philosophical text, the Chinese I Chinq, or Book of Changes, which casts the universe in

terms of contrasting dualities of dark and light, male and female, and so forth. Leibniz

never developed a calculator based on the binary system, though he did give some

thought to it. Undoubtedly, the long strings of digits discouraged him. For example, the

decimal 8 becomes 1000 in the binary code because only one and zero are used. The

binary equivalent of 1,000 is a cumbersome 1111101000. The binary system came to

have mystical significance for Leibniz: the one representing God, and the zero

representing the void. Just as one and zero could express all mathematical ideas, so

too, it could represent everything in the universe.

b. **Boolean Logic (1854). **George Boole, a self-made mathematician,

continued with the search for a universal language. In 1854, he devised a system for

stripping logical argument of all words by expressing it in mathematical terms. Using

Boolean algebra any statement could be expressed symbolically and could be

manipulated like ordinary numbers. Using three basic operations (logic gates), AND,

OR, and NOT, he could add, subtract, multiply, divide, and compare symbols or

numbers. The logic gates are binary since they involve either truth or falsity, yes or no,

closed or open, one or zero. He believed that by stripping logic of words, it would be

easier to arrive at sound conclusions.

c. **Charles Pierce Brings Boolean Logic to the United States. **In 1867,

Charles Sanders Pierce, an American logician, introduced Boolean logic in a paper

delivered to the American Academy of Arts and Sciences. He realized that Boole's two-

state logic lent itself to the description of electrical circuits, because currents were either

"one or "off," just as propositions were either true or false. He designed, but never built,

a logic circuit using electricity. His real contribution was in introducing Boolean logic

into American university courses in logic and philosophy, so that it eventually worked its

way into the innovations of key thinkers.

d. **Claude Shannon (1936). **Claude Shannon was just such a key thinker. A

brilliant mathematician, he had the insight to translate Boolean algebra into practical

terms. Working at the Massachusetts Institute of Technology, with a cumbersome

mechanical calculating device, called the differential analyzer, he recognized that the

machine's bulk was dictated by the need to compute with all 10 digits of the decimal

numbering system. Recalling Boolean algebra, he saw its similarity to an electric circuit,

and recognized in that similarity the potential for streamlining computer design. Electric

circuits could be laid out according to Boolean principles, and they could express logic,

test the truth of propositions and carry out complex calculations. Using electric circuits

instead of shafts and gears would streamline design. Shannon's master's thesis (1938),

which outlined his thoughts about Boolean algebra and binary numbers, had an

immediate impact on the design of telephone systems. A subsequent paper, "A

Mathematical Theory of Communication" described what later came to be known as

information theory. This was a method of defining and measuring information in

mathematical terms, as yes-no choices represented by binary digits, that became the

basis of modern telecommunications.

MD0058

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