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.
Contents 
Computing is intimately tied to the representation of numbers. But long before abstractions like the number arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as :
Eventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with singsong mnemonics to teach sequences to others. All the known languages have words for at least "one" and "two" (although this is disputed: see Piraha language), and even some animals like the blackbird can distinguish a surprising number of items.^{[1]}
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 HinduArabic 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.
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 BC, 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 BC known as the Chinese abacus).
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. Panini used metarules, transformations and recursions with such sophistication that his grammar had the computing power equivalent to a Turing machine. Between 200 BC and 400 AD, 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.^{[2]} 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,^{[3]} the mechanical geared astrolabe by Abū Rayhān alBīrūnī,^{[4]} and the torquetum by Jabir ibn Aflah.^{[5]} Muslim mathematicians also made important advances in cryptography, such as the development of cryptanalysis and frequency analysis by Alkindus.^{[6]}^{[7]} Programmable machines were also invented by Muslim engineers, such as the automatic flute player by the Banū Mūsā brothers,^{[8]} and AlJazari's humanoid robots^{[9]} and castle clock, which is considered to be the first programmable analog computer.^{[10]}
During the Middle Ages, several european philosophers made attempts to produce analog computer devices. Influenced by the arabs and Scholasticism, majorcan philosopher Ramon Llull (12321315) devoted a great part of his life to define and design several logical machines that, by combining simple and undeniable philosophical truths, could produce all the possible knowledge. This machines were never really built, for they were more of a thought experiment devoted to the production of new knowledge by systematic ways; however they could make simple logical operations, they still needed a human being for interpretation of results. Moreover, they lacked of a versatile architecture, each machine serving only to very concrete purposes. No matter what, Llull's work had a severe impact on Gottfried Leibniz (early 18th century), who redeveloped his ideas further and could build several calculating tools with them.
Indeed, 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. A planimeter is a device which does integrals, using distance as the analog quantity. Until the 1980s, HVAC systems used air both as the analog quantity and the controlling element. Unlike modern digital computers, analog computers are not very flexible, and need to be reconfigured (i.e., reprogrammed) manually to switch them from working on one problem to another. Analog computers had an advantage over early digital computers in that they could be used to solve complex problems using behavioral analogues while the earliest attempts at digital computers were quite limited.
Since computers were rare in this era, the solutions were often hardcoded into paper forms such as nomograms,^{[11]} which could then produce analog solutions to these problems, such as the distribution of pressures and temperatures in a heating system.
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.
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 Nbody 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.
The numerical solution of differential equations, notably the NavierStokes 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.
By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass collegelevel 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.
This article may need to be wikified to meet Wikipedia's quality standards. Please help by adding relevant internal links, or by improving the article's layout. (August 2010) 
History of computing 
Hardware before 1960 
Hardware 1960s to present 
Hardware in Soviet Bloc countries 
Artificial intelligence 
Computer science 
Operating systems 
Programming languages 
Software engineering 
Graphical user interface 
Internet 
Personal computers 
Laptops 
Video games 
World Wide Web 
Timeline of computing

More... 
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.
Contents 
Computing is intimately tied to the representation of numbers. But long before abstractions like the number arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as :
Eventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with singsong mnemonics to teach sequences to others. All the known languages have words for at least "one" and "two" (although this is disputed: see Piraha language), and even some animals like the blackbird can distinguish a surprising number of items.^{[1]}
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 HinduArabic 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.^{[citation needed]} 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.^{[citation needed]}
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 BC, 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 BC known as the Chinese abacus).
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. Panini used metarules, transformations and recursions.
