Logicomix: An Epic Search for Truth

It is hard to imagine that the quest for the ultimate logical foundations of mathematics would make for a good graphic novel, but the authors and artists of Logicomix clearly pulled it off! I may be partial here because Bertrand Russell - the main character of the story - is one of my all-time favorite philosophers, but the fact is that the book is historically accurate (as much as a novel needs to be, anyhow), beautifully drawn, and intellectually rigorous (again, by a novel's standard - this is no logics textbook). Some of the minor characters are among the most influential philosophers and logicians of the 20th century, from Frege to Wittgenstein to Godel. What makes them interesting is that their passions show through the work, both in terms of their human frailties and of their almost mad pursuit for logic. Indeed, madness plays a constant background role throughout the story, with a not so subtle investigation of its link to genius, and to mathematics and logic in particular. The authors do a very good job at explaining the basic concepts for the reader with no background knowledge of logic or philosophy through the sometime a bit annoying, but ultimately effective, device of featuring themselves as occasional commentators in the story. Of course, this means that the novel is partly self-referential, with all the obvious implications in terms of logical paradoxes...

Logicomix is a 335 page, beautifully produced and artfully drawn, comic book. Unlike most comic books, the heroes are several of the most prominent mathematicians and logicians of the twentieth century. Also unlike most comics, the subject matter is not fantastic and juvenile, but rather tells the story of the quest for the axiomatization of logic and mathematics in the first half of the twentieth century. The period is passionately interesting because late-nineteenth century innovations, especially Cantor's set theory, opened new vistas for the working mathematician, but the foundations of the new ideas was more than a little shaky. Cantor himself had proved that the power set of any set is strictly larger than the set, which means that the power set of the set of all sets is larger than the set of all sets! This is of course absurd. Bertrand Russell later located a fatal flaw in Frege's axiomatization of logic, famously known as Russell's Paradox. Cantor's paradox, and the related Burali-Forti paradox, are quite simple to expound, but not simple enough for the authors, but their exposition of Russell's paradox is well done. Somewhat later Goedel proved that any system complex enough to included the elementary axioms of arithmetic were such that there are sentences that are true but cannot be proved within the system. Moreover, he showed that if a system of sufficient complexity could prove its own consistency, then it must be inconsistent! Logicomix describes Goedel's incompleteness theorem, but does not explain the difference between `provable' and `true.' Russell's paradox is absurdly simple. Some sets are members of themselves---e.g., the set of abstract ideas is an abstract idea. Some sets are not---e.g., the set of all bluebirds is not a bluebird. What about the set S of all sets that are not members of themselves. If S is a member of itself, then it is not in S, so it is not a member of itself, a contradiction. Thus S is not a member of itself, from which we conclude that it is a member of itself. Thus S both is and is not a member of itself so the logic leading to this result is inconsistent, and hence can `prove' anything. The story line is a biographical account of Bertrand Russell's quest for a firm foundation for logic, and a reduction of mathematics to logic. This led to the monumental Principia Mathematica, coauthored with Alfred Whitehead. This book made Russell even more famous than his paradox, but it was not well received, and most logicians do not believe it solves the problems it poses. Moreover, there was an alternative developed by Zermelo and Fraenkel that appears to have solved the problem, in the sense that now, a century later, no one has found an inconsistency in the Zermelo-Frankel system. The general problem can be easily stated. Frege had an axiom that says that if P is any predicate, then the ensemble of all things that satisfy P form a set. Since sets can be elements of other sets in Frege's system, this led

As an avid reader of all genres: sci-fi, economics, contemporary and classic fiction, fantasy, graphic novels, even science, I never thought I could be surprised by a book. Logicomix has done it. This is a genre-shattering work of genius. Logicomix is a graphic novel of the story of Bertrand Russell's pursuit of the "foundations of mathematics." The authors (math geniuses in their own right) explore how the intellectual giants of the 20th century struggled with the fundamental questions of math, logic, and philosophy. Before reading this book, I only knew Bertrand Russell through his dry "History of Western Philosophy." Logicomix creates a semi-fictional account of his efforts to find out if mathematics can be absolutely logical, provable, consistent, "real." This book gives us brief introductions to Boolean logic, the seminal Mathematica Principia, Euclidean geometry, and philosophy. It's the first time in which I've had to put a graphic novel down to think about the implications of what I'd just read. The authors are ambitious, asking many questions such as "does pure logical thought have to lead to madness?" "Why is there a thin line between mathematical genius and insanity?" Some of the questions are very timely with the current Wall Street meltdown due to over-reliance on mathematical models. "What is the limit of human understanding? What is the meaning of infinity?" Russell pursues the hope that everything in mathematics and the physical world can ultimately be explained by rational thought, by pure logic. We still don't know if math is absolutely true and logical. Pure logic powers our computers, running millions of them successfully around the world. So it seems obvious that math is consistent. Russell, with his paradox, concludes that his quest for absolute truth is a failure, and that even mathematics cannot be considered "complete" and logical. The authors reach their ultimate conclusion on page 296 when Russell says: "Reflect on this please: if even in Logic and Mathematics, the paragons of certainty, we cannot have perfect assurances of Reason, then even less can this be achieved in the messy business of human affairs - either private, or public!" He continues: "Even now, I believe that Logic is a most powerful tool... as far as it goes. When it comes to talking about human life, it certainly isn't!... All the facts of science are not enough to understand the world's meaning....Listen: take my story as a cautionary tale...it tells you that applying formulas is not good enough - not, that is, when you're faced with really hard problems." Logicomix comes to a dramatic finale with the Greek tragedy Orestia, adding even more explanation to Russell's (and mankind as a whole's) quest for perfect rational thought. Don't let the subject matter of Logicomix scare you away! Of course, if I was a college or high school math instructor, I would have all of my students read this book on day one of the course.

