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These include: Dean of the Advanced School for Computing and Imaging. In the early 1990s, the Dutch government began setting up a number of thematically oriented research schools that spanned multiple universities. These schools were intended to bring professors and PhD students from different Dutch (and later, foreign) universities together to help them cooperate and enhance their research. Tanenbaum was one of the cofounders and first Dean of the Advanced School for Computing and Imaging (ASCI). This school initially consisted of nearly 200 faculty members and PhD students from the Vrije Universiteit, University of Amsterdam, Delft University of Technology, and Leiden University. They were especially working on problems in advanced computer systems such as parallel computing and image analysis and processing. Tanenbaum remained dean for 12 years, until 2005, when he was awarded an Academy Professorship by the Royal Netherlands Academy of Arts and Sciences, at which time he became a full-time research professor.
Projects. Amsterdam Compiler Kit. The Amsterdam Compiler Kit is a toolkit for producing portable compilers. It was started sometime before 1981 and Andrew Tanenbaum was the architect from the start until version 5.5. MINIX. In 1987, Tanenbaum wrote a clone of UNIX, called MINIX (MINi-unIX), for the IBM PC. It was targeted at students and others who wanted to learn how an operating system worked. Consequently, he wrote a book that listed the source code in an appendix and described it in detail in the text. The source code itself was available on a set of floppy disks. Within three months, a Usenet newsgroup, comp.os.minix, had sprung up with over 40,000 subscribers discussing and improving the system. One of these subscribers was Linus Torvalds, who began adding new features to MINIX and tailoring it to his own needs. On October 5, 1991, Torvalds announced his own (POSIX-like) kernel, called Linux, which originally used the MINIX file system but is not based on MINIX code. Electoral-vote.com. In 2004, Tanenbaum created Electoral-vote.com, a web site analyzing opinion polls for the 2004 U.S. presidential election, using them to project the outcome in the Electoral College. He stated that he created the site as an American who "knows first hand what the world thinks of America and it is not a pretty picture at the moment. I want people to think of America as the land of freedom and democracy, not the land of arrogance and blind revenge. I want to be proud of America again." The site provided a color-coded map, updated each day with projections for each state's electoral votes. Through most of the campaign period Tanenbaum kept his identity secret, referring to himself as "the Votemaster" and acknowledging only that he personally preferred John Kerry. Mentioning that he supported the Democrats, he revealed his identity on November 1, 2004, the day before the election, and also stating his reasons and qualifications for running the website.
Through the site he also covered the 2006 midterm elections, correctly predicting the winner of all 33 Senate races that year. For the 2008 elections, he got every state right except for Indiana, which he said McCain would win by 2% (Obama won by 1%) and Missouri, which he said was too close to call (McCain won by 0.1%). He correctly predicted all the winners in the Senate except for Minnesota, where he predicted a 1% win by Norm Coleman over Al Franken. After 7 months of legal battling and recounts, Franken won by 312 votes (0.01%). In 2010, he correctly projected 35 out of 37 Senate races in the Midterm elections on the website. The exceptions were Colorado and Nevada. Electoral-vote.com incorrectly predicted Hillary Clinton would win the 2016 United States presidential election. The website incorrectly predicted Clinton would win Wisconsin, Michigan, Pennsylvania, North Carolina, and Florida. Electoral-vote.com did not predict a winner for Nevada, which Clinton would win. The website predicted the winners of the remaining 44 states and the District of Columbia correctly. Clinton however, won the popular vote, but lost the electoral vote. Tanenbaum–Torvalds debate. The Tanenbaum–Torvalds debate was a famous debate between Tanenbaum and Linus Torvalds regarding kernel design on Usenet in 1992.
Ariane 5 Ariane 5 is a retired European heavy-lift space launch vehicle operated by Arianespace for the European Space Agency (ESA). It was launched from the Guiana Space Centre (CSG) in French Guiana. It was used to deliver payloads into geostationary transfer orbit (GTO), low Earth orbit (LEO) or further into space. The launch vehicle had a streak of 82 consecutive successful launches between 9 April 2003 and 12 December 2017. Since 2014, Ariane 6, a direct successor system, first launched in 2024. The system was designed as an expendable launch vehicle by the "Centre national d'études spatiales" (CNES), the French government's space agency, in cooperation with various European partners. Despite not being a direct derivative of its predecessor launch vehicle program, it was classified as part of the Ariane rocket family. Aérospatiale, and later ArianeGroup, was the prime contractor for the manufacturing of the vehicles, leading a multi-country consortium of other European contractors. Ariane 5 was originally intended to launch the Hermes spacecraft, and thus it was rated for human space launches.
Since its first launch, Ariane 5 was refined in successive versions: "G", "G+", "GS", "ECA", and finally, "ES". The system had a commonly used dual-launch capability, where up to two large geostationary belt communication satellites can be mounted using a SYLDA ("Système de Lancement Double Ariane", meaning "Ariane Double-Launch System") carrier system. Up to three, somewhat smaller, main satellites are possible depending on size using a SPELTRA ("Structure Porteuse Externe Lancement Triple Ariane", which translates to "Ariane Triple-Launch External Carrier Structure"). Up to eight secondary payloads, usually small experiment packages or minisatellites, could be carried with an ASAP (Ariane Structure for Auxiliary Payloads) platform. Following the launch of 15 August 2020, Arianespace signed the contracts for the last eight Ariane 5 launches, before it was succeeded by the new Ariane 6 launcher, according to Daniel Neuenschwander, director of space transportation at the ESA. Ariane 5 flew its final mission on 5 July 2023.
Vehicle description. Cryogenic main stage. Ariane 5's cryogenic H173 main stage (H158 for Ariane 5G, G+, and GS) was called the EPC ("Étage Principal Cryotechnique" — Cryotechnic Main Stage). It consisted of a diameter by high tank with two compartments, one for liquid oxygen and one for liquid hydrogen, and a Vulcain 2 engine at the base with a vacuum thrust of . The H173 EPC weighed about , including of propellant. After the main cryogenic stage runs out of fuel, it re-entered the atmosphere for an ocean splashdown. Solid boosters. Attached to the sides were two P241 (P238 for Ariane 5G and G+) solid rocket boosters (SRBs or EAPs from the French "Étages d'Accélération à Poudre"), each weighing about full and delivering a thrust of about . They were fueled by a mix of ammonium perchlorate (68%) and aluminium fuel (18%) and HTPB (14%). They each burned for 130 seconds before being dropped into the ocean. The SRBs were usually allowed to sink to the bottom of the ocean, but, like the Space Shuttle Solid Rocket Boosters, they could be recovered with parachutes, and this was occasionally done for post-flight analysis. Unlike Space Shuttle SRBs, Ariane 5 boosters were not reused. The most recent attempt was for the first Ariane 5 ECA mission in 2009. One of the two boosters was successfully recovered and returned to the Guiana Space Center for analysis. Prior to that mission, the last such recovery and testing was done in 2003.
The French M51 submarine-launched ballistic missile (SLBM) shared a substantial amount of technology with these boosters. In February 2000, the suspected nose cone of an Ariane 5 booster washed ashore on the South Texas coast, and was recovered by beachcombers before the government could get to it. Second stage. The second stage was on top of the main stage and below the payload. The original Ariane — Ariane 5G — used the EPS ("Étage à Propergols Stockables" — Storable Propellant Stage), which was fueled by monomethylhydrazine (MMH) and nitrogen tetroxide, containing of storable propellant. The EPS was subsequently improved for use on the Ariane 5G+, GS, and ES. The EPS upper stage was capable of repeated ignition, first demonstrated during flight V26 which was launched on 5 October 2007. This was purely to test the engine, and occurred after the payloads had been deployed. The first operational use of restart capability as part of a mission came on 9 March 2008, when two burns were made to deploy the first Automated Transfer Vehicle (ATV) into a circular parking orbit, followed by a third burn after ATV deployment to de-orbit the stage. This procedure was repeated for all subsequent ATV flights.
Ariane 5ECA used the ESC ("Étage Supérieur Cryotechnique" — Cryogenic Upper Stage), which was fueled by liquid hydrogen and liquid oxygen. The ESC used the HM7B engine previously used in the Ariane 4 third stage. The propellent load of 14.7 tonne allowed the engine to burn for 945 seconds while providing 6.5 tonne of thrust. The ESC provided roll control during powered flight and full attitude control during payload separation using hydrogen gas thrusters. Oxygen gas thrusters allowed longitudinal acceleration after engine cutoff. The flight assembly included the Vehicle Equipment Bay, with flight electronics for the entire rocket, and the payload interface and structural support. Fairing. The payload and all upper stages were covered at launch by a fairing for aerodynamic stability and protection from heating during supersonic flight and acoustic loads. It was jettisoned once sufficient altitude has been reached, typically above . It was made by Ruag Space and since flight VA-238 it was composed of 4 panels.
Launch pricing and market competition. , the Ariane 5 commercial launch price for launching a "midsize satellite in the lower position" was approximately €50 million, competing for commercial launches in an increasingly competitive market. The heavier satellite was launched in the upper position on a typical dual-satellite Ariane 5 launch and was priced higher than the lower satellite, on the order of €90 million . Total launch price of an Ariane 5 – which could transport up to two satellites to space, one in the "upper" and one in the "lower" positions – was around €150 million . Cancelled plans for future developments. Ariane 5 ME. The Ariane 5 ME (Mid-life Evolution) was in development into early 2015, and was seen as a stopgap between Ariane 5ECA/Ariane 5ES and the new Ariane 6. With first flight planned for 2018, it would have become ESA's principal launcher until the arrival of the new Ariane 6 version. ESA halted funding for the development of Ariane 5ME in late 2014 to prioritize development of Ariane 6.
The Ariane 5ME was to use a new upper stage, with increased propellant volume, powered by the new Vinci engine. Unlike the HM-7B engine, it was to be able to restart several times, allowing for complex orbital maneuvers such as insertion of two satellites into different orbits, direct insertion into geosynchronous orbit, planetary exploration missions, and guaranteed upper stage deorbiting or insertion into graveyard orbit. The launcher was also to include a lengthened fairing up to and a new dual launch system to accommodate larger satellites. Compared to an Ariane 5ECA model, the payload to GTO was to increase by 15% to and the cost-per-kilogram of each launch was projected to decline by 20%. Development. Originally known as the Ariane 5ECB, Ariane 5ME was to have its first flight in 2006. However, the failure of the first ECA flight in 2002, combined with a deteriorating satellite industry, caused ESA to cancel development in 2003. Development of the Vinci engine continued, though at a lower pace. The ESA Council of Ministers agreed to fund development of the new upper stage in November 2008.
In 2009, EADS Astrium was awarded a €200 million contract, and on 10 April 2012 received another €112 million contract to continue development of the Ariane 5ME with total development effort expected to cost €1 billion. On 21 November 2012, ESA agreed to continue with the Ariane 5ME to meet the challenge of lower priced competitors. It was agreed the Vinci upper stage would also be used as the second stage of a new Ariane 6, and further commonality would be sought. Ariane 5ME qualification flight was scheduled for mid-2018, followed by gradual introduction into service. On 2 December 2014, ESA decided to stop funding the development of Ariane 5ME and instead focus on Ariane 6, which was expected to have a lower cost per launch and allow more flexibility in the payloads (using two or four P120C solid boosters depending on total payload mass). Solid propellant stage. Work on the Ariane 5 EAP motors was continued in the Vega programme. The Vega 1st stage engine – the P80 engine – was a shorter derivation of the EAP. The P80 booster casing was made of filament wound graphite epoxy, much lighter than the current stainless steel casing. A new composite steerable nozzle was developed while new thermal insulation material and a narrower throat improved the expansion ratio and subsequently the overall performance. Additionally, the nozzle had electromechanical actuators which replaced the heavier hydraulic ones used for thrust vector control.
These developments could maybe have made their way back into the Ariane programme, but this was most likely an inference based on early blueprints of the Ariane 6 having a central P80 booster and 2-4 around the main one. The incorporation of the ESC-B with the improvements to the solid motor casing and an uprated Vulcain engine would have delivered to LEO. This would have been developed for any lunar missions but the performance of such a design might not have been possible if the higher Max-Q for the launch of this launch vehicle would have posed a constraint on the mass delivered to orbit. Ariane 6. The design brief of the next generation launch vehicle Ariane 6 called for a lower-cost and smaller launch vehicle capable of launching a single satellite of up to to GTO. However, after several permutations the finalized design was nearly identical in performance to the Ariane 5, focusing instead on lowering fabrication costs and launch prices. , Ariane 6 was projected to be launched for about €70 million per flight, about half of the Ariane 5 price.
