{"id":2218,"date":"2015-02-18T11:56:31","date_gmt":"2015-02-18T16:56:31","guid":{"rendered":"http:\/\/blogs.law.harvard.edu\/pamphlet\/?p=2218"},"modified":"2021-02-21T18:04:49","modified_gmt":"2021-02-21T23:04:49","slug":"the-two-guildford-mathematicians","status":"publish","type":"post","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2015\/02\/18\/the-two-guildford-mathematicians\/","title":{"rendered":"The two Guildford mathematicians"},"content":{"rendered":"\n\n\n\n
\"\u2026the<\/a><\/td>\n<\/tr>\n
\u2026the huge ledger\u2026<\/span>
\nStill from Codebreaker<\/em> showing Turing’s checkout of three Carroll books.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The charming town of Guildford<\/a>, 40 minutes southwest of London on South West Trains<\/a>, is associated with two famous British logician-mathematicians. Alan Turing<\/strong> (on whom I seem to perseverate<\/a>) spent time there after 1927, when his parents purchased a home at 22 Ennismore Avenue<\/a> just outside the Guildford town center. Although away at his boarding school, the Sherborne School<\/a> in Dorset, which he attended from 1926 to 1931, Turing spent school holidays at the family home in Guildford. The house bears a blue plaque<\/a> commemorating the connection with Turing, the \u201cfounder of computer science\u201d as it aptly describes him, which you can see in the photo at right, taken on a pilgrimage I took this past June.<\/p>\n\n\n\n\n
\"\u2026the<\/a><\/td>\n<\/tr>\n
\u2026the family home\u2026<\/span>
\nThe Turing residence at 22 Ennismore Avenue, Guildford<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

And this brings us to the second famous Guildford mathematician, who it turns out Turing was reading while at Sherborne. In the Turing docudrama Codebreaker<\/em><\/a>, one of Turing\u2019s biographers David Leavitt visits Sherborne and displays the huge ledger used for the handwritten circulation records of the Sherborne School library. There (Leavitt remarks), in an entry dated 11 April 1930, Turing has checked out three books, including Alice in Wonderland<\/em> and Through the Looking Glass, and What Alice Found There<\/em>. (We\u2019ll come back to the third book shortly.) The books were, of course, written by the Oxford mathematics don Charles Lutwidge Dodgson under his better known pen name Lewis Carroll<\/strong>. Between the 1865 and 1871 publications of these his two most famous works, Carroll leased \u201cThe Chestnuts<\/a>\u201d in Guildford in 1868 to serve as a home for his sisters. The house sits at the end of Castle Hill Road adjacent to the Guildford Castle, which is as good a landmark as any to serve as the center of town. Carroll visited The Chestnuts on many occasions over the rest of his life; it was his home away from Christ Church<\/a> home. He died there 30 years later and was buried at the Guildford Mount Cemetery<\/a>.<\/p>\n\n\n\n\n
\"\u2026through<\/a><\/td>\n<\/tr>\n
\u2026through the looking glass\u2026<\/span>
\nStatue of Alice passing through the looking glass, Guildford Castle Park, Guildford<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Guildford plays up its connection to Carroll much more than its Turing link. In the park surrounding Guildford Castle sits a statue of Alice passing through the looking glass, and the adjacent museum devotes considerable space to the Dodgson family. A statue<\/a> depicting the first paragraphs<\/a> of Alice\u2019s adventures (Alice, her sister reading next to her, noticing a strange rabbit) sits along the bank of the River Wey. The Chestnuts itself, however, bears no blue plaque nor any marker of its link to Carroll. (A plaque formerly marking the brick gatepost has been removed, evidenced only by the damage to the brick where it had been.)<\/p>\n\n\n\n\n
\"\u2026The<\/a><\/td>\n<\/tr>\n
\u2026The Chestnuts\u2026<\/span>
\nThe Dodgson family home in Guildford<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Who knows whether Turing was aware that Carroll, whose two Alice<\/em> books he was reading, had had a home a mere mile from where his parents were living.\u00a0The Sherborne library entry provides yet another convergence between the two British-born, Oxbridge-educated, permanent bachelors with sui generis demeanors, questioned sexualities, and occasional stammers, interested in logic and mathematics.<\/p>\n

