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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. 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 :
NUMBERS Eventually, the concept of numbers became concrete and familiar enough for Counting to arise, at times with sing-song mnemonics to teach Sequence s 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. 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 medieval times, 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 Expression s, and the tabulation of Mathematical Function s such as the Square Root and the Common Logarithm (for use in multiplication and division) and the Trigonometric Function s. 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 innate 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. NAVIGATION AND ASTRONOMY Starting with known special cases, the calculation of logarithms and trigonometric functions can be performed by looking up numbers in a 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, the most powerful computer systems of the Earth are used for Weather Forecast s. SYMBOLIC COMPUTATIONS By the late 1960s , computer systems could perform symbolic algebraic manipulations well enough to pass college-level Calculus courses. Using programs like '' Maple '', '' Macsyma (now Maxima )'' and '' Mathematica '', including some open source programs like '' Yacas '', it is now possible to visualize concepts such as Modular Form s which were only accessible to the Mathematical imagination before this. BOOKS FOR FURTHER READING See List Of Books On The History Of Computing . JOURNALS
Writing computer history The professionalization of computer Historiography is a fairly recent phenomenon. "Until the 1990s, this literature consisted almost entirely of memoirs by computer professionals, often tightly focused on the invention and design of particular machines or on the business history of early computer companies. A few important scholarly books, such as Williams’ ''A History of Computing Technology'', attempted to cover the whole sweep of computer history. Even these, however, generally focused on the computer as a technological object, rather than on applications or (especially) on the evolving social role of computers and networks." Paul N. Edwards, " Making History: New Directions in Computer Historiography ", ''IEEE Annals of the History of Computing'', January-March, 2001 Edward urges his colleagues to think "outside the box" to understand the social dynamics of the development and use of computers. Recent studies have begun to tell the story of the role of computers in the history of administration, business, communication and warfare. NOTES SEE ALSO
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