The Laws of Thought

by Nicholas Mee on September 30, 2017

George Boole was the son of a cobbler. Born in 1815 in Lincoln, he was largely self-taught, with little more than a primary school education. Despite these humble beginnings, Boole would become one of the leading mathematicians of his day. He founded a school in Waddington near Lincoln when just 19. Soon he was exchanging letters with established mathematicians and his research was appearing in academic journals. Eventually, this would lead to his appointment as the first Professor of Mathematics at Queen’s College Cork, now University College Cork, in 1849.

In Cork, Boole was introduced to Mary Everest, the young niece of the Surveyor General of India Colonel Sir George Everest, remembered today with the world’s highest monument. Boole agreed to tutor Mary in mathematics whenever they could meet in Cork or London. In 1855, despite their 17 year age difference, they married.

Boole is famous for devising a method of converting logical statements into algebraic expressions, as set out in his book The Laws of Thought. Once an arcane and abstract topic of interest to just a few specialists, Boolean algebra is now an applied science built into the software and hardware within our computers and other electronic devices.

Boole was a sensitive and mellow man who was totally absorbed in his work. According to Mary the educated people of Cork regarded him as some sort of saint, while the poorer people thought him so simple that it would be unsporting to cheat him. An old lady said to her:

They tell me your husband is a very learned man, my dear. I never saw a learned man before that one could talk to. He’s as innocent as a child, bless him, and as good as an angel, but I never should have guessed that he was clever.

Storm Clouds

On a cold wintry day in November 1864, Boole walked three miles in a heavy downpour from home to the university. The stoical Boole lectured all day soaked in his wet clothes, but on returning home he fell ill and developed a severe cold with a high temperature. Unfortunately, Mary held rather naive beliefs about illnesses and the best ways to treat them. Imagining the best remedy would resemble the cause, she put George to bed and poured buckets of cold water over him as it was the rain that had brought on his illness. This did little to improve Boole’s health. His condition worsened seriously and on 8 December 1864 he died, with his death attributed to a fever-induced pleural effusion. He was 49 years old.

George Boole’s bust at University College Cork.

Boole left five daughters. The widowed Mary, still just 32, returned to London with Mary Ellen, Margaret, Lucy and Ethel Lily, leaving Alice with her grandmother and great uncle in Cork. Alice would rejoin the family seven years later. Mary obtained a job as librarian at Queen’s College, the first women’s college in England.

Free Love and Mathematics

Queen’s College was located in Harley Street, famous as the heart of London’s medical profession, and Mary was soon befriended by James Hinton, a Harley Street ear surgeon. Hinton was a controversial figure, a radical promoter of polygamy and free love, and a founder member of the Metaphysical Society. Hinton’s circle of friends included the author George Eliot, the critic John Ruskin, the poet Alfred Lord Tennyson and the writer and sexuality researcher Havelock Ellis. Mary Boole’s daughters grew up in dirty and overcrowded lodgings in what must have been a rather Bohemian, but very stimulating environment.

Geometrical curved stitch design. Credit: Carnaxcce.

Mary had learnt mathematics from the great George Boole and she was keen to develop mathematical skills in her daughters. She wrote:

As soon as the hands can hold steadily compasses and set-square the child should be encouraged both in copying diagrams and in inventing others. It is desirable that, before any systematic teaching of mathematics begins, the compass, set-square, and ruler marked in fractions of an inch should be as familiar implements as the fork and spoon.

Mary believed that teachers should never simply state a result, but children should be led towards their own discoveries. She also realised that an intuition for geometry could be developed with visual and tactile aids, such as geometrical models and stitched curves. Mary advertised for private pupils and became an unofficial tutor at Queen’s College, where she also organised student meetings with James Hinton. The college authorities disapproved of these meetings, however, and Mary lost her job. Following her dismissal, James Hinton employed her as his secretary.

Revolution and Mysticism

Mary would later publish books explaining her educational methods. Some of her ideas were very influential and well ahead of their time, while others seem wildly eccentric. Mary was a pacifist and an outspoken critic of imperialism and organised religion and a supporter of the Russian anti-Tsarist cause. But she was also a convinced spiritualist and occultist. Her books, such as The Philosophy and Fun of Algebra, are strange mixtures of religious and mystical ideas that have little, if anything, to do with mathematics. But perhaps the fairest way to judge the success of her methods is through the careers of her daughters and their children.

