Reflections on Jim Holt's When Einstein Walked With Godel: Excursions to the Edge of Thought

When Einstein Walked with Godel: Excursions to the Edge of Thought is a collection of 24 full length essays plus several shorter pieces written by Jim Holt, the author of the thought-provoking 2013 book Why Does the World Exist? Holt discusses a wide range of subjects that relate to at least one of three categories: "our most general conception of the world (metaphysics), how we come to obtain and justify our knowledge (epistemology), and even on how we conduct our lives (ethics)" (p. x). 

When Einstein Walked with Godel: Excursions to the Edge of Thought is a fascinating book. I will not review each essay, but I will single out a few of my favorites to whet your appetite to read them all.

The book begins with the title essay. It is a fun fact that two of the greatest geniuses of all-time regularly took walks together, and it is touching that Einstein once said that he went to his office at the Institute for Advanced Study "just to have the privilege of walking home with Kurt Godel." I don't take Einstein's statement as false modesty--like most, if not all, geniuses, Einstein was quite aware of his capabilities--but rather as a genuine statement of affection and admiration for his friend Godel. 

Einstein and Godel were not only geniuses but also--regardless of the fame and acclaim that both received--outsiders. Holt notes that after Einstein initially failed to receive his doctorate in physics he gave up on pursuing an academic career, declaring "the whole comedy has become boring." Einstein worked as a patent clerk, but he followed closely the scientific questions of the time, and he read with interest about what Henri Poincare termed the three greatest unsolved questions: (1) the photoelectric effect, (2) Brownian motion, and (3) the nature of the "luminiferous ether" which had yet to be detected experimentally but was supposed to be the medium through which light waves traveled. Holt explains, "Working alone, apart from the scientific community, the unknown junior clerk rapidly managed to dispatch all three" questions in a series of papers published in 1905, when Einstein was just 26 years old (p. 5). Einstein received the 1921 Nobel Prize in physics for his work on the photoelectric effect, but his equation E=MC² forever transformed our understanding of space, time, and energy.

Einstein had already finished most of the work for which he would be most remembered prior to Godel's birth: "In 1906, the year after Einstein's annus mirabilis, Kurt Godel was born in the city of Brno (now in the Czech Republic). Kurt was both an inquisitive child--his parents and brother gave him the nickname Herr Warum, 'Mr Why?'--and a nervous one. At the age of five, he seems to have suffered a mild anxiety neurosis. At eight, he had a terrible bout of rheumatic fever, which left him with the lifelong conviction that his heart had been fatally damaged" (p. 8).

Godel developed two incompleteness theorems that had profound implications for mathematics and epistemology. The first incompleteness theorem is that no logical system can capture all the truths of mathematics; within any mathematical system there will always be at least one statement that cannot be proven or disproven within that system. The second incompleteness theorem is that no mathematical system can be proven, within its own devices, to be free from inconsistency. When Godel first presented his theorems, few people understood them, and some of the people who understood vigorously objected because they disliked the implications about the nature and limitations of knowledge.

The nature of time is one of the subjects that Einstein and Godel discussed. For Einstein's 70th birthday, Godel presented to him a gift: a solution to Einstein's General Relativity equations demonstrating the theoretical possibility of time travel in a rotating universe. Einstein did not like the idea of a rotating universe in which time travel is possible, but he found no flaws in Godel's math. Holt notes that Godel presented the solution as proof that, in Holt's words, "time itself is impossible. A past that can be revisited has not really passed. And the fact that the universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undetermined in every possible universe, including our own" (p. 13).

The unanswered and perhaps unanswerable question is that if time is impossible then why do we feel its passage so intensely and so vividly? That question leads to other unanswered and perhaps unanswerable questions. Is everything that we consider to be real and to be meaningful an illusion, or a collective delusion/hallucination? If so, what is the purpose of such a grand deception?

Einstein and Godel could not answer those questions, but that did not stop them from walking, talking, and thinking together.

"The Riemann Zeta Conjecture and the Laughter of the Primes" begins with a discussion of the "Copernican Principle": the "Copernican Principle," first formalized as a mathematical equation by astrophysicist J. Richard Gott III in 1993, postulates that at any given time we are not privileged observers of an event, which in simple terms means that when you see something you are not in the first 2.5% of observers and you are not in the final 2.5% of observers. In other words (to borrow Holt's example from pp. 36-37), if you are attending a play that has had n showings then there is a 95% chance that the play will have no more than 39 x n showings and a 95% chance that the play will have no fewer than n/39 showings. Something that has already existed for a long time is statistically more likely to continue to exist for a long time than something that has only existed for a short time.  

Holt demonstrates that laughter and numbers are things that we share with species who have a common ancestor with us several million years ago. Since laughter and numbers have already existed for millions of years, based on the "Copernican Principle" it is more likely than not that laughter and numbers will exist one million years from now. 

What is the Riemann Zeta Conjecture and what does it have to do with any of this? The Riemann Zeta Conjecture is a hypothesis about prime numbers. If Bernhard Riemann was correct, then prime numbers have a hidden harmony, but if he was not correct then the provisional proofs of thousands of theorems "conditioned" on the correctness of his conjecture will be falsified and, as Holt puts it, "the part of higher mathematics that is built upon it will collapse" (p. 43). In layman's terms, the distribution of prime numbers seems at first sight to be random, but Riemann suggested that when one considers the full (i.e., infinite) set of prime numbers then order emerges from what looks to be chaos. The Riemann Zeta Conjecture has been one of the great unsolved math problems for more than 160 years. Applying the Copernican Principle, Holt suggests that there is a 95% chance that it will be solved within the next six millenia. Holt further argues that once the secret of prime numbers is understood then mathematics will be revealed to be, as Bertrand Russell proposed, "as trivial as the statement that a four-footed animal is an animal." Or, put another way, Holt believes that laughter has a better chance of being an integral part of human existence a million years from now that mathematics does. One could object that his opinion is based too much on speculation, but if you read the entire chapter you will be intrigued even if you remain skeptical.

