Lesson 1.3

• 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.
• 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.
• With the invention of zero in India, may have inspired the invention of the Hindu-Arabic number system.
• 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.
• 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.
• 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.
• 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.
• The Jacquard loom, invented in 1804–05 by a French weaver, Joseph Marie Jacquard.
• 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.
• The Analytical Engine - While working on the Difference Engine, Babbage began to imagine ways to improve it. Chiefly he thought about generalizing its operation so that it could perform other kinds of calculations. By the time the funding had run out in 1833, he had conceived of something far more revolutionary: a general purpose computing machine called the Analytical Engine.
• Herman Hollerith - It was while employed at the Census Office that Hollerith first saw the pressing need for automating the tabulation of statistical data. He invented census tabulator.
• Howard Aiken’s digital calculators - While Bush was working on analog computing at MIT, across town Harvard professor Howard Aiken was working with digital devices for calculation. He had begun to realize in hardware something like Babbage’s Analytical Engine, which he had read about.
• Starting in 1937, Howard Aiken laid out detailed plans for a series of four calculating machines of increasing sophistication, based on different technologies, from the largely mechanical Mark I to the electronic Mark IV.
• The Turing Machine - Alan Turing, while a mathematics student at the University of Cambridge, was inspired by German mathematician David Hilbert’s formalist program, which sought to demonstrate that any mathematical problem can potentially be solved by an algorithm—that is, by a purely mechanical process.
• Electronic Numerical Integrator and Computer (ENIAC) - All-electronic computer. World’s first general-purpose, nonmechanical computer. 
• One implication of the stored-program model was that programs could read and operate on other programs as data; that is, they would be capable of self-modification. Konrad Zuse had looked upon this possibility as “making a contract with the Devil” because of the potential for abuse, and he had chosen not to implement it in his machines. But self-modification was essential for achieving a true general-purpose machine.
• It was an interpreter, meaning that it translated HLL statements and executed, or performed, them one at a time—a slow process. Because of their slow execution, interpreters are now rarely used outside of program development, where they may help a programmer to locate errors quickly.
• HLL coding was attempted right from the start of the stored-program era in the late 1940s. Shortcode, or short-order code, was the first such language actually implemented.
• Shortcode was uggested by John Mauchly in 1949, it was implemented by William Schmitt for the BINAC computer in that year and for UNIVAC in 1950.
• Compiler - the entire HLL program is converted to machine language and stored for later execution. Although translation may take many hours or even days, once the translated program is stored, it can be recalled anytime in the form of a fast-executing machine-language program.
• What is FORTRAN? A programming language that was developed in the 1950s and is still widely used today. Allow comments in the program. Programs written in FORTRAN looked a lot more like mathematics than machine instructions.
• COBOL About the time that Backus and his team invented FORTRAN, Hopper’s group at UNIVAC released Math-matic, a FORTRAN-like language for UNIVAC computers. It was slower than FORTRAN and not particularly successful. Another language developed at Hopper’s laboratory at the same time had more influence. Flow-matic used a more English-like syntax and vocabulary.
• ALGOL During the late 1950s a multitude of programming languages appeared. This proliferation of incompatible specialized languages spurred an interest in the United States and Europe to create a single “second-generation” language. A transatlantic committee soon formed to determine specifications for ALGOL (Algorithmic Language),
• Control programs - In order to make the early computers truly useful and efficient, two major innovations in software were needed. One was high-level programming languages (as described in the preceding section, FORTRAN, COBOL, and ALGOL). The other was control. Today the systemwide control functions of a computer are generally subsumed under the term operating system, or OS. An OS handles the behind-the-scenes activities of a computer, such as orchestrating the transitions from one program to another and managing access to disk storage and peripheral devices.
• The IBM 360 - IBM had been selling business machines since early in the century and had built Howard Aiken’s computer to his architectural specifications. But the company had been slow to implement the stored-program digital computer architecture of the early 1950s. It did develop the IBM 650, a (like UNIVAC) decimal implementation of the IAS plan—and the first computer to sell more than 1,000 units.
• Minicomputers - About 1965, roughly coterminous with the development of time-sharing, a new kind of computer came on the scene. Small and relatively inexpensive (typically one-tenth the cost of the Big Iron machines), the new machines were stored-program computers with all the generality of the computers then in use but stripped down.
• The new machines were called minicomputers. (About the same time, the larger traditional computers began to be called mainframes.) Minicomputers were designed for easy connection to scientific instruments and other input/output devices, had a simplified architecture, were implemented using fast transistors, and were typically programmed in assembly language with little support for high-level languages.
• The microprocessor

  Commodore and Tandy enter the field

  In late 1976, Commodore Business Machines, an established electronics firm that had been active in producing electronic calculators, bought a small hobby-computer company named MOS Technology. For the first time, an established company with extensive distribution channels would be selling a microcomputer.
• Apple Incorporated was founded by Stephen G. Wozniak and Steven P. Jobs.
• In 1982 Apple introduced its Lisa computer, a much more powerful computer with many innovations. The Lisa used a more advanced microprocessor, the Motorola 68000. It also had a different way of interacting with the user, called a graphical user interface (GUI). The GUI replaced the typed command lines common on previous computers with graphical icons on the screen that invoked actions when pointed to by a handheld pointing device called the mouse.
• The Lisa was not successful, but Apple was already preparing a scaled-down, lower-cost version called the Macintosh. Introduced in 1984, the Macintosh became wildly successful and, by making desktop computers easier to use, further popularized personal computers.
• In 1985 Microsoft came out with its Windows operating system, which gave PC compatibles some of the same capabilities as the Macintosh. Year after year, Microsoft refined and improved Windows so that Apple, which failed to come up with a significant new advantage, lost its edge. IBM tried to establish yet another operating system, OS/2, but lost the battle to Gates’s company. In fact, Microsoft also had established itself as the leading provider of application software for the Macintosh.
• Founder of Microsoft is Bill Gates
• calculation underlies many activities that are not normally thought of as mathematical. Walking across a room, for instance, requires many complex, albeit subconscious, calculations.
• Leibniz was a strong advocate of the binary number system.
• Binary numbers are ideal for machines because they require only two digits, which can easily be represented by the on and off states of a switch.
• When computers became electronic, the binary system was particularly appropriate because an electrical circuit is either on or off. This meant that on could represent true, off could represent false, and the flow of current would directly represent the flow of logic.
• Calculators such as the Arithmometer remained a fascination after 1820, and their potential for commercial use was well understood.