Initially development of Ariane 6 was projected to cost €3.6 billion. In 2017, the ESA set 16 July 2020 as the deadline for the first flight. The Ariane 6 successfully completed its maiden flight on 9 July 2024. Notable launches. Ariane 5's first test flight (Ariane 5 Flight 501) on 4 June 1996 failed, with the rocket self-destructing 37 seconds after launch because of a malfunction in the control software. A data conversion from 64-bit floating-point value to 16-bit signed integer value to be stored in a variable representing horizontal bias caused a processor trap (operand error) because the floating-point value was too large to be represented by a 16-bit signed integer. The software had been written for the Ariane 4 where efficiency considerations (the computer running the software had an 80% maximum workload requirement) led to four variables being protected with a handler while three others, including the horizontal bias variable, were left unprotected because it was thought that they were "physically limited or that there was a large margin of safety". The software, written in Ada, was included in the Ariane 5 through the reuse of an entire Ariane 4 subsystem despite the fact that the particular software containing the bug, which was just a part of the subsystem, was not required by the Ariane 5 because it has a different preparation sequence than the Ariane 4.
The second test flight (L502, on 30 October 1997) was a partial failure. The Vulcain nozzle caused a roll problem, leading to premature shutdown of the core stage. The upper stage operated successfully, but it could not reach the intended orbit. A subsequent test flight (L503, on 21 October 1998) proved successful and the first commercial launch (L504) occurred on 10 December 1999 with the launch of the XMM-Newton X-ray observatory satellite. Another partial failure occurred on 12 July 2001, with the delivery of two satellites into an incorrect orbit, at only half the height of the intended GTO. The ESA Artemis telecommunications satellite was able to reach its intended orbit on 31 January 2003, through the use of its experimental ion propulsion system. The next launch did not occur until 1 March 2002, when the Envisat environmental satellite successfully reached an orbit of above the Earth in the 11th launch. At , it was the heaviest single payload until the launch of the first ATV on 9 March 2008, at . The first launch of the ECA variant on 11 December 2002 ended in failure when a main booster problem caused the rocket to veer off-course, forcing its self-destruction three minutes into the flight. Its payload of two communications satellites (STENTOR and Hot Bird 7), valued at about €630 million, was lost in the Atlantic Ocean. The fault was determined to have been caused by a leak in coolant pipes allowing the nozzle to overheat. After this failure, Arianespace SA delayed the expected January 2003 launch for the Rosetta mission to 26 February 2004, but this was again delayed to early March 2004 due to a minor fault in the foam that protects the cryogenic tanks on the Ariane 5. The failure of the first ECA launch was the last failure of an Ariane 5 until flight 240 in January 2018.
On 27 September 2003, the last Ariane 5G boosted three satellites (including the first European lunar probe, SMART-1), in Flight 162. On 18 July 2004, an Ariane 5G+ boosted what was at the time the heaviest telecommunication satellite ever, Anik F2, weighing almost . The first successful launch of the Ariane 5ECA took place on 12 February 2005. The payload consisted of the XTAR-EUR military communications satellite, a 'SLOSHSAT' small scientific satellite and a MaqSat B2 payload simulator. The launch had been scheduled for October 2004, but additional testing and a military launch (of a Helios 2A observation satellite) delayed the attempt. On 11 August 2005, the first Ariane 5GS (featuring the Ariane 5ECA's improved solid motors) boosted Thaicom 4, the heaviest telecommunications satellite to date at , into orbit. On 16 November 2005, the third Ariane 5ECA launch (the second successful ECA launch) took place. It carried a dual payload consisting of Spaceway F2 for DirecTV and Telkom-2 for PT Telekomunikasi of Indonesia. This was the launch vehicle's heaviest dual payload to date, at more than .
On 27 May 2006, an Ariane 5ECA launch vehicle set a new commercial payload lifting record of . The dual-payload consisted of the Thaicom 5 and Satmex 6 satellites. On 4 May 2007, the Ariane 5ECA set another new commercial record, lifting into transfer orbit the Astra 1L and Galaxy 17 communication satellites with a combined weight of , and a total payload weight of . This record was again broken by another Ariane 5ECA, launching the Skynet 5B and Star One C1 satellites, on 11 November 2007. The total payload weight for this launch was of . On 9 March 2008, the first Ariane 5ES-ATV was launched to deliver the first ATV called "Jules Verne" to the International Space Station (ISS). The ATV was the heaviest payload ever launched by a European launch vehicle, providing supplies to the space station with necessary propellant, water, air and dry cargo. This was the first operational Ariane mission which involved an engine restart in the upper stage. The ES-ATV Aestus EPS upper stage was restartable while the ECA HM7-B engine was not.
On 1 July 2009, an Ariane 5ECA launched TerreStar-1 (now EchoStar T1), which was then, at , the largest and most massive commercial telecommunication satellite ever built at that time until being overtaken by Telstar 19 Vantage, at , launched aboard Falcon 9. The satellite was launched into a lower-energy orbit than a usual GTO, with its initial apogee at roughly . On 28 October 2010, an Ariane 5ECA launched Eutelsat's W3B (part of its W Series of satellites) and Broadcasting Satellite System Corporation (B-SAT)'s BSAT-3b satellites into orbit. But the W3B satellite failed to operate shortly after the successful launch and was written off as a total loss due to an oxidizer leak in the satellite's main propulsion system. The BSAT-3b satellite, however, is operating normally. The VA253 launch on 15 August 2020 introduced two small changes that increased lift capacity by about ; these were a lighter avionics and guidance-equipment bay, and modified pressure vents on the payload fairing, which were required for the subsequent launch of the James Webb Space Telescope. It also debuted a location system using Galileo navigation satellites.
On 25 December 2021, VA256 launched the James Webb Space Telescope towards a Sun–Earth L2 halo orbit. The precision of trajectory following launch led to fuel savings credited with potentially doubling the lifetime of the telescope by leaving more hydrazine propellant on board for station-keeping than was expected. According to Rudiger Albat, the program manager for Ariane 5, efforts had been made to select components for this flight that had performed especially well during pre-flight testing, including "one of the best Vulcain engines that we've ever built." GTO payload weight records. On 22 April 2011, the Ariane 5ECA flight VA-201 broke a commercial record, lifting Yahsat 1A and Intelsat New Dawn with a total payload weight of to transfer orbit. This record was later broken again during the launch of Ariane 5ECA flight VA-208 on 2 August 2012, lifting a total of into the planned geosynchronous transfer orbit, which was broken again 6 months later on flight VA-212 with sent towards geosynchronous transfer orbit. In June 2016, the GTO record was raised to , on the first rocket in history that carried a satellite dedicated to financial institutions. The payload record was pushed a further , up to on 24 August 2016 with the launch of Intelsat 33e and Intelsat 36. On 1 June 2017, the payload record was broken again to carrying ViaSat-2 and Eutelsat-172B. In 2021 VA-255 put 11,210 kg into GTO.
VA241 anomaly. On 25 January 2018, an Ariane 5ECA launched SES-14 and Al Yah 3 satellites. About 9 minutes and 28 seconds after launch, a telemetry loss occurred between the launch vehicle and the ground controllers. It was later confirmed, about 1 hour and 20 minutes after launch, that both satellites were successfully separated from the upper stage and were in contact with their respective ground controllers, but that their orbital inclinations were incorrect as the guidance systems might have been compromised. Therefore, both satellites conducted orbital procedures, extending commissioning time. SES-14 needed about 8 weeks longer than planned commissioning time, meaning that entry into service was reported early September instead of July. Nevertheless, SES-14 is still expected to be able to meet the designed lifetime. This satellite was originally to be launched with more propellant reserve on a Falcon 9 launch vehicle since the Falcon 9, in this specific case, was intended to deploy this satellite into a high inclination orbit that would require more work from the satellite to reach its final geostationary orbit. The Al Yah 3 was also confirmed healthy after more than 12 hours without further statement, and like SES-14, Al Yah 3's maneuvering plan was also revised to still fulfill the original mission. As of 16 February 2018, Al Yah 3 was approaching the intended geostationary orbit, after series of recovery maneuvers had been performed. The investigation showed that invalid inertial units' azimuth value had sent the vehicle 17° off course but to the intended altitude, they had been programmed for the standard geostationary transfer orbit of 90° when the payloads were intended to be 70° for this supersynchronous transfer orbit mission, 20° off norme. This mission anomaly marked the end of 82nd consecutive success streak since 2003. Launch history. Launch statistics. Ariane 5 launch vehicles had accumulated 117 launches, 112 of which were successful, yielding a success rate. Between April 2003 and December 2017, Ariane 5 flew 83 consecutive missions without failure, but the launch vehicle suffered a partial failure in January 2018. List of launches. All launches are from Guiana Space Centre, ELA-3.
Arianespace Arianespace SA is a French company founded in March 1980 as the world's first commercial launch service provider. It operates two launch vehicles: Vega C, a small-lift rocket, and Ariane 6, a medium-to-heavy-lift rocket. Arianespace is a subsidiary of ArianeGroup, a joint venture between Airbus and Safran. European space launches are carried out as a collaborative effort between private companies and government agencies. The role of Arianespace is to market Ariane 6 launch services, prepare missions, and manage customer relations. At the Guiana Space Centre (CSG) in French Guiana, the company oversees the team responsible for integrating and preparing launch vehicles. The rockets themselves are designed and manufactured by other companies: ArianeGroup for the Ariane 6 and Avio for the Vega. The launch infrastructure at the CSG is owned by the European Space Agency, while the land itself belongs to and is managed by CNES, the French national space agency. , Arianespace had launched more than 850 satellites in 287 missions spanning 41 years. The company's first commercial launch was Spacenet 1, which took place on 23 May 1984. In addition to its facilities at the CSG, the company's main offices are in Évry-Courcouronnes, a suburb of Paris.
History. The formation of Arianespace SA is closely associated with the desire of several European nations to pursue joint collaboration in the field of space exploration and the formation of a pan-national organisation, the European Space Agency (ESA), to oversee such undertaking during 1973. Prior to the ESA's formation, France had been lobbying for the development of a new European expendable launch system to serve as a replacement for the Europa rocket. Accordingly, one of the first programmes launched by the ESA was the Ariane heavy launcher. The express purpose of this launcher was to facilitate the delivery of commercial satellites into geosynchronous orbit. France was the largest stakeholder in the Ariane development programme. French aerospace manufacturer Aérospatiale served as the prime contractor and held responsibility for performing the integration of all sections of the vehicle, while French engine manufacturer Société Européenne de Propulsion (SEP) provided the first, second and third stage engines (the third stage engines were produced in partnership with German aerospace manufacturer MBB). Other major companies involved included the French firms Air Liquide and Matra, Swedish manufacturer Volvo, and German aircraft producer Dornier Flugzeugwerke. Development of the third stage was a major focus point for the project - prior to Ariane, only the United States had ever flown a launcher that utilised hydrogen-powered upper stages.
Immediately following the successful first test launch of an Ariane 1 on 24 December 1979, the French space agency Centre national d'études spatiales (CNES) and the ESA created a new company, "Arianespace", for the purpose of promoting, marketing, and managing Ariane operations. According to Arianespace, at the time of its establishment, it was the world's first launch services company. Following a further three test launches, the first commercial launch took place on 10 September 1982, which ended in failure as a result of a turbopump having failed in the third stage. The six remaining flights of the Ariane 1 were successful, with the final flight occurring during February 1986. As a result of these repeated successes, orders for the Ariane launcher quickly mounted up; by early 1984, a total of 27 satellites had been booked to use Ariane, which was estimated to be half of the world's market at that time. As a result of the commercial success, after the tenth Ariane mission was flown, the ESA formally transferred responsibility for Ariane over to Arianespace.
By early 1986, the Ariane 1, along with its Ariane 2 and Ariane 3 derivates, were the dominant launcher on the world market. The Ariane 2 and Ariane 3 were short-lived platforms while the more extensive Ariane 4 was being developed; it was a considerably larger and more flexible launcher that the earlier members of its family, having been intended from the onset to compete with the upper end of launchers worldwide. In comparison, while the Ariane 1 had a typical weight of 207 tonnes and could launch payloads of up to 1.7 tonnes into orbit; the larger Ariane 4 had a typical weight of 470 tonnes and could orbit payloads of up to 4.2 tonnes. Despite this, the Ariane 4 was actually 15 per cent smaller than the Ariane 3. On 15 June 1988, the first successful launch of the Ariane 4 was conducted. This maiden flight was considered a success, having placed multiple satellites into orbit. For the V50 launch onwards, an improved third stage, known as the "H10+", was adopted for the Ariane 4, which raised the rocket's overall payload capacity by 110 kg and increased its burn time by 20 seconds.