I am a big fan of Doxiadi's book on Goldbach conjecture :Uncle Petros and Goldbach's Conjecture: A Novel of Mathematical Obsession. This book is very different, in manifold ways. The previous book was a novel wrapped around a mathematical idea. In the process of telling a story, Doxiadis explained the mathematical problem. It was pretty straight forward - not the problem, the approach. But this book is a tutorial on logic, a historical review of the most dramatic development in logic, a chronological synopsis of how higher mathematics, philosophy and logic became intertwined and coupled. AND, the book did this in a comic book format. The approach is, of course very ambitious. The question then is: was it successful? This may seem cowardly, but it does echo the book's conclusion: it is really up to the reader. The book poses the question early on: pure logic will lead a rational person to a right conclusion to a difficult moral problem, in this case, whether Britain should enter into WWII against Hitler. The entire book then is predicated upon the literary mechanism to introduce a wide spanning discourse on the development of 20th century logic, the narrative is taken through all of its twists and turns by the narrator in the form of Bertrand Russell, with occasional self referencing vignettes of the writing and drawing teams of this book. Russell is a natural choice, and his life in the higher altitude work in philosophy and mathematics really fits in nicely with the history of the logical arguments. His work, Principia Mathematica - Volume One with Lord Whitehead was also seminal in much of the breakthroughs that followed. The narratives are carried on through conversations with some of the most colorful people in the European philosophical, and mathematical intelligentsia: Frege, Cantor, Wittgenstein, the Vienna, Hilbert, Poincare, and Godels. But, relying on the words of these heavy hitters to carry through the dense and complex ideas is a difficult proposition for the reader because the heavy hitters tend also to have heavy and dense writings, so the authors have thoughtfully provided brief respites featuring the comic book counterparts of the actual writers and animators working on the book, and a welcome respite it is, this mechanism saved the readers from some heavy duty mental headaches and gnashing of teeth. So, after all that work, we return to the original question: were the authors successful? I think they were, by and large, but once again, it is up to the reader to decide because the depths to which the message is delivered depends very much on the reader's depths of understanding of the problems described and the reader's familiarity with the literature. The tutorial on the philosophical works, particularly the Principia and Wittgenstein's Tractatus Logico-Philosophicus (Routledge Classics) was very good, the authors did manage to explain some very important and dense material very cleanly and concisely. As

Dateline Wales: Unusual seismic activity has been reported in the mountains. Reports have been received of areas seemingly 'turning over'. One eye-witness remarked about it being connected with Bertrand Russell's ashes being scattered in the mountains nearly 40 years ago and a new book being released about him - and it's a Comic Book! The thought of Bertrand Russell and comic book being used together is strange. I am using "comic book" because the authors continually used it. It was only in the end notes that "graphic novel" was used by them. There was a very good balance between the art and the text - neither overshadowed the other. The interludes to advance the story were also well done. Though some fiction was employed, this is a very well developed thumb-nail sketch of Russell and his life until the start of World War II. The inclusion of others active in the fields of logic, mathematics and philosophy helped to display both those who influenced Russell and those whose works were influenced by him. I was fortunate to have 'discovered' Russell, through his "History of Western Philosophy", while he was still alive (he died in 1970). Though his appearances on television were few, it was always fascinating to see anything by him or about him. Having this book develop through one of his public appearances was a clever touch that worked well. Like most, I didn't agree with him on everything, and I certainly didn't understand a lot that he wrote. I did, though, recognize genius, and the haggling was over the details. Both his professional life and personal life were filled with controversy. He was one of those who could be described as "bigger than life". Though few today may even recognize his name, he had a significant influence in the first half of the twentieth century; and an impact on thought that continues to today. If you have an interest in logic, math or philosophy, this is an excellent introduction to a fascinating man and his work. If not, you will probably not like this book. While it doesn't require in-depth knowledge (much is explained), some familiarity with the subject will add to your enjoyment. This was an impressive method of presenting this material. Hopefully, the creators will do more in the same manner.