By the second decade of the 19th century, a number of ideas necessary for the invention of the computer were in the air. First, the potential benefits to science and industry of being able to automate routine calculations were appreciated, as they had not been a century earlier. Specific methods to make automated calculation more practical, such as doing multiplication by adding logarithms or by repeating addition, had been invented, and experience with both analog and digital devices had shown some of the benefits of each approach. The Jacquard loom (as described in the previous section, Computer precursors) had shown the benefits of directing a multipurpose device through coded instructions, and it had demonstrated how punched cards could be used to modify those instructions quickly and flexibly. It was a mathematical genius in England who began to put all these pieces together.
The Difference Engine
Charles Babbage was an English mathematician and inventor: he invented the cowcatcher, reformed the British postal system, and was a pioneer in the fields of operations research and actuarial science. It was Babbage who first suggested that the weather of years past could be read from tree rings. He also had a lifelong fascination with keys, ciphers, and mechanical dolls.
As a founding member of the Royal Astronomical Society, Babbage had seen a clear need to design and build a mechanical device that could automate long, tedious astronomical calculations. He began by writing a letter in 1822 to Sir Humphry Davy, president of the Royal Society, about the possibility of automating the construction of mathematical tables—specifically, logarithm tables for use in navigation. He then wrote a paper, “On the Theoretical Principles of the Machinery for Calculating Tables,” which he read to the society later that year. (It won the Royal Society’s first Gold Medal in 1823.) Tables then in use often contained errors, which could be a life-and-death matter for sailors at sea, and Babbage argued that, by automating the production of the tables, he could assure their accuracy. Having gained support in the society for his Difference Engine, as he called it, Babbage next turned to the British government to fund development, obtaining one of the world’s first government grants for research and technological development.
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History Of Computing
A computer might be described with deceptive simplicity as “an apparatus that performs routine calculations automatically.” Such a definition would owe its deceptiveness to a naive and narrow view of calculation as a strictly mathematical process. In fact, calculation underlies many activities that are not normally thought of as mathematical. Walking across a room, for instance, requires many complex, albeit subconscious, calculations. Computers, too, have proved capable of solving a vast array of problems, from balancing a checkbook to even—in the form of guidance systems for robots—walking across a room.
Before the true power of computing could be realized, therefore, the naive view of calculation had to be overcome. The inventors who laboured to bring the computer into the world had to learn that the thing they were inventing was not just a number cruncher, not merely a calculator. For example, they had to learn that it was not necessary to invent a new computer for every new calculation and that a computer could be designed to solve numerous problems, even problems not yet imagined when the computer was built. They also had to learn how to tell such a general problem-solving computer what problem to solve. In other words, they had to invent programming.
They had to solve all the heady problems of developing such a device, of implementing the design, of actually building the thing. The history of the solving of these problems is the history of the computer. That history is covered in this section, and links are provided to entries on many of the individuals and companies mentioned. In addition, see the articles computer science and supercomputer.
Early history
Computer precursors
The abacus
The earliest known calculating device is probably the abacus. It dates back at least to 1100 BCE and is still in use today, particularly in Asia. Now, as then, it typically consists of a rectangular frame with thin parallel rods strung with beads. Long before any systematic positional notation was adopted for the writing of numbers, the abacus assigned different units, or weights, to each rod. This scheme allowed a wide range of numbers to be represented by just a few beads and, together with the invention of zero in India, may have inspired the invention of the Hindu-Arabic number system. In any case, abacus beads can be readily manipulated to perform the common arithmetical operations—addition, subtraction, multiplication, and division—that are useful for commercial transactions and in bookkeeping.
The abacus is a digital device; that is, it represents values discretely. A bead is either in one predefined position or another, representing unambiguously, say, one or zero.
Analog calculators: from Napier’s logarithms to the slide rule
Calculating devices took a different turn when John Napier, a Scottish mathematician, published his discovery of logarithms in 1614. As any person can attest, adding two 10-digit numbers is much simpler than multiplying them together, and the transformation of a multiplication problem into an addition problem is exactly what logarithms enable. This simplification is possible because of the following logarithmic property: the logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers. By 1624, tables with 14 significant digits were available for the logarithms of numbers from 1 to 20,000, and scientists quickly adopted the new labour-saving tool for tedious astronomical calculations.
Most significant for the development of computing, the transformation of multiplication into addition greatly simplified the possibility of mechanization. Analog calculating devices based on Napier’s logarithms—representing digital values with analogous physical lengths—soon appeared. In 1620 Edmund Gunter, the English mathematician who coined the terms cosine and cotangent, built a device for performing navigational calculations: the Gunter scale, or, as navigators simply called it, the gunter. About 1632 an English clergyman and mathematician named William Oughtred built the first slide rule, drawing on Napier’s ideas. That first slide rule was circular, but Oughtred also built the first rectangular one in 1633. The analog devices of Gunter and Oughtred had various advantages and disadvantages compared with digital devices such as the abacus. What is important is that the consequences of these design decisions were being tested in the real world.
Digital calculators: from the Calculating Clock to the Arithmometer
In 1623 the German astronomer and mathematician Wilhelm Schickard built the first calculator. He described it in a letter to his friend the astronomer Johannes Kepler, and in 1624 he wrote again to explain that a machine he had commissioned to be built for Kepler was, apparently along with the prototype, destroyed in a fire. He called it a Calculating Clock, which modern engineers have been able to reproduce from details in his letters. Even general knowledge of the clock had been temporarily lost when Schickard and his entire family perished during the Thirty Years’ War.
Calculating Clock
A reproduction of Wilhelm Schickard's Calculating Clock. The device could add and subtract six-digit numbers (with a bell for seven-digit overflows) through six interlocking gears, each of which turned one-tenth of a rotation for each full rotation of the gear to its right. Thus, 10 rotations of any gear would produce a “carry” of one digit on the following gear and change the corresponding display.
The Computer Museum of America
But Schickard may not have been the true inventor of the calculator. A century earlier, Leonardo da Vinci sketched plans for a calculator that were sufficiently complete and correct for modern engineers to build a calculator on their basis.
The first calculator or adding machine to be produced in any quantity and actually used was the Pascaline, or Arithmetic Machine, designed and built by the French mathematician-philosopher Blaise Pascal between 1642 and 1644. It could only do addition and subtraction, with numbers being entered by manipulating its dials. Pascal invented the machine for his father, a tax collector, so it was the first business machine too (if one does not count the abacus). He built 50 of them over the next 10 years.

Arithmetic Machine, or Pascaline
The Arithmetic Machine, or Pascaline, a French monetary (nondecimal) calculator designed by Blaise Pascal c. 1642. Numbers could be added by turning the wheels (located along the bottom of the machine) clockwise and subtracted by turning the wheels counterclockwise. Each digit in the answer was displayed in a separate window, visible at the top of the photograph.
Courtesy of the Computer Museum History Center
In 1671 the German mathematician-philosopher Gottfried Wilhelm von Leibniz designed a calculating machine called the Step Reckoner. (It was first built in 1673.) The Step Reckoner expanded on Pascal’s ideas and did multiplication by repeated addition and shifting.
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