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George Boole and his Legacy “Standing on the Shoulders of Giants”

George Boole and his Legacy “Standing on the Shoulders of Giants”. Richard Henson University of Worcester r.henson@worc.ac.uk Presentation for BCS 8 th October 2015. Background. Grew up in Lincoln Modest, but not poor…

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George Boole and his Legacy “Standing on the Shoulders of Giants”

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  1. George Boole and his Legacy“Standing on the Shoulders of Giants” Richard Henson University of Worcester r.henson@worc.ac.uk Presentation for BCS 8th October 2015

  2. 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)

  3. 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 (!)

  4. 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!

  5. 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)

  6. 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

  7. 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”

  8. The Genius of George Boole • Massive academic output 1854-1864 • “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… https://www.youtube.com/watch?v=aEjzjLv-YjI

  9. Contents of “Laws of Thought” • 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, • http://staffweb.worc.ac.uk/hensonr/Boolesgreatest.pdf • 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,

  10. 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

  11. 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!

  12. 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

  13. 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… • https://www.youtube.com/watch?v=CyqifpkRjQA • https://www.youtube.com/watch?v=y-eav8-EEY4

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