Transit of Genius
Our brief introduction to Set Theory (aka Transit of Venus, etc.) leads nicely to a brief discussion of Boolean Algebra. Boolean Algebra, or the algebra of logic, was devised by the English mathematician George Boole (1815-64), and embodies the first successful application of algebraic methods to logic.
Boole recognized that the algebraic laws he proposed are essentially those of binary arithmetic, i.e., if the basic symbols are interpreted as taking just the number values 0 and 1. (Note: 0 and 1 can be thought of as “off” and “on” in electrical circuits). In each of these interpretations the basic symbols are conceived as being capable of combination under certain operations: multiplication, corresponding to conjunction of attributes or intersection of classes, addition, corresponding to (exclusive) disjunction or (disjoint) union, and subtraction, corresponding to “excepting” or diifference. Boole’s ideas as outlined here have since undergone extensive development, and the resulting mathematical concept of Boolean algebra now plays a central role in mathematical logic, probability theory and computer design. (see full article here).
I remember our university lecturer telling a compelling story of one electrical engineer who was meeting with a large client in the process of designing a new large office block. The electrical engineer had studies Boolean Algebra and was able to show improvements to the office wiring diagrams to save thousands of dollars for each floor level – simply by applying the above laws.