The Antikythera mechanism is believed to be the earliest known mechanical analog computer.^{[2]} 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,^{[3]} the mechanical geared astrolabe by Abū Rayhān alBīrūnī,^{[4]} and the torquetum by Jabir ibn Aflah.^{[5]} Muslim mathematicians also made important advances in cryptography, such as the development of cryptanalysis and frequency analysis by Alkindus.^{[6]}^{[7]} Programmable machines were also invented by Muslim engineers, such as the automatic flute player by the Banū Mūsā brothers,^{[8]} and AlJazari's humanoid robots^{[9]} and castle clock, which is considered to be the first programmable analog computer.^{[10]}
During the Middle Ages, several European philosophers made attempts to produce analog computer devices. Influenced by the Arabs and Scholasticism, majorcan philosopher Ramon Llull (1232–1315) devoted a great part of his life to define and design several logical machines that, by combining simple and undeniable philosophical truths, could produce all the possible knowledge. This machines were never really built, for they were more of a thought experiment devoted to the production of new knowledge by systematic ways; however they could make simple logical operations, they still needed a human being for interpretation of results. Moreover, they lacked of a versatile architecture, each machine serving only to very concrete purposes. No matter what, Llull's work had a severe impact on Gottfried Leibniz (early 18th century), who redeveloped his ideas further and could build several calculating tools with them.
Indeed, 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. The apex of this early era of formal computing can be seen in the difference engine and its successor the Analytical Engine, which was never completely constructed but was designed in detail, both by Charles Babbage. The analytical engine combined concepts from his work and that of others to create a device that if constructed as designed would have possessed many properties of a modern electronic computer. These properties include such features as an internal "scratch memory" equivalent to RAM, multiple forms of output including a bell, a graphplotter, and simple printer, and a programmable inputoutput "hard" memory of punch cards which it could modify as well as read. The key advancement which Babbage's devices possessed beyond those created before his was that each component of the device was independent of the rest of the machine, much like the components of a modern electronic computer. This was a fundamental shift in thought; previous computational devices served only a single purpose, but had to be at best dissasembled and reconfigured to solve a new problem. Babbage's devices could be reprogramed to solve new problems by the entry of new data, and act upon previous calculations within the same series of instructions. Ada Lovelace took this concept one step further, by creating a program for the analytical engine to calculate Bernoulli numbers, a complex calculation requiring a recursive algorithm. This is considered to the first example of a true computer program, a series of instructions that act upon data not known in full until the program is run.
Several examples of analog compututation survived into recient times. A planimeter is a device which does integrals, using distance as the analog quantity. Until the 1980s, HVAC systems used air both as the analog quantity and the controlling element. Unlike modern digital computers, analog computers are not very flexible, and need to be reconfigured (i.e., reprogrammed) manually to switch them from working on one problem to another. Analog computers had an advantage over early digital computers in that they could be used to solve complex problems using behavioral analogues while the earliest attempts at digital computers were quite limited.
is a wellknown nomogram.]]
Since computers were rare in this era, the solutions were often hardcoded into paper forms such as nomograms,^{[11]} which could then produce analog solutions to these problems, such as the distribution of pressures and temperatures in a heating system.
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.
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 Nbody 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.
The numerical solution of differential equations, notably the NavierStokes 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.
By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass collegelevel calculus courses.
ObjectiveTo familiarize the student with the historical development of the modern computer and its predecessors. In this manner, the student can advance certain knowledge and ideas regarding the computer as a unit in itself. This could help students have a more critical understanding in the development of a computer in terms of sizes, the prices associated when selling individual units, and more importantly how a computer has drasticallychanged society. 
Assignment 
Required Work1. Read the following Wikipedia articles, and write summaries of each that are the specified number of pages.
You may find the Timeline of computing helpful for this part of the assignment. 2. Read about one of the early pioneers in the field: Pascal, Leibniz, Jacquard, Babbage, Lovelace, Hollerith, Eckert, Mauchly, Aiken, Zuse, Atanasoff, Turing, or Von Neumann. Write a 2 pp., single spaced paper describing in detail that person's contribution to computing and computer science. You should consult more than one reputable source outside Wikipedia. Be sure to cite all references! 
Quiz
The statement that "any computer with a certain minimum capability
is, in principle, capable of performing the same tasks that any
other computer can perform" is known as

NotesYou may also find the following pages helpful:

