

In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, and in 1945 to 1947 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics. Returning to France, he obtained his PhD degree in Mathematical Sciences at the University of Paris in 1952.

Research career
From 1949 to 1958, Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey, where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland (to collaborate with Jean Piaget at the International Centre for Genetic Epistemology) and later to the Université Lille Nord de France. In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York. He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow Emeritus.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics.

Randomness and fractals in financial markets
Mandelbrot saw financial markets as an example of "wild randomness", characterized by concentration and long-range dependence. He developed several original approaches for modelling financial fluctuations. In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter. The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'. In later years, after the concept of fractals had matured, the study of financial markets in the context of fractals became possible only after the availability of high frequency data in finance. In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich to apply fractal theory to market microstructure. This cooperation led to the publication of the first comprehensive papers on scaling law in finance. This law shows similar properties at different time scales, confirming Mandelbrot's insight of the fractal nature of market microstructure. Mandelbrot's own research in this area is presented in his books Fractals and Scaling in Finance and The (Mis)behavior of Markets.

Developing "fractal geometry" and the Mandelbrot set
As a visiting professor at Harvard University, Mandelbrot began to study mathematical objects called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the Mandelbrot set which was introduced by him in 1979.

In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas in the French book Les Objets Fractals: Forme, Hasard et Dimension, later translated in 1977 as Fractals: Form, Chance and Dimension. According to computer scientist and physicist Stephen Wolfram, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before". Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals":

"Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called 'fractals', that are equally 'rough' at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space."

Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesque broccoli are two examples from nature." He points out an unexpected conclusion:

"One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot."

Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s psychedelic art with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist Johannes Kepler, who calculated and described the orbits of the planets.

Mandelbrot, however, never felt he was inventing a new idea. He described his feelings in a documentary with science writer Arthur C. Clarke:

"Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science."

According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence":

"the name Mandelbrot, and the word 'mandala'—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas."

In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature. This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division. He joined the Department of Mathematics at Yale, and obtained his first tenured post in 1999, at the age of 75. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences.

Fractals and the "theory of roughness"
Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature. He began by asking himself various kinds of questions related to nature: "Can geometry deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?"

In his paper "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", published in Science in 1967, Mandelbrot discusses self-similar curves that have Hausdorff dimension that are examples of fractals, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.

Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured." Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in The Fractal Geometry of Nature had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new: "The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty."

Fractals are also found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry: "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. —Mandelbrot, in his introduction to The Fractal Geometry of Nature"

Mandelbrot has been called an artist, and a visionary and a maverick. His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.

Awards and honors
Mandelbrot's awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006.

The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Chevalier in France's Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006. An honorary degree from Johns Hopkins University was bestowed on Mandelbrot in the May 2010 commencement exercises.

A partial list of awards received by Mandelbrot:

 * 2004 Best Business Book of the Year Award
 * AMS Einstein Lectureship
 * Barnard Medal
 * Caltech Service
 * Casimir Funk Natural Sciences Award
 * Charles Proteus Steinmetz Medal
 * High School Spelling Bee (1940)
 * Fellow, American Geophysical Union
 * Fellow of the American Statistical Association
 * Fellow of the American Physical Society (1987)
 * Franklin Medal
 * Harvey Prize (1989)
 * Honda Prize
 * Humboldtpreis
 * IBM Fellowship
 * Japan Prize (2003)
 * John Scott Award
 * Légion d'honneur (Legion of Honour)
 * Lewis Fry Richardson Medal
 * Medaglia della Presidenza della Repubblica Italiana
 * Médaille de Vermeil de la Ville de Paris
 * Nevada Prize
 * Member of the Norwegian Academy of Science and Letters.
 * Member of the American Philosophical Society (2004)
 * Science for Art
 * Sven Berggren-Priset
 * Wacław Sierpiński medal of the Polish Mathematical Society (2005)
 * Władysław Orlicz Prize
 * Wolf Foundation Prize for Physics (1993)

Death and legacy
Mandelbrot died from pancreatic cancer at the age of 85 in a hospice in Cambridge, Massachusetts, on 14 October 2010. Reacting to news of his death, mathematician Heinz-Otto Peitgen said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."

