History is filled with extraordinary people. Usually, it is some type of contribution that they make towards society, positive or negative, that makes them memorable. Many times, it is within a specific field or practice that these people make their mark. In the case of George Boole, he is known best within the mathematics community for his success in defining logic by using algebra, or Boolean algebra as it is known today. Boole was born on November 2, 1815, in Lincoln, England, known predominantly as an industrial town. Gasser (2006) states “He was the first of four children born to John Boole, a cobbler, and Mart Ann Boole, nee Joyce, a lady’s maid” (p. 377-78). According to Britannica Online (2015), “He was given his first lessons in mathematics by his father, a tradesman, who also taught him to make optical instrument. Aside from his father’s help and a few years at local schools, however, Boole was self-taught in mathematics.” During the timeframe of Boole’s life, there were many political and social events that took place all around the world. Within England, Victoria took the throne in 1837 and would ultimately rule longer than any other British monarch. In 1838, slavery was abolished in the British empire. Additionally, in Ireland in 1845 the great potato famine began that lasted approximately four years killed about a million people, creating a large emigration to England and North America. In North America, in 1846 the Mexican-American War was fought, as well as the Civil War, although Boole died on December 8, 1864, in Ballintemple, Ireland, before the Civil War ended. Boole is most well-known for his discovery of algebra of logic, known today as Boolean algebra. He stated, “Boole was interested in symbolic analysis years before he wrote his Laws of Thought” (Nahin, 2012). The concept behind symbolic analysis was attempting to condense logic to algebraic form. It can be described and understood using the language of set. Nahin’s (2012) analysis uses intuitive visualizations of sets:
From a “universal” or fundamental set U, say the inhabitants of London, we can symbolize sub-sets by means of selective operators. Thus x(U) may denote the set of blue-eyed inhabitants of London, and y(U) the set of left-handed inhabitants of London, so that x() and y() are selective operators. Then x(y(U)) will select the blue-eyed left handers, and y(x(U)) the left-handed blue-eyed people. Since these two sets are composed of exactly the same elements, we can write x(y(U)) = y(x(U)), or, since the “universe” U is understood, this can be abbreviated to xy = yx. If a third operator z, say, is defined, as for instance, selecting all males, we can show that the operations are associative, x(yz) = (xy)z2.
This example is something that we have recently studied in class. It can be applied to the logical connective of xy = x ∩ y, or “x intersection y”. This is how we denote x and y. It can also be applied similarly to the logical connective of xy = x ∪ y, or “x union y”. However, it can only be applied when specific interpretations of the “Universe” are given.
The contributions of Boole and Boolean algebra are seen today on a large scale. According to Dalakov (2015), “Boolean algebra provides the basis for analyzing the validity of logical propositions because it captures the two-valued character (binary) of statements that may be either true or false.” The field where Boole’s offerings are most widely utilized lie in digital electronics. Dalakov (2015) states “In 1930s, a number of researchers noticed that Boole's two valued logic lent itself to a description of electrical switching circuits. They showed that the binary numbers (0 and 1), combined through Boolean algebra, could be used to analyze electrical switching circuits and thus used to design electronic computers. Today, digital computers and electronic circuits are designed to implement this binary arithmetic.” This is incredibly important in our world today, as mostly everything has become digital in this technological age that we are currently living in. We definitely do things differently because of Boole’s discovery. Without it, much of the advancement in computers as a whole wouldn’t be possible. Taking a look around, Boole’s influence is everywhere and has infiltrated our lives more than we could ever realize. All in all, George Boole and the concept of Boolean algebra has helped propel society from the industrial age into the technological age.

References

Boole, George. (n.d) Britannica Online.

Dalakov, G. (2015, November 30) George Boole. Retrieved from http://history-computer.com/ModernComputer/thinkers/Boole.html

Gasser, J. (2006) BOOLE, George (1815-64). Continuum Encyclopedia of British Philosophy, 377-380.

Nahin, P.J. (2012). The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. Princeton: Princeton University Pre