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Analog computer
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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 to during the Hellenistic period of Greece. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.
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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 of the planisphere and dioptra, the astrolabe was effectively an analog computer capable of working out several different kinds of problems in spherical astronomy. An astrolabe incorporating a mechanical calendar computer and gear-wheels was invented by Abi Bakr of Isfahan, Persia in 1235. Abū Rayhān al-Bīrūnī invented the first mechanical geared lunisolar calendar astrolabe, an early fixed-wired knowledge processing machine with a gear train and gear-wheels, . The castle clock, a hydropowered mechanical astronomical clock invented by Al-Jazari in 1206, was the first programmable analog computer.
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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 calculate the area of a closed figure by tracing over it with a mechanical linkage.
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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 transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Aviation is one of the few fields where slide rules are still in widespread use, particularly for solving time–distance problems in light aircraft.
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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 invented by Sir William Thomson in 1872 was of great utility to navigation in shallow waters. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location.
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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 the ball-and-disk integrators. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output. The torque amplifier was the advance that allowed these machines to work. Starting in the 1920s, Vannevar Bush and others developed mechanical differential analyzers.
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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 Vickers range clock to generate range and deflection data so the gun sights of the ship could be continuously set. A number of versions of the Dumaresq were produced of increasing complexity as development proceeded.
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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 problems too large for analytic methods or hand computation, they were also used to solve problems in nuclear physics and in the design of structures. More than 50 large network analyzers were built by the end of the 1950s.
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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 orientations (measured by gyroscopes) and to stabilize and guide the missile. Mechanical analog computers were very important in gun fire control in World War II, The Korean War and well past the Vietnam War; they were made in significant numbers.
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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 Netherlands (the Delta Works).
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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 over 4000 electron tubes and used 100 dials and 6000 plug-in connectors to program. The MONIAC Computer was a hydraulic model of a national economy first unveiled in 1949.
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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 Locanthi.
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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" analog computer kit of a simple design in the early 1960s consisting of a two transistor tone generators and three potentiometers wired such that the frequency of the oscillator was nulled when the potentiometer dials were positioned by hand to satisfy an equation. The relative resistance of the potentiometer was then equivalent to the formula of the equation being solved. Multiplication or division could be performed, depending on which dials were inputs and which was the output. Accuracy and resolution was limited and a simple slide rule was more accurate—however, the unit did demonstrate the basic principle.
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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 was the flight of a VTOL aircraft like the Harrier jump jet. The altitude and speed of the aircraft were calculated by the analog part of the computer and sent to a PC via a digital microprocessor and displayed on the PC screen.
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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 microprocessors. Electronic analog computers The similarity between linear mechanical components, such as springs and dashpots (viscous-fluid dampers), and electrical components, such as capacitors, inductors, and resistors is striking in terms of mathematics. They can be modeled using equations of the same form.
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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 taking precise mechanical measurements during high-speed tests adds further difficulty.
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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 measurements can be taken directly with an oscilloscope. In the circuit, the (simulated) stiffness of the spring, for instance, can be changed by adjusting the parameters of an integrator. The electrical system is an analogy to the physical system, hence the name, but it is much less expensive than a mechanical prototype, much easier to modify, and generally safer.
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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 described by the equation , with as the vertical position of a mass , the damping coefficient, the spring constant and the gravity of Earth. For analog computing, the equation is programmed as . The equivalent analog circuit consists of two integrators for the state variables (speed) and (position), one inverter, and three potentiometers.
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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 voltages that the circuit can supply —e.g., the expected magnitudes of the velocity and the position of a spring pendulum. Improperly scaled variables can have their values "clamped" by the limits of the supply voltage. Or if scaled too small, they can suffer from higher noise levels. Either problem can cause the circuit to produce an incorrect simulation of the physical system. (Modern digital simulations are much more robust to widely varying values of their variables, but are still not entirely immune to these concerns: floating-point digital calculations support a huge dynamic range, but can suffer from imprecision if tiny differences of huge values lead to numerical instability.)