In "Benoit Mandelbrot and the Discovery of Fractals," Holt, in his typical engaging style, describes Mandelbrot's eventful life, and Mandelbrot's inquisitive spirit that enabled him to find order where others saw only disorder and chaos. Benoit Mandelbrot discovered the Mandelbrot set, and demonstrated that things that had been thought to be rough or chaotic--such as clouds and shorelines--actually have a "degree of order." Mandelbrot coined the word "fractal" (derived from the Latin word for broken) to describe self-similar forms, phenomena that are visible not only in physical objects such as clouds and shorelines but also in the behavior of financial markets. Orthodox thinkers in both mathematics and economics bristled at Mandelbrot's ideas but Mandelbrot was stubborn and undeterred.

Academic tenure eluded Mandelbrot--or he eluded it--until he was 75, but his unorthodox way of thinking about mathematics found a home for many years at, of all places, IBM; for a lengthy period of time, the computer manufacturing giant decided to fund pure research. "We can easily afford a few great scientists during their own thing," the director of research told Mandelbrot (p. 98), and those words were music to Mandelbrot's ears. He worked for IBM from the late 1950s until 1987, when IBM decided it no longer wanted to pay great scientists to do their own thing. Six years later, IBM posted $8 billion in losses, at the time the largest such total in U.S. corporate history. Did IBM stop funding geniuses because it ran out of money, or did it run out of money because it stopped funding geniuses?

Fractals are not only beautiful to observe, but they exist at the nexus of science, math, and art. Here is an example of a fractal:

"The Ada Perplex: Was Byron's Daughter The First Coder?" methodically debunks attempts to elevate Lord Byron's daughter Ava from a person who struggled to learn basic mathematics to someone who supposedly was a pioneering scientific figure. It is important to give proper credit to anyone--man or woman--whose accomplishments merit recognition, but it is dishonest and harmful to rewrite history for the purpose of heaping honor on an individual who is not worthy of such recognition. Holt's effort to set the record straight is important, and hopefully will not only result in a widespread reassessment of Lord Byron's daughter but also inspire a thorough and thoughtful examination of other historical figures who are given too much--or too little--credit.

Holt's curiosity, smooth writing style, and active engagement with any subject that he tackles would probably enable him to communicate engagingly even about uninteresting subject matter, but it is a treat to read his writing about the fascinating subjects briefly described above, as well as the other topics addressed in When Einstein Walked with Godel: Excursions to the Edge of Thought.

Further Reading:

Albert Einstein the Man (December 13, 2015)

Kurt Godel: Mathematician/Philosopher Extraordinaire (August 25, 2016)

Jews, "White Privilege," and Antisemitism

Jews are often not properly acknowledged as a persecuted minority but rather accused of being beneficiaries of "white privilege." The reality is that white supremacists do not classify Jews as white people, and they hate Jews just as much as they hate people of color. 

In Rare Einstein Letter Shows ‘Extreme Anti-Semitism’ in 1930s America, quotes from a letter that Albert Einstein wrote during the 1930s demonstrate how precarious the position of Jewish people was in the United States at that time: "A tremendous degree of anti-Semitism exists here, especially in academia (though also in industry and banking). Mind you, it never takes the form of brutal speech or action, but simmers all the more intensely under the surface. It is, so to speak, an omnipresent enemy, one that is impossible to see, and whose presence you only perceive."

The significant rise in antisemitic violence recently both in the United States and around the world refutes the notion that Jews enjoy some kind of special and protected position; indeed, the truth is that the Jews are a small and vulnerable minority, consisting of less than three percent of the United States' population and a much, much smaller percentage of the world's population. 

It is often stated that the success of individual people of color does not prove that racism is dead, and if you buy that premise then the same premise is also true regarding the success of individual Jews not proving that antisemitism is dead. 

Why do these facts and distinctions matter? They matter because the same people who wrongly assert that Jews benefit from "white privilege" also create and disseminate false narratives about Israel.

Why has it become so prevalent for self-proclaimed "progressives" to label Jews not as a persecuted minority but rather as beneficiaries of "white privilege"? The simplest explanation is the best and most accurate: antisemitism is not only widespread among self-proclaimed "progressives" but in many ways it is inextricably connected to their ideological goals. Why else do marches organized by self-proclaimed "progressives" that have nothing to do with Jews or Israel inevitably feature antisemitic and anti-Zionist rhetoric? 

The success of the Jewish people in quickly transforming their desolate homeland into a regional economic and technological powerhouse induces a lot of fear and shame among groups and nations that have not been similarly successful. It is far easier to accuse Jews and Israel of being beneficiaries of "white privilege" than to recognize the evils that have been committed against Jews and to acknowledge Israel's remarkable triumphs against incredible odds. Israel has the same climate and fewer natural resources (most notably oil) than her neighbors, yet Israel is a thriving democracy with a strong economy while her neighbors are mired in autocracy and economic stagnation. It is absurd to assert that Israel is a product of "white privilege," but other explanations for Israel's success do not fit the preferred narratives of self-proclaimed "progressives." It is worth noting that Asian-Americans face similar targeting by self-proclaimed "progressives" who seek special privileges for certain groups while insisting that Asian-Americans should be treated as if they are members of the white majority.

"The Little Zen Companion"

The Little Zen Companion is a 1994 anthology compiled by David Schiller containing over 300 quotations. In the Introduction, Schiller explains, "This book doesn't presume to define Zen, but instead to offer a taste of Zen's way of looking at the world: where the best moment is now, where things are what they seem to be, where we see with the refreshing directness of a child and not through eyes grown stale from routine." The quotations are not all by Zen masters and many do not even explicitly pertain to Zen, but they all provoke thought about what it means to be human, and how to strive toward living in the now as opposed to dwelling on what was or what might never be.

