Wednesday, August 12, 2009

A journey with the good Lord

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A lively Ludwig Wittgenstein tries to gently persuade Bertrand Russell of the veracity of his ideas in "Logicomix: An Epic Search for Truth"

In the autumn of 1939, as the world in its tormented restlessness perched on the edge of conflict, a tall, lanky man was slowly making his way towards the steps of a prominent American university, his ubiquitous pipe in hand. His face was one of the most recognizable in the world, his mind among the most respected minds of his time. He was slated to give a talk at this august institution, and as he approached he was accosted by protestors who pleaded to him to not give his talk and instead join them in their pacifist protests. Only two decades back the gentleman had been a famously eloquent pacifist, spending time in prison during World War 1 after invoking the ire of his countrymen. Now he hesitated for a moment, and then told the protestors that he would be happy to take up their cause, but only if they first attended his talk, a talk on the role of logic in human affairs.

Such begins "Logicomix: An Epic Search for Truth", a remarkable, unique and highly original graphic novel about Bertrand Russell and the foundations of mathematics. Who would have thought that something as profound and deep as the search for certainty in that most crystalline of human endeavors could be turned into a comic book. And yet Berkeley computer scientist Christos H. Papadimitriou and artist and author Apostolos Doxiadis have achieved this feat. Logicomix traces the history of the foundations of mathematics through the extraordinary life of perhaps its most famous and colorful proponent. The history of the foundations of mathematics is one of the most fascinating expositions of human thought in history, partly because it is the epitome of that ultimate human desire, a search for certainty in a world full of changes of fortune. The field itself is as old as the Greeks, but one would be hard pressed to find anyone else other than Lord Russell who witnessed so much development in the field, and who through his long and eventful life contributed so much to it. I thought that Logicomix, deftly making use of the modern medium of the comic book, provides the best introduction to the foundation of mathematics and its most famous philosopher that I have come across.

The comic book traces the foundations of mathematics through the life of Russell and begins with Russell retelling the story of his life to an audience in America on the eve of the Second World War. Russell's journey toward truth began as a child with a remarkable stay at Pembroke Lodge, where his grandfather, a past Prime Minister of Great Britain, held court with his puritanical and strict grandmother. The amiable and docile grandfather was stark contrast to his wife; sadly he did not live long enough to shield young Bertie from his overbearing grandmother. Privately schooling him at home through hand-picked teachers and drumming Bible lessons into his head, the grandmother actively tried to stifle every inquiry by Russell about his parents, which Russell later found was because of their rather scandalous lifestyle involving a three-way relationship which elicited howls in Victorian England. To escape from his grandmother Russell sought refuge in logic and mathematics. An inspiring teacher introduced Bertie to Euclid's theorems, and the airtight logic inherent in the structure of geometry took hold of Russell's mind like a spirit.

This refuge quickly turned into an all-consuming quest to find absolute certainty in an uncertain world. Russell became utterly fascinated by the fact that different "infinities" could be compared (as did I when I first read George Gamow's "One, two, three, infinity"). Logicomix has him visiting the great mathematicians Gottlob Frege and Georg Cantor who were responsible for crucial developments in the field. Mulling over their work in set theory and logic and inspired by Leibniz, Russell came up with Russell's paradox, a wondrous construct which haunted him to no end and further fueled his intense desire to end contradiction in mathematics. As a student at Cambridge Russell came in contact with Alfred North Whitehead. The result of his friendship and collaboration with Whitehead was one of the most famous works ever produced in the history of human thought, the Principia Mathematica, a book which Russell toiled over like a madman and which used 362 pages to prove 1 + 1 = 2. The book was partly a result of Russell listening to a talk by David Hilbert at the turn of the century in which Hilbert posed 23 famous unsolved fundamental problems in mathematics. Perhaps the loftiest goal advanced by Hilbert was to make mathematics completely self-consistent, so that there would be absolutely no contradiction and paradox and the entire grand edifice would follow precisely and logically from a few axioms. During the process Russell married and also fell for Whitehead's wife. Throughout his life Russell was an impetuous man, and like many other deep thinkers was often cruel and indifferent to his spouses and family.