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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 cases the precision of an analog computer is absolutely sufficient given the uncertainty of the model characteristics and its technical parameters.
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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 1960s, the major manufacturer was Electronic Associates of Princeton, New Jersey, with its 231R Analog Computer (vacuum tubes, 20 integrators) and subsequently its EAI 8800 Analog Computer (solid state operational amplifiers, 64 integrators). Its challenger was Applied Dynamics of Ann Arbor, Michigan.
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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 reversible circuits.
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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 (British Aircraft Corporation).
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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 signal and the output is analog. It acts as an analog potentiometer upgradable digitally. This kind of hybrid technique is mainly used for fast dedicated real time computation when computing time is very critical as signal processing for radars and generally for controllers in embedded systems.
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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 collecting data. The digital computer may also participate to the calculation itself using analog-to-digital and digital-to-analog converters.
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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 integration step where at the beginning everything is simulated, and progressively real components replace their simulated part. Only one company was known as offering general commercial computing services on its hybrid computers, CISI of France, in the 1970s.
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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, even when the problem wasn't time critical. "Programming" a problem meant interconnecting the analog operators; even with a removable wiring panel this was not very versatile. Today there are no more big hybrid computers, but only hybrid components. Implementations Mechanical analog computers
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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, used rotating shafts only for input and output, with precision racks and pinions. The racks were connected to linkages that performed the computation. At least one U.S. Naval sonar fire control computer of the later 1950s, made by Librascope, was of this type, as was the principal computer in the Mk. 56 Gun Fire Control System.
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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, its axis parallel to the disc's surface, provided the output. It was held against the pair of balls by a spring.) Arbitrary functions of one variable were provided by cams, with gearing to convert follower movement to shaft rotation.
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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 the cam. One practical application was ballistics in gunnery.
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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 radius. The other disc, closer to the pin, contained a straight slot in which the block moved. The input angle rotated the latter disc (the face cam disc, for an unchanging radius, rotated with the other (angle) disc; a differential and a few gears did this correction).
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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 mentioned. The plates moved in straight lines, the movement of one plate at right angles to that of the other. The slots were at right angles to the direction of movement. Each plate, by itself, was like a Scotch yoke, known to steam engine enthusiasts.
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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 changed sign; the hypotenuse could coincide with the adjacent side (a zero input), or move beyond the adjacent side, representing a sign change.
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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 vertex between the hypotenuse and the adjacent side.
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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 from the (trig.) adjacent side by an amount proportional to the product.
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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 rollers, quite similar to the mechanism of a rolling-ball computer mouse (in that mechanism, the pick-off rollers were roughly the same diameter as the ball). The pick-off roller axes were at right angles.
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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-transmitter synchros in naval computers. Other readout mechanisms, not directly part of the computation, included internal odometer-like counters with interpolating drum dials for indicating internal variables, and mechanical multi-turn limit stops.
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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 necessarily accurate, nor dependable enough, when these computers were designed). Electronic analog computers
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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 setting up (and, when needed, varying) scale factors. In addition, there is usually a zero-center analog pointer-type meter for modest-accuracy voltage measurement. Stable, accurate voltage sources provide known magnitudes.
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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 precision feedback components that, in operation, all but cancel out the currents arriving from input components. The majority of op amps in a representative setup are summing amplifiers, which add and subtract analog voltages, providing the result at their output jacks. As well, op amps with capacitor feedback are usually included in a setup; they integrate the sum of their inputs with respect to time.
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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 multipliers, nonlinear function generators, and analog comparators.
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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 that higher-quality inductors could be more easily made. Many general-purpose analog computers avoided the use of inductors entirely, re-casting the problem in a form that could be solved using only resistive and capacitive elements, since high-quality capacitors are relatively easy to make.
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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-speed types. Nonlinear functions and calculations can be constructed to a limited precision (three or four digits) by designing function generators—special circuits of various combinations of resistors and diodes to provide the nonlinearity. Typically, as the input voltage increases, progressively more diodes conduct.