Chris Anderson, TED conference curator, described Mandelbrot as "an icon who changed how we see the world". Nicolas Sarkozy, President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".

Best-selling essayist-author Nassim Nicholas Taleb has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published".

In English

 * Fractals: Form, Chance and Dimension, 1977, 2020
 * The Fractal Geometry of Nature, 1982
 * Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615.
 * Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106.
 * Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543.
 * Mandelbrot, B. (1964) Random walks, fire damage amount and other Paretian risk phenomena. Operations Research, 12, 582–585.
 * Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E, 1997 by Benoit B. Mandelbrot and R.E. Gomory
 * Mandelbrot, Benoit B. (1997) Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, Springer.
 * Fractales, hasard et finance, 1959–1997, 1 November 1998
 * Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976) (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot
 * Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot) 14 December 2001 by Benoit Mandelbrot and F.J. Damerau
 * Mandelbrot, Benoit B., Gaussian Self-Affinity and Fractals, Springer: 2002.
 * Fractals and Chaos: The Mandelbrot Set and Beyond, 9 January 2004
 * The Misbehavior of Markets: A Fractal View of Financial Turbulence, 2006 by Benoit Mandelbrot and Richard L. Hudson
 * Mandelbrot, Benoit B. (2010). The Fractalist, Memoir of a Scientific Maverick. New York: Vintage Books, Division of Random House. ISBN 978-0-307-38991-6
 * The Fractalist: Memoir of a Scientific Maverick, 2014
 * Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. ISBN 0-7167-2213-5 (re-published by Films for the Humanities & Sciences, ISBN 978-0-7365-0520-8)
 * "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
 * Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe and Cornelia Zahlten: Fractals: An Animated Discussion (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. ISBN 0-7167-2213-5 (re-published by Films for the Humanities & Sciences, ISBN 978-0-7365-0520-8)
 * "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
 * "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.
 * "Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature", NOVA, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.

title: Benoit Mandelbrot


text:
Benedict of Nursia

Benedict of Nursia (Benedictus Nursiae; Benedetto da Norcia; 2 March 480 – 21 March 547), often known as Saint Benedict, was an Italian Christian monk, writer, and theologian. He is venerated in the Catholic Church, the Eastern Orthodox Church, the Oriental Orthodox Churches, the Lutheran Churches, the Anglican Communion, and Old Catholic Churches. In 1964 Pope Paul VI declared Benedict a patron saint of Europe.

Benedict founded twelve communities for monks at Subiaco in present-day Lazio, Italy (about 65 km to the east of Rome), before moving further south-east to Monte Cassino in the mountains of central Italy. The present-day Order of Saint Benedict emerged later and, moreover, is not an "order" as the term is commonly understood, but a confederation of autonomous  congregations.

Benedict's main achievement, his Rule of Saint Benedict, contains a set of rules for his monks to follow. Heavily influenced by the writings of John Cassian (c. 360 – c. 435), it shows strong affinity with the earlier Rule of the Master, but it also has a unique spirit of balance, moderation and reasonableness (ἐπιείκεια, epieíkeia), which persuaded most Christian religious communities founded throughout the Middle Ages to adopt it. As a result, Benedict's Rule became one of the most influential religious rules in Western Christendom. For this reason, Giuseppe Carletti regarded Benedict as the founder of Western Christian monasticism.

Biography
Apart from a short poem attributed to Mark of Monte Cassino, the only ancient account of Benedict is found in the second volume of Pope Gregory I's four-book Dialogues, thought to have been written in 593, although the authenticity of this work is disputed.

Gregory's account of Benedict's life, however, is not a biography in the modern sense of the word. It provides instead a spiritual portrait of the gentle, disciplined abbot. In a letter to Bishop Maximilian of Syracuse, Gregory states his intention for his Dialogues, saying they are a kind of floretum (an anthology, literally, 'flowers') of the most striking miracles of Italian holy men.

