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48-490: Marin Mersenne , OM (also known as Marinus Mersennus or le Père Mersenne ; French: [maʁɛ̃ mɛʁsɛn] ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those written in the form M n = 2 − 1 for some integer n . He also developed Mersenne's laws , which describe

96-723: A "spontanéité indéfinie"—anything could happen naturally" Mersenne mentions Martin Del Rio 's Investigations into Magic and criticises Marsilio Ficino for claiming power for images and characters. He condemns astral magic and astrology and the anima mundi , a concept popular amongst Renaissance neo-platonists . Whilst allowing for a mystical interpretation of the Cabala, he wholeheartedly condemned its magical application, particularly angelology . He also criticises Pico della Mirandola , Cornelius Agrippa , Francesco Giorgio and Robert Fludd , his main target. Harmonie universelle

144-514: A black wool tunic , with broad sleeves, a hood, and a short scapular . It has a thick, black cord (with four knots that signify the four vows) with a tassel to gird the robe. The Order of the Minims spread throughout Italy in the fifteenth century and was introduced to France in 1482, and later to Spain and to Germany in 1497. The houses in Spain, Germany, and France were suppressed during

192-412: A life of solitude and penance as a hermit . In 1435, two followers joined Francis and began the community, which was first called the "Poor Hermits of St. Francis of Assisi." Francis and his followers founded hermitages at Paterno in 1444 and Milazzo , Sicily , in 1469. The Archbishop of Cosenza approved the group and established them as a religious order on November 30, 1470, and this approval

240-471: A manuscript copy of the Meditations on First Philosophy , and defended its orthodoxy against numerous clerical critics. In later life, he gave up speculative thought and turned to scientific research, especially in mathematics, physics and astronomy. In this connection, his best known work is Harmonie universelle of 1636, dealing with the theory of music and musical instruments . It is regarded as

288-524: A reputation as one of the most educated men of his era. He was offered a professorship at Cambridge , but rejected the proposal, due to the requirement to acknowledge the Trinity . He moved to Poland in 1614 and was appointed rector of the Racovian Academy for three years in the 1620s, but resigned because of the burdens of the teaching and administration. In 1631 Ruar moved to Gdańsk, where he

336-443: A small group who were reasonably knowledgeable about the sciences of the day, and their main theme was to promote educational reform (they were anti-Aristotelian). These pamphlets also promoted an occult view of science containing elements of Paracelsian philosophy , neo-Platonism , Christian Cabala and Hermeticism . In effect, they sought to establish a new form of scientific religion with some pre-Christian elements. Mersenne led

384-524: A source of information on 17th-century music, especially French music and musicians, to rival even the works of Pietro Cerone . One of his many contributions to musical tuning theory was the suggestion of as the ratio for an equally-tempered semitone ( 2 12 {\displaystyle {\sqrt[{12}]{2}}} ). It was more accurate (0.44 cents sharp) than Vincenzo Galilei 's 18/17 (1.05 cents flat), and could be constructed using straightedge and compass . Mersenne's description in

432-728: Is a separate institute founded in 1867 in Guanajuanto, Mexico, by Pablo de Anda Padilla . The sisters work in schools and medical centers in Mexico, Cuba, Ecuador, Rome, and Nogales, Arizona. Marcin Ruar Marcin Ruar (German Martin Ruar , Latin Ruarius ), pseudonym Aretius Crispinus ) (1589–1657) was a Socinian writer, advocate of religious tolerance, and rector of the Racovian Academy from 1620 to 1622. Ruar

480-428: Is also 1 : 2, which in turn is consistent with the source-air-motion-frequency-equivalence hypothesis. He also performed extensive experiments to determine the acceleration of falling objects by comparing them with the swing of pendulums , reported in his Cogitata Physico-Mathematica in 1644. He was the first to measure the length of the seconds pendulum , that is a pendulum whose swing takes one second, and

528-514: Is also remembered today thanks to his association with the Mersenne primes . The Mersenne Twister , named for Mersenne primes, is frequently used in computer engineering and in related fields such as cryptography. However, Mersenne was not primarily a mathematician; he wrote about music theory and other subjects. He edited works of Euclid , Apollonius , Archimedes , and other Greek mathematicians . But perhaps his most important contribution to

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576-414: Is perhaps Mersenne's most influential work. It is one of the earliest comprehensive works on music theory, touching on a wide range of musical concepts, and especially the mathematical relationships involved in music. The work contains the earliest formulation of what has become known as Mersenne's laws , which describe the frequency of oscillation of a stretched string. This frequency is: The formula for