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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 convex hull of a set of points; and strings tied together as a model of finding the shortest path in a network. These are all described in Dewdney (1984). Components
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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 shafts for carrying data within the computer, miter gear differentials, disc/ball/roller integrators, cams (2-D and 3-D), mechanical resolvers and multipliers, and torque servos.
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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
exponentiation
logarithm
division In some analog computer designs, multiplication is much preferred to division. Division is carried out with a multiplier in the feedback path of an Operational Amplifier.
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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 frequency response, noise floor, non-linearities, temperature coefficient, and parasitic effects within semiconductor devices. For commercially available electronic components, ranges of these aspects of input and output signals are always figures of merit.
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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 universities still use analog computers to teach control system theory. The American company Comdyna manufactured small analog computers. At Indiana University Bloomington, Jonathan Mills has developed the Extended Analog Computer based on sampling voltages in a foam sheet. At the Harvard Robotics Laboratory, analog computation is a research topic. Lyric Semiconductor's error correction circuits use analog probabilistic signals. Slide rules are still popular among aircraft personnel.
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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 hybrid computer (65 nm) developed by Ning Guo in 2015, both targeting at energy-efficient ODE/PDE applications. Glenn's chip contains 16 macros, in which there are 25 analog computing blocks, namely integrators, multipliers, fanouts, few nonlinear blocks. Ning's chip contains one macro block, in which there are 26 computing blocks including integrators, multipliers, fanouts, ADCs, SRAMs and DACs. Arbitrary nonlinear function generation is made possible by the ADC+SRAM+DAC chain, where the SRAM block stores the nonlinear function data. The experiments from the related publications revealed that VLSI analog/hybrid computers demonstrated about 1–2 orders magnitude of advantage in both solution time and energy while achieving accuracy within 5%, which points to the promise of using analog/hybrid computing techniques in the area of energy-efficient approximate computing. In 2016, a team of researchers developed a compiler to solve differential equations using analog circuits.
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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 constructed or practically used:
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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
Nomogram
Norden bombsight
Rangekeeper, and related fire control computers
Scanimate
Torpedo Data Computer
Torquetum
Water integrator
MONIAC, economic modelling
Ishiguro Storm Surge Computer
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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 analog computer users in US. It is now known as The Society for Modeling and Simulation International. The Simulation Council newsletters from 1952 to 1963 are available online and show the concerns and technologies at the time, and the common use of analog computers for missilry. See also
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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.
Jackson, Albert S., "Analog Computation". London & New York: McGraw-Hill, 1960.
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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)
Large collection of old analog and digital computers at Old Computer Museum
A great disappearing act: the electronic analogue computer Chris Bissell, The Open University, Milton Keynes, UK Accessed February 2007
German computer museum with still runnable analog computers
Analog computer basics
Analog computer trumps Turing model
Jonathan W. Mills's Analog Notebook
Harvard Robotics Laboratory Analog Computation
The Enns Power Network Computer – an analog computer for the analysis of electric power systems (advertisement from 1955)
Librascope Development Company – Type LC-1 WWII Navy PV-1 "Balance Computor"
Kronis Technology More information on Analog and Hybrid computers
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History of computing hardware
Chinese inventions
Greek inventions
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Aegean civilization
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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 Age. The Cycladic civilization converges with the mainland during the Early Helladic ("Minyan") period and with Crete in the Middle Minoan period. From c. 1450 BC (Late Helladic, Late Minoan), the Greek Mycenaean civilization spreads to Crete, probably by military conquest.
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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 groups arrived to northern France and Germany already around 5000 BC. About 1000 years later, they arrived in Britain. When they left the Aegean, these populations quickly split into two groups with somewhat different cultures. One group went north along the Danube, while the other took a southerly route along the Mediterranean and reached Iberia. This latter group then arrived in Britain.
