Although cyber attacks on department stores have become a common place occurance in our lives, unprecedented scale hack on Sony was a new experience for the entertainment industry. This hack in a way has shown that how film is still a powerful expression tool (Even making people who call themselves supreme leaders to get agitated) and of course motivated many of us to go and see a movie. I knew this movie called ‘Theory of Everything‘ about the life of Stephen Hawking coming to theaters soon. While I googled about this movie, the powerful mind reader of all time i.e. Google showed some other movies that “I might like”. One of which was ‘The Imitation Game.’ It was a movie about one of the brilliant mathematician & computer scientist & cryptanalyst Alan Turing (After all these &’s there are very very few people who satisfy these criteria !).
I first got to know about Alan Turing as an athlete from the picture below. There was an article on Time magazine about honoring Alan Turing during the London olympics in 2012. The picture shows the olympic torch being passed on between athletes on Turing’s 100th birthday (He was born on 23rd June 1912). Alan Turing was a great long distance runner and the movies also shows some scenes where he was depicted as a runner.
Later on I came across several of his works like Turing test, LU decomposition and Turing machine in classes or from other sources. Although most of his work is in very complex fields of mathematics, this movie The Imitation Game shows how it was used in a practical manner to achieve a practical goal.
Overall the movie is wonderful. First half of the movie has several moments where you can chuckle about the interaction between Turing and his coworkers, Commander Denniston (Turing’s boss) and Joan Clarke. Second half of the movie has the scenes on how Alan Turing succeeded in breaking the Enigma and his miserable life after the conviction for indecency. Cast has excelled in their roles. Benedict Cumberbatch and Keira Knightly has shown some of their best career performances. Not only the main roles but also the supporting actors like Alex Lawther who played young Alan Turing has done a really good job in the movie. My intention is not to critique further about this movie but rather to show the basis of math shown in the movie.
The main theme of the movie and the motive for the ‘Bletchley Park‘ during World War II was to break the Enigma code. Although Enigma machine shown below was a commercial encrypting machine it was adopted by Nazi intelligence and they converted it into what they thought was an unbrekable encryption machine.
In one of the early scenes of the movie when mathematicians are recruited to break the enigma code they talk about all the combinations of encryption. Turing said that there are 150 million-million-million (18 zeros after 150) combinations but Hugh Alexander corrects him by saying it was 159 million-million-million precisely. In the video below Dr. James Grimes from Cambridge University explains how this many combinations are possible with an enigma machine very clearly.
Also movie depicts there is only one kind of Enigma machine. However, German Navy had an enigma machine with 8 rotors compared to 5 rotors in German Army and Airforce. They also show scenes about plug boards and plug board settings in the movie. In the video below professor Brailsford from University of Nottingham explains about how they work together and how different branches of German military had different enigma machine setup (It’s nice that he references the movie several times !).
Also the machine that Turing and his colleagues built in order to break the enigma code was called ‘Bombe‘ named after its predecessor ‘Bomba Kryptologiczna‘, a polish code breaking machine. In the movie it is depicted as Turing naming it after his best friend from school Christopher. Although people might point it out as a historical inaccuracy in the movie, I think it gives a touching story especially when Turing says he choses to go through hormonal therapy rather than prison sentence so that he doesn’t have to leave Christopher (Machine).
Finally in a bar scene Turing serendipitously discovers the way to crack the Enigma code from recurring words from the weather reports and the phrase ‘Heil Hitler’. One other thing that was a huge flaw of Enigma was that a particular letter never maps to it self. For example regardless of how many times you type letter ‘a’ in the keyboard letter ‘a’ never appears in the encrypted message. Here Dr. James Grimes explain the flaws in the enigma code.
Finally the name of the movie itself is a game related to the Turing test (The title of this post is my favorite quote from the movie). I hope this post helped anyone looking to know more about the maths shown in the movie or kindled their passion on maths and cryptography.
Finally, I would like to end with what Times magazine stated about Alan Turing when it chose him as one of the hundred most important people of 20th century.
“The fact remains that everyone who taps at a keyboard, opening a spreadsheet or a word-processing program, is working on an incarnation of a Turing machine.”
So if you are reading this you owe something to Mr.Turing !