The tome that Russell and Whitehead laboriously produced was so dense that nobody could critique it, and the two had to embarrassingly publish it themselves. To this day it is doubtful whether more than a handful have digested its contents; one person who Russell was convinced was the only person he had met who had read the work, was to prove his undoing. After this monumental work Russell felt a little burnt out and, as the drums of war sounded in Europe, took refuge again in pure thought and contemplation. He also became interested in social activism. He spoke against the war and went to jail for his protests. He decided on a bicycle ride that he no longer wanted to live with his wife. His greatest discovery however was yet to come.

Just before World War 1 a young man walked into his rooms at Cambridge. Ludwig Wittgenstein had an intensity and interest in philosophy that bordered on madness. A singular character of the twentieth century who gave away all his great wealth, deliberately asked to go to the front, and composed his greatest work lying in the trenches of the Great War, Wittgenstein saw the essence of philosophy and our perception of our world lying in language. With his arrival Russell started a new chapter in his life, but his admiration and buoyant enthusiasm for his disciple soon turned to chagrin when Wittgenstein who would never mince words started telling him that the entire basis of his Principia Mathematica was flawed. Deeply shaken, Russell emerged from the war more of a writer and a public intellectual, with his best years behind him

He still commanded respect of the highest degree, and was the patron saint of the famous Vienna Circle of the 1930s, whose philosophy of logical positivism strove to put the entire world into the constraints of science, and whose luminaries included Moritz Schlick, John von Neumann, and for a time as a sort of external admirer, Karl Popper. However, it was a diffident young member of the circle who was to signal the coup de grace for Bertrand Russell. In 1932, Austrian logician Kurt Gödel produced what is perhaps the single most profound and remarkable idea of the twentieth century, and perhaps of the entire history of intellectual thought. Gödel showed that even arithmetic, the basis of all mathematics and everything that follows, that purest of pure constructs, is essentially full of unprovable statements and paradoxes; it is essentially an incomplete system. Gödel's Incompleteness Theorem dealt a death knell to hundreds of years of fond hope that mathematics could be put on a complete, secure and logically perfectly consistent foundation. Along with Heisenberg's uncertainty principle and Einstein's principle of relativity, it signaled the end of certainty for human beings. In one fell swoop Gödel dashed the hopes of Hilbert, Russell and countless others away to oblivion. Right after Godel's talk, the famous polymath von Neumann simply said "It's over"; a more literal interpretation of the phrase has rarely been expressed in history. Godel's talk signaled the most significant break in Russell's life. After this, he never produced a single significant work in mathematics and spent the rest of his life campaigning against war and nuclear weapons, pontificating on everything from happiness to Christianity to marriage, writing best-selling books on all these topics, and becoming a signature symbol of the rational life for countless in the world. He remains one of the most important intellectuals in history.

So how is all of this captured in a comic book? The answer is, most impressively. There are moving passages where Russell literally goes insane trying to search for certainty in mathematics. The book also explores the troubling connection between genius and insanity, and especially between mathematical genius and insanity. Consider the evidence; Russell's son descended into schizophrenia and his brother committed suicide, Russell himself constantly worried that he was descending into madness in the great toil of his labors, Wittgenstein was nothing short of bona fide crazy and so was Georg Cantor, Gödel became so paranoid toward the end of his life in Princeton that he starved himself to death, convinced that the doctors were trying to poison him through his food. All these men were also acknowledged geniuses. Perhaps it is not a coincidence that John Nash, after he won the Nobel Prize, indicated that there was a deep connection somewhere between his schizophrenia and his remarkable mathematical achievements, accurately observing that neuroses and genius have been commonly connected with each other throughout history; according to Nash there might even be a necessary condition between genius and what we may perceive as irrational obsession.
"...rationality of thought imposes a limit on a person's concept of his relation to the cosmos. For example, a non-Zoroastrian could think of Zarathustra as simply a madman who led millions of naive followers to adopt a cult of ritual fire worship. But without his "madness" Zarathustra would necessarily have been only another of the millions or billions of human individuals who have lived and then been forgotten
Perhaps there is indeed a price that one pays for daring to soar into the highest heights of abstract human thought.