Gregory did not set out to write a chronological, historically anchored story of Benedict, but he did base his anecdotes on direct testimony. To establish his authority, Gregory explains that his information came from what he considered the best sources: a handful of Benedict's disciples who lived with him and witnessed his various miracles. These followers, he says, are Constantinus, who succeeded Benedict as Abbot of Monte Cassino, Honoratus, who was abbot of Subiaco when St. Gregory wrote his Dialogues, Valentinianus, and Simplicius.

In Gregory's day, history was not recognised as an independent field of study; it was a branch of grammar or rhetoric, and historia was an account that summed up the findings of the learned when they wrote what was, at that time, considered history. Gregory's Dialogues, Book Two, then, an authentic medieval hagiography cast as a conversation between the Pope and his deacon Peter, is designed to teach spiritual lessons.

Early life
He was the son of a Roman noble of Nursia, the modern Norcia, in Umbria. If 480 is accepted as the year of his birth, the year of his abandonment of his studies and leaving home would be about 500. Gregory's narrative makes it impossible to suppose him younger than 20 at the time.

Benedict was sent to Rome to study, but was disappointed by urban academic life. Seeking to escape the great city, he left with his servant and settled in Enfide. Enfide, which the tradition of Subiaco identifies with the modern Affile, is in the Simbruini mountains, about forty miles from Rome and two miles from Subiaco.

A short distance from Enfide is the entrance to a narrow, gloomy valley, penetrating the mountains and leading directly to Subiaco. The path continues to ascend, and the side of the ravine on which it runs becomes steeper until a cave is reached, above this point the mountain now rises almost perpendicularly; while on the right, it strikes in a rapid descent down to where, in Benedict's day, 500 ft below, lay the blue waters of a lake. The cave has a large triangular-shaped opening and is about ten feet deep. On his way from Enfide, Benedict met a monk, Romanus of Subiaco, whose monastery was on the mountain above the cliff overhanging the cave. Romanus discussed with Benedict the purpose which had brought him to Subiaco, and gave him the monk's habit. By his advice Benedict became a hermit and for three years lived in this cave above the lake.

Later life
Gregory tells little of Benedict's later life. He now speaks of Benedict no longer as a youth (puer), but as a man (vir) of God. Romanus, Gregory states, served Benedict in every way he could. The monk apparently visited him frequently, and on fixed days brought him food.

During these three years of solitude, broken only by occasional communications with the outer world and by the visits of Romanus, Benedict matured both in mind and character, in knowledge of himself and of his fellow-man, and at the same time he became not merely known to, but secured the respect of, those about him; so much so that on the death of the abbot of a monastery in the neighbourhood (identified by some with Vicovaro), the community came to him and begged him to become its abbot. Benedict was acquainted with the life and discipline of the monastery, and knew that "their manners were diverse from his and therefore that they would never agree together: yet, at length, overcome with their entreaty, he gave his consent". The experiment failed; the monks tried to poison him. The legend goes that they first tried to poison his drink. He prayed a blessing over the cup and the cup shattered. Thus he left the group and went back to his cave at Subiaco.

There lived in the neighborhood a priest called Florentius who, moved by envy, tried to ruin him. He tried to poison him with poisoned bread. When he prayed a blessing over the bread, a raven swept in and took the loaf away. From this time his miracles seem to have become frequent, and many people, attracted by his sanctity and character, came to Subiaco to be under his guidance. Having failed by sending him poisonous bread, Florentius tried to seduce his monks with some prostitutes. To avoid further temptations, in about 530 Benedict left Subiaco. He founded 12 monasteries in the vicinity of Subiaco, and, eventually, in 530 he founded the great Benedictine monastery of Monte Cassino, which lies on a hilltop between Rome and Naples.

Veneration
Benedict died of a fever at Monte Cassino not long after his sister, Scholastica, and was buried in the same tomb. According to tradition, this occurred on 21 March 547. He was named patron protector of Europe by Pope Paul VI in 1964. In 1980, Pope John Paul II declared him co-patron of Europe, together with Cyril and Methodius. Furthermore, he is the patron saint of speleologists. On the island of Tenerife (Spain) he is the patron saint of fields and farmers. An important romeria (Romería Regional de San Benito Abad) is held on this island in his honor, one of the most important in the country.

