anthr_of_comp4

anthr_of_comp4 - 21A.350 / SP.484J / STS.086 The...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
21A.350 / SP.484J / STS.086 The Anthropology of Computing Fall 2004 MIT WORLD WAR TWO: CYBERNETICS, COMMUNICATION, AND CONTROL Lecture 4. October 4 Another 19 th century person we need to know about: George Boole (1815-1864) Beginning as an elementary school instructor, Boole opened his own school at age 20. Unsatisfied with mathematics texts of the time, he set about reading Laplace, Leibniz, and others. He emerged with new ideas on the calculus of variations and, even as an outsider, succeeded in having them published in The Cambridge Mathematical Journal . 1854 An Investigation into the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities . Boole approached logic in a new way reducing it to algebra, incorporating logic into mathematics. He pointed out an analogy between algebraic symbols and those representing logical forms. LOGIC WAS A FORM OF MATH, NOT OF PHILOSOPHY. “We ought no longer to associate Logic and Metaphysics, but Logic and Mathematics” Remember Ada Lovelace’s notion that the Analytical Engine made use of operations and objects of operations and that it could be a completely general machine if both were written in the same language? Boole’s idea was that mathematizing logic would translate operations (logic) and objects of operations (mathematical objects for example) into the same language. You could represent logical statements (like syllogisms and other things with sets of AND, OR, and NOTs) as mathematical statements that were TRUE or FALSE, and then represent this outcome as on or off, 1 or 0. Boolean algebra was algebra on logic statements, not numbers (even though statements could be written in numbered code, like a binary code). As you saw in the Norbert Wiener, Claude Shannon, while a grad student ay MIT, recognized the analogy between electronic circuits and Boolean algebra that became essential to the design of digital computers. Shannon showed that Boole’s TRUE & FALSE could represent functions of switches in electronic circuits. Boolean logic can be used to describe electromagnetically charged memory locations or circuit states that are either charged (1 or true) or not charged (0 or false). Computer can use an AND gate or OR gate operation to obtain a result that can be used for further processing. Two things that Boole did became important for later CS: 1. his logical system — or rather, the reduction of logic to math
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. and the use of a binary representation
Background image of page 2
Bush , Vannevar. 1945. As We May Think. ‘‘Born in Massachusetts, educated at Tufts, graduating in 1913. Joined ± the Department of Electrical Engineering at MIT in 1919, and was a ± professor from 1923-± -32. He constructed a Differential Analyser, an ± analog computer that could solve differential equations with as many as ± 18 independent variables, based on Charles Babbage's Difference Engine. ± An offshoot of the Differential Analyser was the birth of digital ±
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 10

anthr_of_comp4 - 21A.350 / SP.484J / STS.086 The...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online