Even prior to the first flight of the Ariane 4 in 1988, development of a successor, designated as the Ariane 5, had already commenced. In January 1985, the Ariane 5 was officially adopted as an ESA programme, and began an eleven-year development and test program to the first launch in 1996. It lacked the high levels of commonality that the Ariane 4 had with its predecessors, and had been designed not only for launching heavier payloads of up to 5.2 tonnes and at a 20 per cent cost reduction over the Ariane 4, but for a higher margin of safety due to the fact that the Ariane 5 was designed to conduct crewed space launches as well, being intended to transport astronauts using the proposed Hermes space vehicle. Development of the Ariane 5 was not without controversy as some ESA members considered the mature Ariane 4 platform to be more suited for meeting established needs for such launchers; it was reportedly for this reason that Britain chose not to participate in the Ariane 5 programme. For several years, Ariane 4 and Ariane 5 launchers were operated interchangeably; however, it was eventually decided to terminate all Ariane 4 operations in favour of concentrating on the newer Ariane 5.
During the mid-1990s, French firms Aérospatiale and SEP, along with Italian firm Bombrini-Parodi-Delfino (BPD), held discussions on the development of a proposed Ariane Complementary Launcher (ACL). Simultaneously, Italy championed the concept of a new solid-propellant satellite launcher, referred to as Vega. During March 2003, contracts for Vega's development were signed by the ESA and CNES; Italy provided 65 per cent of funding while six additional nations contributed the remainder. In May 2004, it was reported that a contract was signed between commercial operator Arianespace and prime contractor ELV to perform vehicle integration at Kourou, French Guiana. On 13 February 2012, the first launch of the Vega took place; it was reported as being an "apparently perfect flight". Since entering commercial service, Arianespace markets Vega as a launch system tailored for missions to polar and Sun-synchronous orbits. During 2002, the ESA announced the Arianespace Soyuz programme in cooperation with Russia; a launch site for Soyuz was constructed as the Guiana Space Centre, while the Soyuz launch vehicle was modified for use at the site. On 4 February 2005, both funding and final approval for the initiative were granted. Arianespace had offered launch services on the modified Soyuz ST-B to its clients. On 21 October 2011, Arianespace launched the first Soyuz rocket ever from outside former Soviet territory. The payload consisted of two Galileo navigation satellites. Since 2011, Arianespace has ordered a total of 23 Soyuz rockets, enough to cover its needs until 2019 at a pace of three to four launches per year.
On 21 January 2019, ArianeGroup and Arianespace announced that it had signed a one-year contract with the ESA to study and prepare for a mission to the Moon to mine regolith. In 2020, Arianespace suspended operations for nearly two months due to the COVID-19 pandemic. Operations were suspended on 18 March and are, as of 29 April, expected to resume on 11 May. The return to operations will observe a number of new health and safety guidelines including social distancing in the workplace. In 2023, Ariane 5 was retired with the introduction of new Ariane 6, that conducted its maiden flight on 9 July 2024. In August 2024, the ESA agreed to allow Avio—the prime contractor for the ESA-funded Vega—to directly commercialize Vega C and seek non-governmental customers. Arianespace had handled marketing of Vega launches prior to that time. The transition is anticipated to be complete by the end of 2025. Company and infrastructure. Arianespace "is the marketing and sales organization for the European space industry and various component suppliers."
The primary shareholders of Arianespace are its suppliers, in various European nations. Arianespace had 24 shareholders in 2008, 21 in 2014, and just 17 . In 2015, Arianespace shareholding was restructured due to the creation of Airbus Safran Launchers (later renamed ArianeGroup), which is tasked with developing and manufacturing the Ariane 6 carrier rocket. Industrial groups Airbus and Safran pooled their shares along with the French government's CNES stake to form a partnership company holding just under 74% of Arianespace shares, while the remaining 26% is spread across suppliers in nine countries including further Airbus subsidiaries. Competition and pricing. By 2004, Arianespace reportedly held more than 50% of the world market for boosting satellites to geostationary transfer orbit (GTO). During the 2010s, the disruptive force represented by the new sector entrant SpaceX forced Arianespace to cut back on its workforce and focus on cost-cutting to decrease costs to remain competitive against the new low-cost entrant in the launch sector. In the midst of pricing pressure from such companies, during November 2013, Arianespace announced that it was enacting pricing flexibility for the "lighter satellites" that it carries to Geostationary orbits aboard its Ariane 5. According to Arianespace's managing director: "It's quite clear there's a very significant challenge coming from SpaceX (...) therefore things have to change (...) and the whole European industry is being restructured, consolidated, rationalised and streamlined."
During early 2014, Arianespace was considering requesting additional subsidies from European governments to face competition from SpaceX and unfavorable changes in the Euro-Dollar exchange rate. The company had halved subsidy support by €100m per year since 2002 but the fall in the value of the US Dollar meant Arianespace was losing €60m per year due to currency fluctuations on launch contracts. SpaceX had reportedly begun to take market share from Arianespace, Eutelsat CEO Michel de Rosen, a major customer of Arianespace, stated that: "Each year that passes will see SpaceX advance, gain market share and further reduce its costs through economies of scale." By September 2014, Arianespace had reportedly to sign four additional contracts for lower slots on an Ariane 5 SYLDA dispenser for satellites that otherwise could be flown on a SpaceX launch vehicle; this was claimed to have been allowed via cost reductions; it had signed a total of 11 contracts by that point, while two additional ones that were under advanced negotiations. At the time, Arianespace has a backlog of launches worth billion with 38 satellites to be launched on Ariane 5, 7 on Soyuz and 9 on Vega, claiming 60% of the global satellite launch market. However, since 2017, Arianespace's market share has been passed by SpaceX in commercial launches. Launch vehicles. Currently, Arianespace operates three launch vehicles: Ariane launch vehicles. Since the first launch in 1979, there have been several versions of the Ariane launch vehicle:
Accumulator (computing) In a computer's central processing unit (CPU), the accumulator is a register in which intermediate arithmetic logic unit results are stored. Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to cache or main memory, perhaps only to be read right back again for use in the next operation. Accessing memory is slower than accessing a register like an accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register. Early electronic computer systems were often split into two groups, those with accumulators and those without. Modern computer systems often have multiple general-purpose registers that can operate as accumulators, and the term is no longer as common as it once was. However, to simplify their design, a number of special-purpose processors still use a single accumulator. Basic concept. Mathematical operations often take place in a stepwise fashion, using the results from one operation as the input to the next. For instance, a manual calculation of a worker's weekly payroll might look something like:
A computer program carrying out the same task would follow the same basic sequence of operations, although the values being looked up would all be stored in computer memory. In early computers, the number of hours would likely be held on a punch card and the pay rate in some other form of memory, perhaps a magnetic drum. Once the multiplication is complete, the result needs to be placed somewhere. On a "drum machine" this would likely be back to the drum, an operation that takes considerable time. Then the very next operation has to read that value back in, which introduces another considerable delay. Accumulators dramatically improve performance in systems like these by providing a scratchpad area where the results of one operation can be fed to the next one for little or no performance penalty. In the example above, the basic weekly pay would be calculated and placed in the accumulator, which could then immediately be used by the income tax calculation. This removes one save and one read operation from the sequence, operations that generally took tens to hundreds of times as long as the multiplication itself.
Accumulator machines. An accumulator machine, also called a 1-operand machine, or a CPU with "accumulator-based architecture", is a kind of CPU where, although it may have several registers, the CPU mostly stores the results of calculations in one special register, typically called "the accumulator". Almost all computers were accumulator machines with only the high-performance "supercomputers" having multiple registers. Then as mainframe systems gave way to microcomputers, accumulator architectures were again popular with the MOS 6502 being a notable example. Many 8-bit microcontrollers that are still popular , such as the PICmicro and 8051, are accumulator-based machines. Modern CPUs are typically 2-operand or 3-operand machines. The additional operands specify which one of many general-purpose registers (also called "general-purpose accumulators") are used as the source and destination for calculations. These CPUs are not considered "accumulator machines". The characteristic that distinguishes one register as being the accumulator of a computer architecture is that the accumulator (if the architecture were to have one) would be used as an "implicit" operand for arithmetic instructions. For instance, a CPU might have an instruction like: codice_1 that adds the value read from memory location "memaddress" to the value in the accumulator, placing the result back in the accumulator. The accumulator is not identified in the instruction by a register number; it is implicit in the instruction and no other register can be specified in the instruction. Some architectures use a particular register as an accumulator in some instructions, but other instructions use register numbers for explicit operand specification.
History of the computer accumulator. Any system that uses a single "memory" to store the result of multiple operations can be considered an accumulator. J. Presper Eckert refers to even the earliest adding machines of Gottfried Leibniz and Blaise Pascal as accumulator-based systems. Percy Ludgate was the first to conceive a multiplier-accumulator (MAC) in his Analytical Machine of 1909. Historical convention dedicates a register to "the accumulator", an "arithmetic organ" that literally accumulates its number during a sequence of arithmetic operations: Just a few of the instructions are, for example (with some modern interpretation): No convention exists regarding the names for operations from registers to accumulator and from accumulator to registers. Tradition (e.g. Donald Knuth's (1973) hypothetical MIX computer), for example, uses two instructions called "load accumulator" from register/memory (e.g. "LDA r") and "store accumulator" to register/memory (e.g. "STA r"). Knuth's model has many other instructions as well.
Notable accumulator-based computers. The 1945 configuration of ENIAC had 20 accumulators, which could operate in parallel. Each one could store an eight decimal digit number and add to it (or subtract from it) a number it received. Most of IBM's early binary "scientific" computers, beginning with the vacuum tube IBM 701 in 1952, used a single 36-bit accumulator, along with a separate multiplier/quotient register to handle operations with longer results. The IBM 650, a decimal machine, had one 10 digit distributor and two ten-digit accumulators; the IBM 7070, a later, transistorized decimal machine had three accumulators. The IBM System/360, and Digital Equipment Corporation's PDP-6, had 16 general-purpose registers, although the PDP-6 and its successor, the PDP-10, call them accumulators. The 12-bit PDP-8 was one of the first minicomputers to use accumulators, and inspired many later machines. The PDP-8 had but one accumulator. The HP 2100 and Data General Nova had 2 and 4 accumulators. The Nova was created when this follow-on to the PDP-8 was rejected in favor of what would become the PDP-11. The Nova provided four accumulators, AC0-AC3, although AC2 and AC3 could also be used to provide offset addresses, tending towards more generality of usage for the registers. The PDP-11 had 8 general-purpose registers, along the lines of the System/360 and PDP-10; most later CISC and RISC machines provided multiple general-purpose registers.
Early 4-bit and 8-bit microprocessors such as the 4004, 8008 and numerous others, typically had single accumulators. The 8051 microcontroller has two, a primary accumulator and a secondary accumulator, where the second is used by instructions only when multiplying (MUL AB) or dividing (DIV AB); the former splits the 16-bit result between the two 8-bit accumulators, whereas the latter stores the quotient on the primary accumulator A and the remainder in the secondary accumulator B. As a direct descendant of the 8008, the 8080, and the 8086, the modern ubiquitous Intel x86 processors still uses the primary accumulator EAX and the secondary accumulator EDX for multiplication and division of large numbers. For instance, MUL ECX will multiply the 32-bit registers ECX and EAX and split the 64-bit result between EAX and EDX. However, MUL and DIV are special cases; other arithmetic-logical instructions (ADD, SUB, CMP, AND, OR, XOR, TEST) may specify any of the eight registers EAX, ECX, EDX, EBX, ESP, EBP, ESI, EDI as the accumulator (i.e. left operand and destination). This is also supported for multiply if the upper half of the result is not required. x86 is thus a fairly general register architecture, despite being based on an accumulator model. The 64-bit extension of x86, x86-64, has been further generalized to 16 instead of 8 general registers.
Abu Zubaydah Abu Zubaydah ( ; , "Abū Zubaydah"; born March 12, 1971, as Zayn al-Abidin Muhammad Husayn) is a Saudi citizen and alleged terrorist born in Saudi Arabia currently held by the U.S. in the Guantanamo Bay detention camp in Cuba. He is held under the authority of Authorization for Use of Military Force Against Terrorists (AUMF). Zubaydah was captured in Pakistan in March 2002 and has been in United States custody ever since, including years in the secret prison network of the Central Intelligence Agency (CIA). He was transferred among prisons in various countries including a year in Poland, as part of a United States extraordinary rendition program. During his time in CIA custody, Zubaydah was extensively interrogated; he was waterboarded 83 times and subjected to numerous other torture techniques including forced nudity, sleep deprivation, confinement in small dark boxes, deprivation of solid food, stress positions, and physical assaults. Videotapes of some of Zubaydah's interrogations are allegedly amongst those destroyed by the CIA in 2005.