In the pre-1970 General Roman Calendar, his feast is kept on 21 March, the day of his death according to some manuscripts of the Martyrologium Hieronymianum and that of Bede. Because on that date his liturgical memorial would always be impeded by the observance of Lent, the 1969 revision of the General Roman Calendar moved his memorial to 11 July, the date that appears in some Gallic liturgical books of the end of the 8th century as the feast commemorating his birth (Natalis S. Benedicti). There is some uncertainty about the origin of this feast. Accordingly, on 21 March the Roman Martyrology mentions in a line and a half that it is Benedict's day of death and that his memorial is celebrated on 11 July, while on 11 July it devotes seven lines to speaking of him, and mentions the tradition that he died on 21 March.

The Eastern Orthodox Church commemorates Saint Benedict on 14 March.

The Lutheran Churches celebrate the Feast of Saint Benedict on July 11.

The Anglican Communion has no single universal calendar, but a provincial calendar of saints is published in each province. In almost all of these, Saint Benedict is commemorated on 11 July. Benedict is remembered in the Church of England with a Lesser Festival on 11 July.

Rule of Saint Benedict
Benedict wrote the Rule for monks living communally under the authority of an abbot. The Rule comprises seventy-three short chapters. Its wisdom is twofold: spiritual (how to live a Christocentric life on earth) and administrative (how to run a monastery efficiently). More than half of the chapters describe how to be obedient and humble, and what to do when a member of the community is not. About one-fourth regulate the work of God (the "opus Dei"). One-tenth outline how, and by whom, the monastery should be managed. Benedictine asceticism is known for its moderation.

Saint Benedict Medal
This devotional medal originally came from a cross in honor of Saint Benedict. On one side, the medal has an image of Saint Benedict, holding the Holy Rule in his left hand and a cross in his right. There is a raven on one side of him, with a cup on the other side of him. Around the medal's outer margin are the words "Eius in obitu nostro praesentia muniamur" ("May we be strengthened by his presence in the hour of our death"). The other side of the medal has a cross with the initials CSSML on the vertical bar which signify "Crux Sacra Sit Mihi Lux" ("May the Holy Cross be my light") and on the horizontal bar are the initials NDSMD which stand for "Non-Draco Sit Mihi Dux" ("Let not the dragon be my guide"). The initials CSPB stand for "Crux Sancti Patris Benedicti" ("The Cross of the Holy Father Benedict") and are located on the interior angles of the cross. Either the inscription "PAX" (Peace) or the Christogram "IHS" may be found at the top of the cross in most cases. Around the medal's margin on this side are the Vade Retro Satana initials VRSNSMV which stand for "Vade Retro Satana, Nonquam Suade Mihi Vana" ("Begone Satan, do not suggest to me thy vanities") then a space followed by the initials SMQLIVB which signify "Sunt Mala Quae Libas, Ipse Venena Bibas" ("Evil are the things thou profferest, drink thou thine own poison").

This medal was first struck in 1880 to commemorate the fourteenth centenary of Benedict's birth and is also called the Jubilee Medal; its exact origin, however, is unknown. In 1647, during a witchcraft trial at Natternberg near Metten Abbey in Bavaria, the accused women testified they had no power over Metten, which was under the protection of the cross. An investigation found a number of painted crosses on the walls of the abbey with the letters now found on St Benedict medals, but their meaning had been forgotten. A manuscript written in 1415 was eventually found that had a picture of Benedict holding a scroll in one hand and a staff which ended in a cross in the other. On the scroll and staff were written the full words of the initials contained on the crosses. Medals then began to be struck in Germany, which then spread throughout Europe. This medal was first approved by Pope Benedict XIV in his briefs of 23 December 1741 and 12 March 1742.

Benedict has been also the motif of many collector's coins around the world. The Austria 50 euro 'The Christian Religious Orders', issued on 13 March 2002 is one of them.

