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The Organum Mathematicum was an information device or teaching machine that was invented by the Jesuit polymath and scholar Athanasius Kircher in the middle of the 17th century. With proper instruction and use, the device could assist in a wide assortment of calculations, including arithmetic, cryptography, and music.
Kircher adopted some of the ideas in the Organum from preexisting inventions like Napier's bones, almanacs, and his own Arca Musarithmica. Like other calculating devices of the period, the Organum prefigures modern computing technology. Yet, due to its general lack of adoption, it remains an interesting but obscure footnote in the history of information technology. [1]
The Organum Mathematicum was a box or chest divided into nine or more compartments. Each compartment was filled with wooden rods or slats (called "tariffa" by Kircher). The compartments were organized according to the nine functions they performed (see #Topics). To use the organum, you would remove the rods you needed, manipulate them or rearrange them as needed to perform your calculation, and then return the rods to the box. Some of the rods were simple tables, as one might find in an almanac. Other rods, in particular the music, cryptography, and arithmetic rods, were more complex in design and intended to be used in combination. [2]
In 1661, 11 years after the publication of Musurgia Universalis , which contains a description of a similar, but more limited device, the Arca Musarithmica, Kircher sent an Organum Mathematicum to Gottfried Aloys Kinner, the tutor to the 12-year-old Charles Joseph, Archduke of Habsburg, for whom the Organum was likely intended. Kircher enclosed instructions in a drawer in the base of the device, as well as a set of mathematical instruments. [3]
The Organum Mathematicum was later described in a 1668 book of the same title by Gaspar Schott, who was Kircher's pupil. The book includes numerous excerpts from the original manual. [2] There is also a portrait of the young Charles Joseph who had died four years earlier. [4] There are no surviving Organums which closely resemble the device illustrated in Schott's book, but there are three known devices, likely of Jesuit manufacture, which contain essentially the same content.
The device described in Schott's book was divided by functionality into 9 main sections, each of which contained approximately 24 rods.
The arithmetic rods included a set of Napier's Bones. They were capable of assisting with the multiplication of multi-digit numbers and producing quotients.
The rods in this section could aid in determining heights, by use of a geometric square.
The rods in this section could aid in determining the design of bulwarks in fortification plans.
The rods in this section could be used to determine the date of Easter and other church holidays which were positioned relative to it. These rods simply contained a table of upcoming dates.
The rods in this section contained information needed to construct sundials.
This compartment had tablets which resembled those found in an almanac. For each day of the year, the length of the day and night, the times for sunrise and sunset, and the duration of morning and evening twilight were provided. All the information was based on measurements taken at 48 degrees latitude (Vienna).
This section had tables describing movements for the visible planets, and the constellation Draco, and also provided astrological interpretations for the 12 zodiac signs.
The rods in this section could be used to encrypt and decrypt text using a cyclic transposition cypher, based on a keyword.
The rods in this section could be used by non musicians to compose church music. The system used was the same as that used for Kircher's previous device, the Arca Musarithmica. They contained sets of musical phrases which could be combined randomly to set verses to music, producing millions of hymns in 4-part harmony.
There are few surviving examples of the Organum. There are no surviving Organums which closely resemble the device illustrated in Schott's book, but there are three known 17th-century devices which contain essentially the same content. Most of them appear to have been built to impress important patrons to the Jesuits. It is unclear if any of them saw regular use.
This Organum has a steep slope which presents all the rods attractively. There is a dial in the front which can be used to find local time in 24 different cities around the world (the dial duplicates an illustration from Kircher's Ars Magna Lucis et Umbra). The rods are cut to resemble obelisks, perhaps playing on Kircher's reputed expertise in Egyptology.
This Organum appears identical to the Florence model. Some photos show an additional metal frame which may have been added later for protection.
This Organum is the 'odd man out' - it is very different in appearance from the Florence and Prague devices, which are essentially identical. The chest is not sloped, and there are a lot of extra drawers on the pedestal.