Zubaydah and ten other "high-value detainees" were transferred to Guantanamo in September 2006. He and other former CIA detainees are held in Camp 7, where conditions are the most isolating. On July 24, 2014, the European Court of Human Rights ordered the Polish government to pay Zubaydah damages. Zubaydah stated through his US lawyer that he would be donating the awarded funds to victims of torture. Biography and early activities. According to his younger brother Hesham, they had eight siblings. Hesham remembers his older brother "as a happy-go-lucky guy, and something of a womanizer". Born in Saudi Arabia, Zubaydah is reported to have studied computer science in Mysore, India, prior to his travel to Afghanistan/Pakistan at the age of 20 in 1991. In 1991 he joined the mujahideen and fought against Afghan Communist Government forces during the Afghan Civil War, perhaps serving under Mohamad Kamal Elzahabi. In 1992, Zubaydah was injured in an Afghan mortar attack, which left shrapnel in his head and caused severe memory loss, as well as the loss of the ability to speak for over one year.
Zubaydah eventually became involved in the training camp known as the Khalden training camp, where he oversaw the flow of recruits and obtained passports and paperwork for men transferring out of Khalden. He may also have worked as an instructor there. Although originally described as an al-Qaeda training camp, this alleged connection, which has been used as justification for holding Zubaydah and others as enemy combatants, has come under scrutiny from multiple sources, and the camp may have shut its doors in 2001 in response to an ideological division with al-Qaeda. By 1999, the United States government was attempting to surveil Zubaydah. By March 2000, United States officials were reporting that Zubaydah was a "senior bin Laden official", the "former head of Egypt-based Islamic Jihad", a "trusted aide" to bin Laden with "growing power", who had "played a key role in the East Africa embassy attacks". Zubaydah was convicted "in absentia" in Jordan and sentenced to death by a Jordanian court for his role in plots to bomb U.S. and Israeli targets there. A senior Middle East security official said Zubaydah had directed the Jordanian cell and was part of "bin Laden's inner circle".
In August 2001, the classified FBI report, "Bin Ladin Determined To Strike in US", said that the foiled millennium bomber, Ahmed Ressam, had confessed that Zubaydah had encouraged him to blow up the Los Angeles airport and facilitated his mission. The report said that Zubaydah was also planning his own attack on the U.S. However, when Ressam was tried in December 2001, federal prosecutors did not try to connect him to Zubaydah or refer to any of this supposed evidence in its case. After the trial, Ressam recanted his confession, saying he had been coerced into giving it. According to a psychological evaluation conducted upon his capture, Zubaydah allegedly served as Osama bin Laden's senior lieutenant and counter-intelligence officer (i.e. third or fourth highest-ranking member of al Qaeda), managed a network of training camps, was involved in every major terrorist operation carried out by al Qaeda (including the planning of 9/11), and was engaged in planning future terrorist attacks against U.S. interests. These statements were widely echoed by members of the George W. Bush administration and other US officials. Zubaydah's perceived "value" as a detainee would later be used by George W. Bush to justify the use of "enhanced interrogation techniques" and Zubaydah's detention in secret CIA prisons around the world. However, Zubaydah's connection to al Qaeda is now often said to have beenaccording to Rebecca Gordon writing about "The al Qaeda Leader Who Wasn't"a fictitious charge. Others have said instead that it is merely overstated, and in response to his habeas corpus petition, the U.S. Government stated in 2009 that it did not contend Zubaydah had any involvement with the 9/11 attacks, or that he had even been a member of al Qaeda, simply because they did not have to: "In simple terms, the issue in this habeas corpus action is Petitioner's conduct", rather than membership or inclination: "Petitioner's personal philosophy is not relevant except to the extent that it is reflected in his actions".
Capture. On March 28, 2002, CIA and FBI agents, in conjunction with Pakistani intelligence, raided several safe houses in Pakistan searching for Zubaydah. Zubaydah was apprehended from one of the targeted safe houses in Faisalabad, Pakistan. The Pakistani intelligence service had paid a small amount for a tip on his whereabouts. The United States paid far more to Pakistan for its assistance; a CIA source later said: "We paid $10 million for Zubaydah." During the raid, Zubaydah was shot in the thigh, the testicle, and the stomach with rounds from a Kalashnikov assault rifle. Not recognized at first, he was piled into a pickup truck along with other prisoners by the Pakistani forces until a senior CIA officer identified him. He was taken by the Pakistanis to a Pakistani hospital nearby and treated for his wounds. The attending doctor told the CIA lead officer of the group which apprehended Zubaydah that he had never before seen a patient survive such severe wounds. The CIA flew in a doctor from Johns Hopkins University to ensure Zubaydah would survive during transit out of Pakistan.
His pocket litter supposedly contained two bank cards, which showed that he had access to Saudi and Kuwaiti bank accounts; most al-Qaeda members used the preferred, untraceable hawala banking. According to James Risen: "It is not clear whether an investigation of the cards simply fell through the cracks, or whether they were ignored because no one wanted to know the answers about connections between al Qaeda and important figures in the Middle East—particularly in Saudi Arabia." One of Risen's sources chalks up the failure to investigate the cards to incompetence rather than foul play: "The cards were sent back to Washington and were never fully exploited. I think nobody ever looked at them because of incompetence." When Americans investigated the cards, Risen wrote that they worked with a Muslim financier with a questionable past, and with connections to the Afghan Taliban, al Qaeda, and Saudi intelligence. ... Saudi intelligence officials had seized all of the records related to the card from the Saudi financial institution in question; the records then disappeared. There was no longer any way to trace the money that had gone into the account.
A search of the safehouse turned up Zubaydah's 10,000-page diaries, in which he recorded his thoughts as a young boy, older man, and at his current age. What appears to be multiple separate identities is how Zubaydah was piecing his memories together after his 1992 shrapnel head wound. As part of his therapy to regain his memories, he began recording a diary that detailed his life, emotions, and what people were telling him. He split information into categories, such as what he knew about himself and what people told him, and listed them under different names to distinguish one set from the other. This was later interpreted by some analysts reviewing the diary as symptoms of Dissociative Identity Disorder, which some others disputed and said to be incorrect. Zubaydah was handed to the CIA. Reports later alleged that he was transferred to secret CIA-operated prisons, known as black sites, in Pakistan, Thailand, Afghanistan, Poland, Northern Africa, and Diego Garcia. Historically, renditions of prisoners to countries which commit torture have been illegal. A memo written by John Yoo and signed by Jay Bybee of the Office of the Legal Counsel, DOJ, days before Zubaydah's capture, provided a legal opinion providing for CIA renditions of detainees to places such as Thailand. In March 2009, the U.S. Senate Intelligence Committee launched a year-long study on how the CIA operated the secret prisons, or black sites, around the world.
Top U.S. officials approved torture techniques. In the spring of 2002, immediately following the capture of Zubaydah, top Bush administration officials, Vice President Dick Cheney, Secretary of State Colin Powell, CIA Director George Tenet, National Security Adviser Condoleezza Rice, Secretary of Defense Rumsfeld, and US Attorney General John Ashcroft discussed at length whether or not the CIA could legally use harsh techniques against him. Condoleezza Rice specifically mentioned the SERE program during the meeting, saying, "I recall being told that U.S. military personnel were subjected to training to certain physical and psychological interrogation techniques". In addition, in 2002 and 2003, the administration briefed several Democratic Congressional leaders on the proposed "enhanced interrogation techniques". These congressional leaders included Nancy Pelosi, the future Speaker of the House, and Representative Jane Harman. Congressional officials have stated that the attitude in the briefings ranged from "quiet acquiescence, if not downright support". The documents show that top U.S. officials were intimately involved in the discussion and approval of the harsher interrogation techniques used on Zubaydah. Condoleezza Rice ultimately told the CIA the harsher interrogation tactics were acceptable, and Dick Cheney stated, "I signed off on it; so did others." During the discussions, US Attorney General John Ashcroft is reported as saying, "Why are we talking about this in the White House? History will not judge this kindly."
Torture drawings. In December 2019, "The New York Times" published an article in partnership with the Pulitzer Center on Crisis Reporting which was based upon drawings made by Zubaydah, showing how he was tortured in "vivid and disturbing ways". The article includes some of the drawings as well as a link to a 61-page report titled "How America Tortures", and asserts that Zubaydah was never a member of Al Qaeda. In the article Zubaydah gives gruesome details of numerous types of torture including being locked up inside a small box called "the dog box" for "countless hours", which caused muscle contractions. "The very strong pain", he said, "made me scream unconsciously". According to the Senate Intelligence Committee report on CIA torture, over a single 20 day period, Zubaydah spent over 11 days locked in a "coffin size" box, and 29 hours in a box measuring 21 inches wide, 2 feet deep, and 2 feet high (). On May 9, 2023, Zubaydah's former attorney, Mark Denbeaux of Seton Hall Law School, published a detailed report annotating the drawings.
Interrogation of Zubaydah. Zubaydah was interrogated by two separate interrogation teams: the first from the FBI and one from the CIA. Ali Soufan, one of the FBI interrogators, later testified in 2009 on these issues to the Senate Committee that was investigating detainee treatment. Soufan, who witnessed part of the CIA interrogation of Zubaydah, described his treatment under the CIA as torture. The International Committee of the Red Cross and others later reached the same conclusion. While in CIA custody, Zubaydah's previously damaged left eye was surgically removed. Because of the urgency felt about the interrogation of Zubaydah, the CIA had consulted with the president about how to proceed. The General Counsel of the CIA asked for a legal opinion from the Office of Legal Counsel, Department of Justice about what was permissible during interrogation. August 2002 memo. In early July 2002, the Associate General Counsel CTC/Legal Group started drafting a memo to the Attorney General requesting the approval of "aggressive" interrogation methods, which otherwise would be prohibited under the provisions of Section 2340-2340B, Title 18, United States Code, on Abu Zubaydah. This memo, drafted by Office of Legal Counsel, Jay Bybee and his assistant John Yoo, is also referred to as the first Torture Memo. Addressed to CIA acting General Counsel John A. Rizzo at his request, the purpose of the memo was to describe and authorize specific "enhanced interrogation techniques" to be used on Zubaydah. On July 26, 2002, Deputy Assistant Attorney General John Yoo informed the CIA that Attorney General John Ashcroft had approved waterboarding of Abu Zubaydah.
Journalists including Jane Mayer, Joby Warrick and Peter Finn, and Alex Koppelman have reported the CIA was already using these harsh tactics before the memo authorizing their use was written, and that it was used to provide after-the-fact legal support for harsh interrogation techniques. A Department of Justice 2009 report regarding prisoner abuses reportedly stated the memos were prepared one month after Zubaydah had already been subjected to the specific techniques authorized in an August 1, 2002, memo. John Kiriakou stated in July 2009 that Zubaydah was waterboarded in the early summer of 2002, months before the August 1, 2002, memo was written. The memo described ten techniques which the interrogators wanted to use: "(1) attention grasp, (2) walling, (3) facial hold, (4) facial slap (insult slap), (5) cramped confinement, (6) wall standing, (7) stress positions, (8) sleep deprivation, (9) insects placed in a confinement box, and (10) the waterboard." Many of the techniques were, until then, generally considered illegal. Many other techniques developed by the CIA were held to constitute inhumane and degrading treatment and torture under the United Nations Convention against Torture and Article 3 of the European Convention on Human Rights.
As reported later, many of these interrogation techniques were previously considered illegal under U.S. and international law and treaties at the time of Zubaydah's capture. For instance, the United States had prosecuted Japanese military officials after World War II and American soldiers after the Vietnam War for waterboarding. Since 1930, the United States had defined sleep deprivation as an illegal form of torture. Many other techniques developed by the CIA constitute inhuman and degrading treatment and torture under the United Nations Convention against Torture, and Article 3 of the European Convention on Human Rights. Ensuing interrogation. At a CIA black site in Thailand, Zubaydah was subjected to various forms of increasingly harsh interrogation techniques, including temperature extremes, music played at debilitating volumes, and sexual humiliation. Zubaydah was also subjected to beatings, isolation, waterboarding, long-time standing, continuous cramped confinement, and sleep deprivation. Former CIA analyst and case officer John Kiriakou asserted that while Zubaydah was in CIA custody, a box of cockroaches was poured on him inside of a coffin he was confined to for two weeks, because of an irrational fear Zubaydah has of cockroaches.
During Zubaydah's interrogation, Bush learned he was on painkillers for his wounds and was proving resistant. He said to the CIA director George Tenet, "Who authorized putting him on pain medication?" It was later reported that Zubaydah was denied painkillers during his interrogation. Waterboarding. Zubaydah was one of three or more high-value detainees to be waterboarded. The Bush administration in 2007 said that Zubaydah had been waterboarded once. John Kiriakou, a CIA officer who had seen the cables regarding Zubaydah's interrogation, publicly said in 2009 that Zubaydah was waterboarded once for 35 seconds before he started talking. Intelligence sources claimed as early as 2008 that Zubaydah had been waterboarded no less than ten times in the span of one week. Zubaydah was waterboarded 83 times within the month of August 2002, the month the CIA was authorized to use this enhanced interrogation techniques on him. In January 2010, Kiriakou, in a memoir, said, "Now we know that Zubaydah was waterboarded eighty-three times in a single month, raising questions about how much useful information he actually supplied." 2003 transfer to Guantanamo.
