![]() Panini used metarules, transformations and recursions. In the 5th century BC in ancient India, the grammarian Pāṇini formulated the grammar of Sanskrit in 3959 rules known as the Ashtadhyayi which was highly systematized and technical. The Chinese also invented a more sophisticated abacus from around the 2nd century BC known as the Chinese abacus. It was the first known geared mechanism to use a differential gear, which was later used in analog computers. 1050–771 BC, the south-pointing chariot was invented in ancient China. This was the first known calculator and most advanced system of calculation known to date - preceding Archimedes by 2,000 years. Abaci, of a more modern design, are still used as calculation tools today. ![]() Its original style of usage was by lines drawn in sand with pebbles. The earliest known tool for use in computation is the Sumerian abacus, and it was thought to have been invented in Babylon c. ![]() These kinds of statements have existed for thousands of years, and across multiple civilizations, as shown below: This allows the repeatable, verifiable statements which are the hallmark of mathematics and science. ![]() Mathematical statements need not be abstract only when a statement can be illustrated with actual numbers, the numbers can be communicated and a community can arise. 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 by 1976 Feynman had purchased an HP-25 calculator with a 49 program-step capacity if a differential equation required more than 49 steps to solve, he could just continue his computation by hand. 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. 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. See, for example, Euclid's algorithm for finding the greatest common divisor of two numbers.īy the High Middle Ages, the positional Hindu–Arabic numeral system had reached Europe, which allowed for systematic computation of numbers. Eventually the operations were formalized, and concepts about the operations became understood well enough to be stated formally, and even proven. Īdvances 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. All known human languages, except the Piraha language, have words for at least "one" and "two", and even some animals like the blackbird can distinguish a surprising number of items. Įventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with sing-song mnemonics to teach sequences to others. The 3-4-5 right triangle was a device for assuring a right angle, using ropes with 12 evenly spaced knots, for example.Comparison to a standard, a method for assuming reproducibility in a measurement, for example, the number of coins.on a tally stick, eventually abstracted into numbers. One-to-one correspondence, a rule to count how many items, e.g.These concepts are implicit in concrete practices such as: But long before abstractions like the number arose, there were mathematical concepts to serve the purposes of civilization. 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.ĭigital computing is intimately tied to the representation of numbers. Further information: Timeline of computing History of computing
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