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Analog computer
The Antikythera mechanism was an orrery and is considered an early mechanical analog computer, according to Derek J. de Solla Price. It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated ...
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Many mechanical aids to calculation and measurement were constructed for astronomical and navigation use. The planisphere was first described by Ptolemy in the 2nd century AD. The astrolabe was invented in the Hellenistic world in either the 1st or 2nd centuries BC and is often attributed to Hipparchus. A combination o...
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The sector, a calculating instrument used for solving problems in proportion, trigonometry, multiplication and division, and for various functions, such as squares and cube roots, was developed in the late 16th century and found application in gunnery, surveying and navigation. The planimeter was a manual instrument to...
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The slide rule was invented around 1620–1630, shortly after the publication of the concept of the logarithm. It is a hand-operated analog computer for doing multiplication and division. As slide rule development progressed, added scales provided reciprocals, squares and square roots, cubes and cube roots, as well as tr...
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In 1831–1835, mathematician and engineer Giovanni Plana devised a perpetual-calendar machine, which, through a system of pulleys and cylinders could predict the perpetual calendar for every year from AD 0 (that is, 1 BC) to AD 4000, keeping track of leap years and varying day length. The tide-predicting machine invente...
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The differential analyser, a mechanical analog computer designed to solve differential equations by integration, used wheel-and-disc mechanisms to perform the integration. In 1876 James Thomson had already discussed the possible construction of such calculators, but he had been stymied by the limited output torque of t...
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Modern era The Dumaresq was a mechanical calculating device invented around 1902 by Lieutenant John Dumaresq of the Royal Navy. It was an analog computer that related vital variables of the fire control problem to the movement of one's own ship and that of a target ship. It was often used with other devices, such as a ...
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By 1912 Arthur Pollen had developed an electrically driven mechanical analog computer for fire-control systems, based on the differential analyser. It was used by the Imperial Russian Navy in World War I.
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Starting in 1929, AC network analyzers were constructed to solve calculation problems related to electrical power systems that were too large to solve with numerical methods at the time. These were essentially scale models of the electrical properties of the full-size system. Since network analyzers could handle proble...
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World War II era gun directors, gun data computers, and bomb sights used mechanical analog computers. In 1942 Helmut Hölzer built a fully electronic analog computer at Peenemünde Army Research Center as an embedded control system (mixing device) to calculate V-2 rocket trajectories from the accelerations and orientatio...
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In the period 1930–1945 in the Netherlands Johan van Veen developed an analogue computer to calculate and predict tidal currents when the geometry of the channels are changed. Around 1950 this idea was developed into the Deltar, an analogue computer supporting the closure of estuaries in the southwest of the Netherland...
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The FERMIAC was an analog computer invented by physicist Enrico Fermi in 1947 to aid in his studies of neutron transport. Project Cyclone was an analog computer developed by Reeves in 1950 for the analysis and design of dynamic systems. Project Typhoon was an analog computer developed by RCA in 1952. It consisted of ov...
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Computer Engineering Associates was spun out of Caltech in 1950 to provide commercial services using the "Direct Analogy Electric Analog Computer" ("the largest and most impressive general-purpose analyzer facility for the solution of field problems") developed there by Gilbert D. McCann, Charles H. Wilts, and Bart Loc...
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Educational analog computers illustrated the principles of analog calculation. The Heathkit EC-1, a $199 educational analog computer, was made by the Heath Company, US . It was programmed using patch cords that connected nine operational amplifiers and other components. General Electric also marketed an "educational" a...
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Analog computer designs were published in electronics magazines. One example is the PE Analogue Computer, published in Practical Electronics in the September 1978 edition. Another more modern hybrid computer design was published in Everyday Practical Electronics in 2002. An example described in the EPE Hybrid Computer ...
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In industrial process control, analog loop controllers were used to automatically regulate temperature, flow, pressure, or other process conditions. The technology of these controllers ranged from purely mechanical integrators, through vacuum-tube and solid-state devices, to emulation of analog controllers by microproc...
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However, the difference between these systems is what makes analog computing useful. Complex systems often are not amenable to pen-and-paper analysis, and require some form of testing or simulation. Complex mechanical systems, such as suspensions for racing cars, are expensive to fabricate and hard to modify. And takin...