Influence

The early Middle Ages have been called "the Benedictine centuries." In April 2008, Pope Benedict XVI discussed the influence St Benedict had on Western Europe. The pope said that "with his life and work St Benedict exercised a fundamental influence on the development of European civilization and culture" and helped Europe to emerge from the "dark night of history" that followed the fall of the Roman empire.

Benedict contributed more than anyone else to the rise of monasticism in the West. His Rule was the foundational document for thousands of religious communities in the Middle Ages. To this day, The Rule of St. Benedict is the most common and influential Rule used by monasteries and monks, more than 1,400 years after its writing.

A basilica was built upon the birthplace of Benedict and Scholastica in the 1400s. Ruins of their familial home were excavated from beneath the church and preserved. The earthquake of 30 October 2016 completely devastated the structure of the basilica, leaving only the front facade and altar standing.

Gallery

 * See also Category:Paintings of Benedict of Nursia.

The Rule

 * , translated by Leonard J. Doyle
 * , translated by Leonard J. Doyle

Publications

 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).
 * Marett-Crosby, A., ed., The Benedictine Handbook (Norwich: Canterbury Press, 2003).

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Benedict of Nursia


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Battle of Pharsalus

The Battle of Pharsalus was the decisive battle of Caesar's Civil War fought on 9 August 48 BC near Pharsalus in Central Greece. Julius Caesar and his allies formed up opposite the army of the Roman Republic under the command of Pompey. Pompey had the backing of a majority of Roman senators and his army significantly outnumbered the veteran Caesarian legions.

Pressured by his officers, Pompey reluctantly engaged in battle and suffered an overwhelming defeat, ultimately fleeing the camp and his men, disguised as an ordinary citizen. Eventually making his way to Egypt, he was assassinated upon his arrival at the order of Ptolemy XIII.

Prelude
Following the start of the Civil War, Caesar had captured Rome, forced Pompey and his allies to withdraw from Italy, and defeated Pompey's legates in Spain. In the campaign season for 48 BC, Caesar crossed the Adriatic and advanced on Dyrrachium. There, he besieged it, but was defeated.

Caesar then withdrew east into Thessaly, partly to relieve one of his legates from attack by Metellus Scipio's forces arriving from Syria. He besieged Gomphi after it resisted him. Pompey pursued, seeking to spare Italy from invasion by concluding the war on Greek soil, to prevent Caesar from defeating Metellus Scipio's forces arriving from Syria, and under pressure from his overconfident allies who accused him of prolonging the war to extend his command.

Date
The decisive battle took place on 9 August 48 BC according to the Republican calendar.

Location
The location of the battlefield was for a long time the subject of controversy among scholars. Caesar himself, in his Commentarii de Bello Civili, mentions few place-names; and although the battle is called after Pharsalos by modern authors, four ancient writers – the author of the Bellum Alexandrinum (48.1), Frontinus (Strategemata 2.3.22), Eutropius (20), and Orosius (6.15.27) – place it specifically at Palaepharsalus ("Old" Pharsalus). Strabo in his Geographica (Γεωγραφικά) mentions both old and new Pharsaloi, and notes that the Thetideion, the temple to Thetis south of Scotoussa, was near both. In 198 BC, in the Second Macedonian War, Philip V of Macedon sacked Palaepharsalos (Livy, Ab Urbe Condita 32.13.9), but left new Pharsalos untouched. These two details perhaps imply that the two cities were not close neighbours. Many scholars, therefore, unsure of the site of Palaepharsalos, followed Appian (2.75) and located the battle of 48 BC south of the Enipeus or close to Pharsalos (today's Pharsala). Among the scholars arguing for the south side are Béquignon (1928), Bruère (1951), and Gwatkin (1957).