Kircher's earlier Arca Musarithmica was a music composing device of similar design to the Organum. The content of the rods was essentially the same as the musical rods in the Organum (although there was room for more of them). The Organum can be thought of as an improved and generalized version of the Arca.
The magic lantern, also known by its Latin name lanterna magica, was an early type of image projector that used pictures—paintings, prints, or photographs—on transparent plates, one or more lenses, and a light source. Because a single lens inverts an image projected through it, slides were inserted upside down in the magic lantern, rendering the projected image correctly oriented.
Athanasius Kircher was a German Jesuit scholar and polymath who published around 40 major works of comparative religion, geology, and medicine. Kircher has been compared to fellow Jesuit Roger Joseph Boscovich and to Leonardo da Vinci for his vast range of interests, and has been honoured with the title "Master of a Hundred Arts". He taught for more than 40 years at the Roman College, where he set up a wunderkammer. A resurgence of interest in Kircher has occurred within the scholarly community in recent decades.
Gaspar Schott was a German Jesuit and scientist, specializing in the fields of physics, mathematics and natural philosophy, and known for his industry.
Hugh Sempill was a Scottish Jesuit mathematician and linguist. He describes himself in his work as Craigbaitaeus, having inherited landholdings at Craigbait from his grandfather.
The stylus fantasticus is a style of early baroque music, especially for the instrumental music.
A cat organ, also called cat piano, is a hypothetical musical instrument which consists of a line of cats fixed in place with their tails stretched out underneath a keyboard so that they cry out when a key is pressed. The cats would be arranged according to the natural tone of their voices.
Musurgia Universalis, sive Ars Magna Consoni et Dissoni is a 1650 work by the Jesuit scholar Athanasius Kircher. It was printed in Rome by Ludovico Grignani and dedicated to Archduke Leopold Wilhelm of Austria. It was a compendium of ancient and contemporary thinking about music, its production and its effects. It explored, in particular, the relationship between the mathematical properties of music with health and rhetoric. The work complements two of Kircher's other books: Magnes sive de Arte Magnetica had set out the secret underlying coherence of the universe and Ars Magna Lucis et Umbrae had explored the ways of knowledge and enlightenment. What Musurgia Universalis contained, through its exploration of dissonance within harmony, was an explanation of the presence of evil in the world.
Kunstkammer is the title of Jeffrey Ching's Fifth Symphony, composed in Berlin from 12 October 2004 to 6 February 2005, and revised in December 2005
The Arca Musarithmica is an information device that was invented by Jesuit scholar Athanasius Kircher in the mid 17th century. Its purpose was to enable non musicians to compose church music. Through simple combinatoric techniques it is capable of producing millions of pieces of 4-part polyphonic music. Like other calculating aids of the period, the Arca prefigures modern computing technology. It is among the earliest examples of "Artificial Creativity". The device anticipates aleatoric and computer compositional techniques of the 20th century, and can be thought of as a kind of music composition algorithm in physical form.
Arca Noë is a book published in 1675 by the Jesuit scholar Athanasius Kircher. It is a study of the biblical story of Noah's Ark, published by the cartographer and bookseller Johannes van Waesbergen in Amsterdam. Kircher's aim in Arca Noë was to reconcile recent discoveries in nature and geography with the text of the Bible. This demonstration of the underlying unity and truth between revelation and science was a fundamental task of Catholic scholarship at the time. Together with its sister volume Turris Babel, Arca Noë presented a complete intellectual project to demonstrate how contemporary science supported the account of the Book of Genesis.
Phonurgia Nova is a 1673 work by the Jesuit scholar Athanasius Kircher. It is notable for being the first book ever dedicated entirely to the science of acoustics, and for containing the earliest description of an aeolian harp. It was dedicated to the Holy Roman Emperor Leopold I and printed in Kempten by Rudoph Dreherr.