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By contrast, it is very inexpensive to build an electrical equivalent of a complex mechanical system, to simulate its behavior. Engineers arrange a few operational amplifiers (op amps) and some passive linear components to form a circuit that follows the same equations as the mechanical system being simulated. All meas...
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The electronic circuit can also be made to run faster or slower than the physical system being simulated. Experienced users of electronic analog computers said that they offered a comparatively intimate control and understanding of the problem, relative to digital simulations.
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Electronic analog computers are especially well-suited to representing situations described by differential equations. Historically, they were often used when a system of differential equations proved very difficult to solve by traditional means. As a simple example, the dynamics of a spring-mass system can be describe...
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Electronic analog computers have drawbacks: the value of the circuit's supply voltage limits the range over which the variables may vary (since the value of a variable is represented by a voltage on a particular wire). Therefore, each problem must be scaled so its parameters and dimensions can be represented using volt...
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The precision of the analog computer readout was limited chiefly by the precision of the readout equipment used, generally three or four significant figures. (Modern digital simulations are much better in this area. Digital arbitrary-precision arithmetic can provide any desired degree of precision.) However, in most ca...
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Many small computers dedicated to specific computations are still part of industrial regulation equipment, but from the 1950s to the 1970s, general-purpose analog computers were the only systems fast enough for real time simulation of dynamic systems, especially in the aircraft, military and aerospace field. In the 196...
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Although the basic technology for analog computers is usually operational amplifiers (also called "continuous current amplifiers" because they have no low frequency limitation), in the 1960s an attempt was made in the French ANALAC computer to use an alternative technology: medium frequency carrier and non dissipative ...
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In the 1970s every big company and administration concerned with problems in dynamics had a big analog computing center, for example: In the US: NASA (Huntsville, Houston), Martin Marietta (Orlando), Lockheed, Westinghouse, Hughes Aircraft In Europe: CEA (French Atomic Energy Commission), MATRA, Aérospatiale, BAC (Br...
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Analog–digital hybrids Analog computing devices are fast, digital computing devices are more versatile and accurate, so the idea is to combine the two processes for the best efficiency. An example of such hybrid elementary device is the hybrid multiplier where one input is an analog signal, the other input is a digital...
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In the early 1970s analog computer manufacturers tried to tie together their analog computer with a digital computer to get the advantages of the two techniques. In such systems, the digital computer controlled the analog computer, providing initial set-up, initiating multiple analog runs, and automatically feeding and...
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The largest manufacturer of hybrid computers was Electronics Associates. Their hybrid computer model 8900 was made of a digital computer and one or more analog consoles. These systems were mainly dedicated to large projects such as the Apollo program and Space Shuttle at NASA, or Ariane in Europe, especially during the...
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The best reference in this field is the 100,000 simulation runs for each certification of the automatic landing systems of Airbus and Concorde aircraft.
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After 1980, purely digital computers progressed more and more rapidly and were fast enough to compete with analog computers. One key to the speed of analog computers was their fully parallel computation, but this was also a limitation. The more equations required for a problem, the more analog components were needed, e...
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While a wide variety of mechanisms have been developed throughout history, some stand out because of their theoretical importance, or because they were manufactured in significant quantities.
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Most practical mechanical analog computers of any significant complexity used rotating shafts to carry variables from one mechanism to another. Cables and pulleys were used in a Fourier synthesizer, a tide-predicting machine, which summed the individual harmonic components. Another category, not nearly as well known, u...
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Online, there is a remarkably clear illustrated reference (OP 1140) that describes the fire control computer mechanisms. For adding and subtracting, precision miter-gear differentials were in common use in some computers; the Ford Instrument Mark I Fire Control Computer contained about 160 of them.
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Integration with respect to another variable was done by a rotating disc driven by one variable. Output came from a pick-off device (such as a wheel) positioned at a radius on the disc proportional to the second variable. (A carrier with a pair of steel balls supported by small rollers worked especially well. A roller,...
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Functions of two variables were provided by three-dimensional cams. In one good design, one of the variables rotated the cam. A hemispherical follower moved its carrier on a pivot axis parallel to that of the cam's rotating axis. Pivoting motion was the output. The second variable moved the follower along the axis of t...