But there’s more. What of the third book that Turing checked out of the Sherborne library at the same time? Leavitt finds the third book remarkable because the title, The Game of Logic<\/a><\/em>, presages Turing\u2019s later work in logic and the foundations of computer science. What Leavitt doesn\u2019t seem to be aware of is that it is no surprise that this book would accompany the Alice<\/em> books; it has the same author. Carroll published The Game of Logic<\/em> in 1886. It serves to make what I believe to be the deepest connection between the two mathematicians, one that has to my knowledge never been noted before.<\/p>\n\n\n\n\n
\"\u2026Carroll\u2019s<\/a><\/td>\n<\/tr>\n
\u2026Carroll\u2019s own copy\u2026<\/span>
\nTitle page of Lewis Carroll,\u00a0The Game of Logic<\/em>, 1886.<\/em>\u00a0EC85.D6645.886g<\/a>, Houghton Library, Harvard University.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

After watching Codebreaker<\/em> and noting the Game of Logic<\/em> connection, I decided to refresh my memory about the book. I visited Harvard\u2019s Houghton Library<\/a>, which happens to have Carroll\u2019s own copy<\/a> of the book. The title page is shown at right, with the facing page visible showing a sample card to be used in the game. The book was sold together with a copy of the\u00a0card made of pasteboard and counters of two colors (red and grey) to be used to mark the squares on the card.<\/p>\n

The Houghton visit and the handling of the game pieces jogged my memory as to the point of Carroll\u2019s book. Carroll\u2019s goal in The Game of Logic<\/em> was to describe a system for carrying out syllogistic reasoning that even a child could master. Towards that goal, the system was intended to be completely mechanical<\/em>. It involved the card marked off in squares and the two types of counters placed on the card in various configurations. Any of a large class of syllogisms over arbitrary properties can be characterized in this way, given a large enough card and enough counters, though it becomes unwieldy quite quickly after just a few.<\/p>\n\n\n\n\n
\"\u2026<\/a><\/td>\n<\/tr>\n
\u2026 marked off in squares\u2026<\/span>
\nThe game card depicting a syllogism.\u00a0Lewis Carroll,\u00a0The Game of Logic<\/em>, 1886.<\/em>\u00a0EC85.D6645.886g<\/a>, Houghton Library, Harvard University.<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

(The photo at right shows the card and counters that came with the book. I’ve placed the counters in such a way as to depict the syllogism:<\/p>\n

\n\n\n\n\n\n\n
No red apples are unripe.<\/td>\n<\/tr>\n
Some wholesome apples are red.<\/td>\n<\/tr>\n
\n
\n<\/td>\n<\/tr>\n
\u2234 Some ripe apples are red. \u00a0 \u00a0 \u00a0 \u00a0 )<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/blockquote>\n

To computer scientists, this ought to sound familiar. Just six years after checking out The Game of Logic<\/em> from his school library, Turing would publish his groundbreaking paper \u201cOn computable numbers<\/a>\u201d, in which he describes a system for carrying out computations in a way that is completely mechanical<\/em>. It involves a paper tape marked off in squares, and markings of at least two types placed on the tape in various configurations. Any of a large class of computations over arbitrary values can be characterized in this way, given a large enough tape and enough markings, though it becomes unwieldy quite quickly. We now call this mechanical device with tape and markings a Turing machine, and recognize it as the first universal model of computation. Turing\u2019s paper serves as the premier work in the then nascent field of computer science.<\/p>\n

Of course, there are differences both superficial and fundamental between Carroll\u2019s game and Turing\u2019s machine. Carroll\u2019s card is two-dimensional with squares marked off in a lattice pattern, and counters are placed both within the squares and on the edges between squares. Turing\u2019s tape is one-dimensional (though two-dimensional Turing machines have been defined and analyzed) and the markings are placed only within the squares. Most importantly, nothing even approaching the ramifications that Turing developed on the basis of his model came from Carroll\u2019s simple game. (As a mathematician, Carroll was no Turing.) Nonetheless, in a sense the book that Turing read at 17 attempts to do for logic what Turing achieved six years later for computation.<\/p>\n

I have no idea whether Lewis Carroll\u2019s The Game of Logic<\/em> influenced Alan Turing\u2019s thinking about computability. But it serves as perhaps the strongest conceptual bond between Guildford\u2019s two great mathematicians.<\/p>\n