Logicomix explores this troubling association. The illustrations in it are endearing, although they could perhaps have been better (I was reminded of the marvelous artwork in "Watchmen"). Also importantly, although almost all the characters and events are real, their placement and chronology is often fictional. For instance Russell never actually met Hilbert, nor did he attend the devastating talk by Gödel. Plus, some of the dialogue is rather unlikely; for instance did Wittgenstein really call Hilbert a "bloody ass"? The book also perhaps lacked the kind of depth that I expected at first, but then it is geared toward a popular audience after all, and concepts like Russell's paradox, countable and uncountable infinity and Gödel's theorems are difficult for laymen to understand even when simplified. Nonetheless, these are minor quibbles which don't detract from the uniqueness and substance in the book.

Keeping true to its emphasis on logic, the book follows a recursive self-referential kind of theme and cycles between two stories. The major story is of Bertrand Russell and the foundations of mathematics, and the side story is the story of the writers planning the book. Both authors are Greek and their story takes a stroll, both literally and figuratively, through the scenic gardens of Athens and through the great plays of Sophocles and Aeschylus. The writers' and artists' story is interspersed with the main story line, even as they grapple with the concepts and their presentation.

The book ends with the artists and writers attending a performance of Aeschylus's The Eumenides in the great Acropolis of Athens. Aeschylus's play extolled logic and reason, qualities that Russell and many of the book's protagonists held dearer than life. In the end, logic and reason are not enough. But they are candles in the dark, threads of Ariadne, ephemeral wisps of the human mind that keep us from wandering too far from the straight line. For this we can be grateful to the men who spent their lives struggling for certainty, and we can continue to join them in their quest.

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Blogger Harmanjit Singh said...

You (or perhaps the comic book as well) didn't emphasize enough the contribution of Wittgenstein, who reduced mathematics to a set of tautologies which could not in itself reveal any facts about the world.

This was a greater blow to Russell than that of Godel. Godel showed that any aximaotic system which is consistent and sufficiently powerful would have to be incomplete, but Wittgenstein made a more devastating critique of Russell by pointing at logic and mathematics as primarily symbol manipulation.

As for Russell being pulverized by these discoveries, Ray Monk in his two-volume biography, and especially in vol 2 (The Ghost of Madness) of Russell points to certain other motivations for his politicking and activism than his logical Waterloos.

12:07 AM  
Blogger Vivek Gupta said...

Great article! Just what a man needs during another boring afternoon in the corporate prison. Did you pick up the book in Strand? It is an awesome place indeed. Since you live so close to the city, why don't we get acquainted. Give me a call at 404-368-5192 when you are in the City or Jersey city.

12:01 PM  
Blogger Wavefunction said...

Harmanjit: The book indeed does not dwell too much on Wittgenstein which it should have. I personally consider Godel's achievement as more devastating and profound, if for no other reason than because it was grounded in much more rigorous mathematics.
I still have to read Monk's magisterial Russell bio.

Vivek: Thanks, and tell me about a boring afternoon in the corporate world! I would be happy to meet up and am reachable at 908-231-5837 and by email at

5:26 PM  
Blogger Harmanjit Singh said...

Hi Ashutosh:

Godel's achievement is stunning and utterly remarkable, but ultimately, of theoretical interest. And to be sure, it is much, much, cleverer than what W did.

However, Wittgenstein's work has a wider and deeper implication as it deals with real world use of language and symbols.

But anyhow, great article. Keep 'em coming.

6:39 PM  
Blogger Wavefunction said...

Thanks, and you are right. Wittgenstein's work is quite special and incidentally I picked up Ray Monk's "How To Read Wittgenstein" yesterday. So far it looks really good.

8:58 PM  

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