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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 ancestry with the transition to farming. The Chalcolithic (Copper Age) started in Europe about 5500 BC. Numerous megalithic structures and monuments were also erected in this period. Periodization Mainland
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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 very close commerce with Egypt, and Aegean goods found their way to all coasts of the Mediterranean. No traces of currency have come to light, excluding certain axeheads, too slight for practical use, had that character. Standard weights have been found, as well as representations of ingots. The Aegean written documents have not yet proved (by being found outside the area) to be epistolary (letter writing) correspondence with other countries. Representations of ships are not common, but several have been observed on Aegean gems, gem-sealings, frying pans and vases. These vases are of low free-board, with masts and oars. Familiarity with the sea is proved by the free use of marine motifs in decoration. The most detailed illustrations are to be found on the 'ship fresco' at Akrotiri on the island of Thera (Santorini) preserved by the ash fall from the volcanic eruption which destroyed the town there.
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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 classical civilization. Next in importance come Hissarlik, Mycenae, Phaestus, Hagia Triada, Tiryns, Phylakope, Palaikastro and Gournia.
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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 near Palaikastro by J. L. Myres in 1904) are represented on intaglios and frescoes. From the sources and from inlay-work we have also representations of palaces and houses.
Structural decoration: Architectural features, such as columns, friezes and various mouldings; mural decoration, such as fresco-paintings, coloured reliefs and mosaic inlay. Roof tiles were also occasionally employed, as at early Helladic Lerna and Akovitika, and later in the Mycenaean towns of Gla and Midea.
Furniture: (a) Domestic furniture, such as vessels of all sorts and in many materials, from huge store jars down to tiny unguent pots; culinary and other implements; thrones, seats, tables, etc., these all in stone or plastered terracotta. (b) Sacred furniture, such as models or actual examples of ritual objects; of these we have also numerous pictorial representations. (c) Funerary furniture, for example, coffins in painted terracotta.
Art products: for example, plastic objects, carved in stone or ivory, cast or beaten in metals (gold, silver, copper and bronze), or modelled in clay, faience, paste, etc. Very little trace has yet been found of large free-standing sculpture, but many examples exist of sculptors' smaller work. Vases of all kinds, carved in marble or other stones, cast or beaten in metals or fashioned in clay, the latter in enormous number and variety, richly ornamented with coloured schemes, and sometimes bearing moulded decoration. Examples of painting on stone, opaque and transparent. Engraved objects in great number for example, ring-bezels and gems; and an immense quantity of clay impressions, taken from these.
Weapons, tools and implements: In stone, clay and bronze, and at the last iron, sometimes richly ornamented or inlaid. Numerous representations also of the same. No actual body armour, except such as was ceremonial and buried with the dead, like the gold breastplates in the circle-graves at Mycenae or the full length body armour from Dendra.
Articles of personal use: for example, brooches (fibulae), pins, razors, tweezers, etc., often found as dedications to a deity, for example, in the Dictaean Cavern of Crete. No textiles have survived other than impressions in clay.
Written documents: for example, clay tablets and discs (so far in Crete only), but nothing of more perishable nature, such as skin, papyrus, etc.; engraved gems and gem impressions; legends written with pigment on pottery (rare); characters incised on stone or pottery. These show a number of systems of script employing either ideograms or syllabograms (see Linear B).
Excavated tombs: Of either the pit, chamber or the tholos kind, in which the dead were laid, together with various objects of use and luxury, without cremation, and in either coffins or loculi or simple wrappings.
Public works: Such as paved and stepped roadways, bridges, systems of drainage, etc.
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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 civilizations: Especially the Hellenic; such as, for example, those embodied in the Homeric poems, the legends concerning Crete, Mycenae, etc.; statements as to the origin of gods, cults and so forth, transmitted to us by Hellenic antiquarians such as Strabo, Pausanias, Diodorus Siculus, etc.
Traces of customs, creeds, rituals, etc.: In the Aegean area at a later time, discordant with the civilization in which they were practiced and indicating survival from earlier systems. There are also possible linguistic and even physical survivals to be considered.
