I watched Dangerous Knowledge, a 90-minute BBC video documentary from 2007 which explores the imaginations of four great thinkers. (It’s in two parts. Watch Part Two) These guys opened doors to areas of mathematics that enable today’s technology. And then . . . then, these intellectual giants’ lives spun out of control, toward madness and suicide.
Georg Cantor (1845 – 1918), mathematician. Inventor of set theory, he created the Continuum Hypothesis, which explored the possible sizes of infinite sets. He suffered from manic depression and spent long periods in sanitoria.
Ludwig Boltzmann (1844 – 1906), physicist. Made sense of disorder. Probability theory pioneer.
Kurt Gödel (1906 – 1978), shook mathematics, philosophy, and logic, with his incompleteness theorem. Close friend of Albert Einstein while at Princeton Institute for Advanced Studies.
Alan Turing (1912 – 1954), “the father of modern computing”
(Originally published October, 2014) The new British film The Imitation Game illustrates the remarkable life of mathematician and computer science pioneer Alan Turing. It will open in theaters on November 21.
This 30-minute video interview with the film’s director Morten Tyldum, actors Benedict Cumberbatch and Keira Knightley, and screenwriter Graham Moore, is worth watching. I can’t wait to see the movie. I’m happy that the screenplay is based on Andrew Hodges’ definitive biography Alan Turing: The Enigma. (Hodges is a mathematician, so if you’d like, he can walk you through Turing’s reasoning based on number theory that led to the routine decryption of messages that were encrypted by the German Navy’s Enigma machines.) Hodges’ biography is a wonderful book that I use as a reference.
Screenwriter Moore describes Mr. Turing as “the outsider’s outsider”. Director Tyldum calls The Imitation Game “a story about outsiders, those who are different.” “The mission of the movie is to celebrate uniqueness — individuality.”
Update, 28 Dec 2014 Mathematician Simon Singh saw the movie and quipped in a Science Friday interview that it’s “filled with factual errors, full of flaws, and in that respect it’s a terrible, terrible film” but in other ways it’s a “brilliant, great film”. According to Singh, the movie errs in dozens of details. Notable errors:
At Bletchley Park during WW2, Turing is shown building a general purpose computer dubbed “Christopher”, which supposedly was used to decipher scrambled German messages that had been encrypted with the Enigma machine. This is wrong. Turing did create the algorithms for, design, and participate in the construction of multiple dedicated electromechanical single-purpose calculators that were used to decipher Enigma-encrypted messages. These machines were called bombes.
In 1952, through detective work, the Manchester police discovered that Turing was a homosexual. In fact, Alan’s flat was burgled by, he suspected, a homosexual paramour. Outraged, he reported it to police, and mentioned that, yes, he had had a few trysts with the suspect. The police charged him with “lewd and indecent acts” (the same crime that had put Oscar Wilde behind bars a few decades earlier).
I view these errors as serious flaws, but I suppose that Hollywood feels a need to juice up the facts.
November 2015: I’m not going to watch this movie. Reviews by knowledgeable people who’ve seen it decry its many inaccuracies. Just one of many negative reviews on IMDB:
Another Weinstein production that is obvious and sad. Pushing the main Hollywood agenda of homosexuality. Sad and practically comical A very demeaning exploitation of the real heroes and suffering in WWII and woe is the lone gay guy losing the battle to the evil empire of the moral world. Save your money. The acting was made trite by the twisted story and the depth was a deep as a sippy cup. Really disappointing but of course will get tons of attention due to the publicity budget from this group. This once again confirms that you can no longer see a big name production without expecting the story to be trivialized and contain the jaded view of the liberal left who is in a ship going down.
Now that not just one, but two movies (Breaking The Code and The Imitation Game) have been produced about Alan Turing, it’s time we had a movie about Ada Lovelace. She seems to have possessed an unusual combination of precise reasoning and imagination, strong will, and feminine charm. Plus, she was in the middle of a tug o war between her feuding parents, poet Lord Byron and his wife Anne Isabella.
Why is Ada important? She’s acknowledged to be the first computer programmer (c 1840!). Like Mozart and Turing, her life was tragically cut short at a young age. I propose this biopic today because it’s Ada Lovelace Day!
