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52-502: Boa Esperança (literally meaning "good hope" in Portuguese) may refer to the following places: Boa Esperança is the name of a seaworthy replica of a caravel , on display as a museum in the port of Lagos in the Algarve. Replica Replicas have been sometimes sold as originals, a type of fraud . Most replicas have more innocent purposes. Fragile originals need protection, while

104-430: A prop in a film or stage performance, generally for safety reasons. A prop replica is an authentic-looking duplicate of a prop from a video game, movie or television show. "Replicas represent a copy or forgery of another object and we often think of forgeries we think of paintings but, in fact, anything that is collectible and expensive is an attractive item to forge". Replicas have been made by people to preserve

156-524: A difference engine can compute many useful tables . 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, devised and built an adding machine and described the basic principles of

208-504: A difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), 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 (Difference Engine 0). He announced his invention on 14 June 1822, in a paper to the Royal Astronomical Society , entitled "Note on

260-537: A machine for the Nautical Almanac Office which was used as a difference engine of second-order. It was later replaced in 1929 by a Burroughs Class 11 (13-digit numbers and second-order differences, or 11-digit numbers and [at least up to] fifth-order differences). Alexander John Thompson about 1927 built integrating and differencing machine (13-digit numbers and fifth-order differences) for his table of logarithms "Logarithmetica britannica". This machine

312-675: A means of checking the engine's performance. In addition to funding the construction of the output mechanism for the Science Museum's difference engine, Nathan Myhrvold commissioned the construction of a second complete Difference Engine No. 2, which was on exhibit at the Computer History Museum in Mountain View, California , from May 2008 to January 2016. It has since been transferred to Intellectual Ventures in Seattle where it

364-400: A perceived link to the past. This can be linked to a historical past or specific time-period or just to commemorate an experience. Replicas and reproductions of artifacts help provide a material representation of the past for the public. Replicas of artifacts and art have a purpose within museums and research. They are created to help with preserving of original artifacts. In many cases

416-423: A polynomial (and of its finite differences ) is calculated by some means for some value of X , the difference engine can calculate any number of nearby values, using the method generally known as the method of finite differences . For example, consider the quadratic polynomial with the goal of tabulating the values p (0), p (1), p (2), p (3), p (4), and so forth. The table below is constructed as follows:

468-465: A small difference engine (20-digit numbers and third-order differences). American George B. Grant started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz (Schentz). One year later (1870) he learned about difference engines and proceeded to design one himself, describing his construction in 1871. In 1874 the Boston Thursday Club raised a subscription for

520-401: A small working model (one-seventh of the plan), which operated on 6-digit numbers by second-order differences. Lady Byron described seeing the working prototype in 1833: "We both went to see the thinking machine (or so it seems) last Monday. It raised several Nos. to the 2nd and 3rd powers, and extracted the root of a Quadratic equation." Work on the larger engine was suspended in 1833. By

572-454: Is a legal issue related to copyright and trademark ownership. An example of the discussion taking place around the reproduction of art and cultural heritage is the Victoria & Albert Museum's ReACH Initiative. Dialogues on the "first original copy" and the role of blockchain technologies in authenticating replicas, and ownership is taking shape. Difference Engine A difference engine

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624-533: Is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was first created by Charles Babbage . The name difference engine is derived from the method of divided differences , a way to interpolate or tabulate functions by using a small set of polynomial co-efficients. Some of the most common mathematical functions used in engineering, science and navigation are built from logarithmic and trigonometric functions , which can be approximated by polynomials, so

676-428: Is important for public access and knowledge. Replicas and their original representation can be seen as fake or real depending on the viewer. Good replicas take much education related to understanding all the processes and history that go behind the culture and the original creation. To create a good and authentic replica of an object, there is to be a skilled artisan or forger to create the same authentic experience that

728-399: Is on display just outside the main lobby. The difference engine consists of a number of columns, numbered from 1 to N . The machine is able to store one decimal number in each column. The machine can only add the value of a column n  + 1 to column n to produce the new value of n . Column N can only store a constant, column 1 displays (and possibly prints ) the value of