An increasing number of scholars, however, have argued for a location on the north side of the river. These include Perrin (1885), Holmes (1908), Lucas (1921), Rambaud (1955), Pelling (1973), Morgan (1983), and Sheppard (2006). John D. Morgan in his definitive "Palae-pharsalus – the Battle and the Town", shows that Palaepharsalus cannot have been at Palaiokastro, as Béquignon thought (a site abandoned c. 500 BC), nor the hill of Fatih-Dzami within the walls of Pharsalus itself, as Kromayer (1903, 1931) and Gwatkin thought; and Morgan argues that it is probably also not the hill of Khtouri (Koutouri), some 7 miles north-west of Pharsalus on the south bank of the Enipeus, as Lucas and Holmes thought, although that remains a possibility. However, Morgan believes it is most likely to have been the hill just east of the village of Krini Larisas (Krini Larisas, formerly Driskoli) very close to the ancient highway from Larisa to Pharsalus. This site is some 6 mi north of Pharsalus, and three miles north of the river Enipeus, and not only has remains dating back to neolithic times but also signs of habitation in the 1st century BC and later. The identification seems to be confirmed by the location of a place misspelled "Palfari" or "Falaphari" shown on a medieval route map of the road just north of Pharsalus. Morgan places Pompey's camp a mile to the west of Krini, just north of the village of Avra (formerly Sarikayia), and Caesar's camp some four miles to the east-south-east of Pompey's. According to this reconstruction, therefore, the battle took place not between Pharsalus and the river, as Appian wrote, but between Old Pharsalus and the river.

An interesting side-note on Palaepharsalus is that it was sometimes identified in ancient sources with Phthia, the home of Achilles. Near Old and New Pharsalus was a "Thetideion", or temple dedicated to Thetis, the mother of Achilles. However, Phthia, the kingdom of Achilles and his father Peleus, is more usually identified with the lower valley of the Spercheios river, much further south.

Name of the battle
Although it is often called the Battle of Pharsalus by modern historians, this name was rarely used in the ancient sources. Caesar merely calls it the proelium in Thessaliā ("battle in Thessalia"); Marcus Tullius Cicero and Hirtius call it the Pharsālicum proelium ("Pharsalic battle") or pugna Pharsālia ("Pharsalian battle"), and similar expressions are also used in other authors. But Hirtius (if he is the author of the de Bello Alexandrino) also refers to the battle as having taken place at Palaepharsalus, and this name also occurs in Strabo, Frontinus, Eutropius, and Orosius. Lucan in his poem about the Civil War regularly uses the name Pharsālia, and this term is also used by the epitomiser of Livy and by Tacitus. The only ancient sources to refer to the battle as being at Pharsalus are a certain calendar known as the Fasti Amiternini and the Greek authors Plutarch, Appian, and Polyaenus. It has therefore been argued by some scholars that "Pharsalia" would be a more accurate name for the battle than Pharsalus.

Opposing armies
The total number of soldiers on each side is unknown because ancient accounts of the battle focused primarily on giving the numbers of Italian legionaries only, regarding allied non-citizen contingents as inferior and inconsequential. According to Caesar, his own army included 22,000 Roman legionaries distributed throughout 80 cohorts (8 legions), alongside 1,000 Gallic and Germanic cavalry. All of Caesar's legions were understrength; some only had about a thousand men at the time of Pharsalus, due partly to losses at Dyrrhachium and partly to Caesar's wish to rapidly advance with a picked body as opposed to a ponderous movement with a large army. Another source adds that he had recruited Greek light infantry from Dolopia, Acarnania and Aetolia; these numbered no more than a few thousand. Caesar, Appian and Plutarch give Pompey an army of 45,000 Roman infantry. Osorius describes Pompey as having 88 cohorts of Roman infantry, which at full strength would come to 44,000 men, while Brunt and Wylie estimated Pompey's Roman infantry as being as 38,000 men, and Greenhalgh said they contained a maximum of 36,000.

It was in his auxiliary troops and in particular his cavalry, all of which vastly outnumbered Caesar's own, that Pompey had his greatest advantage. He seems to have had at his disposal anywhere between 5,000 and 7,000 cavalry, and thousands of archers, slingers and light infantrymen in general. These all formed a remarkably diverse group, including Gallic and Germanic horsemen alongside all polyglot peoples of the east – namely Greeks, Thracians, and Anatolians from the Balkans and Syrians, Phoenicians and Jews from the Levant. To this heterogeneous force Pompey added horsemen conscripted from his own slaves. Many of the foreigners were serving under their own rulers, for more than a dozen despots and petty kings under Roman influence in the east were Pompey's personal clients and some elected to attend in person, or send proxies.