In August 2010, the Associated Press reported that the CIA, having concluded its agents had gotten most of the information from Zubaydah, in September 2003 transferred him and three other high-value detainees to Guantanamo. They were held at what was informally known as "Strawberry Fields", a secret camp within the complex built especially for former CIA detainees. Concerned that a pending Supreme Court decision, "Rasul v. Bush" (2004), might go against the Bush administration and require providing the prisoners with counsel and having to reveal data about them, on March 27, 2004, the CIA took the four men back into custody and transported them out of Guantanamo to one of their secret sites. At the time, the moves were all kept secret. International Committee of the Red Cross report. In February 2007, the International Committee of the Red Cross concluded a report on the treatment of "14 high-value detainees", who had been held by the CIA and, after September 2006, by the military at Guantanamo. The ICRC described the twelve enhanced interrogation techniques covered in the OLC memos to the CIA: suffocation by water (which is described as "torture" by numerous US officials), prolonged stress standing position, beatings by use of a collar, beating and kicking, confinement in a box, prolonged nudity, sleep deprivation, exposure to cold temperature, prolonged shackling, threats of ill-treatment, forced shaving, and deprivation/restricted provision of solid food. Zubaydah was the only detainee of the 14 interviewed who had been subjected to all 12 of these interrogation techniques. He was also the only one of the 14 detainees to be put into close confinement.
May 30, 2005, memo. The final memo mentioned Zubaydah several times. It claimed that due to the enhanced interrogation techniques, Zubaydah "provided significant information on two operatives, [including] José Padilla[,] who planned to build and detonate a 'dirty bomb' in the Washington DC area." This claim is strongly disputed by Ali Soufan, the FBI interrogator who first interrogated Zubaydah following his capture, by traditional means. He said the most valuable information was gained before torture was used. Other intelligence officers have also disputed that claim. Soufan, when asked in 2009 by Senator Sheldon Whitehouse during a Congressional hearing if the memo was incorrect, testified that it was. The memo noted that not all of the waterboarding sessions were necessary for Zubaydah, since the on-scene interrogation team determined he had stopped producing actionable intelligence. The memo reads: This is not to say that the interrogation program has worked perfectly. According to the IG Report, the CIA, at least initially, could not always distinguish detainees who had information but were successfully resisting interrogation from those who did not actually have the information. See IG Report at 83–85. On at least one occasion, this may have resulted in what might be deemed in retrospect to have been the unnecessary use of enhanced techniques. On that occasion, although the on-scene interrogation team judged Zubaydah to be compliant, elements within CIA Headquarters still believed he was withholding information. See id at 84. At the direction of CIA Headquarters, interrogators therefore used the waterboard one more time on Zubaydah.
John McLaughlin, former acting CIA director, stated in 2006, "I totally disagree with the view that the capture of Zubaydah was unimportant. Zubaydah was woven through all of the intelligence prior to 9/11 that signaled a major attack was coming, and his capture yielded a great deal of important information." In his 2007 memoir, former CIA Director George Tenet writes: A published report in 2006 contended that Zubaydah was mentally unstable and that the administration had overstated his importance. Baloney. Zubaydah had been at the crossroads of many al-Qa'ida operations and was in position to—and did—share critical information with his interrogators. Apparently, the source of the rumor that Zubaydah was unbalanced was his personal diary, in which he adopted various personas. From that shaky perch, some junior Freudians leapt to the conclusion that Zubaydah had multiple personalities. In fact, Agency psychiatrists eventually determined that in his diary he was using a sophisticated literary device to express himself.
Intelligence obtained from Zubaydah and its after effects. Zubaydah's capture was touted as the biggest of the War on Terror until that of Khalid Sheikh Mohammed. The director of the FBI stated Zubaydah's capture would help deter future attacks. In a speech in 2006, Bush claimed that Zubaydah revealed useful intelligence when enhanced interrogation was used, including identification of two important suspects and information that allegedly helped foil a terrorist attack on American soil. These claims directly conflict with the reports of the FBI agents who first interrogated Zubaydah. He gave them the names before torture was used, and the third piece of information came from other sources who had been receiving crucial pieces of information from him without the use of harsher techniques, as well as other government officials. Iraq War (2003). The Bush administration relied on some of Zubaydah's claims in justifying the invasion of Iraq. U.S. officials stated that the allegations that Iraq and al-Qaeda were linked in the training of people on chemical weapons came from Zubaydah. The officials noted there was no independent verification of his claims.
The U.S. government included statements made by Zubaydah in regards to al Qaeda's ability to obtain a dirty bomb to show a link between Iraq and al Qaeda. According to a Senate Intelligence Committee report of 2004, Zubaydah said that "he had heard that an important al Qaeda associate, Abu Musab al Zarqawi, and others had good relationships with Iraqi intelligence." However, the year before, in June 2003, Zubaydah and Khalid Sheikh Mohammed were reported as saying there was no link between Saddam Hussein and al Qaeda. In the Senate Armed Services Committee 2008 report on the abuses of detainees, the Bush administration was described as having applied pressure to interrogators to find a link between Iraq and al Qaeda prior to the Iraq War. Major Paul Burney, a psychiatrist with the United States Army, said to the committee, "while we were [at Guantanamo] a large part of the time we were focused on trying to establish a link between al Qaeda and Iraq and we were not being successful." He said that higher-ups were "frustrated" and applied "more and more pressure to resort to measures that might produce more immediate results."
Colonel Lawrence B. Wilkerson, the former chief of staff for former Secretary of State Colin Powell said: Likewise, what I have learned is that as the administration authorized harsh interrogation in April and May 2002—well before the Justice Department had rendered any legal opinion—its principal priority for intelligence was not aimed at pre-empting another terrorist attack on the U.S. but discovering a smoking gun linking Iraq and al-Qa'ida. So furious was this effort that on one particular detainee, even when the interrogation team had reported to Cheney's office that their detainee "was compliant" (meaning the team recommended no more torture), the VP's office ordered them to continue the enhanced methods. The detainee had not revealed any al-Qa'ida-Baghdad contacts yet. This ceased only after Ibn al-Shaykh al-Libi, under waterboarding in Egypt, "revealed" such contacts. Of course, later we learned that al-Libi revealed these contacts only to get the torture to stop. Concerns. In 2004, media coverage of Abu Zubaydah began listing him as a "disappeared" prisoner, stating he had no access to the International Red Cross. In February 2005, the CIA was reported as uncomfortable keeping Zubaydah in indefinite custody. Less than 18 months later, Zubaydah and the thirteen other high-value detainees who had been in secret CIA custody were transferred to the Guantanamo Bay detention camp.
After his transfer, the CIA denied access to Zubaydah. In 2008, the Office of the Inspector General, Department of Justice, complained that it had been prevented from seeing him, although it was conducting a study of the US treatment of its detainees. Zubaydah's mental health. Some people are concerned about Zubaydah's mental stability and how that has affected information he has given to interrogators. Ron Suskind noted in his book, "The One Percent Doctrine: Deep Inside America's Pursuit of Its Enemies Since 9/11" (2006), that Zubaydah was mentally ill or disabled due to a severe head injury. He described Zubaydah as keeping a diary "in the voice of three people: Hani 1, Hani 2, and Hani 3"—a boy, a young man and a middle-aged alter ego. Zubaydah's diaries spanned ten years and recorded in numbing detail "what he ate, or wore, or trifling things [people] said". Dan Coleman, then the FBI's top al-Qaeda analyst, told a senior bureau official, "This guy is insane, certifiable, split personality." According to Suskind, this judgment was "echoed at the top of CIA and was briefed to the President and Vice President." Coleman stated Zubaydah was a "safehouse keeper" with mental problems, who "claimed to know more about al-Qaeda and its inner workings than he really did."
Joseph Margulies, Zubaydah's co-counsel, wrote in an op-ed in the "Los Angeles Times" in 2009: Partly as a result of injuries he suffered while he was fighting the communists in Afghanistan, partly as a result of how those injuries were exacerbated by the CIA and partly as a result of his extended isolation, Zubaydah's mental grasp is slipping away. Today, he suffers blinding headaches and has permanent brain damage. He has an excruciating sensitivity to sounds, hearing what others do not. The slightest noise drives him nearly insane. In the last two years alone, he has experienced about 200 seizures. Already, he cannot picture his mother's face or recall his father's name. Gradually, his past, like his future, eludes him. Legal status. President Bush referred to Zubaydah in a speech to Congress September 2006 requesting a bill to authorize military commissions, following the U.S. Supreme Court ruling in "Hamdan v. Rumsfeld" (2006) that held the tribunals as formulated by the executive branch were unconstitutional. Congress rapidly passed legislation that was signed by the president.
Less than one month after Zubaydah's capture, Justice Department officials said Zubaydah was "a near-ideal candidate for a tribunal trial". Several months later in 2002, US officials said there was "no rush" to try Zubaydah via military commission. At his Combatant Status Review Tribunal in 2007, Zubaydah said he was told that the CIA realized he was not significant. "They told me, 'Sorry, we discover that you are not Number 3, not a partner, not even a fighter, said Zubaydah, speaking in broken English, according to the new transcript of a Combatant Status Review Tribunal held at the U.S. military prison in Guantanamo Bay, Cuba. Abu Zubaydah's lawyers, including Joseph Margulies and George Brent Mickum IV, filed a lawsuit in July 2008 challenging his detention at Guantanamo Bay detention camps after the "Boumediene v. Bush" ruling. The judge overseeing the case, Richard W. Roberts, failed to rule on any motions related to the case, even the preliminary ones. This led Zubaydah's lawyers to file a motion asking Judge Roberts to recuse himself for nonfeasance in January 2015. On March 16, 2016, Roberts retired early from the federal bench, citing unspecified health issues.
The U.S. government has not officially charged Zubaydah with any crimes. The Senate Intelligence Committee report on CIA torture reported that Zubaydah's CIA interrogators wanted him to "remain in isolation and incommunicado for the remainder of his life." Joint Review Task Force. When he assumed Presidential office in January 2009, Barack Obama made a number of promises about the future of Guantanamo. He promised the use of torture would cease at the camp and to institute a new review system composed of officials from six departments, where the OARDEC reviews were conducted entirely by the Department of Defense. When it reported back, a year later, the Joint Review Task Force classified some individuals as too dangerous to be transferred from Guantanamo, even though there was no evidence to justify laying charges against them. On April 9, 2013, that document was made public after a Freedom of Information Act request. Zayn al-lbidin Muhammed Husayn was one of the 71 individuals deemed too innocent to charge but too dangerous to release. Although Obama promised that those deemed too innocent to charge but too dangerous to release would start to receive reviews from a Periodic Review Board, less than a quarter of men have received a review. Husayn was denied approval for transfer on September 22, 2016.
European Court of Human Rights decision. On 24 July 2014, the European Court of Human Rights (ECHR) ruled that Poland had violated the European Convention on Human Rights when it cooperated with US allowing the CIA to hold and torture Zubaydah and Abd al-Rahim al-Nashiri on its territory in 2002–2003. The court ordered the Polish government to pay each of the men €100,000 in damages. It also awarded Zubaydah €30,000 to cover his costs. On 31 May 2018, the ECHR ruled that Romania and Lithuania also violated the rights of Abu Zubaydah and Abd al-Rahim al-Nashiri in 2003–2005 and in 2005–2006 respectively, and Lithuania and Romania were ordered to pay €100,000 in damages each to Abu Zubaydah and Abd al-Nashiri. U.S. Supreme Court decision. In connection with the European Court of Human Rights proceedings, Zubaydah filed suit in the U.S. seeking disclosure of information related to the matter. The U.S. government intervened, seeking to assert a state secrets privilege. The U.S. district court decided in favor of the government and dismissed the case. On appeal, the dismissal was reversed on a ruling that the state secrets privilege did not apply to information that was already publicly known. The Supreme Court reversed the appeal ruling in "United States v. Zubaydah", explaining that the state secrets privilege applies to the existence (or nonexistence) of a secret CIA facility and that revelation by government would confirm or deny that state secret.
Arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers. Real number arithmetic is about calculations with real numbers, which include both rational and irrational numbers. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Computer arithmetic deals with the specificities of the implementation of binary arithmetic on computers. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic.
