History of computing

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The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. The timeline of computing presents a summary list of major developments in computing by date.

1 Concrete devices
2 Numbers
3 Early computation
4 Navigation and astronomy
5 Weather prediction
6 Symbolic computations
7 References
8 See also
9 External links
- 9.1 Computer History Museums

Concrete devices

Computing is intimately tied to the representation of numbers. But long before abstractions like number arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as :

one-to-one correspondence, a rule to count how many items, say on a tally stick, which was eventually abstracted into number;
comparison to a standard, a method for assuming reproducibility in a measurement, for example, the number of coins;
the 3-4-5 right triangle was a device for assuring a right angle, using ropes with 12 evenly spaced knots, for example.

Numbers

Eventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with sing-song mnemonics to teach sequences to others. All the known languages have words for at least "one" and "two", and even some animals like the blackbird can distinguish a surprising number of items.^{[citation needed]}

Advances in the numeral system and mathematical notation eventually led to the discovery of mathematical operations such as addition, subtraction, multiplication, division, squaring, square root, and so forth. Eventually the operations were formalized, and concepts about the operations became understood well enough to be stated formally, and even proven. See, for example, Euclid's algorithm for finding the greatest common divisor of two numbers.

By the High Middle Ages, the positional Hindu-Arabic numeral system had reached Europe, which allowed for systematic computation of numbers. During this period, the representation of a calculation on paper actually allowed calculation of mathematical expressions, and the tabulation of mathematical functions such as the square root and the common logarithm (for use in multiplication and division) and the trigonometric functions. By the time of Isaac Newton's research, paper or vellum was an important computing resource, and even in our present time, researchers like Enrico Fermi would cover random scraps of paper with calculation, to satisfy their curiosity about an equation. Even into the period of programmable calculators, Richard Feynman would unhesitatingly compute any steps which overflowed the memory of the calculators, by hand, just to learn the answer.

Early computation

Main article: Timeline of computing 2400 BC–1949

The earliest known tool for use in computation was the abacus, and it was thought to have been invented in Babylon circa 2400 BC. Its original style of usage was by lines drawn in sand with pebbles. Abaci, of a more modern design, are still used as calculation tools today. This was the first known computer and most advanced system of calculation known to date - preceding Greek methods by 2,000 years.

In 1115 BCE, the South Pointing Chariot was invented in ancient China. It was the first known geared mechanism to use a differential gear, which was later used in analog computers. The Chinese also invented a more sophisticated abacus from around the 2nd century BCE known as the Chinese abacus).

In the 5th century BCE in ancient India, the grammarian Pāṇini formulated the grammar of Sanskrit in 3959 rules known as the Ashtadhyayi which was highly systematized and technical. Panini used metarules, transformations and recursions with such sophistication that his grammar had the computing power equivalent to a Turing machine. Between 200 BCE and 400 CE, Jaina mathematicians in India invented the logarithm. From the 13th century, logarithmic tables were produced by Muslim mathematicians.

The Antikythera mechanism is believed to be the earliest known mechanical analog computer.^[1] 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 circa 100 BC.

Mechanical analog computer devices appeared again a thousand years later in the medieval Islamic world and were developed by Muslim astronomers, such as the equatorium by Arzachel,^[2] the mechanical geared astrolabe by Abū Rayhān al-Bīrūnī,^[3] and the torquetum by Jabir ibn Aflah.^[4] The first programmable machines were also invented by Muslim engineers, such as the automatic flute player by the Banū Mūsā brothers^[5] and the humanoid robots by Al-Jazari.^[6] Muslim mathematicians also made important advances in cryptography, such as the development of cryptanalysis and frequency analysis by Alkindus.^[7]^[8]

When John Napier discovered logarithms for computational purposes in the early 17th century, there followed a period of considerable progress by inventors and scientists in making calculating tools.

None of the early computational devices were really computers in the modern sense, and it took considerable advancement in mathematics and theory before the first modern computers could be designed.

Navigation and astronomy

Starting with known special cases, the calculation of logarithms and trigonometric functions can be performed by looking up numbers in a mathematical table, and interpolating between known cases. For small enough differences, this linear operation was accurate enough for use in navigation and astronomy in the Age of Exploration. The uses of interpolation have thrived in the past 500 years: by the twentieth century Leslie Comrie and W.J. Eckert systematized the use of interpolation in tables of numbers for punch card calculation.

In our time, even a student can simulate the motion of the planets, an N-body differential equation, using the concepts of numerical approximation, a feat which even Isaac Newton could admire, given his struggles with the motion of the Moon.

Weather prediction

The numerical solution of differential equations, notably the Navier-Stokes equations was an important stimulus to computing, with Lewis Fry Richardson's numerical approach to solving differential equations. To this day, some of the most powerful computer systems of the Earth are used for weather forecasts.

Symbolic computations

By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass college-level calculus courses. Using programs like Mathematica and others it is now possible to visualize concepts such as modular forms which were only accessible to the mathematical imagination before this.