Mycenae and Tiryns are the two principal sites on which evidence of a prehistoric civilization was remarked long ago by the ancient Greeks.
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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 civilization. It was not until Schliemann exposed the contents of the graves which lay just inside the gate, that scholars recognized the advanced stage of art which prehistoric dwellers in the Mycenaean citadel had attained.
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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 Dynasty tomb of Rekhmara at Egyptian Thebes as bearing vases of peculiar forms, were of some Mediterranean race, neither their precise habitat nor the degree of their civilization could be determined while so few actual prehistoric remains were known in the Mediterranean lands. Nor did the Aegean objects which were lying obscurely in museums in 1870, or thereabouts, provide a sufficient test of the real basis underlying the Hellenic myths of the Argolid, the Troad and Crete, to cause these to be taken seriously. Aegean vases have been exhibited both at Sèvres and Neuchatel since about 1840, the provenance (i.e. source or origin) being in the one case Phylakope in Melos, in the other Cephalonia.
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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 demonstrated these to be no strayed Phoenician products. In 1866 primitive structures were discovered on the island of Therasia by quarrymen extracting pozzolana, a siliceous volcanic ash, for the Suez Canal works. When this discovery was followed up in 1870, on the neighbouring Santorini (Thera), by representatives of the French School at Athens, much pottery of a class now known immediately to precede the typical late Aegean ware, and many stone and metal objects, were found. These were dated by the geologist Ferdinand A. Fouqué, somewhat arbitrarily, to 2000 BC, by consideration of the superincumbent eruptive stratum.
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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 Asiatic fabric of uncertain date. Nor was a connection immediately detected between them and the objects found four years later in a tomb at Menidi in Attica and a rock-cut "bee-hive" grave near the Argive Heraeum.
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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 presently to spread far outside the narrow circle of scholars. As soon as Schliemann came on the Mycenae graves three years later, light poured from all sides on the prehistoric period of Greece. It was recognized that the character of both the fabric and the decoration of the Mycenaean objects was not that of any well-known art. A wide range in space was proved by the identification of the Inselsteine and the Ialysus vases with the new style, and a wide range in time by collation of the earlier Theraean and Hissarlik discoveries. A relationship between objects of art described by Homer and the Mycenaean treasure was generally allowed, and a correct opinion prevailed that, while certainly posterior, the civilization of the Iliad was reminiscent of the Mycenaean.
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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 at Hissarlik in 1892 after the first explorer's death. But by laying bare in 1884 the upper stratum of remains on the rock of Tiryns, Schliemann made a contribution to our knowledge of prehistoric domestic life which was amplified two years later by Christos Tsountas's discovery of the palace at Mycenae. Schliemann's work at Tiryns was not resumed till 1905, when it was proved, as had long been suspected, that an earlier palace underlies the one he had exposed.
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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-tombs, most already pillaged but retaining some of their furniture, were excavated at Arkina and Eleusis in Attica, at Dimini near Volos in Thessaly, at Kampos on the west of Mount Taygetus, and at Maskarata in Cephalonia. The richest grave of all was explored at Vaphio in Laconia in 1889, and yielded, besides many gems and miscellaneous goldsmiths' work, two golden goblets chased with scenes of bull-hunting, and certain broken vases painted in a large bold style which remained an enigma until the excavation of Knossos.
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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 Larissa. During the Acropolis excavations in Athens, which terminated in 1888, many potsherds of the Mycenaean style were found; but Olympia had yielded either none, or such as had not been recognized before being thrown away, and the temple site at Delphi produced nothing distinctively Aegean (in dating). The American explorations of the Argive Heraeum, concluded in 1895, also failed to prove that site to have been important in the prehistoric time, though, as was to be expected from its neighbourhood to Mycenae itself, there were traces of occupation in the later Aegean periods.
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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 representative that is known in the Aegean. Melos, long marked as a source of early objects but not systematically excavated until taken in hand by the British School at Athens in 1896, yielded at Phylakope remains of all the Aegean periods, except the Neolithic.