780-421: Is the crucial fact behind the success of the method. This table was built from left to right, but it is possible to continue building it from right to left down a diagonal in order to compute more values. To calculate p (5) use the values from the lowest diagonal. Start with the fourth column constant value of 4 and copy it down the column. Then continue the third column by adding 4 to 11 to get 15. Next continue

832-457: Is to produce stereotype plates for use in printing presses, which it does by pressing type into soft plaster to create a flong . Babbage intended that the Engine's results be conveyed directly to mass printing, having recognized that many errors in previous tables were not the result of human calculating mistakes but from slips in the manual typesetting process. The printer's paper output is mainly

884-569: The Difference and Analytical Engines at the Science Museum library in London. This work led the Science Museum to construct a working calculating section of difference engine No. 2 from 1985 to 1991, under Doron Swade , the then Curator of Computing. This was to celebrate the 200th anniversary of Babbage's birth in 1991. In 2002, the printer which Babbage originally designed for the difference engine

936-562: The Rosetta Stone or prints and museum-quality copies of the Mona Lisa and other famous pieces of art. For example, Difference Engine No. 2, designed by Charles Babbage in the 19th century, was reconstructed from original drawings studied by Allan Bromley in the 1980s and is now on display at the Science Museum in London , England . A second example is Stephenson's Rocket where a replica

988-464: The application of machinery to the computation of astronomical and mathematical tables". This machine used the decimal number system and 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

1040-521: The authentic feelings that they are supposed to get from the originals. Through the context and experience that a replica can provide in a museum setting, people can be fooled into seeing it as "original". The authenticity of a replica is important for the impression it gives off to tourists or observers. "According to Trilling, the original use of authenticity in tourism was in museums where experts wanted to determine 'whether objects of art are what they appear to be or are claimed to be, and therefore worth

1092-488: The calculation on the current iteration . The engine is programmed by setting initial values to the columns. Column 1 is set to the value of the polynomial at the start of computation. Column 2 is set to a value derived from the first and higher derivatives of the polynomial at the same value of X . Each of the columns from 3 to N is set to a value derived from the ( n − 1 ) {\displaystyle (n-1)} first and higher derivatives of

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1144-550: The construction of a large-scale model, which was built in 1876. It could be expanded to enhance precision and weighed about 2,000 pounds (910 kg). Christel Hamann built one machine (16-digit numbers and second-order differences) in 1909 for the "Tables of Bauschinger and Peters" ("Logarithmic-Trigonometrical Tables with eight decimal places"), which was first published in Leipzig in 1910. It weighed about 40 kilograms (88 lb). Burroughs Corporation in about 1912 built

1196-441: The crank directly on the main shaft, it was later realized that the force required to crank the machine would have been too great for a human to handle comfortably. Therefore, the two models that were built incorporate a 4:1 reduction gear at the crank, and four revolutions of the crank are required to perform one full cycle. Each iteration creates a new result, and is accomplished in four steps corresponding to four complete turns of

1248-434: The creation of replicas of their pieces. With replica artifacts the copies to be "museum-quality" have to reach a high standard and can cost a lot of money to be produced. Replica artifacts (copies) can provide an authentic view but represents more of the subjectivities of what people expect and desire from their museum experiences and the cultures they learn about. With copies of retail and other counterfeit goods there

1300-552: The cultures that are being represented and make them seem static. For luxury goods, the same authentic feel has to be present for consumers to want to buy a "fake" designer bag or watch that provides them with the same feelings and desired experiences, but as well achieves the look of higher class. Replicas and reproductions are also for purely consumption and personal value. Through souvenirs people can own their very own physical representation of their experience or passions. People can buy on-line full size replicas (museum-quality) of

1352-446: The engine will give exact results for first N steps. After that, the engine will only give an approximation of the function. The Taylor series expresses the function as a sum obtained from its derivatives at one point. For many functions the higher derivatives are trivial to obtain; for instance, the sine function at 0 has values of 0 or ± 1 {\displaystyle \pm 1} for all derivatives. Setting 0 as

1404-507: The function and by backtracking (i.e. calculating the required differences). Col 1 0 {\displaystyle 1_{0}} gets the value of the function at the start of computation f ( 0 ) {\displaystyle f(0)} . Col 2 0 {\displaystyle 2_{0}} is the difference between f ( 1 ) {\displaystyle f(1)} and f ( 0 ) {\displaystyle f(0)} ... If

