Devices have been used to aid computation for thousands of years, mostly using one-to-one correspondence with fingers. The earliest counting device was probably a form of tally stick.
The Lebombo bone from the mountains between Eswatini and South Africa may be the oldest known mathematical artifact. It dates from 35,000 BCE and consists of 29 distinct notches that were deliberately cut into a baboon's fibula.
Later record keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers. The use of counting rods is one example.
The abacus was early used for arithmetic tasks. What we now call the Roman abacus was used in Babylonia as early as c. 2700-2300 BC. Since then, many other forms of reckoning boards or tables have been invented.
Several analog computers were constructed in ancient and medieval times to perform astronomical calculations. These included the astrolabe and Antikythera mechanism from the Hellenistic world (c. 150-100 BC).
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In Roman Egypt, Hero of Alexandria (c. Other early mechanical devices used to perform one or another type of calculations include the planisphere and other mechanical computing devices invented by Al-Biruni (c. AD 1000); the equatorium and universal latitude-independent astrolabe by Al-Zarqali (c. AD 1015); the astronomical analog computers of other medieval Muslim astronomers and engineers; and the astronomical clock tower of Su Song (1094) during the Song dynasty.
Scottish mathematician and physicist John Napier discovered that the multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the logarithms of those numbers.
While producing the first logarithmic tables, Napier needed to perform many tedious multiplications. Since real numbers can be represented as distances or intervals on a line, the slide rule was invented in the 1620s, shortly after Napier's work, to allow multiplication and division operations to be carried out significantly faster than was previously possible.
Slide Rule
Edmund Gunter built a calculating device with a single logarithmic scale at the University of Oxford. His device greatly simplified arithmetic calculations, including multiplication and division.
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William Oughtred greatly improved this in 1630 with his circular slide rule. He followed this up with the modern slide rule in 1632, essentially a combination of two Gunter rules, held together with the hands.
In 1609, Guidobaldo del Monte made a mechanical multiplier to calculate fractions of a degree. Based on a system of four gears, the rotation of an index on one quadrant corresponds to 60 rotations of another index on an opposite quadrant.
Thanks to this machine, errors in the calculation of first, second, third and quarter degrees can be avoided. Wilhelm Schickard, a German polymath, designed a calculating machine in 1623 which combined a mechanized form of Napier's rods with the world's first mechanical adding machine built into the base.
Gottfried Wilhelm von Leibniz invented the stepped reckoner and his famous stepped drum mechanism around 1672. He attempted to create a machine that could be used not only for addition and subtraction but would use a moveable carriage to enable multiplication and division.
Leibniz once said "It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used." However, Leibniz did not incorporate a fully successful carry mechanism.
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Leibniz also described the binary numeral system, a central ingredient of all modern computers.
Around 1820, Charles Xavier Thomas de Colmar created what would over the rest of the century become the first successful, mass-produced mechanical calculator, the Thomas Arithmometer. It could be used to add and subtract, and with a moveable carriage the operator could also multiply, and divide by a process of long multiplication and long division.
It utilised a stepped drum similar in conception to that invented by Leibniz.
In 1804, French weaver Joseph Marie Jacquard developed a loom in which the pattern being woven was controlled by a paper tape constructed from punched cards. The paper tape could be changed without changing the mechanical design of the loom.
This was a landmark achievement in programmability. His machine was an improvement over similar weaving looms. Punched cards were preceded by punch bands, as in the machine proposed by Basile Bouchon.
In the late 1880s, the American Herman Hollerith invented data storage on punched cards that could then be read by a machine. To process these punched cards, he invented the tabulator and the keypunch machine.
His machines used electromechanical relays and counters. Hollerith's method was used in the 1890 United States census.
By 1920, electromechanical tabulating machines could add, subtract, and print accumulated totals. Machine functions were directed by inserting dozens of wire jumpers into removable control panels.
Leslie Comrie's articles on punched-card methods and W. J. Eckert's publication of Punched Card Methods in Scientific Computation in 1940, described punched-card techniques sufficiently advanced to solve some differential equations or perform multiplication and division using floating-point representations, all on punched cards and unit record machines.
Such machines were used during World War II for cryptographic statistical processing, as well as a vast number of administrative uses.
By the 20th century, earlier mechanical calculators, cash registers, accounting machines, and so on were redesigned to use electric motors, with gear position as the representation for the state of a variable.