Here are a few quotations that resonated deeply with me; in some instances, I have added my own brief comments (in italics, after the pertinent quotation):

• "In the beginner's mind there are many possibilities, but in the expert's mind there are few." Shunryu Suzuki. Studies have shown that the best chess players look at fewer moves than weaker players, but the best players look at those moves more deeply and more accurately. The expert chess player understands that there are only a few optimal ways--and, sometimes, only one optimal way--to play a given position. 
• "Before a person studies Zen, mountains are mountains, and waters are waters; after a first glimpse into the truth of Zen, mountains are no longer mountains and waters are not waters; after enlightenment, mountains are once again mountains and waters once again waters." Zen saying.
• "Ring the bells that can still ring. Forget your perfect offering. There is a crack in everything. That's how the light gets in." Leonard Cohen.
• "The raindrops patter on the basho leaf, but these are not tears of grief; this is only the anguish of him who is listening to them." Zen saying.
• "If you seek, how is that different from pursuing sound and form? If you don't seek, how are you different from earth, wood, or stone? You must seek without seeking." Wu-men.
• "Where do we come from? What are we? Where are we going?" Gauguin, inscription on one of his paintings. This quotation reminds me of Prince's song "The Ladder," which has the following lyrics: 
  "Everybody's looking for the answers
  How the story started and how it will end
  What's the use in half a story, half a dream
  You have to climb all of the steps in between (yeah, we ride)
  Everybody's looking for the ladder
  Everybody wants salvation of the soul
  The steps you take are no easy road
  But the reward is great
  For those who want to go (I do)" 
  
• "In walking, just walk. In sitting, just sit. Above all, don't wobble. " Yun-men.
• "If you wish to drown, do not torture yourself with shallow water." Bulgarian saying. After breaking Joe Theismann's leg during a tackle on Monday Night Football, Lawrence Taylor visited Theismann in the hospital. "Did you know you broke my leg in two places?" Theismann asked. "I never do anything halfway," Taylor replied. For better or worse, halfway is nowhere; commit 100% to an action, or don't take action at all. This also brings to mind Sheriff Buck's conversation on "American Gothic" with the bungling criminal he dismissed as "Half-Ted"; Buck declared that if "Half-Ted" were a real criminal he would have killed all witnesses and escaped and if he were not a criminal at all then he would have never ended up in that particular predicament, so he was not really Ted but just "Half-Ted."
• "One cannot step twice into the same river." Herakleitos.
• "To set up what you like against what you dislike--this is the disease of the mind." Seng-T'San.
• "How shall I grasp it? Do not grasp it. That which remains when there is no more grasping is the Self." Panchadasi.
• "In dwelling, live close to the ground. In thinking, keep to the simple. In conflict, be fair and generous. In governing, don't try to control. In work, do what you enjoy. In family life, be completely present." Tao Te Ching.
• "When hungry, eat your rice; when tired, close your eyes. Fools may laugh at me, but wise men will know what I mean." Lin-Chi.
• "Sit, rest, work. Alone with yourself, never weary. On the edge of the forest, live joyfully, without desire." The Buddha.
• "This is what you shall do: Love the earth and sun and the animals, despise riches, give alms to everyone that asks, stand up for the stupid and crazy, devote your income and labor to others, hate tyrants, argue not concerning God..." Walt Whitman.
• "Barn's burnt down--now I can see the Moon." Masahide. The ability to see hope in crisis and the faith/optimism to look to the future with confidence represent a very rare and special form of grace.
• "We walk, and our religion is shown (even to the dullest and most insensitive person) in how we walk. Or to put it more accurately, living in this world means choosing, choosing to walk, and the way we choose to walk is infallibly and perfectly expressed in the walk itself. Nothing can disguise it. The walk of an ordinary man and of an enlightened man are as different as that of a snake and a giraffe." R. H. Blyth.
• "Things derive their being and nature by mutual dependence and are nothing in themselves." Nagarjuna, second century Buddhist philosopher.
• "An elementary particle is not an independently existing, unanalyzable entity. It is, in essence, a set of relationships that reach outward to other things." H.P. Stapp, twentieth century physicist. 
• "The most terrifying thing is to accept oneself completely." Carl Jung.
• "If you gaze for long into the abyss, the abyss also gazes into you." Nietzsche.
• "He who knows others is wise. He who knows himself is enlightened." Tao Te Ching.
• "1. Out of clutter, find simplicity. 2. From discord, find harmony. 3. In the middle of difficulty lies opportunity." Albert Einstein, three rules of work. 
• "If you study Japanese art, you see a man who is undoubtedly wise, philosophic, and intelligent, who spends his time how? In studying the distance between the earth and the moon? No. In studying the policy of Bismarck? No. He studies a single blade of grass. But this blade of grass leads him to draw every plant and then the seasons, the wide aspects of the countryside, then animals, then the human figure. So he passes his life, and life is too short to do the whole." Vincent Van Gogh. Van Gogh is speaking the truth that an artist's greatness is not only in his hands but also in his eyes, and his mind's eye--in his ability to truly see, and to intensely focus with a calm gaze.

Kurt Godel: Mathematician/Philosopher Extraordinaire

If you have heard the name Kurt Godel at all, you probably heard it in connection with Douglas Hofstadter's masterful (and massive) Gödel, Escher, Bach: An Eternal Golden Braid. Unless you read and remember the contents of that more than 30 year old book, you probably have no idea who Godel was and why his work is so significant.

John W. Dawson's article Godel and the Limits of Logic provides a sensitive and perceptive glimpse at the accomplishments and inner life of one of the most eminent mathematicians of all time. Dawson explains that Godel was a Platonist: "he believed that in addition to objects, there exists a world of concepts to which humans have access by intuition. For Plato, who lived around 400 BC, concepts such as truth were not products of the human mind which can change according to the thinker's point of view, as some philosophers believe, but existed independently of the human observer. Thus, a statement could have a definite 'truth value'--be true or not--whether or not it had been proved or could be empirically confirmed or refuted by humans. Gödel subscribed to this philosophy, and, in his own view, this was an aid to his remarkable mathematical insights."

Mental illness plagued Godel for much of his life and ultimately led to his untimely demise but Godel nevertheless made an indelible impact on mathematics, logic and philosophy. Dawson declares:

Gödel proved that the mathematical methods in place since the time of Euclid (around 300 BC) were inadequate for discovering all that is true about the natural numbers. His discovery undercut the foundations on which mathematics had been built up to the 20th century, stimulated thinkers to seek alternatives and generated a lively philosophical debate about the nature of truth. Gödel's innovative techniques, which could readily be applied to algorithms for computations, also laid the foundation for modern computer science...

Although Gödel's work irrefutably proves that "undecidable" statements do exist within number theory, not many examples of such statements have been found. One example comes from the sentence:

This statement is unprovable
You can see why this is a prime candidate: if you could prove this statement to be true, then it would be false! It is true only if it is unprovable, and unprovable only if it is true. As it stands, this is not a statement about the natural numbers. But Gödel had devised an ingenious way to assign numbers to English-language phrases like this one, so that finding whether the statement is true or not translates to solving numerical equations. He proved that, within the axioms of number theory, it is impossible to prove whether or not the equation corresponding to the sentence above holds true, thus confirming our "common-sense" analysis.

