April 2016
Intermediate to advanced
451 pages
13h 37m
English
Chapter 1
Over many centuries, tools of increasing sophistication have been developed to serve the human race. Physical tools such as chisels, hammers, spears, arrows, guns, carts, cars, and aircraft all have their place in the history of civilization. Humanity has also developed tools of communication—spoken language, written language, and the language of mathematics. These tools have not only enabled the exchange and storage of information but have also allowed the expression of concepts that simply could not exist outside of language.
The last century saw the arrival of a new tool—the digital computer. Computers are able to perform the same sort of numerical and symbolic manipulations that an ordinary ...
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