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05 July 2010

Logicomix: An Epic Search For an Epic Search For Truth

Logicomix, An Epic Search For Truth
By Apostolos Doxiadis, Christos Papadimitriou, Alecos Papadatos and Annie Di Donna

I have enjoyed comics since I was a child, when, immersed in Hergé's Adventures of Tintin, I argued heatedly with my friends, who all preferred Asterix.

I still read Tintin occasionally, and I enjoy more consciously grown-up graphic novels, but I never thought I’d be treated to a comic-book account of Bertrand Russell’s quest to establish the foundations of mathematics. The idea of such a book is incredible, yet here it is, a story told passionately and illustrated beautifully, which does justice to the men and their ideas. And they’re all in here: Frege, Hilbert, Cantor, Gödel and Wittgenstein.

Self-reference

In the spirit of these folks, the book is a story within a story within a story, one of them being the story of the creation of the book. The creators appear as characters in present-day Athens, debating how to go about their task; then, in the next layer, there is Russell at the outbreak of the Second World War, giving a lecture in which he describes his quest to establish firm foundations for mathematics (and eventually knowledge) using a new, formalized and symbol-based kind of logic; and it is this quest that forms the inner, central story.

So we are welcomed into the book on the first page by Apostolos, the author himself, and the inner stories are often interrupted to allow us to see the debates that he is having with his collaborators about what’s going on and where they should take things next. In including the creation of the book within the book, it is self-referential, and given the significance of that notion to Russell’s central story, this seems appropriate. On the other hand, it makes the story feel unfinished, as if they didn’t know what to do with it, and in a flash of inspiration thought, “hey, let’s put our story, about writing the book, in the book! Get it?”

However, I can’t say this made the story any less gripping. Perhaps, on the contrary, it was the only way that they could have properly conveyed the logico-mathematical ideas, and the excitement they can generate: by presenting us with conversations featuring Christos, the computer scientist co-author, explaining the theories and problems to his lay colleagues, fleshing out the discussions that are going on amongst the logicians in the central story. And as things progress we too begin to feel part of these conversations.

The messy, unfinished feeling is heightened fascinatingly when the self-referential device reveals conflicts between the writers. Apostolos, the originator of the project, is interested in the interplay between the foundational quest and the personal motivations of – and psychological consequences for – the protagonists. Christos, on the other hand, is more interested in the logical and mathematical drama that would lead to the glory of computer science.

The preoccupations of a computer science professor

This leads me say something about a few passages towards the end, in which Christos, in present-day Athens, expresses some worries about the direction the book has taken.

Until this point Russell’s quest is presented as heroic and tragic, one that was motivated by the highest of intentions but which was doomed to fail. Kurt Gödel, appearing in the inner story as an earnest, respectful young man, proves mathematically that Russell’s Holy Grail would always, of necessity, be just out of reach. The logical foundations of a mathematical system can never be both all-encompassing and consistent.

This view, of the foundational quest as a failure, is fairly common amongst philosophers and historians of ideas, but Christos insists that it was a great success, because it led to a “new beginning”: the invention of the computer.

At the time of reading, I felt rather let down by this. Apostolos seems to give way here, to lose confidence in his vision of heroism and tragedy, and to give his co-author the last word. Christos, who is a professor at Berkeley, is presented as the expert in the field, dismissive of the mere human, dramatic, and even philosophical concerns of the others. His enthusiasm about the “triumph” of formal logic is that of a narrow computer scientist rather than that of a philosopher.

“So, 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!”

Russell’s quest, via Gödel, may indeed have given Turing the tools with which to invent the modern computer – and this may be interesting in its own right – but in no way does this refute the thesis that the foundational quest was a failure. By its own stated aims the quest certainly did fail: it turned out that a firm logical foundation for mathematics was an impossible dream.

In mathematics, logic, computing and linguistics, Russell’s contributions became important, and they have served as foundational in their own way. But Russell did not achieve what he set out to achieve. His quest was philosophical, and Christos’s preoccupations with computer science bring to mind Russell’s earlier frustration with the mathematicians who were unconcerned that their axioms were unproven. Christos dismisses not only the human aspects of the story, but the foundational and philosophical character of the quest.*

When the history is understood as a story of a philosophical quest that real people undertook, its dramatic and human aspects cannot be dismissed in the way that Christos seems to want to. If it is true that he sees this story as only a precusror to later triumph, then the philosophical view – as opposed to the logico-mathematical view – is better represented by Apostolos. Personally I think that the foundational quest told as a heroic tragedy is a brilliant idea that sheds light both on the heroes themselves and on their theories. Christos seems close to completely subverting what makes the book so exciting and original.

On the other hand, what struck me as a rant about computer science on reflection does tell us something that might easily be doubted by amateurs like me, that the formalization of logic did have an influence outside of a tiny group of eccentrics, and, more than that, that it had practical uses. And what is more relevant, the narrative of heroic triumph is very fitting for a comic book: Christos represents the unreconstructed superhero era of comics against Apostolos’ postmodern ambiguity.

Furthermore, all of this makes for an engrossing read: the fact that I want to dive into the page and join in the debate reveals how engaging and exciting it is, even in its confusions.

Logic → Madness, or Madness → Logic?

