The silent heroes of WW2, still saving lives in 2020.
After seemingly months of lockdown, this weekend my family and I were fortunate enough to visit Bletchley Park, Buckinghamshire. This now famous park, was the site where Alan Turing and thousands of others cracked the infamous Enigma, the notorious encryption device used by the Axis powers during World War 2. The decryption of this machine as well many other devices gave the British and allied forces a huge advantage in what could be debated as being the ultimate turning point in the war. Additionally, the basis of the work these mathematicians performed laid the foundations of modern computing. Their use of logic and early forms of programming allowed them to perform the seemingly impossible task of cracking the uncrackable code possessing literally hundreds of millions of possible combinations.
Image credit – Bletchley Park: two operators working to break German ciphers.
Whilst learning more about these codebreakers, I stumbled across a piece of research by revered mathematician William Thomas Tutte and his work on Graph theory. In mathematics, Graphs are used to study relationships between vertices (or points) with edges (or lines) and look very different to the graphs we are used to. Tutte’s work with Graph Theory lead to him creating a proof still well regarded today about the existence of a perfect matching between these vertices.
A perfect match is described as being such that every point is connected to at least one other and that no point is connected to more than one other.
Image credit – Math world: 9 different perfect matches for the same 8 objects
This perfect matching boils down to the calculation of the most efficient path between all these points and has led to the development of many different computational methodologies. One such methodology includes Nobel prize winner Alvin Roth’s development of Game Theory, using graphs to identify the interdependencies of competing players. In fact, Tutte’s theorem has numerous relevancies today across multiple different industries, including: Navigational software like Google Maps to find the shortest path between two points (or is it vertices?). As well as software to model and predict behaviours of compounds in chemistry; to applications in healthcare allowing the most efficient donor paths for kidney transplants when donors aren’t a match for their loved ones.
A two-way kidney paired donation exchange being the simplest, but can be infinitely more complex, requiring long chains of calculation and dependency. The existence and location of a perfect match is crucial to this endeavour, as it creates a mutualistic relationship between all involved parties, which in turn reduces the chance of a single party dropping out and inadvertently preventing another from getting sufficient treatment. Additionally, perfectly matched kidney is more likely to be longer lasting and require less immunosuppression than an unmatched kidney.
Image Credit – Liver Cancer Genomics: traditional paired kidney exchanges (left) versus complex chains (right) calculated by software.
As Venture capitalists, we are fascinated by the idea of the existence of a perfect matching. As it indicates that if we understand the space we are operating in (the Graph) and which companies occupying that space (the vertices); there must then exist a perfect matching between all the important players using funding (the edges). Meaning we can fully understand our environment using Graph Theory. Does this mean that one day a VC firm might be able work out who they should fund using just an algorithm?
The answer to that question is still unclear. However, what is clear from my experience of this topic, is that one good idea is never just one idea, it is a culmination of paths to reach the end goal and that Turing and his colleagues proved, the greatest of odds can be overcome with the powers of collaboration and persistence.