I saw The Imitation Game last week ““ the biopic of Alan Turing ““ and it prompted me to write something about Jack Good, one of the Bletchley park codebreakers depicted in the movie.

In April 2003, while researching my unpublished probability book, I visited him in Blacksburg, Virginia. I was in New York on financial journalism business and had only one day to spare, so I took an early morning flight to DC and rented a car, driving at breakneck speed down the interstate (At one point, a highway patrol car flashed its lights at me; I quickly slammed on the brakes, bringing my speed down and he let me go).

Good was a sprightly 87-year old with a grey moustache and clipped tones of an old-school English gentleman, although by background he was the son of a Polish Jewish watchmaker. He ended up emeritus professor at Virginia Tech and was one of the last century’s most distinguished Bayesian statisticians. But I was there to talk to him about Bletchley, in particular the way he and Turing deployed Bayes’ theorem to measure the strength of their hunches about Enigma messages, in order to save time and win the Second World War.

Our conversation lasted a couple of hours and was one of the most interesting experiences of my life. Good’s memory was photographic and listening to him was as close as you could get to sitting in Hut 8 in 1941. It was a highly technical conversation and I couldn’t follow much of it. He peppered his talk with terms like grundstellung, steckerboard and Banburismus, interspersed with anecdotes about his former codebreaking colleagues. (One thing he would not talk about was his post-war work for GCHQ). Coincidences delighted him and he mused about them in combinatoric terms ““ what were the odds that such and such could happen?

He thought this during the bleakest moment of the war. Having received his Cambridge maths PhD before the outbreak of hostilities, Good was placed on the ‘reserve list’ as being a scientist exempt from military service. In 1940 he watched as Hitler’s armies conquered Europe, and decided that the probability of Germany winning the war was more than 95 per cent. As a Jew, he knew the personal consequences such a victory would have. Like Walter Benjamin fleeing through France, he wondered if it was rational to carry on.

“I was frustrated”, Good told me. “But I felt we should fight on nevertheless, even though it was 20-1 against us winning, because there was too much to gain. Rather like Pascal’s argument for being religious”. In May 1941 he arrived at Bletchley, a quiet Jew about to arm-wrestle Hitler.

Breaking Enigma was all about combinations and coincidences. The background is well documented (read Alan Hodges’ Turing biography for a good introduction). Hitler’s forces felt confident about transmitting messages over the airwaves because they had extremely good encryption systems: Enigma’s wheels and plugboards scrambled text so effectively that it would take longer than the duration of the war to go through the possible combinations of letters.

Turing and the others at Bletchley Park defeated Enigma not by using a brute force approach (for which they never had the resources) but with the help of weaknesses in the system that only mathematicians could tease out. The most obvious were ‘cribs’: hunches about the content of messages that could be tested against the intercepted code text (this is dramatized in The Imitation Game by an unseen German radio operator who uses the name of his girlfriend).

Subtler still were the indicator settings that Enigma operators would have to encrypt and transmit in order for the receiving operators to read the messages. This process that introduced a slight non-random relation between one message and the next that Bletchley mathematicians could attack. These weaknesses greatly reduced the scale of cracking Enigma from near-impossibility to merely immense difficulty.

In the language of probability, they flipped the ordering of terms on either side of the conditionality operator: rather than looking for the source plaintext given a fragment of code (the needle-in-a-haystack problem), find the code that Enigma would generate given a fragment of plaintext. At Bletchley they did this using ‘Bombes’, machines based on electrical relays that churned through possible Enigma combinations. If you succeeded you would get to read all the Enigma messages that day, before the Germans next changed the settings.

At Bletchley in 1941 there were barely enough Bombes to do the job (this is what prompted Turing and his colleagues Hugh Alexander and Gordon Welchman to write their famous letter to Churchill demanding more resources). It meant that a method for weighting the importance of coincidences was essential to prevent wasting the Bombes’ time going down blind alleys. This was Banburismus – the Bayesian ¹⁾some commentators have said it wasn’t Bayesian but Good told me it was which was enough for me decision system that Turing invented and Good refined in Hut 8. After Enigma, Good adapted Turing’s algorithms to help crack the German army’s Lorenz cipher machines, using Colossus, which may have been the world’s first programmable computer.

There was a lot more to Good than his work at Bletchley, and I find myself delving into his post-war ruminations on artificial intelligence and probability again and again. I was sad to hear of his death in 2009 at the age of 92. He may have fought the war in Turing’s shadow, but for me he was one of the greatest of ‘the greatest generation’.

Watching The Imitation Game was a very poor imitation (excuse the pun) of my conversation with Good 11 years ago. Perhaps it is inevitable that the demands of commercial drama would inject so many inaccuracies, some more annoying than others. But at least the film conveyed something of Bletchley, if in a mashed-up way.

That brings me to The Interview. Not the film itself but its metadata ““ the hacking attack by North Koreans against Sony Corporation that severely embarrassed the company and led to the cancellation disruption of the film’s release. We don’t yet know the details of how the attack took place, but for now let’s imagine that Sony executives received those little plastic key fobs that give them access to corporate virtual private networks. There might have been something like “RSA” embossed on the outside ““ an indication of an encryption scheme far superior to Enigma. And so those executives tapped out all those emails thinking they were invisible to the outside world.

The lesson of Enigma is that there is always a way into an apparently secure system. Weaknesses in the way it is used, combined with sufficient determination and skill on the part of an adversary, make published brute force odds meaningless. I use the word sufficient because the effort requires resources.

It was clear to Good and his colleagues that the rewards of breaking Enigma deserved the resources that Churchill allocated to it, even though the odds of success initially seemed slim. In the case of The Interview, it took a paranoid, hypersensitive dictator to see things in the same way, and decide that Hollywood was making war on him. The result was an improbable scenario that not even Hollywood could have invented.