624-643: The Dutch Republic . He was a staunch defender of Galileo, assisting him in translations of some of his mechanical works. For four years, Mersenne devoted himself entirely to philosophic and theological writing, and published Quaestiones celeberrimae in Genesim ( Celebrated Questions on the Book of Genesis ) (1623); L'Impieté des déistes ( The Impiety of the Deists ) (1624); La Vérité des sciences ( Truth of

672-637: The Friars Minor founded by his patron saint . Francis composed a rule for the community in 1493, which was approved under the name of "Hermits of the Order of the Minims". The definitive version of the rule was solemnly approved by Pope Julius II in the Bull Inter ceteros , July 28, 1506, who also simplified the name of the community to the Order of Minims ( Latin : Ordo Minimorum ). In addition to

720-677: The Polish brethren from Raków and closed the Racovian Academy , the Gdańsk city council moved to exile Ruar. However, as a lawyer Ruar demanded an official trial, appealing to the support of the Polish magnates who were patrons of the Polish Brethren . Ruar argued that the doctrine of his faith, wrongly called "Arianism," was in reality based on the Bible. The city council relented, providing Ruar

768-518: The Spanish ambassador , Don Pedro de Lucena, who was a very pious man, grew to know and admire him. He sent reports of the holy friar to his family back in Jaén . His daughter, Elena, and her two daughters, Maria and Francisca, felt so inspired by Don Pedro's reports, they wanted to dedicate themselves to the way of life Francis had established. Through the ambassador, they communicated their interest to

816-580: The United States of America . The Munich friary of the German Minims brewed beer as means of support, but after the friars were expelled, the brewery continued independently. It continues to brew the Paulaner brand of beer, which draws its name from Francis of Paola. Francis was called to France in 1483 by King Louis XI to serve as his deathbed confessor . While he was there,

864-404: The nomological determinism of Lucilio Vanini ("God acts on sublunary beings (humans) using the sky as a tool"), and Gerolamo Cardano 's idea that martyrs and heretic were compelled to self-harm by the stars; Historian of science William Ashworth explains "Miracles, for example, were endangered by the naturalists, because in a world filled with sympathies and occult forces—with what Lenoble calls

912-405: The 1636 Harmonie universelle of the first absolute determination of the frequency of an audible tone (at 84 Hz) implies that he had already demonstrated that the absolute-frequency ratio of two vibrating strings, radiating a musical tone and its octave , is 1 : 2. The perceived harmony ( consonance ) of two such notes would be explained if the ratio of the air oscillation frequencies

960-601: The European scholarly community boosted their own prestige by claiming to be among the selected members of the Brotherhood. However, it is now generally agreed among historians that there is no evidence that an order of Rosicrucians existed at the time, with later Rosicrucian Orders drawing on the name, with no relation to the writers of the Rosicrucian Manifestoes. During the mid-1630s Mersenne gave up

1008-607: The French mathematician and philosopher René Descartes (1596–1650) to manifest his international network of mathematicians. Mersenne's philosophical works are characterized by wide scholarship and the narrowest theological orthodoxy. His greatest service to philosophy was his enthusiastic defence of Descartes, whose agent he was in Paris and whom he visited in exile in the Netherlands . He submitted to various eminent Parisian thinkers

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1056-660: The German Socinian Marcin Ruar concerning the Copernican ideas of Pierre Gassendi , finding Ruar already a supporter of Gassendi's position. Among his correspondents were Descartes, Galileo, Roberval, Pascal , Beeckman and other scientists. He died on 1 September 1648 of complications arising from a lung abscess . Quaestiones celeberrimae in Genesim was written as a commentary on the Book of Genesis and comprises uneven sections headed by verses from

1104-571: The Monastery of Jesus and Mary. This was first and remains the oldest monastery of the Minim nuns. Francisca was elected as the first corrector ( religious superior ) of the community. She spent many years as the corrector of the monastery, gaining a reputation for holiness, and is today honored as Blessed Francisca. Their proper rule was approved by the Holy See in 1506, at the same time as that of

1152-631: The Royal Society in London, which were founded about twenty years after Mersenne's death, were direct descendants of Mersenne's activities." In 1635 Mersenne met with Tommaso Campanella but concluded that he could "teach nothing in the sciences ... but still he has a good memory and a fertile imagination." Mersenne asked if Descartes wanted Campanella to come to Holland to meet him, but Descartes declined. He visited Italy fifteen times, in 1640, 1641 and 1645. In 1643–1644 Mersenne also corresponded with

1200-591: The Sciences Against the Sceptics , 1624). It is sometimes incorrectly stated that he was a Jesuit . He was educated by Jesuits, but he never joined the Society of Jesus . He taught theology and philosophy at Nevers and Paris. In 1635 he set up the informal Académie Parisienne (Academia Parisiensis), which had nearly 140 correspondents, including astronomers and philosophers as well as mathematicians, and

