While writing this blog my theme develops around “there isn’t a single truth”, so reading a book that features “an epic search for truth” might not exactly be my thing. Well, in fact, it is. I read Logicomix in one stretch and I was delighted. It contains insights I wished I had known before.
A story about people
Logicomix is a book that treats a very heavy-handed subject in a light way. It is about complicated science, it is about the foundations of science and – whatever we feel about it – it is about knowledge that ultimately influences all and everything around us. So normally this kind of subject is handled in a very serious, sacred atmosphere where full rational attention would be required and any frivolous dissipation would be considered out of bounds.
The writers of Logicomix however chose to give their story a form that is eminently frivolous: a comic book.
A frivolous form does not mean it is a sloppy work, the writers very well explain who they are and what they’re up to. Their intention is to write a story about people, a story like all other stories that is about people, fate and human passion. This is a brilliant angle. Only when you see the result, you realize what a shortcoming it has been the exact sciences have never been treated this way.
Yet the paradox lies in the fact it has been the exact sciences themselves that tried to get rid of the lack of objectiveness, precision and control that goes with emotion, frivolity and story telling. At the heart of exact science culture lies the search for mathematical truth, the subject of this book.
Self-reference
The book has three layers. The top layer is about the writers themselves, writing and drawing the book. The second layer is about Bertrand Rusell, giving a lecture in 1939 in which he tells the real story of the book and third layer: his life among great mathematicians.
The fact the book has layers, one referring to the other, is a very mathematical starting point. Referencing is the exact same thing that the logical formulas, that their characters are inquiring, do. Then, the top layer references to the book itself, a clear hint to the principle that the characters of the book find so difficult to deal with: self-reference.
This self-reference is not out of vanity, it is absolutely essential for the book. It is the only way they can escape themselves the big trap that their protagonists are falling in, the search of some unreachable external force to justify their work. The story begins and ends in Athens, Greece, at the beginning of the 21st Century with a couple of friends who have just each other to justify their crazy plan. It may seem futile but this is what liberates them from the burden of absolute accuracy and allows them to tell the story from their own perspective.
Poor social behavior
One of the drives of the writers has been the curious fact that the majority of the protagonists of this great intellectual adventure ended up insane. The hypothesis they formulate is that it was the other way around, that these men were already insane, or at least troubled, and that was the reason searching for the grip of a fundamental truth in the first place.
They are making a clear statement, showing young Bertrand Rusell being raised by his loveless grandmother, while surrounded by an unruly and scary environment. It is no surprise this boy is searching for ways to get grip on reality, so we can understand when he find out about mathematics later on, that he puts his hope on rational logics as the sole way to access reality.
Yet there seems to be incompatibility somehow between strict logical reasoning and social behavior. What we see is that these mathematicians, who embrace strict rationality and, for that matter, denounce “irrational” human intuition and emotion, are getting out of touch. They fail to make a connection with their loved ones and show poor social behavior.
So maybe these irrational things are quite useful after all, how could that be?
The incompleteness theorem
Well, the book doesn’t say anything about the usefulness of emotions but it does show where the search for truth ended: the 1931 incompleteness theorem of Gödel. While Rusell and Whitehead tried to prove an irrefutable foundation of logics, Gödel turned it the other way around and proved that such a proof would never be possible.
What he basically did was write down in logical notation: “This thesis cannot be proved.” Either this thesis is false, which would contradict the logical system in which it has been written, or it is true but incomplete. Or you can also say: once you have a powerful system of logical notation the amount of possibilities within the system is infinite so there will always be possibilities you haven’t been able to evaluate yet.
I was happy to read this, it is exactly what I have been trying to say with my previous posts about one-truth. It is amazing it has already been found in 1931 while it hasn’t had that much of an impact yet.
See: Logicomix website