Alan Turing (1912–1954), often recognized as the father of modern computer science and artificial intelligence, holds a foundational though abstract, connection to modern banking, which was explicitly acknowledged with his selection as the face of the Bank of England’s £50 note in 2021.
Turing’s intellectual legacy is indeed too enormous for any article, let alone a blog post. Today’s AI-driven world would not have been possible were it not for his pioneering work on the concept of a “universal machine”, capable of executing any algorithm. Turing’s universal machine provides the logical underpinnings for all modern computing, including the systems used for digital banking, high-speed trading, data processing and AI-algorithms. Mind you, he came up with this “wild” idea in the 1930s and early 1940s, well before the world had seen the first computer.
Apart from his abstract universal machine concept, Turing also did more practical work involving code-breaking. Specifically, he was hired by the British government during WWII to lead the effort to crack German (“Enigma”) codes, increasing the chance of victory for the Allied Forces. Working at Bletchley Park in the UK, Turing’s brief was to design an electro-mechanical machine that could automate the search for trillions of Enigma machine settings, reducing these huge number of combinations to just a few.
Central to his efforts to speed up the identification of correct code settings was a statistical technique called Bayesian analysis. For seventy years, the details of this was kept top-secret by the British Intelligence. The secret documents were declassified only in 2012 when two of Turing’s papers on military decryption were released for public access. One of these papers, entitled, The Applications of Probability to Cryptography is now in the public domain. A line in that paper reads: “Nearly all applications of probability to cryptography depend on the factor principle (or Bayes’ Theorem).”
That is a remarkable claim and it is what I will focus on today. We now know that Turing cracked German codes by applying (and in some ways reinventing) Bayesian analysis, named after Thomas Bayes, an Englishman whose celebrated paper was published posthumously in 1763 with the title, Essay towards Solving a Problem in the Doctrine of Chance.
The actual formula that Turing used is very complex but at the heart lies Bayes’ Theorem, something that I personally think every educated person should have knowledge of. Thomas Bayes’ key insight was to put prior probabilities on a random event of interest, then update them with data about how frequently that event occurs to a final posterior probability. In effect, this procedure gives the decision maker a judgement about the probability of an event that is informed by the data. The three key elements of Bayesian inference (prior probability, data, and posterior probability) that make up Bayes’ formula, are without question, one of the most greatest discoveries in statistics.
Bayes’ formula or Bayes’ Theorem (as it is interchangeable known), is expressed by the following equation:
where 
Students of statistics are typically taught this result using the examples of coin flips. These are but toy examples of an unfamiliar concept. The real power of Bayes’ theorem comes when it is cleverly put into use when prior probabilities and good data are available (please refer to the technical notes for details). And of course, Turing was brilliant enough to know that it could be useful for decrypting enemy codes. Using Bayes’ theorem, he worked with an assortment of information, even fuzzy ones, asking questions like where did the message came from, what time did it came through, whether it was the length of a standard ‘noisy message’ to confuse the British, whether the sender always signed off with a standard-length ending and so on. He was able to combine all this information with prior frequencies in the messages to eventually sift through the trillions of codes to detect the probabilistically more truthful ones, thus shortening the war. The world would be a very different place were not for his brilliant efforts.
From Bayes to Banking
But even Turing could not have foreseen how his decryption analysis would also prove to be extremely useful for modern finance. The intersection of Turing’s work, Bayesian analysis, and modern banking represents a direct evolution from his wartime codebreaking to the algorithms governing contemporary finance. Here are three areas for which his analysis provides the foundation of modern finance:
- Risk Modeling & Management: Banks use Bayesian frameworks to estimate risks that could lead to bankruptcy, combining historical data with new, real-time market data to predict future volatility.
- Investment & Asset Management: Bayesian forecasting enables investors to make precise probabilistic forecasts by updating their views on stocks or sectors based on incoming news or market trends.
- Fraud Detection: Similar to how Turing filtered out impossible settings to find the correct one, modern banking employs Bayesian techniques combined with AI to “filter” through billions of transactions to identify fraudulent activities in real-time.
So, the next time you do an online banking transaction, give a thought to Alan Turing, the father of modern computing and artificial intelligence.
Technical Notes
[1] Bayes’ theorem is sometimes expressed in terms of odds (a terminology familiar to gamblers):
where x denotes the data and H1 and H0 are your hypothesis of some event. This equation says that the posterior odds of H1 over H0 is the prior odds (the second term after the equal sign) times the ratio of two likelihoods. This ratio is known as the Bayes Factor. It has a natural interpretation as a weight of evidence. Here is a concrete example of how to use the odds version of Bayes’ formula. Suppose you are assessing whether a fund manager whom you may entrust your money, is a truly skillful investor. Suppose after doing some research, you decide to work with a Bayes Factor of 2. At the same time, you recall from one of your MBA lessons that on average, only 40% of fund managers “beat the market” every year. You should take this “base information” into account because not doing so will skew your subjective assessment of the fund manager, in your case towards the optimistic side. Using 0.67 as your prior odds (40% divided by 60%) and multiplying this by the Bayes factor of 2 gives a posterior odds of 1.34. The posterior probability that the fund manager is skillful can be backed out from the posterior odds. It is 1.34/(1+ 1.34) which gives 57.3%. Not bad, but nothing to shout about either.
Further study:
Sharon B. McGrayne, The Theory that Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy, Yale University Press, 2012.