1248-817: The Socinian cause, arguing that his deportation was the beginning of religious persecution in Poland. Although he was conditionally allowed to return to Gdańsk, henceforth Ruar preferred to live outside the city, in Straszyn, where he spent the rest of his life, writing, preaching, corresponding with the congregation in Gdansk, and with scholars abroad under the protection of the hetman Stanisław Koniecpolski . During this period he again travelled widely and freely, visiting England and Italy. He died in Straszyn near Gdańsk. Ruar

1296-462: The advance of learning was his extensive correspondence (in Latin ) with mathematicians and other scientists in many countries. At a time when the scientific journal had not yet come into being, Mersenne was the centre of a network for exchange of information. It has been argued that Mersenne used his lack of mathematical specialty, his ties to the print world, his legal acumen, and his friendship with

1344-627: The fight against acceptance of these ideas, particularly those of Rosicrucian promoter Robert Fludd , who had a lifelong battle of words with Johannes Kepler . Fludd responded with Sophia cum moria certamen (1626), wherein he discusses his involvement with the Rosicrucians . The anonymous Summum bonum (1629), another critique of Mersenne, is a Rosicrucian-themed text. The cabalist Jacques Gaffarel joined Fludd's side, while Pierre Gassendi defended Mersenne. The Rosicrucian ideas were defended by many prominent men of learning, and some members of

1392-475: The first three chapters of that book. At first sight the book appears to be a collection of treatises on various miscellaneous topics. However Robert Lenoble has shown that the principle of unity in the work is a polemic against magical and divinatory arts, cabalism , and animistic and pantheistic philosophies. Mersenne was concerned with the teachings of some Italian naturalists that all things happened naturally and determined astrologically; for example,

1440-444: The first to observe that a pendulum's swings are not isochronous as Galileo thought, but that large swings take longer than small swings. Two German pamphlets that circulated around Europe in 1614–15, Fama fraternitatis and Confessio Fraternitatis , claimed to be manifestos of a highly select, secret society of alchemists and sages called the Brotherhood of Rosicrucians . The books were allegories, but were obviously written by

1488-709: The friars. The Federation of Minim Nuns of Saint Francis of Paola includes 14 monasteries in Spain, Italy, Mexico, and the Philippines. A new community was established in Barcelona on Easter 1623. In 1936, the 25 members of the community in Barcelona were arrested by soldiers of the Republic of Spain . Charged with treason, nine choir nuns and an extern Sister were executed on July 23. They were beatified by Pope Francis on October 13, 2013, and are commemorated on July 23. The Minim Daughters of Mary Immaculate

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1536-506: The harmonics of a vibrating string (such as may be found on guitars and pianos ), and his seminal work on music theory , Harmonie universelle , for which he is referred to as the "father of acoustics ". Mersenne, an ordained Catholic priest , had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s" and, because of his ability to make connections between people and ideas, "the post-box of Europe". He

1584-419: The lowest frequency is where f is the frequency [Hz], L is the length [m], F is the force [N] and μ is the mass per unit length [kg/m]. In this book, Mersenne also introduced several innovative concepts that can be considered the basis of modern reflecting telescopes: Because of criticism that he encountered, especially from Descartes, Mersenne made no attempt to build a telescope of his own. Mersenne

1632-561: The minister of Hazerswoude , Samuel Naeranus , on the Trinity. In 1643 Ruar had married the daughter of Martin Voss, from a well-off and prominent Gdańsk family and converted his wife, her family, friends and many citizens. These conversions did not escape the attentions of the city council, most of whom belonged to the local Lutheran Church. Following the 1638 decision of the Sejm which drove

1680-441: The order, Francis of Paola , was born in 1416 and named in honor of Francis of Assisi . The boy became ill when he was only one month old, and his mother prayed to Saint Francis and promised that her son would spend a year in a Franciscan friary if he were healed. Francis recovered, which she believed meant that God had granted her prayer. At 13 years of age Francis fulfilled that votive year. After this year he dedicated himself to

1728-780: The period following the French Revolution . By the turn of the 20th century, only 19 friaries remained, all but one of them in Italy. On December 31, 2010, the order had 46 communities with 174 members, 112 of them priests. The majority of these were in Italy, but they are also established in Brazil , Cameroon , Colombia , the Democratic Republic of the Congo , the Czech Republic , India , Mexico , Spain , and

1776-405: The saint, and asked for a rule of life which they might follow. Francis welcomed their request heartily, and, to this end, he adapted the rule of the friars for them to live as cloistered nuns. Don Pedro donated a portion of his estate to the young women, and there they formed a small monastic community. They received the Minim religious habit from a Friar Lionet on June 11, 1495, and established