Caesarian legions
Caesar had the following legions with him:
 * the VI legion (later called Ferrata) veterans of his Gallic Wars
 * the VII legion (later called Claudia Pia Fidelis) veterans of his Gallic Wars
 * the VIII legion (later called Augusta) veterans of his Gallic Wars
 * the IX legion (later called Hispania) veterans of his Gallic Wars
 * the X legion (Equestris, later called Gemina) veterans of his Gallic Wars
 * the XI legion (later called Paterna and Claudia Pia Fidelis, the same title as the seventh) veterans of his Gallic Wars
 * the XII legion (later called Fulminata) veterans of his Gallic Wars
 * the XIII legion (later also called Gemina, the 'twin' to the tenth) veterans of his Gallic Wars

The bulk of Caesar's army at Pharsalus was made up of his veterans from the Gallic Wars; very experienced, battle-hardened troops who were absolutely devoted to their commander.

Deployment

The two generals deployed their legions in the traditional three lines (triplex acies), with Pompey's right and Caesar's left flanks resting on river Enipeus. As the stream provided enough protection to that side, Pompey moved almost all of his cavalry, archers, and slingers to the left, to make the most of their numerical strength. Only a small force of 500–600 Pontic cavalry and some Cappadocian light infantry was placed on his right flank. Pompey stationed his strongest legions in the center and wings of his infantry line, and dispersed some 2,000 re-enlisted veterans throughout the entire line in order to inspire the less experienced. The Pompeian cohorts were arrayed in an unusually thick formation, 10 men deep: their task was just to tie down the enemy foot while Pompey's cavalry, his key to victory, swept through Caesar's flank and rear. The column of legions was divided under command of three subordinates, with Lentulus in charge of the left, Scipio of the center and Ahenobarbus the right. Labienus was entrusted with command of the cavalry charge, while Pompey himself took up a position behind the left wing in order to oversee the course of the battle.

Caesar also deployed his men in three lines, but, being outnumbered, had to thin his ranks to a depth of only six men, in order to match the frontage presented by Pompey. His left flank, resting on the Enipeus River, consisted of his battle-worn IX legion supplemented by the VIII legion, these were commanded by Mark Antony. The VI, XII, XI and XIII formed the centre and were commanded by Domitius, then came the VII and upon his right he placed his favored X legion, giving Sulla command of this flank – Caesar himself took his stand on the right, across from Pompey. Upon seeing the disposition of Pompey's army Caesar grew discomforted, and further thinned his third line in order to form a fourth line on his right: this to counter the onslaught of the enemy cavalry, which he knew his numerically inferior cavalry could not withstand. He gave this new line detailed instructions for the role they would play, hinting that upon them would rest the fortunes of the day, and gave strict orders to his third line not to charge until specifically ordered.

Battle
There was significant distance between the two armies, according to Caesar. Pompey ordered his men not to charge, but to wait until Caesar's legions came into close quarters; Pompey's adviser Gaius Triarius believed that Caesar's infantry would be fatigued and fall into disorder if they were forced to cover twice the expected distance of a battle march. Also, stationary troops were expected to be able to defend better against pila throws. Seeing that Pompey's army was not advancing, Caesar's infantry under Mark Antony and Gnaeus Domitius Calvinus started the advance. As Caesar's men neared throwing distance, without orders, they stopped to rest and regroup before continuing the charge; Pompey's right and centre line held as the two armies collided.