Arithmetic operations form the basis of many branches of mathematics, such as algebra, calculus, and statistics. They play a similar role in the sciences, like physics and economics. Arithmetic is present in many aspects of daily life, for example, to calculate change while shopping or to manage personal finances. It is one of the earliest forms of mathematics education that students encounter. Its cognitive and conceptual foundations are studied by psychology and philosophy. The practice of arithmetic is at least thousands and possibly tens of thousands of years old. Ancient civilizations like the Egyptians and the Sumerians invented numeral systems to solve practical arithmetic problems in about 3000 BCE. Starting in the 7th and 6th centuries BCE, the ancient Greeks initiated a more abstract study of numbers and introduced the method of rigorous mathematical proofs. The ancient Indians developed the concept of zero and the decimal system, which Arab mathematicians further refined and spread to the Western world during the medieval period. The first mechanical calculators were invented in the 17th century. The 18th and 19th centuries saw the development of modern number theory and the formulation of axiomatic foundations of arithmetic. In the 20th century, the emergence of electronic calculators and computers revolutionized the accuracy and speed with which arithmetic calculations could be performed.
Definition, etymology, and related fields. Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and logarithm. The term "arithmetic" has its root in the Latin term which derives from the Ancient Greek words ("arithmos"), meaning , and ("arithmetike tekhne"), meaning . There are disagreements about its precise definition. According to a narrow characterization, arithmetic deals only with natural numbers. However, the more common view is to include operations on integers, rational numbers, real numbers, and sometimes also complex numbers in its scope. Some definitions restrict arithmetic to the field of numerical calculations. When understood in a wider sense, it also includes the study of how the concept of numbers developed, the analysis of properties of and relations between numbers, and the examination of the axiomatic structure of arithmetic operations.
Arithmetic is closely related to number theory and some authors use the terms as synonyms. However, in a more specific sense, number theory is restricted to the study of integers and focuses on their properties and relationships such as divisibility, factorization, and primality. Traditionally, it is known as higher arithmetic. Numbers. Numbers are mathematical objects used to count quantities and measure magnitudes. They are fundamental elements in arithmetic since all arithmetic operations are performed on numbers. There are different kinds of numbers and different numeral systems to represent them. Kinds. The main kinds of numbers employed in arithmetic are natural numbers, whole numbers, integers, rational numbers, and real numbers. The natural numbers are whole numbers that start from 1 and go to infinity. They exclude 0 and negative numbers. They are also known as counting numbers and can be expressed as formula_1. The symbol of the natural numbers is formula_2. The whole numbers are identical to the natural numbers with the only difference being that they include 0. They can be represented as formula_3 and have the symbol formula_4. Some mathematicians do not draw the distinction between the natural and the whole numbers by including 0 in the set of natural numbers. The set of integers encompasses both positive and negative whole numbers. It has the symbol formula_5 and can be expressed as formula_6.
Based on how natural and whole numbers are used, they can be distinguished into cardinal and ordinal numbers. Cardinal numbers, like one, two, and three, are numbers that express the quantity of objects. They answer the question "how many?". Ordinal numbers, such as first, second, and third, indicate order or placement in a series. They answer the question "what position?". A number is rational if it can be represented as the ratio of two integers. For instance, the rational number formula_7 is formed by dividing the integer 1, called the numerator, by the integer 2, called the denominator. Other examples are formula_8 and formula_9. The set of rational numbers includes all integers, which are fractions with a denominator of 1. The symbol of the rational numbers is formula_10. Decimal fractions like 0.3 and 25.12 are a special type of rational numbers since their denominator is a power of 10. For instance, 0.3 is equal to formula_11, and 25.12 is equal to formula_12. Every rational number corresponds to a finite or a repeating decimal.
Irrational numbers are numbers that cannot be expressed through the ratio of two integers. They are often required to describe geometric magnitudes. For example, if a right triangle has legs of the length 1 then the length of its hypotenuse is given by the irrational number formula_13. is another irrational number and describes the ratio of a circle's circumference to its diameter. The decimal representation of an irrational number is infinite without repeating decimals. The set of rational numbers together with the set of irrational numbers makes up the set of real numbers. The symbol of the real numbers is formula_14. Even wider classes of numbers include complex numbers and quaternions. Numeral systems. A numeral is a symbol to represent a number and numeral systems are representational frameworks. They usually have a limited amount of basic numerals, which directly refer to certain numbers. The system governs how these basic numerals may be combined to express any number. Numeral systems are either positional or non-positional. All early numeral systems were non-positional. For non-positional numeral systems, the value of a digit does not depend on its position in the numeral.
The simplest non-positional system is the unary numeral system. It relies on one symbol for the number 1. All higher numbers are written by repeating this symbol. For example, the number 7 can be represented by repeating the symbol for 1 seven times. This system makes it cumbersome to write large numbers, which is why many non-positional systems include additional symbols to directly represent larger numbers. Variations of the unary numeral systems are employed in tally sticks using dents and in tally marks. Egyptian hieroglyphics had a more complex non-positional numeral system. They have additional symbols for numbers like 10, 100, 1000, and 10,000. These symbols can be combined into a sum to more conveniently express larger numbers. For instance, the numeral for 10,405 uses one time the symbol for 10,000, four times the symbol for 100, and five times the symbol for 1. A similar well-known framework is the Roman numeral system. It has the symbols I, V, X, L, C, D, M as its basic numerals to represent the numbers 1, 5, 10, 50, 100, 500, and 1000.
A numeral system is positional if the position of a basic numeral in a compound expression determines its value. Positional numeral systems have a radix that acts as a multiplicand of the different positions. For each subsequent position, the radix is raised to a higher power. In the common decimal system, also called the Hindu–Arabic numeral system, the radix is 10. This means that the first digit is multiplied by formula_15, the next digit is multiplied by formula_16, and so on. For example, the decimal numeral 532 stands for formula_17. Because of the effect of the digits' positions, the numeral 532 differs from the numerals 325 and 253 even though they have the same digits. Another positional numeral system used extensively in computer arithmetic is the binary system, which has a radix of 2. This means that the first digit is multiplied by formula_18, the next digit by formula_19, and so on. For example, the number 13 is written as 1101 in the binary notation, which stands for formula_20. In computing, each digit in the binary notation corresponds to one bit. The earliest positional system was developed by ancient Babylonians and had a radix of 60.
Operations. Arithmetic operations are ways of combining, transforming, or manipulating numbers. They are functions that have numbers both as input and output. The most important operations in arithmetic are addition, subtraction, multiplication, and division. Further operations include exponentiation, extraction of roots, and logarithm. If these operations are performed on variables rather than numbers, they are sometimes referred to as algebraic operations. Two important concepts in relation to arithmetic operations are identity elements and inverse elements. The identity element or neutral element of an operation does not cause any change if it is applied to another element. For example, the identity element of addition is 0 since any sum of a number and 0 results in the same number. The inverse element is the element that results in the identity element when combined with another element. For instance, the additive inverse of the number 6 is -6 since their sum is 0. There are not only inverse elements but also inverse operations. In an informal sense, one operation is the inverse of another operation if it undoes the first operation. For example, subtraction is the inverse of addition since a number returns to its original value if a second number is first added and subsequently subtracted, as in formula_21. Defined more formally, the operation "formula_22" is an inverse of the operation "formula_23" if it fulfills the following condition: formula_24 if and only if formula_25.
Commutativity and associativity are laws governing the order in which some arithmetic operations can be carried out. An operation is commutative if the order of the arguments can be changed without affecting the results. This is the case for addition, for instance, formula_26 is the same as formula_27. Associativity is a rule that affects the order in which a series of operations can be carried out. An operation is associative if, in a series of two operations, it does not matter which operation is carried out first. This is the case for multiplication, for example, since formula_28 is the same as formula_29. Addition and subtraction. Addition is an arithmetic operation in which two numbers, called the addends, are combined into a single number, called the sum. The symbol of addition is formula_30. Examples are formula_31 and formula_32. The term summation is used if several additions are performed in a row. Counting is a type of repeated addition in which the number 1 is continuously added. Subtraction is the inverse of addition. In it, one number, known as the subtrahend, is taken away from another, known as the minuend. The result of this operation is called the difference. The symbol of subtraction is formula_33. Examples are formula_34 and formula_35. Subtraction is often treated as a special case of addition: instead of subtracting a positive number, it is also possible to add a negative number. For instance formula_36. This helps to simplify mathematical computations by reducing the number of basic arithmetic operations needed to perform calculations.
The additive identity element is 0 and the additive inverse of a number is the negative of that number. For instance, formula_37 and formula_38. Addition is both commutative and associative. Multiplication and division. Multiplication is an arithmetic operation in which two numbers, called the multiplier and the multiplicand, are combined into a single number called the product. The symbols of multiplication are formula_39, formula_40, and *. Examples are formula_41 and formula_42. If the multiplicand is a natural number then multiplication is the same as repeated addition, as in formula_43. Division is the inverse of multiplication. In it, one number, known as the dividend, is split into several equal parts by another number, known as the divisor. The result of this operation is called the quotient. The symbols of division are formula_44 and formula_45. Examples are formula_46 and formula_47. Division is often treated as a special case of multiplication: instead of dividing by a number, it is also possible to multiply by its reciprocal. The reciprocal of a number is 1 divided by that number. For instance, formula_48.
The multiplicative identity element is 1 and the multiplicative inverse of a number is the reciprocal of that number. For example, formula_49 and formula_50. Multiplication is both commutative and associative. Exponentiation and logarithm. Exponentiation is an arithmetic operation in which a number, known as the base, is raised to the power of another number, known as the exponent. The result of this operation is called the power. Exponentiation is sometimes expressed using the symbol ^ but the more common way is to write the exponent in superscript right after the base. Examples are formula_51 and formula_52^formula_53. If the exponent is a natural number then exponentiation is the same as repeated multiplication, as in formula_54. Roots are a special type of exponentiation using a fractional exponent. For example, the square root of a number is the same as raising the number to the power of formula_7 and the cube root of a number is the same as raising the number to the power of formula_56. Examples are formula_57 and formula_58.
Logarithm is the inverse of exponentiation. The logarithm of a number formula_59 to the base formula_60 is the exponent to which formula_60 must be raised to produce formula_59. For instance, since formula_63, the logarithm base 10 of 1000 is 3. The logarithm of formula_59 to base formula_60 is denoted as formula_66, or without parentheses, formula_67, or even without the explicit base, formula_68, when the base can be understood from context. So, the previous example can be written formula_69. Exponentiation and logarithm do not have general identity elements and inverse elements like addition and multiplication. The neutral element of exponentiation in relation to the exponent is 1, as in formula_70. However, exponentiation does not have a general identity element since 1 is not the neutral element for the base. Exponentiation and logarithm are neither commutative nor associative. Types. Different types of arithmetic systems are discussed in the academic literature. They differ from each other based on what type of number they operate on, what numeral system they use to represent them, and whether they operate on mathematical objects other than numbers.
Integer arithmetic. Integer arithmetic is the branch of arithmetic that deals with the manipulation of positive and negative whole numbers. Simple one-digit operations can be performed by following or memorizing a table that presents the results of all possible combinations, like an addition table or a multiplication table. Other common methods are verbal counting and finger-counting. For operations on numbers with more than one digit, different techniques can be employed to calculate the result by using several one-digit operations in a row. For example, in the method addition with carries, the two numbers are written one above the other. Starting from the rightmost digit, each pair of digits is added together. The rightmost digit of the sum is written below them. If the sum is a two-digit number then the leftmost digit, called the "carry", is added to the next pair of digits to the left. This process is repeated until all digits have been added. Other methods used for integer additions are the number line method, the partial sum method, and the compensation method. A similar technique is utilized for subtraction: it also starts with the rightmost digit and uses a "borrow" or a negative carry for the column on the left if the result of the one-digit subtraction is negative.
A basic technique of integer multiplication employs repeated addition. For example, the product of formula_71 can be calculated as formula_72. A common technique for multiplication with larger numbers is called long multiplication. This method starts by writing the multiplier above the multiplicand. The calculation begins by multiplying the multiplier only with the rightmost digit of the multiplicand and writing the result below, starting in the rightmost column. The same is done for each digit of the multiplicand and the result in each case is shifted one position to the left. As a final step, all the individual products are added to arrive at the total product of the two multi-digit numbers. Other techniques used for multiplication are the grid method and the lattice method. Computer science is interested in multiplication algorithms with a low computational complexity to be able to efficiently multiply very large integers, such as the Karatsuba algorithm, the Schönhage–Strassen algorithm, and the Toom–Cook algorithm. A common technique used for division is called long division. Other methods include short division and chunking.