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Coordinate conversion from polar to rectangular was done by a mechanical resolver (called a "component solver" in US Navy fire control computers). Two discs on a common axis positioned a sliding block with pin (stubby shaft) on it. One disc was a face cam, and a follower on the block in the face cam's groove set the ra...
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Referring to the mechanism's frame, the location of the pin corresponded to the tip of the vector represented by the angle and magnitude inputs. Mounted on that pin was a square block. Rectilinear-coordinate outputs (both sine and cosine, typically) came from two slotted plates, each slot fitting on the block just ment...
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During World War II, a similar mechanism converted rectilinear to polar coordinates, but it was not particularly successful and was eliminated in a significant redesign (USN, Mk. 1 to Mk. 1A).
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Multiplication was done by mechanisms based on the geometry of similar right triangles. Using the trigonometric terms for a right triangle, specifically opposite, adjacent, and hypotenuse, the adjacent side was fixed by construction. One variable changed the magnitude of the opposite side. In many cases, this variable ...
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Typically, a pinion-operated rack moving parallel to the (trig.-defined) opposite side would position a slide with a slot coincident with the hypotenuse. A pivot on the rack let the slide's angle change freely. At the other end of the slide (the angle, in trig. terms), a block on a pin fixed to the frame defined the ve...
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At any distance along the adjacent side, a line perpendicular to it intersects the hypotenuse at a particular point. The distance between that point and the adjacent side is some fraction that is the product of 1 the distance from the vertex, and 2 the magnitude of the opposite side.
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The second input variable in this type of multiplier positions a slotted plate perpendicular to the adjacent side. That slot contains a block, and that block's position in its slot is determined by another block right next to it. The latter slides along the hypotenuse, so the two blocks are positioned at a distance fro...
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To provide the product as an output, a third element, another slotted plate, also moves parallel to the (trig.) opposite side of the theoretical triangle. As usual, the slot is perpendicular to the direction of movement. A block in its slot, pivoted to the hypotenuse block positions it.
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A special type of integrator, used at a point where only moderate accuracy was needed, was based on a steel ball, instead of a disc. It had two inputs, one to rotate the ball, and the other to define the angle of the ball's rotating axis. That axis was always in a plane that contained the axes of two movement pick-off ...
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A pair of rollers "above" and "below" the pick-off plane were mounted in rotating holders that were geared together. That gearing was driven by the angle input, and established the rotating axis of the ball. The other input rotated the "bottom" roller to make the ball rotate.
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Essentially, the whole mechanism, called a component integrator, was a variable-speed drive with one motion input and two outputs, as well as an angle input. The angle input varied the ratio (and direction) of coupling between the "motion" input and the outputs according to the sine and cosine of the input angle.
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Although they did not accomplish any computation, electromechanical position servos were essential in mechanical analog computers of the "rotating-shaft" type for providing operating torque to the inputs of subsequent computing mechanisms, as well as driving output data-transmission devices such as large torque-transmi...
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Considering that accurately controlled rotational speed in analog fire-control computers was a basic element of their accuracy, there was a motor with its average speed controlled by a balance wheel, hairspring, jeweled-bearing differential, a twin-lobe cam, and spring-loaded contacts (ship's AC power frequency was not...
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Electronic analog computers typically have front panels with numerous jacks (single-contact sockets) that permit patch cords (flexible wires with plugs at both ends) to create the interconnections that define the problem setup. In addition, there are precision high-resolution potentiometers (variable resistors) for set...
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Typical electronic analog computers contain anywhere from a few to a hundred or more operational amplifiers ("op amps"), named because they perform mathematical operations. Op amps are a particular type of feedback amplifier with very high gain and stable input (low and stable offset). They are always used with precisi...
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Integrating with respect to another variable is the nearly exclusive province of mechanical analog integrators; it is almost never done in electronic analog computers. However, given that a problem solution does not change with time, time can serve as one of the variables. Other computing elements include analog multip...
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Electrical elements such as inductors and capacitors used in electrical analog computers had to be carefully manufactured to reduce non-ideal effects. For example, in the construction of AC power network analyzers, one motive for using higher frequencies for the calculator (instead of the actual power frequency) was th...
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The use of electrical properties in analog computers means that calculations are normally performed in real time (or faster), at a speed determined mostly by the frequency response of the operational amplifiers and other computing elements. In the history of electronic analog computers, there were some special high-spe...
