By classifying thought and codifying it using algebraic language, Boole invented a new kind of mathematics. A century later, boolean algebra would provide an ideal foundation for designing the electronic structure of computers, and for manipulating information within computers.
Can Boole in any way have foreseen such developments before his premature death in 1864?
The practical application of his ideas, and the eventual societal benefit for work, learning and communication, would certainly have pleased Boole. He was a practical scientist, dedicated to ‘understanding the thought processes of the human mind’, an author who tested each idea exhaustively before committing to print and, in boyhood, a pupil in mathematics and optics who ‘learnt by doing’ with his father, calculating the focal length of a lens for a new telescope.
Boole’s biographer, Professor Desmond MacHale, believes he did sense an approaching revolution in computing. MacHale cites a revealing passage in Mary Boole’s 1868 book The Message of Psychic Science, in which she appears to paraphrase her late husband’s views:
" . . . if I were asked to point out the two greatest benefactors to humanity that this century has produced, I think I should be inclined to mention Mr Babbage, who made a machine for working out series, and Mr Jevons, who made a machine for stringing together syllogisms. Between them they have conclusively proved, by unanswerable logic of facts, that calculation and reasoning, like weaving and ploughing, are work, not for human souls, but for clever combinations of iron and wood. If you spend time in doing work that a machine could do faster than yourselves, it should only be for exercise . . . "
A letter in the Boole archive written by Joseph Hill records Boole’s meeting with Charles Babbage (1791-1871) at the Great London Exposition of 1862. Among the large machinery exhibits were parts of the Analytical Engine, which Babbage had been developing since the 1830s. Boole’s conversation with Babbage about the ‘thinking engine’ was witnessed by Hill.
Babbage conceived the Analytical Engine in 1833. It was to be the first general purpose mechanical computer, programmed using loops of punched cards like the Jacquard loom. Part of the Analytical Engine was displayed at the King George III Museum at King’s College London in 1843, but Babbage never ceased modifying his designs and it was not completed.
On 15th October 1862, Boole wrote to Babbage concerning their meeting:
"My dear Sir, It is a source of regret to me that I was quite unable to avail myself of your kind invitation to call upon you on my return from Cambridge to London . . . Meanwhile, I shall endeavour to acquaint myself with Menabrea’s paper and the principle of the Jacquard loom. But I cannot allow this opportunity of writing to you to pass without thanking you very warmly for the kind explanations you gave me of the working of the Difference Engine, and without saying that it was a pleasure and an honour to me to meet you."
MacHale has speculated on this encounter as one of the great ‘what-ifs’ of science. What if Boole had decided to collaborate with Babbage . . . would Boole have coded software to programme Babbage’s hardware? Could there have been a mechanical analog computer by 1875, and even an electro-mechanical version by 1900?
It should be noted that Boole had ideal skills for tackling information storage and retrieval. He had a remarkable memory, and credited this to his ability to categorise information:
‘the power of arrangement, which provides its proper place in the mind for every fact and idea, and thus enables me to find at once what I want, just as you would know in a well-ordered set of drawers where to lay your hand in a moment upon any article you required’.
Mary Boole’s book, quoted earlier, mentions a second name, that of William Stanley Jevons (1835-82), a logician and economist with whom Boole came into contact in August 1863.
Jevons was a sincere admirer of Boole’s symbolic logic, but he was not a mathematician. In 1864 he published a short book, Pure Logic; or, the Logic of Quality apart from Quantity which contained a critique of Boole’s system.
Here Jevons attempted to explain the processes of reasoning by once again divesting logic of mathematics. He stated extravagantly; ’the mathematical dress into which he [Boole] threw his discoveries is not proper to them, and his quasi-mathematical processes are vastly more complicated than they need have been’.
Correspondence between Boole and Jevons survives at the Royal Society in London, showing that Boole was unable to make Jevons (twenty years his junior) comprehend his viewpoint.
In 1866, Jevons conceived a ‘universal principle of reasoning’, which he published in 1869 as The Substitution of Similars. In parallel with this research, he was exploring the construction of a ‘logical machine’ through which the processes of logical inference might be mechanised.
In 1870, Jevons exhibited his ‘Logic Piano’ at the Royal Society. Jevons remarked wryly that it was ‘quite as likely to be laughed at as admired’. It is now recognised as the first mechanical computer to solve problems with an accuracy and speed that exceeds the human brain.
The ‘Logic Piano’ delivers a conclusion that is derivable from any given set of premises. Resembling a small upright piano, with twenty-one keys to input classes and operations in equational logic, the original device can be seen at the Oxford Museum of Science.
It was not until 1937 that Howard Aiken, inspired by Babbage’s Analytical Engine, persuaded IBM to fund a huge electro-mechanical computer programmed with punched cards, the Harvard Mark 1. A year later at MIT, Claude Shannon published his seminal paper A Symbolic Analysis of Relay and Switching Circuits, inspired by Boole’s work on symbolic logic which had lain largely unappreciated for 70 years.
Shannon’s recognition of the importance of boolean logic for circuit design is discussed in more detail on this website at His Legacy: Engineering.