Integer arithmetic is not closed under division. This means that when dividing one integer by another integer, the result is not always an integer. For instance, 7 divided by 2 is not a whole number but 3.5. One way to ensure that the result is an integer is to round the result to a whole number. However, this method leads to inaccuracies as the original value is altered. Another method is to perform the division only partially and retain the remainder. For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions. A simple method to calculate exponentiation is by repeated multiplication. For instance, the exponentiation of formula_73 can be calculated as formula_74. A more efficient technique used for large exponents is exponentiation by squaring. It breaks down the calculation into a number of squaring operations. For example, the exponentiation formula_75 can be written as formula_76. By taking advantage of repeated squaring operations, only 7 individual operations are needed rather than the 64 operations required for regular repeated multiplication. Methods to calculate logarithms include the Taylor series and continued fractions. Integer arithmetic is not closed under logarithm and under exponentiation with negative exponents, meaning that the result of these operations is not always an integer.
Number theory. Number theory studies the structure and properties of integers as well as the relations and laws between them. Some of the main branches of modern number theory include elementary number theory, analytic number theory, algebraic number theory, and geometric number theory. Elementary number theory studies aspects of integers that can be investigated using elementary methods. Its topics include divisibility, factorization, and primality. Analytic number theory, by contrast, relies on techniques from analysis and calculus. It examines problems like how prime numbers are distributed and the claim that every even number is a sum of two prime numbers. Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers. Examples are the use of fields and rings, as in algebraic number fields like the ring of integers. Geometric number theory uses concepts from geometry to study numbers. For instance, it investigates how lattice points with integer coordinates behave in a plane. Further branches of number theory are probabilistic number theory, which employs methods from probability theory, combinatorial number theory, which relies on the field of combinatorics, computational number theory, which approaches number-theoretic problems with computational methods, and applied number theory, which examines the application of number theory to fields like physics, biology, and cryptography.
Influential theorems in number theory include the fundamental theorem of arithmetic, Euclid's theorem, and Fermat's Last Theorem. According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number or can be represented as a unique product of prime numbers. For example, the number 18 is not a prime number and can be represented as formula_77, all of which are prime numbers. The number 19, by contrast, is a prime number that has no other prime factorization. Euclid's theorem states that there are infinitely many prime numbers. Fermat's Last Theorem is the statement that no positive integer values exist for formula_78, formula_60, and formula_80 that solve the equation formula_81 if formula_82 is greater than formula_83. Rational number arithmetic. Rational number arithmetic is the branch of arithmetic that deals with the manipulation of numbers that can be expressed as a ratio of two integers. Most arithmetic operations on rational numbers can be calculated by performing a series of integer arithmetic operations on the numerators and the denominators of the involved numbers. If two rational numbers have the same denominator then they can be added by adding their numerators and keeping the common denominator. For example, formula_84. A similar procedure is used for subtraction. If the two numbers do not have the same denominator then they must be transformed to find a common denominator. This can be achieved by scaling the first number with the denominator of the second number while scaling the second number with the denominator of the first number. For instance, formula_85.
Two rational numbers are multiplied by multiplying their numerators and their denominators respectively, as in formula_86. Dividing one rational number by another can be achieved by multiplying the first number with the reciprocal of the second number. This means that the numerator and the denominator of the second number change position. For example, formula_87. Unlike integer arithmetic, rational number arithmetic is closed under division as long as the divisor is not 0. Both integer arithmetic and rational number arithmetic are not closed under exponentiation and logarithm. One way to calculate exponentiation with a fractional exponent is to perform two separate calculations: one exponentiation using the numerator of the exponent followed by drawing the nth root of the result based on the denominator of the exponent. For example, formula_88. The first operation can be completed using methods like repeated multiplication or exponentiation by squaring. One way to get an approximate result for the second operation is to employ Newton's method, which uses a series of steps to gradually refine an initial guess until it reaches the desired level of accuracy. The Taylor series or the continued fraction method can be utilized to calculate logarithms.
The decimal fraction notation is a special way of representing rational numbers whose denominator is a power of 10. For instance, the rational numbers formula_89, formula_90, and formula_91 are written as 0.1, 3.71, and 0.0044 in the decimal fraction notation. Modified versions of integer calculation methods like addition with carry and long multiplication can be applied to calculations with decimal fractions. Not all rational numbers have a finite representation in the decimal notation. For example, the rational number formula_56 corresponds to 0.333... with an infinite number of 3s. The shortened notation for this type of repeating decimal is 0.. Every repeating decimal expresses a rational number. Real number arithmetic. Real number arithmetic is the branch of arithmetic that deals with the manipulation of both rational and irrational numbers. Irrational numbers are numbers that cannot be expressed through fractions or repeated decimals, like the root of 2 and . Unlike rational number arithmetic, real number arithmetic is closed under exponentiation as long as it uses a positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1.
Irrational numbers involve an infinite non-repeating series of decimal digits. Because of this, there is often no simple and accurate way to express the results of arithmetic operations like formula_93 or In cases where absolute precision is not required, the problem of calculating arithmetic operations on real numbers is usually addressed by truncation or rounding. For truncation, a certain number of leftmost digits are kept and remaining digits are discarded or replaced by zeros. For example, the number has an infinite number of digits starting with 3.14159... If this number is truncated to 4 decimal places, the result is 3.141. Rounding is a similar process in which the last preserved digit is increased by one if the next digit is 5 or greater but remains the same if the next digit is less than 5, so that the rounded number is the best approximation of a given precision for the original number. For instance, if the number is rounded to 4 decimal places, the result is 3.142 because the following digit is a 5, so 3.142 is closer to than 3.141. These methods allow computers to efficiently perform approximate calculations on real numbers.
Approximations and errors. In science and engineering, numbers represent estimates of physical quantities derived from measurement or modeling. Unlike mathematically exact numbers such as or scientifically relevant numerical data are inherently inexact, involving some measurement uncertainty. One basic way to express the degree of certainty about each number's value and avoid false precision is to round each measurement to a certain number of digits, called significant digits, which are implied to be accurate. For example, a person's height measured with a tape measure might only be precisely known to the nearest centimeter, so should be presented as 1.62 meters rather than 1.6217 meters. If converted to imperial units, this quantity should be rounded to 64 inches or 63.8 inches rather than 63.7795 inches, to clearly convey the precision of the measurement. When a number is written using ordinary decimal notation, leading zeros are not significant, and trailing zeros of numbers not written with a decimal point are implicitly considered to be non-significant. For example, the numbers 0.056 and 1200 each have only 2 significant digits, but the number 40.00 has 4 significant digits. Representing uncertainty using only significant digits is a relatively crude method, with some unintuitive subtleties; explicitly keeping track of an estimate or upper bound of the approximation error is a more sophisticated approach. In the example, the person's height might be represented as meters or .
In performing calculations with uncertain quantities, the uncertainty should be propagated to calculated quantities. When adding or subtracting two or more quantities, add the absolute uncertainties of each summand together to obtain the absolute uncertainty of the sum. When multiplying or dividing two or more quantities, add the relative uncertainties of each factor together to obtain the relative uncertainty of the product. When representing uncertainty by significant digits, uncertainty can be coarsely propagated by rounding the result of adding or subtracting two or more quantities to the leftmost last significant decimal place among the summands, and by rounding the result of multiplying or dividing two or more quantities to the least number of significant digits among the factors. (See .) More sophisticated methods of dealing with uncertain values include interval arithmetic and affine arithmetic. Interval arithmetic describes operations on intervals. Intervals can be used to represent a range of values if one does not know the precise magnitude, for example, because of measurement errors. Interval arithmetic includes operations like addition and multiplication on intervals, as in formula_94 and formula_95. It is closely related to affine arithmetic, which aims to give more precise results by performing calculations on affine forms rather than intervals. An affine form is a number together with error terms that describe how the number may deviate from the actual magnitude.
The precision of numerical quantities can be expressed uniformly using normalized scientific notation, which is also convenient for concisely representing numbers which are much larger or smaller than 1. Using scientific notation, a number is decomposed into the product of a number between 1 and 10, called the "significand", and 10 raised to some integer power, called the "exponent". The significand consists of the significant digits of the number, and is written as a leading digit 1–9 followed by a decimal point and a sequence of digits 0–9. For example, the normalized scientific notation of the number 8276000 is formula_96 with significand 8.276 and exponent 6, and the normalized scientific notation of the number 0.00735 is formula_97 with significand 7.35 and exponent −3. Unlike ordinary decimal notation, where trailing zeros of large numbers are implicitly considered to be non-significant, in scientific notation every digit in the significand is considered significant, and adding trailing zeros indicates higher precision. For example, while the number 1200 implicitly has only 2 significant digits, the number explicitly has 3.
A common method employed by computers to approximate real number arithmetic is called floating-point arithmetic. It represents real numbers similar to the scientific notation through three numbers: a significand, a base, and an exponent. The precision of the significand is limited by the number of bits allocated to represent it. If an arithmetic operation results in a number that requires more bits than are available, the computer rounds the result to the closest representable number. This leads to rounding errors. A consequence of this behavior is that certain laws of arithmetic are violated by floating-point arithmetic. For example, floating-point addition is not associative since the rounding errors introduced can depend on the order of the additions. This means that the result of formula_98 is sometimes different from the result of The most common technical standard used for floating-point arithmetic is called IEEE 754. Among other things, it determines how numbers are represented, how arithmetic operations and rounding are performed, and how errors and exceptions are handled. In cases where computation speed is not a limiting factor, it is possible to use arbitrary-precision arithmetic, for which the precision of calculations is only restricted by the computer's memory.
Tool use. Forms of arithmetic can also be distinguished by the tools employed to perform calculations and include many approaches besides the regular use of pen and paper. Mental arithmetic relies exclusively on the mind without external tools. Instead, it utilizes visualization, memorization, and certain calculation techniques to solve arithmetic problems. One such technique is the compensation method, which consists in altering the numbers to make the calculation easier and then adjusting the result afterward. For example, instead of calculating formula_99, one calculates formula_100 which is easier because it uses a round number. In the next step, one adds formula_52 to the result to compensate for the earlier adjustment. Mental arithmetic is often taught in primary education to train the numerical abilities of the students. The human body can also be employed as an arithmetic tool. The use of hands in finger counting is often introduced to young children to teach them numbers and simple calculations. In its most basic form, the number of extended fingers corresponds to the represented quantity and arithmetic operations like addition and subtraction are performed by extending or retracting fingers. This system is limited to small numbers compared to more advanced systems which employ different approaches to represent larger quantities. The human voice is used as an arithmetic aid in verbal counting.
Tally marks are a simple system based on external tools other than the body. This system relies on mark making, such as strokes drawn on a surface or notches carved into a wooden stick, to keep track of quantities. Some forms of tally marks arrange the strokes in groups of five to make them easier to read. The abacus is a more advanced tool to represent numbers and perform calculations. An abacus usually consists of a series of rods, each holding several beads. Each bead represents a quantity, which is counted if the bead is moved from one end of a rod to the other. Calculations happen by manipulating the positions of beads until the final bead pattern reveals the result. Related aids include counting boards, which use tokens whose value depends on the area on the board in which they are placed, and counting rods, which are arranged in horizontal and vertical patterns to represent different numbers. Sectors and slide rules are more refined calculating instruments that rely on geometric relationships between different scales to perform both basic and advanced arithmetic operations. Printed tables were particularly relevant as an aid to look up the results of operations like logarithm and trigonometric functions.
Mechanical calculators automate manual calculation processes. They present the user with some form of input device to enter numbers by turning dials or pressing keys. They include an internal mechanism usually consisting of gears, levers, and wheels to perform calculations and display the results. For electronic calculators and computers, this procedure is further refined by replacing the mechanical components with electronic circuits like microprocessors that combine and transform electric signals to perform calculations. Others. There are many other types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result in a number outside this finite set then the number is adjusted back into the set, similar to how the hands of clocks start at the beginning again after having completed one cycle. The number at which this adjustment happens is called the modulus. For example, a regular clock has a modulus of 12. In the case of adding 4 to 9, this means that the result is not 13 but 1. The same principle applies also to other operations, such as subtraction, multiplication, and division.
Some forms of arithmetic deal with operations performed on mathematical objects other than numbers. Interval arithmetic describes operations on intervals. Vector arithmetic and matrix arithmetic describe arithmetic operations on vectors and matrices, like vector addition and matrix multiplication. Arithmetic systems can be classified based on the numeral system they rely on. For instance, decimal arithmetic describes arithmetic operations in the decimal system. Other examples are binary arithmetic, octal arithmetic, and hexadecimal arithmetic. Compound unit arithmetic describes arithmetic operations performed on magnitudes with compound units. It involves additional operations to govern the transformation between single unit and compound unit quantities. For example, the operation of reduction is used to transform the compound quantity 1 h 90 min into the single unit quantity 150 min. Non-Diophantine arithmetics are arithmetic systems that violate traditional arithmetic intuitions and include equations like formula_102 and formula_103. They can be employed to represent some real-world situations in modern physics and everyday life. For instance, the equation formula_102 can be used to describe the observation that if one raindrop is added to another raindrop then they do not remain two separate entities but become one.