1456-473: The function to be calculated is a polynomial function , expressed as the initial values can be calculated directly from the constant coefficients a 0 , a 1 , a 2 , ..., a n without calculating any data points. The initial values are thus: Many commonly used functions are analytic functions , which can be expressed as power series , for example as a Taylor series . The initial values can be calculated to any degree of accuracy; if done correctly

1508-684: 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, and 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 later designed an improved "Difference Engine No. 2" design (31-digit numbers and seventh-order differences), between 1846 and 1849. Babbage

1560-406: The handle shown at the far right in the picture below. The four steps are: The engine represents negative numbers as ten's complements . Subtraction amounts to addition of a negative number. This works in the same manner that modern computers perform subtraction, known as two's complement . The principle of a difference engine is Newton's method of divided differences . If the initial value of

1612-425: The original artifact may be too fragile and too much at risk of further damage to be on display, posing a risk to the artifact from light, environmental agents, and other risks greater than in secure storage. Replicas are created for the purpose of experimental archaeology where archaeologists and material analysts try to understand the ways that an artifact was created and what technologies and skills were needed for

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1664-450: The original object provides. This process takes time and much money to be done correctly for museum standards. Authenticity or real feeling presented by an object can be "described as the experience of an 'aura' of an original." An aura of an object is what an object represents through its previous history and experience. Replicas work well in museum settings because they have the ability to look so real and accurate that people can feel

1716-419: The past. With works of art museums assert their intellectual property rights for replicas and reproduction of images which many museums use commercial licensing for providing access to images. Issues are arising with more images being available on the internet and it being free access. Artists can claim copyright infringement related to displays of their work in a context they did not approve of which can be

1768-414: The people to create the artifact on display. Another reason for the creation of replica artifacts, is for museums to be able to send originals around the globe or allow other museums or events to educate people on the history of specific artifacts. Replicas are also put on display in museums when further research is being conducted on the artifact, but further display of the artifact in real or replica form

1820-672: The polynomial are produced without ever having to multiply. A difference engine only needs to be able to add. From one loop to the next, it needs to store 2 numbers—in this example (the last elements in the first and second columns). To tabulate polynomials of degree n , one needs sufficient storage to hold n numbers. Babbage's difference engine No. 2, finally built in 1991, can hold 8 numbers of 31 decimal digits each and can thus tabulate 7th degree polynomials to that precision. The best machines from Scheutz could store 4 numbers with 15 digits each. The initial values of columns can be calculated by first manually calculating N consecutive values of

1872-499: The polynomial. In the Babbage design, one iteration (i.e. one full set of addition and carry operations) happens for each rotation of the main shaft. Odd and even columns alternately perform an addition in one cycle. The sequence of operations for column n {\displaystyle n} is thus: Steps 1,2,3,4 occur for every odd column, while steps 3,4,1,2 occur for every even column. While Babbage's original design placed

1924-514: The price that is asked for them or   ... worth the admiration they are being given'." These reproductions and the values of authenticity presented to the public through artifacts in museums provide "truth". However, authenticity has a way of also being represented in what the public expects in a predictable manner or based on stereotypes within museums. This idea of authenticity also relates to cultural artifacts like food, cultural activities, festivals, housing, and dress that helps to homogenize

1976-502: 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. According to the 1830 design for Difference Engine No. 1, it would have about 25,000 parts, weigh 4 tons , and operate on 20-digit numbers by sixth-order differences. In 1832, Babbage and Joseph Clement produced

2028-635: The public can examine a replica in a museum. Replicas are often manufactured and sold as souvenirs. Not all incorrectly attributed items are intentional forgeries . In the same way that a museum shop might sell a print of a painting or a replica of a vase , copies of statues , paintings, and other precious artifacts have been popular through the ages. However, replicas have often been used illegally for forgery and counterfeits , especially of money and coins, but also commercial merchandise such as designer label clothing, luxury bags and accessories, and luxury watches . In arts or collectible automobiles,

