George Boole and his Legacy “Standing on the Shoulders of Giants” Richard Henson University of Worcester Presentation for BCS 8 th October 2015

Background Grew up in Lincoln Modest, but not poor… father owned a small business but his real interest was Science & Maths exceled in Maths at school also excellent in Latin & Greek! Became a Maths Teacher family business failed; had to support them ran a school! (at 18!) opened his own (at 19)

Development into Adulthood Continued to manage schools… took his family with him each time became politically active, lobbying for “Early Closing” decided he wanted to be a priest! tried for 5 years to study Principia Mathematica in his spare time (!)

Development into an Academic Links with Gregory, Cambridge University some impressed with his ideas, influenced by LaPlace (probability) & LaGrange (celestial mechanics) published a Mathematical paper in a Cambridge journal “Researches on the Theory of Analytical Transformations” Paper on Algebra later sent to the Royal Society… support of Prof De Morgan paper accepted… still living “modestly” at his school in Lincoln!

Fame and Academic Recognition Continued working on Algebra… influential work: “On a general method of analysis” (1843) support from famous names: e.g. Prof De Morgan, Lord Kelvin Royal Society medal! seminal work… “Mathematical Analysis of Logic” (1847)

Chair of Mathematics! 1846: Applied for Professorship at one of the Queen’s new non-denominational Colleges 1849: Cork offer… just after his father had died in Lincoln

New Life (Anglican in Cork!?) Dedicated to mathematical study even met his future wife (Mary) through tutoring her on differential calculus Religious disputes… wisely steering clear became Dean of Science (1851) Worked intently on his great work (1854): “An Investigation into the Laws of Thought… on which are founded The Mathematical Theories of Logic and Probabilities”

The Genius of George Boole Massive academic output “Laws of Thought…” guidance from Prof De Morgan brought together logic & probability, using algebra, set theory to develop his new digital mathematics Inspired many other logicians of his era… Boolean Piano Alice in Wonderland And today…

Contents of “Laws of Thought” Signs and their Laws, Derivation of the Laws, Division of Propositions, Principles of Symbolic Reasoning, Of Interpretation, Of Elimination, Methods of Abbreviation, Conditions of a Perfect Method, Of Secondary Propositions, Methods in Secondary Propositions, Clarke and Spinoza, Example of Analysis, Of the Aristotelian Logic, Of the Theory of Probabilities, General Method in Probabilities, Elementary Illustrations, Of Statistical Conditions, Problems on Causes, Probability of Judgments, Constitution of the Intellect, olesgreatest.pdf olesgreatest.pdf

Boolean Algebra & De Morgan’s Laws Algebra based on binary numbers! used to calculate output(s) from any combination of binary inputs Binary = digital = representation of anything De Morgan… easy way for non- Mathematicians to do Boolean Algebra

Logic Gates and Digital Data Processing Started with AND, OR NOT “gates” Results of proposed combinations of gates calculated using Boolean Algebra & de Morgan’s Laws Initially mechanical switches… then relays… valves… transistors Potentially limitless scope to model, and interact with physical world!

Silicon-based Architecture Uses NAND, NOR, and NOT gates primitive circuits used to build modern computers combine in many ways to build higher-level circuits and components. NOT (inverter) can just be a single transistor Simple (but sadly obsolete) resistor-transistor logic (RTL) circuit NAND - two transistors in series NOR - two transistors in parallel

The Legacy of George Boole 10 years was not sufficient to achieve the vision of putting Boolean Logic/Algebra into the real world papers kept, mostly under wraps, at The Royal Society after his premature death… later transferred to Cork…