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When compensated for temperature, the forward voltage drop of a transistor's base-emitter junction can provide a usably accurate logarithmic or exponential function. Op amps scale the output voltage so that it is usable with the rest of the computer.
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Any physical process that models some computation can be interpreted as an analog computer. Some examples, invented for the purpose of illustrating the concept of analog computation, include using a bundle of spaghetti as a model of sorting numbers; a board, a set of nails, and a rubber band as a model of finding the c...
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Analog computers often have a complicated framework, but they have, at their core, a set of key components that perform the calculations. The operator manipulates these through the computer's framework. Key hydraulic components might include pipes, valves and containers. Key mechanical components might include rotating...
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Key electrical/electronic components might include: precision resistors and capacitors operational amplifiers multipliers potentiometers fixed-function generators The core mathematical operations used in an electric analog computer are: addition integration with respect to time inversion multiplication expone...
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Differentiation with respect to time is not frequently used, and in practice is avoided by redefining the problem when possible. It corresponds in the frequency domain to a high-pass filter, which means that high-frequency noise is amplified; differentiation also risks instability. Limitations
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In general, analog computers are limited by non-ideal effects. An analog signal is composed of four basic components: DC and AC magnitudes, frequency, and phase. The real limits of range on these characteristics limit analog computers. Some of these limits include the operational amplifier offset, finite gain, and freq...
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Decline In the 1950s to 1970s, digital computers based on first vacuum tubes, transistors, integrated circuits and then micro-processors became more economical and precise. This led digital computers to largely replace analog computers. Even so, some research in analog computation is still being done. A few universitie...
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Resurgence With the development of very-large-scale integration (VLSI) technology, Yannis Tsividis' group at Columbia University has been revisiting analog/hybrid computers design in standard CMOS process. Two VLSI chips have been developed, an 80th-order analog computer (250 nm) by Glenn Cowan in 2005 and a 4th-order ...
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Analog computers are also used in neuromorphic computing, and in 2021 a group of researchers have shown that a specific type of artificial neural network called a spiking neural network was able to work with analog neuromorphic computers. Practical examples These are examples of analog computers that have been construc...
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Boeing B-29 Superfortress Central Fire Control System Deltar E6B flight computer Kerrison Predictor Leonardo Torres y Quevedo's Analogue Calculating Machines based on "fusee sans fin" Librascope, aircraft weight and balance computer Mechanical computer Mechanical integrators, for example, the planimeter Nomogra...
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Analog (audio) synthesizers can also be viewed as a form of analog computer, and their technology was originally based in part on electronic analog computer technology. The ARP 2600's Ring Modulator was actually a moderate-accuracy analog multiplier. The Simulation Council (or Simulations Council) was an association of...
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Analog neural network Analogical models Chaos theory Differential equation Dynamical system Field-programmable analog array General purpose analog computer Lotfernrohr 7 series of WW II German bombsights Signal (electrical engineering) Voskhod Spacecraft "Globus" IMP navigation instrument XY-writer Notes
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References A.K. Dewdney. "On the Spaghetti Computer and Other Analog Gadgets for Problem Solving", Scientific American, 250(6):19–26, June 1984. Reprinted in The Armchair Universe, by A.K. Dewdney, published by W.H. Freeman & Company (1988), . Universiteit van Amsterdam Computer Museum. (2007). Analog Computers. Jac...
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External links Biruni's eight-geared lunisolar calendar in "Archaeology: High tech from Ancient Greece", François Charette, Nature 444, 551–552(30 November 2006), The first computers Large collection of electronic analog computers with lots of pictures, documentation and samples of implementations (some in German) ...
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History of computing hardware Chinese inventions Greek inventions
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Aegean civilization
Aegean civilization is a general term for the Bronze Age civilizations of Greece around the Aegean Sea. There are three distinct but communicating and interacting geographic regions covered by this term: Crete, the Cyclades and the Greek mainland. Crete is associated with the Minoan civilization from the Early Bronze A...
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The earlier Aegean farming populations of Neolithic Greece brought agriculture to Western Europe already before 5,000 years BC. Aegean Neolithic farmers A DNA study from 2019 indicates that agriculture was brought to Western Europe by the Aegean populations that are known as "Aegean Neolithic farmers". These Neolithic ...