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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 outside Mycenae. E. Chantre in 1894 picked up lustreless ware, like that of Hissariik, in central Phtygia and at Pteria, and the English archaeological expeditions, sent subsequently into north-western Anatolia, have never failed to bring back ceramic specimens of Aegean appearance from the valleys of the Rhyndncus, Sangarius and Halys.
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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 of the Aegean style which can be set off against the many debts which the centres of Aegean culture owed to Egypt. Two Aegean vases were found at Sidon in 1885, and many fragments of Aegean and especially Cypriot pottery have been found during recent excavations of sites in Philistia by the Palestine Fund.
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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 has yielded objects recognized as Aegean from tombs near Cadiz and from Saragossa.
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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 archaeologists by the remarkable archaic Greek bronzes found in a cave on Mount Ida in 1885, as well as by epigraphic monuments such as the famous law of Gortyna (also called Gortyn). But the first undoubted Aegean remains reported from it were a few objects extracted from Cnossus by Minos Kalokhairinos of Candia in 1878. These were followed by certain discoveries made in the S. plain Messara by F. Halbherr. Unsuccessful attempts at Cnossus were made by both W. J. Stillman and H. Schliemann, and A. J. Evans, coming on the scene in 1893, travelled in succeeding years about the island picking up trifles of unconsidered evidence, which gradually convinced him that greater things would eventually be found. He obtained enough to enable him to forecast the discovery of written characters, till then not suspected in Aegean civilization. The revolution of 1897–1898 opened the door to wider knowledge, and much exploration has ensued, for which see Crete.
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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 the eastern Mediterranean area in Syria and Egypt. Regarding the Cyrenaica, we are still insufficiently informed. Fall
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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 Aegean writing. In Cyprus, and perhaps on the south-west Anatolian coasts, there is some reason to think that the cataclysm was not complete, and Aegean art continued to languish, cut off from its fountain-head. Such artistic faculty as survived elsewhere issued in the lifeless geometric style which is reminiscent of the later Aegean, but wholly unworthy of it. Cremation took the place of burial of the dead. This great disaster, which cleared the ground for a new growth of local art, was probably due to yet another incursion of northern tribes, in possession of superior iron weaponsthose tribes which later Greek tradition and Homer knew as the Dorians. They crushed a civilization already hard hit; and it took two or three centuries for the artistic spirit, instinct in the Aegean area, and probably preserved in suspended animation by the survival of Aegean racial elements, to blossom anew. On this conquest seems to have ensued a long period of unrest and popular movements, known to Greek tradition as the Ionian Migration and the Aeolic and Dorian "colonizations", and when once more we see the Aegean area clearly, it is dominated by Hellenes, though it has not lost all memory of its earlier culture.
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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 and Balkan Prehistory: Articles, site-reports and bibliography database concerning the Aegean, Balkans and Western Anatolia
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Atlas Autocode
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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. Features
AA featured explicitly typed variables, subroutines, and functions. It omitted some ALGOL features such as passing parameters by name, which in ALGOL 60 means passing the memory address of a short subroutine to recalculate a parameter each time it is mentioned.
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Atlas Autocode
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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 efficient or to effect some operation which otherwise cannot be done easily.
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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. The complex data type was dropped when Atlas Autocode later evolved into the language Edinburgh IMP. IMP was an extension of AA and was used to write the Edinburgh Multiple Access System (EMAS) operating system.
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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 continuously at Edinburgh from the 60's until almost the year 2000. Other Autocodes were developed for the Titan computer, a prototype Atlas 2 at Cambridge, and the Ferranti Mercury.
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Atlas Autocode
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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 characters could be overstruck as a single symbol. For example, the character set had no ↑ symbol, so exponentiation was an overstrike of | and *. The aforementioned underlining of reserved words (keywords) could also be done using overstriking. The language is described in detail in the Atlas Autocode Reference Manual.
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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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