2080-783: The same ancient method." These warriors can come in a variety of sizes and provide a very realistic and authentic experience with their own personal warrior. The Barcelona Pavilion was built in 1929 and demolished in 1930. In 1986 a replica was built on the same site. As the white mark prestige comes from the imitation of iPhone, the white marks are the most popular brands in the world. Knock-off brand label fashions and accessories like Louis Vuitton, Coach, Chanel, and Rolex are major labels that often are copied. Replicas can also be used for re-enactment purposes, for example replicas of steel helmets and leather equipment used in WW2. Controversies with replicas (used in museums), are associated with who owns

2132-440: The second column by taking its previous value, 22 and adding the 15 from the third column. Thus p (5) is 22 + 15 = 37. In order to compute p (6), we iterate the same algorithm on the p (5) values: take 4 from the fourth column, add that to the third column's value 15 to get 19, then add that to the second column's value 37 to get 56, which is p (6). This process may be continued ad infinitum . The values of

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2184-412: The second column contains the values of the polynomial, the third column contains the differences of the two left neighbors in the second column, and the fourth column contains the differences of the two neighbors in the third column: The numbers in the third values-column are constant. In fact, by starting with any polynomial of degree n , the column number n  + 1 will always be constant. This

2236-407: The start of computation we get the simplified Maclaurin series The same method of calculating the initial values from the coefficients can be used as for polynomial functions. The polynomial constant coefficients will now have the value The problem with the methods described above is that errors will accumulate and the series will tend to diverge from the true function. A solution which guarantees

2288-463: The style of racers, and often carry the highest performance and safety specifications of any street-legal products. These high-performance race-look products termed "Replica", are priced higher and are usually more sought-after than plain colours of the same product. Because of gun ownership restrictions in some locales, gun collectors create non-functional legal replicas of illegal firearms. Such replicas are also preferred to real firearms when used as

2340-518: The term "replica" is used for discussing the non-original recreation, sometimes hiding its real identity. In motor racing, especially motorcycling, often manufacturers will produce a street version product with the colours of the vehicle or clothing of a famous racer. This is not the actual vehicle or clothing worn during the race by the racer, but a fully officially approved brand-new street-legal product in similar looks. Typically found in helmets, race suits/clothing, and motorcycles, they are coloured in

2392-467: 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 (economically produced tables), not the development (at unpredictable cost) of the machine itself. Babbage refused to recognize that predicament. Meanwhile, Babbage's attention had moved on to developing an analytical engine , further undermining

2444-461: Was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more quickly 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, and in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, which

2496-588: Was also completed. The conversion of the original design drawings into drawings suitable for engineering manufacturers' use revealed some minor errors in Babbage's design (possibly introduced as a protection in case the plans were stolen), which had to be corrected. The difference engine and printer were constructed to tolerances achievable with 19th-century technology, resolving a long-standing debate as to whether Babbage's design could have worked using Georgian-era engineering methods. The machine contains 8,000 parts and weighs about 5 tons. The printer's primary purpose

2548-428: Was built in 1979, following the original design fairly closely, but with some adaptations. In China the terra-cotta warriors can be recreated to be personalized for customers. The "Talented craftspeople use their hands and proper tools reproducing every masterwork precisely in the same manner as the royal craftsmen did 2200 years ago. They are made from the same local clay as the originals and constructed essentially in

2600-577: Was composed of four modified Triumphator calculators. Leslie Comrie in 1928 described how to use the Brunsviga -Dupla calculating machine as a difference engine of second-order (15-digit numbers). He also noted in 1931 that National Accounting Machine Class 3000 could be used as a difference engine of sixth-order. During the 1980s, Allan G. Bromley , an associate professor at the University of Sydney , Australia , studied Babbage's original drawings for

2652-633: Was later extended to third-order (1842). In 1843, after adding the printing part, the model was completed. In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853. The machine was demonstrated at the World's Fair in Paris, 1855 and then sold in 1856 to the Dudley Observatory in Albany, New York . Delivered in 1857, it

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2704-653: Was the first printing calculator sold. In 1857 the British government ordered the next Scheutz's difference machine, which was built in 1859. It had the same basic construction as the previous one, weighing about 10  cwt (1,100  lb ; 510  kg ). Martin Wiberg improved Scheutz's construction ( c.  1859 , his machine has the same capacity as Scheutz's: 30-digit and sixth-order) but used his device only for producing and publishing printed tables (interest tables in 1860, and logarithmic tables in 1875). Alfred Deacon of London in c.  1862 produced

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