English mathematician Alan Turing, who in 1952 was convicted of “gross indecency” (read: homosexuality), today received a pardon from Queen Elizabeth. His death in 1954 was ruled a suicide. His work at Bletchley Park had led to the breaking of the German naval Enigma code during WW2. BBC story: http://www.bbc.co.uk/news/technology-25495315
In 1953, the world contained 5 kilobytes of electronic memory.
George Dyson, son of physicist Freeman Dyson and brother of I.T. pundit Esther Dyson, tells the story of electronic computers’ early days. I loved listening to his 52-minute aural presentation. He describes the early post-war activities of computer pioneers John von Neumann, Kurt Gödel, Alan Turing, and Paul Erdős. George’s father rubbed elbows with these guys at the Princeton Institute for Advanced Studies, so George has personal childhood memories of some of these giants.
He points out that Alan Turing’s hypothetical Turing Machine (which stored instructions and data sequentially on a tape) of 1936 gave us a one-dimensional computing model. With 1945’s EDVAC design, John von Neumann gave us a two-dimensional model (which stored instructions and data in a matrix). Today’s computers are just very fast iterations of 1945’s von Neumann model.
Von Neumann was at the center of not just computing, but also development of the hydrogen bomb, study of climate change, and exploration of DNA.
Back in 1953, von Neumann and crew at the Princeton Institute for Advanced Studies explored nuclear fission, shock waves, weather prediction, biological evolution, and stellar evolution — in just 5 kilobytes of memory!
Von Neumann died in 1957. Princeton’s Institute for Advanced Studies pulled the plug on his computer in 1958.
George Dyson is an outdoorsman and master kayak builder. (For 3 years he lived 90 feet up in a tree house.) He mixes a love of the outdoors with knowledge of science and technology. He discusses his life and interests in this 67-minute audio interview. Here’s a 12-minute interview.
I was vaguely aware that Alan Turing laid the mathematical foundations for computing and was a leader in the wartime breaking of the German Enigma code by the English. Then in the 1980s I read Andrew Hodges’ biography of Turing, titled The Enigma, which helped sharpen my image of Alan Turing. Born in 1912, he thought of numbers as mere symbols, which led to his becoming a powerhouse in number theory. Before World War 2, number theory was a quiet corner of mathematics of seemingly no practical use. Before the war, Alan studied at Cambridge and Princeton, and in a famous paper, proposed a “universal machine”, which he proved mathematically could perform the functions of any other machine. Then Germany attacked England and used Enigma machines to encrypt its military messages . . .
The stack of rotors inside an Enigma machine, consisting of three rotors and Umkehrwalze-B (the reflector).
The story of the decoding of German encrypted messages deserves at least several books. The Wikipedia article entitled Cryptanalysis of the Enigma is excellent. There were multiple generations of Enigma machines, whose encrypted messages became increasingly difficult to crack. Each German service employed different Enigma operating protocols, from weak to robust. Turing’s number theory work led to the development of the bombe, a machine that was used to decode Enigma encrypted messages. From June 1941, the Brits routinely decoded German U-boat messages, which brought the sinking of supply ships to a halt. England would not be starved to death.
The Germans subsequently deployed the Lorenz teleprinter machine, whose encrypted messages were eventually decrypted by a massive electromechanical machine with vacuum tube “valves” the Brits called Colossus.
After the war, Turing worked on the design and development of digital milestones, including the ACE and Manchester Mark 1 computers. He pioneered Artificial Intelligence and used mathematics to model and predict biological behavior. He died in 1954 at age 42. He’s believed to have poisoned himself with cyanide, but there’s evidence that his death may have been accidental.
The biography The Enigma is complete — maybe too complete, but the central character remains fascinating. From a book review on Amazon by Thomas D. Jennings:
“. . . Turing was a difficult person: an unapologetic homosexual in post-Victorian England; ground-breaking mathematician; utterly indifferent to social conventions; arrogantly original (working from first principles, ignoring precedents); with no respect for professional boundaries (a ‘pure’ mathematician who taught himself engineering and electronics).”
Galileo, Newton, Maxwell, Tesla, Einstein, Armstrong, Shannon, Turing . . . the list of Promethean giants is long. What do they have in common? I think that the review by Tom Jennings got it right: they were “utterly indifferent to social conventions; arrogantly original (working from first principles, ignoring precedents)”.