One of the book’s themes, which came mainly from Apostolos, is the connection between logic and madness. Russell himself was surrounded in his family by mental illness, and several of the logicians and philosophers who appear in the story went insane or suffered from mental instability. There might be something interesting in this, but the case made for it here is weak, and the authors lose confidence in it part way through (this is actually acknowledged towards the end in one of the scenes of meta-commentary).

And in attempting to make a case for this link, the authors perform some sleight of hand that might be rather too big of a lie. Gottlob Frege, the father of symbolic logic, is portrayed as a cantankerous but almost loveable old man when Russell meets him for the first time. Years later, when Russell visits him again, he has become a raving anti-semitic conspiracy theorist.

These meetings are a fiction, but I don’t mind that in itself: this and other similar inventions in the book are justified in making the story come to life. The gross misrepresentation is in pretending that Frege became anti-semitic through madness, and only towards the end of his life. From what I have read, it appears that he had long held those views, and that his most extreme ideas on how to expel the Jews from Germany were only the culmination of a gradual trend in his politics.

Maths

On the whole it does a very good job of introducing the technicalities of mathematical logic. Readers who are unfamiliar with these ideas could, I think, really become hooked. Of course, there is only so far you can go in this format if you want to retain a dramatic momentum. Most things are only touched upon, and certain ideas are left hanging. Most frustrating amongst these was the significance of set theory and the idea of infinity, which Russell begins to talk about when he and Alys visit a hotel, but which goes nowhere.

But really, there is far more of logic and philosophy in here than one expects. In fact, there is probably more than you would find in most books about Russell.

I haven’t made up my mind on this, but I felt that one sequence about mathematics slightly missed the mark, namely the explanation of Russell’s Paradox. This paradox is crucial to the story and it is one of the best ways to get inside the subject, in the way that the catchy riffs of Wagner and Stravinsky open up new worlds of music. Russell saw something that nobody had noticed before, that there was a fatal contradiction in the set theory at the heart of the logical foundations of arithmetic, as they had been formulated by Frege. There are several ways of presenting this paradox in a non-mathematical way, because the idea of a set is intuitive and basic, but I felt that while the book’s handling of it was entertaining and clever, it was also slightly clumsy and possibly confusing, especially in the way it was worded. The authors chose to use the Barber to illustrate the paradox, and you can see why, but I never found this the best way to approach it, preferring the library analogy. We each have our own way of thinking about such things and perhaps it was only that theirs did not quite gel with mine.

Wittgenstein

Wittgenstein’s appearances in the book are executed beautifully. With great economy and sensitivity they seem to capture the way that he influenced Russell in real life, as a mysterious and original force of genius that rocked his foundations, his most deeply-held beliefs about logic and knowledge. Wittgenstein is always crucial to any account of Russell’s life or philosophy, but he appears here only fleetingly. That these appearances are so memorable and touching reveals great judgement and care on the part of the authors and artists. The marriage of the illustrations and words here is very powerful, especially the scene in the snow in which Russell, intellectually exhausted, pathetically argues for the cause of philosophical logic in the face of Wittgenstein’s onslaught.

Pictures

The illustration is in the style of Tintin, with clean lines and shapes, but it is much richer, with much more shadow and depth. It has the feel of a sweeping historical film drama with classical cinematography. The present-day scenes in Athens are drawn with love, and, surprisingly as I think about it now, the feeling of Athens in late summer is the ground for the whole thing: it is what one feels is the backdrop for the whole story.

It is also through the illustrations that the central drama comes alive. The recurring theme of the thunderous storm marks two important turning points in Russell’s life, and serves to nicely convey his inner turbulence. This is hardly original in itself, but these devices are powerful and original for the telling of this story. The idea of the tormented comic-book superhero has been done many times, but never with Bertrand Russell cast in the role.

Anyway, the originality of comics lies in the artful way that themes and devices from books, films and other comics are combined, and applied to unusual subjects. Comics wear their influences for all to see, openly and without shame. A good comic book is a beautiful re-use of other forms of story-telling. It might be a cliché or an exaggeration to say that comics achieve some kind of synergy and transcendence in this manner, but it’s something like that.

Conclusion

My most important conclusion is: I loved this book, please read it, it’s great.

But aside from that, I can imagine different reactions to it. One can easily see it as a failure. The link between logic and madness, supposedly a central theme, is totally unconvincing, and this can make one lose faith in the whole book. And you can’t transcend your difficulties just by presenting them, with the clever device of self-reference. Seen like this it has a whiff of postmodern emptiness.

But I don’t think it is empty. The failures and conflicts of the authors mirror those in the inner story: Apostolos is like Russell, his quest to establish the link between logic and madness shown to be a failure by the Gödel-Wittgenstein figure of Christos. In the end, then, they found meaning in reflecting upon the quest as a universal one: certainty versus doubt, reason versus the disturbing forces of irrationality, order versus chaos. And this is brought home by the remarkable ending. Oddly enough, one can say that the book is both a failure and a great success, the story of its creation itself something of a doomed quest.

There is much else to commend: the book is a beautiful object, illustrated and printed to the highest standards; it succeeds in turning mathematical logic into a gripping drama; it actually serves as a good way in to the subject; and words and pictures are combined harmoniously to spectacular effect.

And last but not least, it’s a comic book. About mathematical logic.


*I should point out here that while the foundational quest may have been a philosophical failure, Russell made huge contributions in other areas of philosophy, notably the philosophy of language and epistemology.

Apostolos Doxiadis’s web site
Logicomix official web site
Logicomix on Amazon UK

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