In a similar way, Gödel translated the statement

The axioms of this theory do not contradict each other
into numerical code, and again proved that the translation is unprovable. Any proof that the axioms do not contradict each other--that they are consistent-- must therefore appeal to stronger principles than the axioms themselves. 

The latter result greatly dismayed David Hilbert, who had envisioned a program for securing the foundations of mathematics through a "bootstrapping" process, by which the consistency of complex mathematical theories could be derived from that of simpler, more evident theories. Gödel, on the other hand, saw his incompleteness theorems not as demonstrating the inadequacy of the axiomatic method but as showing that the derivation of theorems cannot be completely mechanized. He believed they justified the role of intuition in mathematical research.

The concepts and methods Gödel introduced in his incompleteness paper are central to all of modern computer science. This is not surprising, since computers are forced to use logical rules mechanically without recourse to intuition or a "birds-eye view" that allows them to see the systems they are using from the outside. Extensions of Gödel's ideas have allowed the derivation of several results about the limits of computational procedures. One is the unsolvability of the halting problem. If you have ever written a computer program, you will know that a programming mistake can cause it to enter an infinite loop: it will run forever and never end. The question is if there can be an algorithm that can examine any computer program and decide whether it will eventually halt or whether it will keep running forever. This is the halting problem and the answer is "no."

Another result that derives from Gödel's ideas is the demonstration that no program that does not alter a computer's operating system can detect all programs that do. In other words, no program can find all the viruses on your computer, unless it interferes with and alters the operating system.

Godel's concepts have wide-ranging implications not only for mathematics, physics and computer science but also for philosophy and metaphysics. David Goodman, writing in First Things, describes Godel's impact as both a mathematician and someone who thought seriously about theological matters:

Kurt Gödel was a believer--or, at least, a knower--whose engagement with God included a reworking of the ontological proof of God’s existence. Born in 1906, Gödel was arguably the great mathematician of his time. Certainly no twentieth-century thinker did more to show that the human mind cannot be reduced to a machine. At twenty-five he ruined the positivist hope of making mathematics into a self-contained formal system with his incompleteness theorems, implying, as he noted, that machines never will be able to think, and computer algorithms never will replace intuition. To Gödel this implies that we cannot give a credible account of reality without God. But Gödel’s God is not the well-behaved deity of the old natural theology, or the happy harmonizer of the intelligent-design subculture. Gödel’s God hides his countenance and can be glimpsed only in paradox and intuition. God is not an abstraction but “can act as a person,” as Gödel once wrote, confronting those who seek him with paradox, uplifting man through glorious insights while guarding his infinitude from human grasp. Gödel’s investigations in number theory and general relativity suggest a similar theological result: that God cannot be reduced to a mere principle of the natural world. Gödel may have seen himself as a successor to Leibniz, whose critique of Spinoza’s atheism set a precedent for much of Gödel’s work.

Rebecca Goldstein's book-length biography Incompleteness: The Proof and Paradox of Kurt Godel further explains Godel's significance: "This man's theorem is the third leg, together with Heisenberg's uncertainty principle and Einstein's relativity, of that tripod of theoretical cataclysms that have been felt to force disturbances deep down in the foundations of the 'exact sciences.' The three discoveries appear to deliver us into an unfamiliar world, one so at odds with our previous assumptions and intuitions that, nearly a century on, we are still struggling to make out where, exactly, we have landed" (p. 22).

Positivists and postmodernists cite Albert Einstein, Kurt Godel and Werner Heisenberg as three figures who destroyed the concept of objective reality but Einstein and Godel rejected this interpretation of their work. In Goldstein's words, "Einstein interpreted his theory as representing the objective nature of space-time, so very different from our human, subjective point of view of space and time" (p. 42). Similarly, Godel's "commitment to the objective existence of mathematical reality is the view known as conceptual, or mathematical, realism. It is also known as mathematical Platonism, in honor of the ancient Greek philosopher whose own metaphysics was a vehement rejection of the Sophist Protagoras' 'man is the measure of all things'" (p. 44). In layman's terms, "For Godel mathematics is a means of unveiling the features of objective mathematical reality, just as for Einstein physics is a means of unveiling aspects of objective physical reality" (p. 45). Einstein and Godel did not believe that they had thrown the world into chaos but rather that they had used their intellect to decipher the true nature of, respectively, space-time and mathematical reality.

Godel was a member of the famous Vienna Circle of intellectuals who regularly met in the 1920s and 1930s but most of the Vienna Circle's members believed in logical positivism while Godel was a Platonist. However, Godel rarely spoke during these meetings and he was one of the younger members of the group, so it appears that the other members did not even realize that Godel opposed their views. Godel first presented his revolutionary Incompleteness Theorem during a 20 minute talk on "Epistemology of the Exact Sciences" during the second day of a scientific conference in Konigsberg. Godel's work was later described as an "amazing intellectual symphony" but because of his mild-mannered presentation and because of the complexity of his ideas it was not immediately apparent even to the esteemed attendees of this conference that Godel had accomplished something monumental.

On the third day of the conference, Godel summarized the meaning of his Incompleteness Theorem: "One can (assuming the [formal] consistency of classical mathematics) even give examples of propositions (and indeed of such a type as Goldbach and Fermat) which are really contextually [materially] true but unprovable in the formal system of classical mathematics." Goldstein describes this sentence as "meticulously crafted, a miniature masterpiece" (p. 157) but adds, "Godel was always disappointed by the abilities of others to draw the implications he had scrupulously prepared for them, and his experience at Konigsberg must have been a magnificent disappointment, for the response was a resounding silence."

The only person present who grasped the implications of what Godel had said was another towering genius, John von Neumann. Von Neumann spoke with Godel afterwards and Von Neumann later informed Godel--who was then still finishing his doctoral studies--that the implication of what Godel had said was that it is impossible to formally prove the consistency of a system of arithmetic within that system of arithmetic. Godel drily replied that not only did he realize this but he had already drafted the mathematical proof of it (this is known as Godel's second Incompleteness Theorem).

After Godel emigrated to the United States, he shared a close friendship with Einstein, despite being separated in age by nearly 30 years. Einstein so enjoyed their daily walks together on the grounds of the Institute of Advanced Study that toward the end of Einstein's life he told the economist Oskar Morgenstern that his own work did not matter much anymore but he came to the Institute primarily for the privilege of walking alongside Godel each day. Einstein was an outgoing, mentally stable (though highly unconventional) person, while Godel was introverted and battled mental illness throughout his life but they shared in common immense genius and insatiable curiosity: Einstein once said, "The most important thing is to not stop questioning," while Godel was known as "Mr. Why" when he was a child because he constantly asked questions.

