Logicomix and the quest for a quest
Logicomix is a graphic novel, no less, that sets out to tell the story of the foundational quest for mathematics. The superhero in question is Bertrand Russell, the British mathematician cum philosopher whose life we follow from austere upbringing to his role as one of the protagonists in the attempt to root the whole of mathematics in a logical framework (more on which below). The attempt to portray this quest in graphic novel form is itself, of course, a highly ambitious project, and the authors reflect this by building their own artistic quest into the narrative. In this way, we are presented with two parallel quests (or a quest within a quest): the foundational quest in mathematics, on the one hand, and the attempt to tell the story of that quest in a 300-page comic, on the other. When I started reading I found this format both slightly irritating and slightly patronising, but actually it works very well as a means not only of showing the difficulty of navigating an artistic project on this scale (involving at least five major players), but also of defusing the tension created by the inevitable liberties that the authors take with some of the events they depict.
The foundational quest in mathematics, for those who like myself had no idea that such a quest even existed (it is apparently also known as the foundational crisis in mathematics), was the concerted effort to find a rigorous logical and philosophical basis for mathematics. The quest started towards the end of the nineteenth century with the growing awareness of so-called “foundational issues”, including inconsistencies between the main branches of mathematics. The goal of finding a complete and consistent set of mathematical axioms from which everything in mathematics can be derived is also known as Hilbert’s programme, after the logician David Hilbert, who identified it in his famous list of problems in mathematics.
Bertrand Russell joined the quest after becoming frustrated with what he saw as unproved assumptions underpinning the study of mathematics. In 1900, he attended the Congress of Philosophy in Paris where he was introduced to the work of Giuseppe Peano, who was busy developing Georg Cantor’s principles of set theory. Russell’s personal attempt to achieve the Holy Grail of foundational mathematics is reflected in the enormous Principia Mathematica, which he co-authored with Alfred North Whitehead and which was eventually published in 1910. Unfortunately for both of them, and for foundational mathematics as a school of thought, Kurt Gödel’s two incompleteness theorems of 1931 proved that for every set of mathematical axioms, there are mathematical statements whose truth cannot be derived from the system itself. The presentation of the two theorems led another great mathematician, John von Neumann, to declare: “it’s all over.”
The rise and fall of foundational mathematics, and the consequences for those involved, is really at the heart of Logicomix, and the authors struggle to find the best way of portraying this in narrative form. The main point of difference between Doxiadis and Papadimitriou is over the issue of whether or not to depict the quest as essentially tragic. Broadly speaking, Doxiadis (a novelist) thinks that it must be seen as a tragedy, whilst Papadimitriou (a computer scientist) disagrees, pointing to the importance of the work of these mathematical crusaders in leading to the development of computer science:
“Follow the ‘quest’ for ten more years…and you get a brand-new, triumphant finale…with the creation of the computer, which is the ‘quest’s’ real hero! Your problem is, simply, that you see it as a story of people!”
As Papadimitriou notes above, the issue is really about whether the quest is seen in personal or impersonal terms. For Russell, the quest in its purest sense was a failure, even if he did live to see his work and that of other logicians inspire Alan Turing’s prototype computer, the theoretical “machine”. Papadimitriou, on the other hand, takes a wider (more contentious) view of events and, understandably perhaps as a professor of computer science, sees the computer as humanity’s great hope for freedom and democracy. To this extent, Russell’s failure was part of the “greater good”. I’m naturally inclined to side with Doxiadis on this one, probably because as a reader of novels I’m drawn to the human aspect of the narrative, and Bertrand Russell makes for a fascinating protagonist. However, the way the schism is ultimately reconciled via a dress rehearsal of Aeschylus’ Oresteia is cunningly staged, and ties in well with the Athenian backdrop. Having said that, perhaps more could have been made of the human/non-human divide, particularly because the limits of mathematics and by extension of human reasoning seem to have led indirectly to the ‘shadow’ humanity that is the world of computing that we have become so accustomed to. After all, without Turing and von Neumann this computer, let alone this online blog, would almost certainly never have come into being. [Ed: I’ve now been advised that this is a whimsical historical counterfactual that doesn’t stand up to rigorous philosophical scrutiny – apologies.]
Finally, it would be wrong to write anything about Logicomix without mentioning the stunning artwork. The two artists, Alecos Papadatos and Annie di Donna, do a fantastic job of recreating scenes from Russell’s life and more generally from the history of mathematics. I was also struck by the depictions of modern-day Athens, which is shown basking under a perpetually clear-blue summer sky. Even when Papadimitriou notes at one stage how much the city has changed in recent years, it still seems like an ideal place from which to write/draw a graphic novel. Inevitably, thinking of Greece nowadays immediately conjures images of queues outside banks and Alexis Tsipras sweating as he attempts to negotiate another bailout package with troika bureaucrats. However trite it may seem though, Logicomix reminded me of the enormous intellectual and artistic debt the rest of the world owes the country.