A difference engine, first created by Charles Babbage, is an automatic mechanical calculator designed to tabulate polynomial functions. Its name is derived from the method of divided differences, a way to interpolate or tabulate functions by using a small set of polynomial coefficients. Most mathematical functions used by engineers and navigators, including logarithmic and trigonometric functions, can be approximated by polynomials, so a difference engine can compute many useful tables of numbers; the historical difficulty in producing error-free tables by teams of mathematicians and human "computers" spurred Charles Babbage's desire to build a mechanism to automate the process. The notion of a mechanical calculator for mathematical functions can be traced back to the Antikythera mechanism of the 2nd century BC, while early modern examples are attributed to Pascal and Leibniz in the 17th century. In 1784 J. H. Müller, an engineer in the Hessian army and built an adding machine and described the basic principles of a difference machine in a book published in 1786, but he was unable to obtain funding to progress with the idea.

Charles Babbage began to construct a small difference engine in c. 1819 and had completed it by 1822. He announced his invention on 14 June 1822, in a paper to the Royal Astronomical Society, entitled "Note on the application of machinery to the computation of astronomical and mathematical tables"; this machine was powered by cranking a handle. The British government was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical. In 1823, the British government gave Babbage £1700 to start work on the project. Although Babbage's design was feasible, the metalworking techniques of the era could not economically make parts in the precision and quantity required, thus the implementation proved to be much more expensive and doubtful of success than the government's initial estimate. In 1832, Babbage and Joseph Clement produced a small working model which operated on 6-digit numbers and second-order differences. Lady Byron described seeing the working prototype in 1833: "We both went to see the thinking machine last Monday.

It raised several Nos. to the 2nd and 3rd powers, extracted the root of a Quadratic equation." Work on the larger engine was suspended in 1833. By the time the government abandoned the project in 1842, Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine; the government valued only the machine's output, not the development of the machine itself. Babbage did not, or was unwilling to, recognize that predicament. Meanwhile, Babbage's attention had moved on to developing an analytical engine, further undermining the government's confidence in the eventual success of the difference engine. By improving the concept as an analytical engine, Babbage had made the difference engine concept obsolete, the project to implement it an utter failure in the view of the government; the incomplete Difference Engine No. 1 was put on display to the public at the 1862 International Exhibition in South Kensington, London. Babbage went on to design his much more general analytical engine, but produced an improved "Difference Engine No. 2" design, between 1846 and 1849.

Babbage was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more while using fewer parts. Inspired by Babbage's difference engine in 1834, Per Georg Scheutz built several experimental models. In 1837 his son Edward proposed to construct a working model in metal, in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, extended to third-order. In 1843, after adding the printing part, the model was completed. In 1851, funded by the government, construction of the larger and improved machine began, finished in 1853; the machine was demonstrated at the World's Fair in Paris, 1855 and sold in 1856 to the Dudley Observatory in Albany, New York. Delivered in 1857, it was the first printing calculator sold.. In 1857 the British government ordered the next Scheutz's difference machine, built in 1859, it had the same basic construction as the previous one. Martin Wiberg improved Scheutz's construction but used his device only for producing and publishing printed tables.

Alfred Deacon of London in c. 1862 produced a small difference engine. American George B. Grant started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz. One year he learned about difference engines and proceed to design one himself, describing his construction in 1871. In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, built in 1876, it weighed about 2,000 pounds. Christel Hamann built one machine in 1909 for the "Tables of Bauschinger and Peters" ("Logarithmic-Trigonometrical Tables with eight d

Frederick Ferdinand, Hereditary Prince of Denmark was grandson of King Frederick V and heir presumptive to the throne from 1848 until his death. Had he lived five months longer, he would have outlived his nephew, King Frederick VII, become King of Denmark. Prince Ferdinand was born at Christiansborg Palace in Copenhagen on 22 November 1792 as the youngest child of Frederick, Hereditary Prince of Denmark and Norway and Sophie Frederikke of Mecklenburg, thus being a grandson of late King Frederick V of Denmark and Norway, his uncle King Christian VII being mentally unstable, his father had acted as regent after the fall of Johann Friedrich Struensee in 1772. But after the coup of 1784, when the king's son Crown Prince Frederick took power and regency, Hereditary Prince Frederick had been without influence at the court. However, Crown Prince Frederick being without male heirs, Hereditary Prince Frederick and his sons were in the immediate line of succession to the throne; when Christiansborg Palace was destroyed by fire in 1794, the young Prince and his family moved to Amalienborg Palace where he was brought up, spending the summers at Sorgenfri Palace.

Prince Ferdinand married at Frederiksberg Palace on 1 August 1829 his first cousin once removed, Princess Caroline of Denmark. She was the eldest daughter of the above-mentioned sonless Crown Prince Frederick, now King Frederick VI of Denmark; when Frederick VI died in 1839, because of the Salic Law Caroline did not succeed to the throne, inherited by the closest male relative, Ferdinand's elder brother Prince Christian Frederick. The number of male members of the Royal House was so low in those decades that Ferdinand himself was always close to the succession. At the death of his brother Christian VIII in 1848, the aged Ferdinand became heir presumptive. Ferdinand died childless, one of the reasons why the main branch of the Danish Royal House soon became extinct, triggering the second war of Schleswig; the Danish Monarchy http://runeberg.org/dbl/5/0127.html

Tsubasa Kato is a Japanese contemporary artist. He made his debut at the "Roppongi Crossing 2010" exhibition at Mori Art Museum and received the Kengo Kuma Prize, after earning M. F. A from the Tokyo University of the Arts. In 2015, he received a fellowship from the Agency for Cultural Affairs of Japan Government and participated in Japan-US Exchange Friendship Program in the Arts as Visitor Research Scholar of University of Washington in Seattle for two years. Since 2007, he is known for his Raise project. 2018 Out in the Cold, University of Warwick, Coventry, UK2018–17 Uprisings, Galerie de l’UQAM and Cinémathèque québécoise, Canada MUAC, Mexico City, Mexico SESC, São Paulo, Brazil Museum of The National University of Tres de Febrero, Buenos Aires, Argentina National Art Museum of Catalonia, Spain2017 Guerrilla Waves, Then Cafe, Vietnam Condition Report: The Mashup Syndicate, Gudang Sarinah Ekosistem, Indonesia2016 East Asian Video Frames: Shades of Urbanization, Pori Art Museum, Finland2015 Art Basel in Hong Kong, Hong Kong Convention and Exhibition Centre, Hong Kong being MAPHILINDO, Sabah Art Gallery, Kota Kinabalu, Malaysia Come Close: Japanese Artists Within their Communities, Bus Projects, Victoria, Australia2013 Why not live for Art?

II – 9 collectors reveal their treasures, Tokyo Opera City Art Gallery, Japan2011 11.3 PROJECT, Toyoma district of Iwaki city, Japan “ Fractions of the Longest Distance at MUJIN-TO Production, Japan” Review by Ryan Holmberg in Artforum "Reenacting History_Collective Actions and Everyday Gestures" National Museum of Modern and Contemporary Art "Uprisings" Jeu de Paume “A conversation with Tsubasa Kato” interview by Laura Thomson in OCULA A documentary film "Mitakuye Oyasin at United Tribes Technical College, Bismarck / Standing Rock Sioux Reservation, North Dakota, USA" directed by Takaharu Eto "Now Japan.