In A World Without Time: The Forgotten Legacy of Godel and Einstein, Palle Yourgrau notes that Godel provided a mathematical solution for Einstein's General Theory of Relativity that demonstrated that in a relativistic universe time travel is theoretically possible. If Godel is correct, then this means that time does not exist, at least not in the linear way that we humans subjectively perceive it, because what is past is not actually past.

Yourgrau laments that mathematicians and physicists have essentially ignored or dismissed Godel's solution even though no one has found any flaw with Godel's math; Einstein disliked the idea that time travel might be possible but he could find no mistakes in Godel's calculations and Einstein admitted that "the problem here involved disturbed me at the time of the building up of the general theory of relativity."

Einstein further stated, "Kurt Godel's essay constitutes, in my opinion, an important contribution to the general theory of relativity, especially to the analysis of the concept of time." However, Einstein questioned whether Godel's model was physically plausible even though it was mathematically and conceptually sound; Godel's theoretical universe rotates and for the remainder of his life after he proposed this solution Godel had a keen interest in whether or not our universe rotates (to this day, astrophysical observations have neither confirmed nor refuted the possibility that our universe may in fact conform to Godel's hypothetical model).

In his younger days, Einstein had questioned other interpretations of general relativity--including the possibility that black holes exist and the possibility that the universe is expanding--on the grounds of being physically implausible only to later be proven wrong. Godel's relentless logic led Godel inexorably to the conclusion that if time does not exist in a theoretically possible universe (such as the rotating universe postulated in his solution to Einstein's General Relativity equations) then it stands to reason that time does not exist in any universe to which General Relativity applies. Physicists and philosophers have mocked Godel's concept for decades but have yet to actually disprove it. We humans subjectively perceive the passage of time but that does not mean that our subjective perception is accurate; Einstein's theory accurately predicted that time passes more slowly as an object is accelerated and thus there is not one universal "now" but rather only various frames of reference, so Godel's suggestion that the passage of time is an illusion is perhaps not so radical a notion as it seems (though, if correct, it does raise an interesting philosophical or perhaps theological question of why our brains are designed/have evolved to believe in the passage of time if the passage of time is actually illusory).

The Einstein-Godel friendship survived any disagreements about theoretical or practical matters and it endured despite differences in age and temperament. While Einstein enjoyed his celebrity status and used his fame as a platform to publicly speak out about a variety of issues, Godel shunned the spotlight and at times seemed stunningly oblivious to anything that did not directly relate to mathematics; during the late 1930s, he innocently asked a refugee scientist who had recently fled the Nazis what had brought him to America. Not surprisingly, many people were not charmed by Godel's singular focus on mathematics to the exclusion of just about anything else. Godel avoided conflict and in time avoided human contact in general (other than with his wife, Einstein and very few others) by utilizing his full-proof escape method: agree to meet a person at a particular place and time and then not show up, thus ensuring that he avoided contact/conflict.

Godel was burdened from an early age with serious psychological problems. He suffered rheumatic fever as a child and when he was a child his research about rheumatic fever revealed that it often causes permanent heart damage. Therefore, Godel concluded that logic dictates that he suffered permanent heart damage, so he spent most of his adult life taking pills for a non-existent heart ailment. Godel also convinced himself that poisonous fumes were emanating from his air conditioner's ducts.

A deep pessimism clouded Godel's thoughts and moods. "We live in a world in which ninety-nine percent of all beautiful things are destroyed in the bud," he lamented. Godel did not believe in the concept of historical progress but instead felt that humanity was regressing: "The world tends to deteriorate. Good things appear from time to time in single persons and events...but the general development tends to be negative."

Taking this concept to what seemed to him to be a logical conclusion, Godel was convinced that there was a conspiracy to rid the world of logical-thinking people and that--as perhaps the foremost logician in the world--he was one of the targets of this conspiracy. Thus, Godel was constantly afraid that his food would be poisoned. Godel's wife Adele allayed those fears by sampling his food first; not long after Adele became too ill to perform this task for him, Godel died of starvation because he refused to eat.

Godel's paranoia is similar to the paranoia exhibited by the great chess champion Bobby Fischer in the sense that both men excelled in disciplines that require the rigorous application of logic and yet, paradoxically, logic failed them in areas outside of their expertise. However, Goldstein does not find Godel's paranoia paradoxical: "Paranoia isn't the abandonment of rationality. Rather, it is rationality run amuck, the inventive search for explanations turned relentless. A psychologist friend of mine put it this way: 'A paranoid person is irrationally rational...Paranoid thinking is characterized not by illogic, but by a misguided logic, by logic run wild" (p. 205).

Goldstein asks a haunting question about Godel that applies equally to Fischer and to other supergeniuses whose strict dedication to misguided logic led them to very dark places: "How can a person, operating within a system of beliefs, including beliefs about beliefs, get outside that system to determine whether it is rational? If your entire system becomes infected with madness, including the very rules by which you reason, then how can you ever reason your way out of your madness?" (p. 204). This is clearly a formidable task even for some of the most brilliant people who ever lived; neither Fischer nor Godel ever figured out how to reason their way out of their particular versions of madness: Fischer's logic extrapolated from the truth that the Soviet Union cheated at chess to create in his mind a vast conspiracy centered on anti-Jewish thought that reached bizarre (but to Fischer completely logical) conclusions such as every single move in every single Kasparov-Karpov game was prearranged; Godel's logic extrapolated from some truths about his early childhood illnesses to some unfounded beliefs about his health and about supposed conspiracies to poison him.

Fischer was only officially the World Chess Champion from 1972-75 but more than 40 years later many people still consider him to be the greatest chess player of all-time. Similarly, Godel published relatively little during his lifetime but because of the depth, quality and influence of what he did publish he has been called the greatest mathematician of the 20th century and perhaps the greatest logician since Aristotle. Godel postulated that the passage of time may be illusory but as long as we humans perceive the passage of time he should and will be remembered as someone who shed some light on the mysteries of the universe.

Further Reading:

1) Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been described as "simply the best and most beautiful book ever written by the human species."