1824-547: The search for physical causes in the Aristotelian sense (rejecting the idea of essences , which were still favoured by the scholastic philosophers ) and taught that true physics could be only a descriptive science of motions ( Mécanisme ), which was the direction set by Galileo Galilei . Mersenne had been a regular correspondent with Galileo and had extended the work on vibrating strings originally developed by his father, Vincenzo Galilei . An air attributed to Mersenne

1872-438: The standard three religious vows of chastity, poverty and obedience , the rule contains the vow of "a Lenten way of life" ( Latin : vita quadragesimalis ), which is considered to be the distinctive feature of the Minims. This vow is for perpetual abstinence from all meat, eggs and dairy products , except in case of grave illness and by order of a physician . The order is also discalced . The Minim habit consists of

1920-809: Was a minister in the German-speaking Socinian congregation. Known for his humanist and liberal views, Ruar was not doctrinaire and tried to reconcile Socinians with the Mennonite Remonstrants. Journeying to the Netherlands Ruar established contacts between the Polish Arians and the Dutch Remonstrant movement and with Jacobus Arminius . However his position against the Trinity remained clear, as in extensive correspondence with Remonstrants, such as

1968-552: Was also a member of the ascetical Minim religious order and wrote and lectured on theology and philosophy . Mersenne was born of Jeanne Moulière, wife of Julien Mersenne, peasants who lived near Oizé , County of Maine (present-day Sarthe , France). He was educated at Le Mans and at the Jesuit College of La Flèche . On 17 July 1611, he joined the Minim Friars and, after studying theology and Hebrew in Paris,

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2016-475: Was an advocate of separation of church authority from natural sciences. In 1643 Marin Mersenne , sought from a J. Fabricius (a student from Gdańsk in Paris, apparently no relation to the astronomer), a Socinian with whom Mersenne could correspond concerning the Copernican heliocentrism of Pierre Gassendi , and was introduced to Ruar. However Ruar was already familiar with Gassendi's works, and replied to Mersenne that such matters should be left to science, not wait

2064-574: Was born in Krempe , Holstein, the son of a Lutheran preacher. He studied in Altdorf , where he became acquainted with and adopted the non-trinitarian of Fausto Sozzini , and then studied law at Leiden. He was a polyglot making frequent travels through Denmark, France, Italy, the Netherlands and the countries of Germany, promoting non-trinitarian teaching and pleas for tolerance, publishing and earning

2112-474: Was confirmed by Pope Sixtus IV in his bull Sedes Apostolica of May 17, 1474. At that time, the pope also changed their status from that of hermits to mendicant friars. The name Minims comes from the Italian word minimo , meaning the smallest or the least, and their founder would call himself il minimo dei minimi . Francis of Paola wanted to distinguish himself as being of even less significance than

2160-546: Was ordained a priest in 1613. Between 1614 and 1618, he taught theology and philosophy at Nevers , but he returned to Paris and settled at the convent of L'Annonciade in 1620. There he studied mathematics and music and met with other kindred spirits such as René Descartes , Étienne Pascal , Pierre Petit , Gilles de Roberval , Thomas Hobbes , and Nicolas-Claude Fabri de Peiresc . He corresponded with Giovanni Doni , Jacques Alexandre Le Tenneur , Constantijn Huygens , Galileo Galilei , and other scholars in Italy, England and

2208-555: Was the precursor of the Académie des sciences established by Jean-Baptiste Colbert in 1666. He was not afraid to cause disputes among his learned friends in order to compare their views, notable among which were disputes between Descartes, Pierre de Fermat , and Jean de Beaugrand . Peter L. Bernstein , in his book Against the Gods: The Remarkable Story of Risk , wrote, "The Académie des Sciences in Paris and

2256-493: Was to cease converting Lutherans. After five years Ruar received from King Władysław IV Vasa a certificate of immunity, and began again to convert Lutheran burghers of the city, which in 1643 resulted in a further banishment from Gdańsk - with his father in law Voss, the doctor Florian Crusius, Daniel Zwicker, the secretary of the council Ladebach and the eighty-year-old barber Werner David Buttel, with their families. Ruar initially went to Warsaw, where he tried to gain support for

2304-457: Was used by Ottorino Respighi in his second suite of Ancient Airs and Dances Minims (religious order) Like the other mendicant orders, there are three separate components, or orders, of the movement: the friars , contemplative nuns and a Third Order of laypeople who live in the spirit of the order in their daily lives. At present there are only two fraternities of the Minim tertiaries ; both are in Italy. The founder of

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