Axiomatic foundations. Axiomatic foundations of arithmetic try to provide a small set of laws, called axioms, from which all fundamental properties of and operations on numbers can be derived. They constitute logically consistent and systematic frameworks that can be used to formulate mathematical proofs in a rigorous manner. Two well-known approaches are the Dedekind–Peano axioms and set-theoretic constructions. The Dedekind–Peano axioms provide an axiomatization of the arithmetic of natural numbers. Their basic principles were first formulated by Richard Dedekind and later refined by Giuseppe Peano. They rely only on a small number of primitive mathematical concepts, such as 0, natural number, and successor. The Peano axioms determine how these concepts are related to each other. All other arithmetic concepts can then be defined in terms of these primitive concepts. Numbers greater than 0 are expressed by repeated application of the successor function formula_105. For example, formula_106 is formula_107 and formula_52 is formula_109. Arithmetic operations can be defined as mechanisms that affect how the successor function is applied. For instance, to add formula_83 to any number is the same as applying the successor function two times to this number.
Various axiomatizations of arithmetic rely on set theory. They cover natural numbers but can also be extended to integers, rational numbers, and real numbers. Each natural number is represented by a unique set. 0 is usually defined as the empty set formula_111. Each subsequent number can be defined as the union of the previous number with the set containing the previous number. For example, formula_112, formula_113, and formula_114. Integers can be defined as ordered pairs of natural numbers where the second number is subtracted from the first one. For instance, the pair (9, 0) represents the number 9 while the pair (0, 9) represents the number −9. Rational numbers are defined as pairs of integers where the first number represents the numerator and the second number represents the denominator. For example, the pair (3, 7) represents the rational number formula_115. One way to construct the real numbers relies on the concept of Dedekind cuts. According to this approach, each real number is represented by a partition of all rational numbers into two sets, one for all numbers below the represented real number and the other for the rest. Arithmetic operations are defined as functions that perform various set-theoretic transformations on the sets representing the input numbers to arrive at the set representing the result.
History. The earliest forms of arithmetic are sometimes traced back to counting and tally marks used to keep track of quantities. Some historians suggest that the Lebombo bone (dated about 43,000 years ago) and the Ishango bone (dated about 22,000 to 30,000 years ago) are the oldest arithmetic artifacts but this interpretation is disputed. However, a basic sense of numbers may predate these findings and might even have existed before the development of language. It was not until the emergence of ancient civilizations that a more complex and structured approach to arithmetic began to evolve, starting around 3000 BCE. This became necessary because of the increased need to keep track of stored items, manage land ownership, and arrange exchanges. All the major ancient civilizations developed non-positional numeral systems to facilitate the representation of numbers. They also had symbols for operations like addition and subtraction and were aware of fractions. Examples are Egyptian hieroglyphics as well as the numeral systems invented in Sumeria, China, and India. The first positional numeral system was developed by the Babylonians starting around 1800 BCE. This was a significant improvement over earlier numeral systems since it made the representation of large numbers and calculations on them more efficient. Abacuses have been utilized as hand-operated calculating tools since ancient times as efficient means for performing complex calculations.
Early civilizations primarily used numbers for concrete practical purposes, like commercial activities and tax records, but lacked an abstract concept of number itself. This changed with the ancient Greek mathematicians, who began to explore the abstract nature of numbers rather than studying how they are applied to specific problems. Another novel feature was their use of proofs to establish mathematical truths and validate theories. A further contribution was their distinction of various classes of numbers, such as even numbers, odd numbers, and prime numbers. This included the discovery that numbers for certain geometrical lengths are irrational and therefore cannot be expressed as a fraction. The works of Thales of Miletus and Pythagoras in the 7th and 6th centuries BCE are often regarded as the inception of Greek mathematics. Diophantus was an influential figure in Greek arithmetic in the 3rd century BCE because of his numerous contributions to number theory and his exploration of the application of arithmetic operations to algebraic equations.
The ancient Indians were the first to develop the concept of zero as a number to be used in calculations. The exact rules of its operation were written down by Brahmagupta in around 628 CE. The concept of zero or none existed long before, but it was not considered an object of arithmetic operations. Brahmagupta further provided a detailed discussion of calculations with negative numbers and their application to problems like credit and debt. The concept of negative numbers itself is significantly older and was first explored in Chinese mathematics in the first millennium BCE. Indian mathematicians also developed the positional decimal system used today, in particular the concept of a zero digit instead of empty or missing positions. For example, a detailed treatment of its operations was provided by Aryabhata around the turn of the 6th century CE. The Indian decimal system was further refined and expanded to non-integers during the Islamic Golden Age by Middle Eastern mathematicians such as Al-Khwarizmi. His work was influential in introducing the decimal numeral system to the Western world, which at that time relied on the Roman numeral system. There, it was popularized by mathematicians like Leonardo Fibonacci, who lived in the 12th and 13th centuries and also developed the Fibonacci sequence. During the Middle Ages and Renaissance, many popular textbooks were published to cover the practical calculations for commerce. The use of abacuses also became widespread in this period. In the 16th century, the mathematician Gerolamo Cardano conceived the concept of complex numbers as a way to solve cubic equations.
The first mechanical calculators were developed in the 17th century and greatly facilitated complex mathematical calculations, such as Blaise Pascal's calculator and Gottfried Wilhelm Leibniz's stepped reckoner. The 17th century also saw the discovery of the logarithm by John Napier. In the 18th and 19th centuries, mathematicians such as Leonhard Euler and Carl Friedrich Gauss laid the foundations of modern number theory. Another development in this period concerned work on the formalization and foundations of arithmetic, such as Georg Cantor's set theory and the Dedekind–Peano axioms used as an axiomatization of natural-number arithmetic. Computers and electronic calculators were first developed in the 20th century. Their widespread use revolutionized both the accuracy and speed with which even complex arithmetic computations can be calculated. In various fields. Education. Arithmetic education forms part of primary education. It is one of the first forms of mathematics education that children encounter. Elementary arithmetic aims to give students a basic sense of numbers and to familiarize them with fundamental numerical operations like addition, subtraction, multiplication, and division. It is usually introduced in relation to concrete scenarios, like counting beads, dividing the class into groups of children of the same size, and calculating change when buying items. Common tools in early arithmetic education are number lines, addition and multiplication tables, counting blocks, and abacuses.
Later stages focus on a more abstract understanding and introduce the students to different types of numbers, such as negative numbers, fractions, real numbers, and complex numbers. They further cover more advanced numerical operations, like exponentiation, extraction of roots, and logarithm. They also show how arithmetic operations are employed in other branches of mathematics, such as their application to describe geometrical shapes and the use of variables in algebra. Another aspect is to teach the students the use of algorithms and calculators to solve complex arithmetic problems. Psychology. The psychology of arithmetic is interested in how humans and animals learn about numbers, represent them, and use them for calculations. It examines how mathematical problems are understood and solved and how arithmetic abilities are related to perception, memory, judgment, and decision making. For example, it investigates how collections of concrete items are first encountered in perception and subsequently associated with numbers. A further field of inquiry concerns the relation between numerical calculations and the use of language to form representations. Psychology also explores the biological origin of arithmetic as an inborn ability. This concerns pre-verbal and pre-symbolic cognitive processes implementing arithmetic-like operations required to successfully represent the world and perform tasks like spatial navigation.
One of the concepts studied by psychology is numeracy, which is the capability to comprehend numerical concepts, apply them to concrete situations, and reason with them. It includes a fundamental number sense as well as being able to estimate and compare quantities. It further encompasses the abilities to symbolically represent numbers in numbering systems, interpret numerical data, and evaluate arithmetic calculations. Numeracy is a key skill in many academic fields. A lack of numeracy can inhibit academic success and lead to bad economic decisions in everyday life, for example, by misunderstanding mortgage plans and insurance policies. Philosophy. The philosophy of arithmetic studies the fundamental concepts and principles underlying numbers and arithmetic operations. It explores the nature and ontological status of numbers, the relation of arithmetic to language and logic, and how it is possible to acquire arithmetic knowledge. According to Platonism, numbers have mind-independent existence: they exist as abstract objects outside spacetime and without causal powers. This view is rejected by intuitionists, who claim that mathematical objects are mental constructions. Further theories are logicism, which holds that mathematical truths are reducible to logical truths, and formalism, which states that mathematical principles are rules of how symbols are manipulated without claiming that they correspond to entities outside the rule-governed activity.
The traditionally dominant view in the epistemology of arithmetic is that arithmetic truths are knowable a priori. This means that they can be known by thinking alone without the need to rely on sensory experience. Some proponents of this view state that arithmetic knowledge is innate while others claim that there is some form of rational intuition through which mathematical truths can be apprehended. A more recent alternative view was suggested by naturalist philosophers like Willard Van Orman Quine, who argue that mathematical principles are high-level generalizations that are ultimately grounded in the sensory world as described by the empirical sciences. Others. Arithmetic is relevant to many fields. In daily life, it is required to calculate change when shopping, manage personal finances, and adjust a cooking recipe for a different number of servings. Businesses use arithmetic to calculate profits and losses and analyze market trends. In the field of engineering, it is used to measure quantities, calculate loads and forces, and design structures. Cryptography relies on arithmetic operations to protect sensitive information by encrypting data and messages.
Arithmetic is intimately connected to many branches of mathematics that depend on numerical operations. Algebra relies on arithmetic principles to solve equations using variables. These principles also play a key role in calculus in its attempt to determine rates of change and areas under curves. Geometry uses arithmetic operations to measure the properties of shapes while statistics utilizes them to analyze numerical data. Due to the relevance of arithmetic operations throughout mathematics, the influence of arithmetic extends to most sciences such as physics, computer science, and economics. These operations are used in calculations, problem-solving, data analysis, and algorithms, making them integral to scientific research, technological development, and economic modeling.
Andersonville, Georgia Andersonville is a city in Sumter County, Georgia, United States. As of the 2020 census, the city had a population of 237. It is located in the southwest part of the state, approximately southwest of Macon on the Central of Georgia railroad. During the American Civil War, it was the site of a prisoner-of-war camp, which is now Andersonville National Historic Site. Andersonville is part of the Americus micropolitan statistical area. History. The hamlet of Anderson was named for John Anderson, a director of the South Western Railroad in 1853 when it was extended from Oglethorpe to Americus. It was known as Anderson Station until the US post office was established in November 1855. The government changed the name of the station from "Anderson" to "Andersonville" in order to avoid confusion with the post office in Anderson, South Carolina. During the Civil War, the Confederate army established Camp Sumter at Andersonville to house incoming Union prisoners of war. The overcrowded Andersonville Prison was notorious for its bad conditions, and nearly 13,000 prisoners died there. After the war, Henry Wirz was convicted for war crimes related to the command of the camp. His trial was later regarded as unfair by several pro-confederacy groups, and a monument in his honor has been erected in Andersonville by the United Daughters of the Confederacy.
The town also served as a supply depot during the war period. It included a post office, a depot, a blacksmith shop and stable, a couple of general stores, two saloons, a school, a Methodist church, and about a dozen houses. Ben Dykes, who owned the land on which the prison was built, was both depot agent and postmaster. Until the establishment of the prison, the area was entirely dependent on agriculture, supported by dark reddish brown sandy loams later mapped as Greenville and Red Bay soil series. After the close of the prison and end of the war, the town continued economically dependent on agriculture, primarily the cultivation of cotton as a commodity crop. It was not until 1968, when the large-scale mining of kaolin, bauxitic kaolin, and bauxite was begun by Mulcoa, Mullite Company of America, that the town was dramatically altered. This operation exploited of scrub oak wilderness into a massive mining and refining operation. The company now ships more than 2000 tons of refined ore from Andersonville each week.
In 1974, long-time mayor Lewis Easterlin and a group of concerned citizens decided to promote tourism in the town, redeveloping Main Street to look much as it did during the American Civil War. The city of Andersonville and the Andersonville National Historic Site, location of the prison camp, are now tourist attractions. Demographics. As of the census of 2000, there were 331 people, 124 households, and 86 families residing in the city. The population density was . There were 142 housing units at an average density of . The racial makeup of the city was 65.26% White and 34.74% African American. Hispanic or Latino of any race were 1.21% of the population. There were 124 households, out of which 34.7% had children under the age of 18 living with them, 46.0% were married couples living together, 17.7% had a female householder with no husband present, and 30.6% were non-families. 26.6% of all households were made up of individuals, and 10.5% had someone living alone who was 65 years of age or older. The average household size was 2.67 and the average family size was 3.21.

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