Specula Melitensis Encyclica is a 1638 book by Fra Salvatore Imbroll, describing a machine invented by a Jesuit scholar Athanasius Kircher. It was printed in Naples by Secundino Roncagliolo and dedicated to Giovanni Paolo Lascaris, Grand Master of the Knights of Malta.
Prodromus Coptus sive Aegyptiacus was a 1636 work by the Jesuit scholar Athanasius Kircher. It was published in Rome by the Sacred Congregation for the Propagation of the Faith and dedicated to the Prefect of the Congregation, Cardinal Francesco Barberini. The book was Kircher's first venture into the field of Egyptology, and it also contained the first ever published grammar of the Coptic language.
Itinerarium exstaticum quo mundi opificium is a 1656 work by the Jesuit scholar Athanasius Kircher. It is an imaginary dialogue in which an angel named Cosmiel takes the narrator, Theodidactus, on a journey through the planets. It is the only work by Kircher devoted entirely to astronomy, and one of only two pieces of imaginative fiction by him. A revised and expanded second edition, entitled Iter Exstaticum, was published in 1660.
Polygraphia nova et universalis ex combinatoria arte directa is a 1663 work by the Jesuit scholar Athanasius Kircher. It was one of Kircher's most highly regarded works and his only complete work on the subject of cryptography, although he made passing references to the topic elsewhere. The book was distributed as a private gift to selected European rulers, some of who also received an arca steganographica, a presentation chest containing wooden tallies used to encrypt and decrypt codes.
Magnes sive de Arte Magnetica is a 1641 work by the Jesuit scholar Athanasius Kircher. It was dedicated to Emperor Ferdinand III and printed in Rome by Hermann Scheuss. It developed the ideas set out in his earlier Ars Magnesia and argued that the universe is governed by universal physical forces of attraction and repulsion. These were, as described in the motto in the book's first illustration, 'hidden nodes' of connection. The force that drew things together in the physical world was, he argued, the same force that drew people's souls towards God. The work is divided into three books: 1.De natura et facultatibus magnetis, 2.Magnes applicatus, 3.Mundus sive catena magnetica. It is noted for the first use of the term 'electromagnetism'.
Pantometrum Kircherianum is a 1660 work by the Jesuit scholars Gaspar Schott and Athanasius Kircher. It was dedicated to Christian Louis I, Duke of Mecklenburg and printed in Würzburg by Johann Gottfried Schönwetter. It was a description, with building instructions, of a measuring device called the pantometer, that Kircher had developed some years before. The first edition include 32 copperplate illustrations.
Latium is a 1669 work by the Jesuit scholar Athanasius Kircher. It was dedicated to Pope Clement X and a 1671 edition was published in Amsterdam by Johannes van Waesbergen. The work was the first to discuss the topography, archeology and history of the Lazio region. It was based partly on Kircher's extensive walks in the countryside around Rome, although it included sites that he had probably not visited in person. The work included many illustrations of the contemporary countryside, as well as reconstructions of ancient buildings. It also included an account of his discovery of the ruined sanctuary at Mentorella, which he had already recounted in his 1665 work Historia Eustachio Mariana.
Diatribe de progidiosis crucibus is a 1661 work by the Jesuit scholar Athanasius Kircher. It was printed in Rome by Blasius Deversin and dedicated to Archduke Leopold Wilhelm of Austria. A second edition of the work was published in Rome in 1666 and a German translation appeared in Gaspar Schott's Joco-seriorum naturae et artis.
Ars Magna Lucis et Umbrae is a 1646 work by the Jesuit scholar Athanasius Kircher. It was dedicated to Ferdinand IV, King of the Romans and published in Rome by Lodovico Grignani. A second edition was published in Amsterdam in 1671 by Johann Jansson. Ars Magna was the first description published in Europe of the illumination and projection of images. The book contains the first printed illustration of Saturn and the 1671 edition also contained a description of the magic lantern.