In the 20th anniversary edition of his Pulitzer Prize winning book, Hofstadter explains his original goals and intentions:

GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter...GEB approaches [this question] by slowly building up an analogy that likens inanimate molecules to meaningless symbols, and further likens selves... to certain special swirly, twisty, vortex-like, and meaningful patterns that arise only in particular types of systems of meaningless symbols. It is these strange, twisty patterns that the book spends so much time on, because they are little known, little appreciated, counterintuitive, and quite filled with mystery [that] I call..."strange loops"...

...the Godelian strange loop that arises in formal systems in mathematics... is a loop that allows such systems to "perceive itself," to talk about itself, to become "self-aware," and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self.

2) A World Without Time: The Forgotten Legacy of Godel and Einstein by Palle Yourgrau focuses on Godel's mathematical solution to Einstein's General Theory of Relativity and the implication of that solution, namely that in a universe governed by the General Theory of Relativity time travel is possible. As Godel realized, if the past is accessible then this means that the past is not really past and therefore time cannot exist as anything other than an ideal concept in such a universe (i.e., in such a universe there is no real distinction between past, present and future).

3) Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein is a very readable yet informative account of Godel's life, though it apparently contains some errors in its descriptions of Godel's work (see below; as I do not have formal, higher level mathematical training I must defer to the experts on this issue).

4) The Incomplete Godel is a review of Yourgrau's book and Goldstein's book by Gregory Moore, a professor of mathematics at McMaster University in Canada. Moore prefers Yourgrau's book to Goldstein's because of several errors he notes in Goldstein's attempts to explain Godel's mathematical work but he states that the definitive Godel biography is Logical Dilemmas: The Life and Work of Kurt Gödel (A K Peters, 1997), by John W. Dawson, Jr.

5) Time and Causation in Godel's Universe describes some of the practical implications of Godel's concept of a universe in which time travel is possible.

6) The theoretical possibility of time travel presents us with the confounding Grandfather Paradox, which Robert Heinlein memorably explored in his classic short story "'--All You Zombies--.'"

Albert Einstein the Man

"Learn from yesterday, live for today, hope for tomorrow. The important thing is not to stop questioning."--Albert Einstein

Albert Einstein the physicist is world-renowned for developing ideas that forever changed how we view space, time and the nature of reality. Albert Einstein the man is much less well known but he was a father, a job-seeker and a person whose understanding/awareness of his cultural identity evolved. It is interesting to explore these lesser known aspects of Einstein that informed and shaped a mind that had such a transformative effect on society.

Einstein the Father

Einstein's first child, a daughter named Lieserl, was born out of wedlock in January 1902 to Mileva Maric, a volatile and emotionally unstable woman who began a relationship with Einstein in 1897. Maric put Lieserl up for adoption shortly after Lieserl's birth--perhaps to avoid the shame of having an out of wedlock child--and Einstein never met his daughter. Lieserl's ultimate fate is unknown, though some reports suggest that she died in infancy of scarlet fever. Einstein and Maric married in January 1903, shortly after the death of Einstein's father (who disapproved of Maric and preferred that Einstein rekindle his previous relationship with Maria Winteler, who was much more emotionally stable than Maric). In 1904, Maric gave birth to a son named Hans Albert. "My husband often spends his free time at home just playing with the boy," Maric wrote in a letter to a friend.

The couple later had a second son, Eduard, but the marriage was ultimately doomed because of Maric's deep-seated psychological issues (one visitor to the Einstein home later remarked that he thought Maric was schizophrenic). In July 1914, Maric moved to Switzerland with their two children; Einstein reportedly cried "all afternoon and evening" after Maric's departure. Einstein wrote, "I have carried these children around innumerable times day and night, taken them out in their pram, played with them, romped around and joked with them. They used to shout with joy when I came..." He later accused Maric of "poisoning" the boys against him.

Albert Einstein put the money from his Nobel Prize into a trust fund that supported Maric and their two children. Hans Albert became a prominent hydraulic engineer who had a good relationship with his father but Eduard was diagnosed with schizophrenia at the age of 20 and spent much of his adult life in various asylums. Albert stayed in regular contact with Eduard and later noted, "The more refined of my sons, the one I considered really of my own nature, was seized by an incurable mental illness."

Einstein the Job-Seeker

The man who transformed physics had trouble obtaining the most basic employment when he was in his 20s. Long after Einstein wrote four seminal papers during his "miracle year" of 1905, he was still supporting himself as a patent clerk. A physicist who had read Einstein's work was aghast when he visited Einstein at the patent office, declaring, "History is full of bad jokes." Einstein applied for an entry level teaching position at the University of Bern but was not hired because he failed to submit a new thesis with his application--despite the fact that he included 17 papers with his application, including the theory of relativity for which he ultimately became world famous! Einstein also applied for a job as a high-school math teacher and out of the 21 applicants he did not even make the list of three finalists. Even when Einstein finally landed a job in academia his troubles were not over; the position paid so poorly that Einstein could not afford to quit his job at the patent office.

Imagine how Einstein must have felt about his life at that time: his emotionally unbalanced wife complained constantly, he could barely support his family and he was being shunned by the academic world even though he knew that he had unparalleled insights about the structure of the universe.

Einstein the Jew

Einstein abhorred conformity and, despite a brief flirtation with observant Judaism during his childhood, he was skeptical of organized religion. Einstein tended to consider himself a citizen of the world more than a member of a particular religious or national group but his perspective changed with the rise of Nazism. Einstein wryly noted that if his theories were proven correct then he would be considered a German but otherwise he would be considered a Jew. As the situation of European Jewry grew more and more perilous, Einstein's sense of identity with the Jewish people strengthened (though he never abandoned his skepticism regarding any form of organized religious practice): "The pursuit of knowledge for its own sake, an almost fanatical love of justice, and the desire for personal independence--these are the features of the Jewish tradition which make me thank the stars I belong to it."

Einstein's solidarity with the Jewish people became even more intense after the Holocaust: "My relationship to the Jewish people has become my strongest human bond, ever since I became aware of our precarious position among the nations of the world." Adolf Hitler showed the futility of a person with any Jewish blood trying to deny that connection; his Nazi party developed an elaborate and detailed set of laws about people of "mischling" (mixed) background, decreeing that in some scenarios the presence of two Jewish grandparents in a person's background is enough to label that person as a Jew worthy of extermination (a person with "only" one Jewish grandparent could marry a so-called pure Aryan and thus avoid Nazi persecution).

