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

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

2. and the use of a binary representation

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 ±
circuit design theory by one of Bush's graduate students, Claude ±
Shannon.±