Companies like Friden, Marchant Calculator and Monroe made desktop mechanical calculators from the 1930s that could add, subtract, multiply and divide.
In 1948, the Curta was introduced by Austrian inventor Curt Herzstark.
The world's first all-electronic desktop calculator was the British Bell Punch ANITA, released in 1961. It used vacuum tubes, cold-cathode tubes and Dekatrons in its circuits, with 12 cold-cathode "Nixie" tubes for its display.
The ANITA sold well since it was the only electronic desktop calculator available, and was silent and quick.
The Industrial Revolution (late 18th to early 19th century) had a significant impact on the evolution of computing hardware, as the era's rapid advancements in machinery and manufacturing laid the groundwork for mechanized and automated computing.
Though Babbage's designs were never fully realized due to technical and financial challenges, they influenced a range of subsequent developments in computing hardware.
The Industrial Revolution's advancements in mechanical systems demonstrated the potential for machines to conduct complex calculations, influencing engineers like Leonardo Torres Quevedo and Vannevar Bush in the early 20th century.
In the first half of the 20th century, analog computers were considered by many to be the future of computing. These devices used the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved, in contrast to digital computers that represented varying quantities symbolically, as their numerical values change.
The first modern analog computer was a tide-predicting machine, invented by Sir William Thomson, later Lord Kelvin, in 1872. It used a system of pulleys and wires to automatically calculate predicted tide levels for a set period at a particular location and was of great utility to navigation in shallow waters.
The differential analyser, a mechanical analog computer designed to solve differential equations by integration using wheel-and-disc mechanisms, was conceptualized in 1876 by James Thomson, the brother of the more famous Lord Kelvin.
An important advance in analog computing was the development of the first fire-control systems for long range ship gunlaying. When gunnery ranges increased dramatically in the late 19th century it was no longer a simple matter of calculating the proper aim point, given the flight times of the shells.
Mk. I Drift Sight
Various spotters on board the ship would relay distance measures and observations to a central plotting station. There the fire direction teams fed in the location, speed and direction of the ship and its target, as well as various adjustments for Coriolis effect, weather effects on the air, and other adjustments; the computer would then output a firing solution, which would be fed to the turrets for laying.
Mechanical devices were also used to aid the accuracy of aerial bombing. Drift Sight was the first such aid, developed by Harry Wimperis in 1916 for the Royal Naval Air Service; it measured the wind speed from the air, and used that measurement to calculate the wind's effects on the trajectory of the bombs.
The art of mechanical analog computing reached its zenith with the differential analyzer, built by H. L. Hazen and Vannevar Bush at MIT starting in 1927, which built on the mechanical integrators of James Thomson and the torque amplifiers invented by H. W. Nieman.
The principle of the modern computer was first described by computer scientist Alan Turing, who set out the idea in his seminal 1936 paper, On Computable Numbers. Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as Turing machines.
He proved that some such machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. He also introduced the notion of a "universal machine" (now known as a universal Turing machine), with the idea that such a machine could perform the tasks of any other machine, or in other words, it is provably capable of computing anything that is computable by executing a program stored on tape, allowing the machine to be programmable.
John von Neumann acknowledged that the central concept of the modern computer was due to this paper. Turing machines are to this day a central object of study in theory of computation.
The era of modern computing began with a flurry of development before and during World War II. Most digital computers built in this period were electromechanical - electric switches drove mechanical relays to perform the calculation.
Parts from four early computers, 1962.
The Z2 was one of the earliest examples of an electric operated digital computer built with electromechanical relays and was created by civil engineer Konrad Zuse in 1940 in Germany.
In the same year, electro-mechanical devices called bombes were built by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II.
The bombe's initial design was created in 1939 at the UK Government Code and Cypher School at Bletchley Park by Alan Turing, with an important refinement devised in 1940 by Gordon Welchman. The engineering design and construction was the work of Harold Keen of the British Tabulating Machine Company.
In 1941, Zuse followed his earlier machine up with the Z3, the world's first working electromechanical programmable, fully automatic digital computer. The Z3 was built with 2000 relays, implementing a 22-bit word length that operated at a clock frequency of about 5-10 Hz.
Program code and data were stored on punched film. It was quite similar to modern machines in some respects, pioneering numerous advances such as floating-point numbers.
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