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Prior to that, these territories were populated by the hunter-gathererer cultures known as the 'western hunter-gatherers', similar to the Cheddar Man. Most of the ancestry of the British population after 4000 BC (74% on average) is attributable to the Aegean Neolithic farmers. This indicates a substantial shift in ance...
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Early Helladic (EH): 3200/3100–2050/2001 BC Middle Helladic (MH): 2000/1900–1550 BC Late Helladic (LH): 1550–1050 BC Crete Early Minoan (EM): 2700–2160 BC Middle Minoan (MM): 2160–1600 BC Late Minoan (LM): 1600-1100 BC Cyclades
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Early Cycladic (EC): 3300–2000 BC Kastri (EH II–EH III): ca. 2500–2100 BC Convergence with MM from ca. 2000 BC
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Commerce Commerce was practiced to some extent in very early times, as is proved by the distribution of Melian obsidian over all the Aegean area. Cretan vessels appeared to be exported to Melos, Egypt and the Greek mainland. In particular, Melian vases, eventually, found their way to Crete. After 1600 BC, there was ver...
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Discoveries, later in the 20th century, of sunken trading vessels such as those at Uluburun and Cape Gelidonya off the south coast of Turkey have brought forth an enormous amount of new information about that culture.
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Evidence For details of monumental evidence the articles on Crete, Mycenae, Tiryns, Troad, Cyprus, etc., must be consulted. The most representative site explored up to now is Knossos (see Crete) which has yielded not only the most various but the most continuous evidence from the Neolithic age to the twilight of classi...
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Internal evidence Structures: Ruins of palaces, palatial villas, houses, built dome- or cist-graves and fortifications (Aegean islands, Greek mainland and northwestern Anatolia), but not distinct temples; small shrines, however, and temene (religious enclosures, remains of one of which were probably found at Petsofa ne...
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External evidence Monuments and records of other contemporary civilizations: for example, representations of alien peoples in Egyptian frescoes; imitation of Aegean fabrics and style in non-Aegean lands; allusions to Mediterranean peoples in Egyptian, Semitic or Babylonian records. Literary traditions of subsequent civ...
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Discovery The curtain-wall and towers of the Mycenaean citadel, its gate with heraldic lions, and the great "Treasury of Atreus" had borne silent witness for ages before Heinrich Schliemann's time; but they were supposed only to speak to the Homeric, or, at farthest, a rude Heroic beginning of purely Hellenic civilizat...
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There had been, however, a good deal of other evidence available before 1876, which, had it been collated and seriously studied, might have discounted the sensation that the discovery of the citadel graves eventually made. Although it was recognized that certain tributaries, represented for example, in the XVIIIth Dyna...
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Ludwig Ross, the German archaeologist appointed Curator of the Antiquities of Athens at the time of the establishment of the Kingdom of Greece, by his explorations in the Greek islands from 1835 onwards, called attention to certain early intaglios, since known as Inselsteine; but it was not until 1878 that C. T. Newton...
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Meanwhile, in 1868, tombs at Ialysus in Rhodes had yielded to Alfred Biliotti many fine painted vases of styles which were called later the third and fourth "Mycenaean"; but these, bought by John Ruskin, and presented to the British Museum, excited less attention than they deserved, being supposed to be of some local A...
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Even Schliemann's first excavations at Hissarlik in the Troad did not excite surprise. But the "Burnt City" of his second stratum, revealed in 1873, with its fortifications and vases, and a hoard of gold, silver and bronze objects, which the discoverer connected with it, began to arouse a curiosity which was destined p...
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Schliemann got to work again at Hissarlik in 1878, and greatly increased our knowledge of the lower strata, but did not recognize the Aegean remains in his "Lydian" city of the sixth stratum. These were not to be fully revealed until Dr. Wilhelm Dorpfeld, who had become Schliemann's assistant in 1879, resumed the work ...
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From 1886 dates the finding of Mycenaean sepulchres outside the Argolid, from which, and from the continuation of Tsountas's exploration of the buildings and lesser graves at Mycenae, a large treasure, independent of Schliemann's princely gift, has been gathered into the National Museum at Athens. In that year tholos-t...