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What can we learn from these vignettes about Einstein the man? "This too shall pass." Dinesh Chandrasekar notes that whether you are going through a good time in your life or a bad one the situation is temporary but he declares, "This isn't a pessimistic view of life. In fact, it is the other way around. Because we know there is death, let us make the most of life. Because we know the day will end, let us make the day count. Because we know the year will end, even before the New Year arrives, let us do something significant to make 2015 memorable. Because we know our tough times too will end, let us endure it with strength and courage. Because we know the best of times too will end, let us be humble even in our success. Because we know every relationship will eventually end, let us give ourselves completely and unconditionally to our loved ones."

Descriptive and Evocative Writing About Joao Magueijo's Varying Speed of Light Theory

Mary Rogan's feature story "Faster Than the Speed of Light" (January/February 2003 issue of Seed) vividly explains complex concepts in an engaging and easy to understand manner. Physicist Joao Magueijo's Varying Speed of Light (VSL) Theory proposes that Albert Einstein's Theory of Relavity--perhaps the most famous and influential theory ever--is incorrect or at least incomplete. Einstein posited that the speed of light is constant but Magueijo contends that in the first moments after the Big Bang light moved faster than it does now. If Magueijo is right, his VSL Theory will upend nearly several decades' worth of developments in theoretical physics and resolve some vexing questions about the creation of the universe.

Rogan's article could easily have been dull, esoteric and/or impossible for a layperson to follow. She took a different approach: conversational, sassy and brimming with indelible images and metaphors. This is her opening paragraph:

Thinking about the universe will fuck you up. Talking with Joao Magueijo won't help. He's the 34-year-old theoretical physicist who's about to take a bite out of Albert Einstein's ass. The more I talk with Joao, the more it feels like talking with Tom Toughey in high school after I've smoked a joint. Tom could shake his eyeballs. Not his eyelids or the corner of his eyes but both his actual eyeballs. He'd corner me in the hall and shake his elecric blue orbs until I'd run screaming into the girl's room to try and splash down my high with cold water. Joao is no Tom Toughey, but he's close. And right now he's poised to jack modern physics into overdrive. Fuck the speed limit of the universe. With Joao at the wheel, there are no speed limits. That'll set your eyeball shaking.

My writing style is much different than that--more formal, less vulgar--but I appreciate Rogan's rhythm and flow; that paragraph is energetic and intriguing: it demands that you keep reading.

The universe is so large--and it expanded so quickly--that a beam of light could not travel all of the way across it at Einstein's theoretical speed of light (186,000 miles per second). This means that far flung regions of the universe should have never been in contact with each other and thus should have differing properties but our observations suggest that this is not the case. This is formally known as the Homogeneity Problem but Rogan explains the concept informally by using a clever analogy:

The universe, despite its vastness, is remarkably similar. In scientific terms, this means the natural laws that govern the universe are the same all over. How is this possible? How can parts of the universe that are eons away from each other speak the same language? How and when were they all in the same room together? Imagine you grew up in the Bronx and someone else grew up in Africa. You're ten-thousand miles apart. You have no plane or boat. No teleporting machine. Presumably, you've never met. But somehow, you speak the same language, wear the same clothes, and eat the same food. That's impossible. That's fucked up.

VSL Theory solves the Homogeneity Problem by asserting that right after the Big Bang light traveled faster than it does now but as the universe cooled light slowed down. Or, as Rogan memorably puts it, "Like a fast and furious friendship, someone stops calling. Two days go by, then a week. Things slow down until you drift apart. Galaxies that were once close are now light years apart." Our universe is cold, vast and aloof, much like a friend who once seemed close but is now distant and unavailable.

Is Magueijo right? Einstein's Theory of Relativity is one of the most well-tested and successful theories ever; more than 100 years after Einstein published it in his annus mirabilis, researchers are still devising new ways to test it and it has yet to fail. It will be interesting to see if Magueijo's concept can similarly withstand such rigorous investigation. Rogan writes that Magueijo has a very pragmatic attitude about this: "Nothing lasts forever. Not an idea or a man. That's why Joao doesn't worry about taking Einstein down. He tells me it's a sign of respect to question everything. Einstein kept asking questions until he found one he couldn't answer. Then he died." Before Einstein penned the final draft of his theory, he toyed with the VSL concept; as a scientist he would approve of Magueijo's questioning and wondering, even if as a proud individual he would believe that his theory most closely mirrors the Old Man's thoughts (as Einstein might put it).

Near the end of the article, Rogan mentions that Magueijo asked her a question: Why did Holocaust survivor/respected writer Primo Levi commit suicide? Here is Rogan's description of that part of their conversation:

Now he's asking me something I can maybe answer. But I don't because before I can tell him what I think, he offers his own explanation. Maybe, after all those years of being at someone else's mercy, Levi wanted control. Wanted to fall down his own stairs before some Nazi pushed him. This idea seems to make Joao feel better. He's talked a lot about getting out of physics while he's still at the top of his game. Maybe get back to music or take up writing full time. He doesn't want to be like Einstein. By the end of his career, Einstein was frustrated and disappointed. He was pushing beyond his limits and he knew it.

I'm listening to Joao and figure I don't need to tell him my theory about Primo Levi. Besides, it's in direct contradiction to his. I imagine Levi was just exhausted. Adversity doesn't make you stronger; it just drains your tank. So by the time Primo Levi killed himself, the everyday insults that life throws at us probably felt like boulders falling on his head.

I will not presume to know what thoughts and emotions tormented Levi but I think that both Magueijo and Rogan may be correct in a larger, more general sense: Levi's final act may have been both a defiant assertion of control and an escape from a world that can be unbearably painful for the highly intelligent and highly sensitive. I suspect that many of the Holocaust survivors who committed suicide decades after the Event did so because they felt disillusioned by how little the world has changed, how little people have learned. If you devote your life to bearing witness to an atrocity and the world neither listens to your story nor heeds your message/warning then life could seem intolerably meaningless and hopeless, if not cosmically absurd.

Cloud Atlas Explores Our Interconnected Lives and Destinies

"All men are caught in an inescapable network of mutuality, tied in a single garment of destiny. Whatever affects one directly affects all indirectly. I can never be what I ought to be until you are what you ought to be and you can never be what you ought to be until I am what I ought to be."--Dr. Martin Luther King, Jr.