Update\u00a0February 25, 2015:<\/strong> Thanks to Houghton Library Blog<\/em><\/a> for reblogging this post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u2026the huge ledger\u2026 Still from Codebreaker showing Turing’s checkout of three Carroll books. The charming town of Guildford, 40 minutes southwest of London on South West Trains, is associated with two famous British logician-mathematicians. Alan Turing (on whom I seem to perseverate) spent time there after 1927, when his parents purchased a home at 22 […]<\/p>\n","protected":false},"author":2110,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[13256,380,62110],"tags":[],"class_list":["post-2218","post","type-post","status-publish","format-standard","hentry","category-alan-turing","category-computer-science","category-lewis-carroll"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p5pLfN-zM","jetpack-related-posts":[{"id":321,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2009\/09\/13\/britain-apologizes-for-treatment-of-alan-turing\/","url_meta":{"origin":2218,"position":0},"title":"Britain apologizes for treatment of Alan Turing","author":"Stuart Shieber","date":"Sunday, September 13, 2009","format":false,"excerpt":"Image by Whimsical Chris via Flickr Prime Minister Gordon Brown has apologized on behalf of the British government for the appalling treatment of Alan Turing, who was obliged to undergo chemical castration for the crime of being gay. Prime Minister Brown's statement in the Telegraph follows an online petition drive\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"Alan Turing","src":"https:\/\/i0.wp.com\/farm3.static.flickr.com\/2081\/2042538753_f102fe97df_m.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":2209,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2014\/11\/30\/the-turing-moment\/","url_meta":{"origin":2218,"position":1},"title":"The Turing moment","author":"Stuart Shieber","date":"Sunday, November 30, 2014","format":false,"excerpt":"\u2026less histrionic\u2026 Ed Stoppard as Alan Turing in Codebreaker We seem to be at the \u201cTuring moment\u201d, what with Benedict Cumberbatch, erstwhile Sherlock Holmes, now starring as a Hollywood Alan Turing in The Imitation Game. The release culminates a series of Turing-related events over the last few years. The centennial\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2271,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2015\/05\/07\/in-support-of-behavioral-tests-of-intelligence\/","url_meta":{"origin":2218,"position":2},"title":"In support of behavioral tests of intelligence","author":"Stuart Shieber","date":"Thursday, May 7, 2015","format":false,"excerpt":"\u2026\u201cblockhead\u201d argument\u2026 \"Blockhead by Paul McCarthy @ Tate Modern\" image from flickr user Matt Hobbs. Used by permission. Alan Turing proposed what is the best known criterion for attributing intelligence, the capacity for thinking, to a computer. We call it the Turing Test, and it involves comparing the computer\u2019s verbal\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1481,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2012\/06\/16\/talmud-and-the-turing-test\/","url_meta":{"origin":2218,"position":3},"title":"Talmud and the Turing Test","author":"Stuart Shieber","date":"Saturday, June 16, 2012","format":false,"excerpt":"...the Golem... Image of the statue of the Golem of Prague at the entrance to the Jewish Quarter of Prague by flickr user D_P_R. Used by permission (CC-BY 2.0). Alan Turing, the patron saint of computer science, was born 100 years ago this week (June 23). I\u2019ll be attending the\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1610,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2013\/01\/13\/aaron-swartzs-legacy\/","url_meta":{"origin":2218,"position":4},"title":"Aaron Swartz’s legacy","author":"Stuart Shieber","date":"Sunday, January 13, 2013","format":false,"excerpt":"Government zealotry in prosecuting brilliant people is a repeating theme. It gave rise to one of the great intellectual tragedies of the 20th century, the death of Alan Turing after his appalling treatment by the British government. Sadly, we have just been presented with another case. Aaron Swartz committed suicide\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":2295,"url":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/2015\/08\/03\/becoming-tin-men\/","url_meta":{"origin":2218,"position":5},"title":"Becoming tin men","author":"Stuart Shieber","date":"Monday, August 3, 2015","format":false,"excerpt":"From the 2015 introduction to the 1965 novel The Tin Men by Michael Frayn: \"I hadn't in those days heard of the Turing Test\u2014Alan Turing's proposal that a computer could be said to think if its conversational powers were shown to be indistinguishable from a human being's\u2014so I didn't realise\u2026","rel":"","context":"In "Alan Turing"","block_context":{"text":"Alan Turing","link":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/category\/computer-science\/alan-turing\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/posts\/2218","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/users\/2110"}],"replies":[{"embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/comments?post=2218"}],"version-history":[{"count":38,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/posts\/2218\/revisions"}],"predecessor-version":[{"id":2443,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/posts\/2218\/revisions\/2443"}],"wp:attachment":[{"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/media?parent=2218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/categories?post=2218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive.blogs.harvard.edu\/pamphlet\/wp-json\/wp\/v2\/tags?post=2218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}