It was an extraordinary family whose activities down the generations would touch on science, educational methods and revolutionary politics in many ways. Mary’s daughters were all rather remarkable. Lucy was a chemist and became the first female fellow of the Royal Institute of Chemistry. Margaret was the mother of the eminent physicist Professor Sir Geoffrey Ingram Taylor, a leading British theorist who developed many aspects of the theory of fluids and investigated a wide range of applications in areas including meteorology, oceanography and even supersonic flight. Taylor was part of the British delegation to the Manhattan project where he worked on the development of the first nuclear weapons. He was one of a handful of theorists who witnessed the first atomic bomb test codenamed Trinity in New Mexico on 16 July 1945.

The Gadfly

Boole’s other daughters lived equally colourful lives. Ethel Lily was just six months old when Boole died. She grew up to become a novelist and musician and, like her mother, was a supporter of various political causes. In 1890, she met a Polish revolutionary Wilfrid Michal Habdank-Wojnicz who had escaped penal servitude in Siberia, after being exiled by the Russian authorities for his anti-Tsarist activities. On reaching London, he anglicised his name to Wilfrid Michael Voynich and became an antiquarian book dealer. Ethel Lily and Voynich lived together for at least seven years before they married in 1902. Voynich is remembered for his discovery of the remarkable Voynich manuscript which he purchased in 1912.

The Voynich Manuscript

Ethel Lily is famous for her novel of 1897 The Gadfly about the struggles of an Italian revolutionary. The novel was an instant international best-seller and would become essential reading in the Soviet Union where millions of copies were sold. In 1955 the novel was made into a film with a score written by Dmitri Shostakovich. Ethel Lily lived until 1960.

Asteroids are often named after scientists and mathematicians, so it is not too surprising that there is an asteroid named after George Boole. Asteroid 17734 Boole was discovered on January 22, 1998 by Paul G. Comba in Prescott, Arizona. But Ethel Lily Voynich née Boole was accorded this honour decades before her father. Asteroid 2032 Ethel was discovered by the Soviet astronomer Tamara Mikhailovna Smirnova in 1970 and is named after her.

What is the Fourth Dimension?

Mary Ellen, Boole’s eldest daughter, married Charles Howard Hinton, the son of Mrs Boole’s friend James Hinton. Charles had been educated at Rugby and Oxford. He was a mathematician and science writer with an interest in the mystical theosophical movement that flourished during the Victorian era.

Crucifixion (Corpus Hypercubus) by Salvador Dali. ©1999 Artists Rights Society (ARS), New York / VEGAP, Madrid.

Hinton popularised the notion of four-dimensional space in a series of texts called Scientific Romances that include pieces such as What is the Fourth Dimension? (1884). Hinton believed there was a spiritual significance to the idea of a fourth spatial dimension and deep intellectual insight could be achieved by its contemplation. He suggested this would enable us to rid ourselves of the familiar ideas of right and left, and up and down, that weld us to a particular viewpoint in a three-dimensional world, a process he referred to as ‘casting out the self‘. According to Hinton this is a step towards sympathising with others and seeing the world from their perspective. In pursuit of this goal he devised mind-bending methods of perceiving higher dimensional space by meditating on sections of four-dimensional cubes known as hypercubes.

Hinton’s writings were very influential, inspiring writers and artists such as H.G. Wells, Joseph Conrad, Robert Heinlein, William James and Salvador Dali and mystics such as Pyotr Demianovich Ouspenskii. Hinton appears briefly in the novel Moonchild by Aleister Crowley and is mentioned in several of the short stories of the great Argentinian writer Jorge Luis Borges.

Alice in Wonderland

That just leaves Alice. She was the most talented daughter of George and Mary Boole. Immersed in the techniques of Charles Howard Hinton she would develop a facility for exploring the world of four dimensions that few people have ever matched. But her story will require another article.

Further Information

Geoffrey Ingram Taylor witnessed the first nuclear explosion and calculated the energy released in the bomb just by studying a film of the explosion: That’s Maths: How Big was the Bomb?

For more about the remarkable Voynich manuscript see: Voynich manuscript.



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