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In 1890 and 1893, Staes cleared out certain less rich tholos-tombs at Thoricus in Attica; and other graves, either rock-cut "bee-hives" or chambers, were found at Spata and Aphidna in Attica, in Aegina and Salamis, at the Argive Heraeum and Nauplia in the Argolid, near Thebes and Delphi, and not far from the Thessalian...
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Prehistoric research had now begun to extend beyond the Greek mainland. Certain central Aegean islands, Antiparos, Ios, Amorgos, Syros and Siphnos, were all found to be singularly rich in evidence of the Middle-Aegean period. The series of Syran-built graves, containing crouching corpses, is the best and most represent...
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A map of Cyprus in the later Bronze Age (such as is given by J. L. Myres and M. O. Richter in Catalogue of the Cyprus Museum) shows more than 25 settlements in and about the Mesaorea district alone, of which one, that at Enkomi, near the site of Salamis, has yielded the richest Aegean treasure in precious metal found o...
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In Egypt in 1887, Flinders Petrie found painted sherds of Cretan style at Kahun in the Fayum, and farther up the Nile, at Tell el-Amarna, chanced on bits of no fewer than 800 Aegean vases in 1889. There have now been recognized in the collections at Cairo, Florence, London, Paris and Bologna several Egyptian imitations...
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Sicily, ever since P. Orsi excavated the Sicel cemetery near Lentini in 1877, has proved a mine of early remains, among which appear in regular succession Aegean fabrics and motives of decoration from the period of the second stratum at Hissarlik. Sardinia has Aegean sites, for example, at Abini near Teti; and Spain ha...
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One land, however, has eclipsed all others in the Aegean by the wealth of its remains of all the prehistoric ages— Crete; and so much so that, for the present, we must regard it as the fountainhead of Aegean civilization, and probably for long its political and social centre. The island first attracted the notice of ar...
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Thus the "Aegean Area" has now come to mean the Archipelago with Crete and Cyprus, the Hellenic peninsula with the Ionian islands, and Western Anatolia. Evidence is still wanting for the Macedonian and Thracian coasts. Offshoots are found in the western Mediterranean area, in Sicily, Italy, Sardinia and Spain, and in t...
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The final collapse of the Mycenaean civilisation appears to have occurred about 1000 BC. The palace at Knossus was once more destroyed, and never rebuilt or re-inhabited. Iron took the place of Bronze, and Aegean art, as a living thing, ceased on the Greek mainland and in the Aegean isles including Crete, together with...
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See also Mycenaean Greece Prehistory of Southeastern Europe References This includes many illustrations, and a more intensive history of the civilizations, as understood in the early 20th century. External links Jeremy B. Rutter, "The Prehistoric Archaeology of the Aegean": chronology, history, bibliography Aegean an...
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Atlas Autocode
Atlas Autocode (AA) is a programming language developed around 1965 at the University of Manchester. A variant of the language ALGOL, it was developed by Tony Brooker and Derrick Morris for the Atlas computer. The word Autocode was basically an early term for programming language. Different autocodes could vary greatly...
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The AA compiler generated range-checking for array accesses, and allowed an array to have dimensions that were determined at runtime, i.e., an array could be declared as integer array Thing (i:j), where i and j were calculated values. AA high-level routines can include machine code, either to make an inner loop more ef...
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Atlas Autocode
AA includes a complex data type to represent complex numbers, partly because of pressure from the electrical engineering department, as complex numbers are used to represent the behavior of alternating current. The imaginary unit square root of -1 was represented by i, which was treated as a fixed complex constant = i....
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Atlas Autocode
AA's second-greatest claim to fame (after being the progenitor of IMP and EMAS) was that it had many of the features of the original Compiler Compiler. A variant of the AA compiler included run-time support for a top-down recursive descent parser. The style of parser used in the Compiler Compiler was in use continuous...
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Atlas Autocode
Syntax Atlas Autocode's syntax was largely similar to ALGOL, though it was influenced by the output device which the author had available, a Friden Flexowriter. Thus, it allowed symbols like ½ for .5 and the superscript 2 for to the power of 2. The Flexowriter supported overstriking and thus, AA did also: up to three ...
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Atlas Autocode
Other Flexowriter characters that were found a use in AA were: α in floating-point numbers, e.g., 3.56α-7 for modern 3.56e-7 ; β to mean the second half of a 48-bit Atlas memory word; π for the mathematical constant pi.
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