As Pompey's infantry fought, Labienus ordered the Pompeian cavalry on his left flank to attack Caesar's cavalry; as expected they successfully pushed back Caesar's cavalry. Caesar then revealed his hidden fourth line of infantry and surprised Pompey's cavalry charge; Caesar's men were ordered to leap up and use their pila to thrust at Pompey's cavalry instead of throwing them. Pompey's cavalry panicked and suffered hundreds of casualties, as Caesar's cavalry came about and charged after them. After failing to reform, the rest of Pompey's cavalry retreated to the hills, leaving the left wing of his legions exposed to the hidden troops as Caesar's cavalry wheeled around their flank. Caesar then ordered in his third line, containing his most battle-hardened veterans, to attack. This broke Pompey's left wing troops, who fled the battlefield.

After routing Pompey's cavalry, Caesar threw in his last line of reserves – a move which at this point meant that the battle was more or less decided. Pompey lost the will to fight as he watched both cavalry and legions under his command break formation and flee from battle, and he retreated to his camp, leaving the rest of his troops at the centre and right flank to their own devices. He ordered the garrisoned auxiliaries to defend the camp as he gathered his family, loaded up gold, and threw off his general's cloak to make a quick escape. As the rest of Pompey's army were left confused, Caesar urged his men to end the day by routing the rest of Pompey's troops and capturing the Pompeian camp. They complied with his wishes; after finishing off the remains of Pompey's men, they furiously attacked the camp walls. The Thracians and the other auxiliaries who were left in the Pompeian camp, in total seven cohorts, defended bravely, but were not able to fend off the assault.

Caesar had won his greatest victory, claiming to have only lost about 200 soldiers and 30 centurions and assigning the Optimate losses to be 60,000 men. These numbers seem suspiciously exaggerated with Appian suggesting the Caesarean losses to be as many as 1,200 men and the Pompeian losses to be 6,000. In his history of the war, Caesar would praise his own men's discipline and experience, and remembered each of his centurions by name. He also questioned Pompey's decision not to charge.

Aftermath
Pompey, despairing of the defeat, fled with his advisors overseas to Mytilene and thence to Cilicia where he held a council of war; at the same time, Cato and supporters at Dyrrachium attempted first to hand over command to Marcus Tullius Cicero, who refused, deciding instead to return to Italy. They then regrouped at Corcyra and went thence to Libya. Others, including Marcus Junius Brutus sought Caesar's pardon, travelling over marshlands to Larissa where he was then welcomed graciously by Caesar in his camp. Pompey's council of war decided to flee to Egypt, which had in the previous year supplied him with military aid.

In the aftermath of the battle, Caesar captured Pompey's camp and burned Pompey's correspondence. He then announced that he would forgive all who asked for mercy. Pompeian naval forces in the Adriatic and Italy mostly withdrew or surrendered.

Hearing of Pompey's flight to Egypt, Caesar remained in hot pursuit, first landing in Asia and reaching Alexandria on 2 October 48 BC, where he learnt of Pompey's murder and then was embroiled in a dynastic dispute between Ptolemy XIII and Cleopatra.

Importance
Paul K. Davis wrote that "Caesar's victory took him to the pinnacle of power, effectively ending the Republic." The battle itself did not end the civil war but it was decisive and gave Caesar a much needed boost in legitimacy. Until then much of the Roman world outside Italy supported Pompey and his allies due to the extensive list of clients he held in all corners of the Republic. After Pompey's defeat former allies began to align themselves with Caesar as some came to believe the gods favored him, while for others it was simple self-preservation. The ancients took great stock in success as a sign of favoritism by the gods. This is especially true of success in the face of almost certain defeat – as Caesar experienced at Pharsalus. This allowed Caesar to parlay this single victory into a huge network of willing clients to better secure his hold over power and force the Optimates into near exile in search for allies to continue the fight against Caesar.

In popular culture
The battle gives its name to the following artistic, geographical, and business concerns:

 * Pharsalia, a poem by Lucan
 * Pharsalia, New York, U.S.
 * Pharsalia Technologies, Inc.

In Alexandre Dumas' The Three Musketeers, the author makes reference to Caesar's purported order that his men try to cut the faces of their opponents – their vanity supposedly being of more value to them than their lives.

In Mankiewicz's 1963 film Cleopatra, the immediate aftermath of Pharsalus is used as an opening scene to set the action in motion.

title: Battle of Pharsalus