Cloud Atlas explores a theme stated by the character Sonmi-451, who declares, "Our lives are not our own. We are bound to others, past and present. And by each crime and every kindness, we birth our future." This is an alluring, attractive and yet frightening concept: it is tempting and comforting to believe that every soul is inextricably bound together, that we are not alone and that a better future can be created by each act of kindness--but it is distressing and frightening to think that perhaps individual free will is constrained by a larger plan and that this larger plan permits (or even specifically includes) evil actions that cause much suffering.

The film tells six parallel narratives set in six different locales/time frames:

1) South Pacific Ocean, 1849
2) England/Scotland, 1936
3) San Francisco, 1973
4) United Kingdom, 2012
5) Neo Seoul, Korea, 2141
6) Hawaiian Islands, 2321 (post-apocalyptic Earth)

Cloud Atlas' journey from a primitive (by 2012 standards) 1849 setting to an advanced (by 2012 standards) 2141 setting culminating in a very primitive (by any standard) post-apocalyptic setting where a horde of cannibals terrorizes a peaceful settlement brings to mind an Albert Einstein quote: "I know not with what weapons World War III will be fought, but World War IV will be fought with sticks and stones." Cloud Atlas never explicitly examines this point but strongly implies that the degenerate nature of the 2141 society resulted in a war, revolution or some other kind of general social upheaval that quite literally brought the world back into the Stone Age.

The quest for freedom--on both an individual level and on a larger level in terms of freedom from mass suffering/oppression--is the driving force in each Cloud Atlas storyline. In the 1849 setting, one character scoffs at the notion of freeing a slave, saying that the would-be emancipator is taking an action that is the equivalent of removing one drop from an ocean and that this action could have dire consequences (ranging from social ostracism to death by lynching) while not making any real difference. The skeptic received the unhesitating reply that the ocean consists of nothing more than drops of water. Similarly, in the 2141 setting, Sonmi-451 is interrogated shortly before being executed. The interrogator asks her what difference her ideas about freedom could possibly make if no one ever hears them or believes them. She calmly replies that at least one person has already heard her (meaning the interrogator).
 
Is it really true that if you remove (or add) enough drops of water that you can reshape society, that one person can significantly change the world? Or is the cynic right that anyone who tries to do so will meet a horrible fate without making a meaningful difference? There have always been brave, visionary leaders willing to risk their lives for the sake of that "one drop" but those leaders frequently suffer immensely--and often make the ultimate sacrifice. Have their sacrifices made the world better or are the trappings of our "civilization" just a thin veneer draped over our true barbaric nature? I fear that Einstein was right and that we are just one war away from heading right back to the Stone Age; our technological capabilities are increasing much faster than our capacity to function on a high moral/ethical level: as Martin Amis put it in Time's Arrow, "[The Holocaust] was unique, not in its cruelty, nor in its cowardice, but in its style--in its combination of the atavistic and the modern. It was, at once, reptilian and 'logistical.' And although the offence was not definingly German, its style was. The National Socialists found the core of the reptile brain, and built an autobahn that went there."

Whether or not reincarnation literally exists as depicted in Cloud Atlas, Dr. King is right that all of humanity is intimately connected--but it is far from clear if we will collectively understand that concept and act accordingly or if we will soon be fighting World War IV with sticks and stones.

Thoughts on Poshlost and the Defining Arrogance of Genius

In Vladimir Nabokov, The Art of Fiction No. 40, interviewer Herbert Gold of the Paris Review asked Nabokov, "What is most characteristic of poshlust in contemporary writing? Are there temptations for you in the sin of poshlust? Have you ever fallen?"

Nabokov replied (emphasis added):

“Poshlust,” or in a better transliteration poshlost, has many nuances, and evidently I have not described them clearly enough in my little book on Gogol, if you think one can ask anybody if he is tempted by poshlost. Corny trash, vulgar clichés, Philistinism in all its phases, imitations of imitations, bogus profundities, crude, moronic, and dishonest pseudo-literature—these are obvious examples. Now, if we want to pin down poshlost in contemporary writing, we must look for it in Freudian symbolism, moth-eaten mythologies, social comment, humanistic messages, political allegories, overconcern with class or race, and the journalistic generalities we all know. Poshlost speaks in such concepts as “America is no better than Russia” or “We all share in Germany's guilt.” The flowers of poshlost bloom in such phrases and terms as “the moment of truth,” “charisma,” “existential” (used seriously), “dialogue” (as applied to political talks between nations), and “vocabulary” (as applied to a dauber). Listing in one breath Auschwitz, Hiroshima, and Vietnam is seditious poshlost. Belonging to a very select club (which sports one Jewish name—that of the treasurer) is genteel poshlost. Hack reviews are frequently poshlost, but it also lurks in certain highbrow essays. Poshlost calls Mr. Blank a great poet and Mr. Bluff a great novelist. One of poshlost's favorite breeding places has always been the Art Exhibition; there it is produced by so-called sculptors working with the tools of wreckers, building crankshaft cretins of stainless steel, Zen stereos, polystyrene stinkbirds, objects trouvés in latrines, cannonballs, canned balls. There we admire the gabinetti wall patterns of so-called abstract artists, Freudian surrealism, roric smudges, and Rorschach blots—all of it as corny in its own right as the academic “September Morns” and “Florentine Flowergirls” of half a century ago. The list is long, and, of course, everybody has his bête noire, his black pet, in the series. Mine is that airline ad: the snack served by an obsequious wench to a young couple—she eyeing ecstatically the cucumber canapé, he admiring wistfully the hostess. And, of course, Death in Venice. You see the range.

Nabokov's statement foreshadowed/predicted much of what is wrong not only with contemporary journalism but also with the ideological perspectives that have become very fashionable in certain circles (i.e., equating the actions of President George Herbert Walker Bush with the crimes against humanity committed by Saddam Hussein is not merely inaccurate--it is perverse, or, as Nabokov would say, an example of "poshlost").

Here are some other Nabokov gems from that interview:

The purpose of a critique is to say something about a book the critic has or has not read. Criticism can be instructive in the sense that it gives readers, including the author of the book, some information about the critic's intelligence, or honesty, or both.

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There is only one school: that of talent.

(Nabokov dismissed the idea that certain Russian poets belonged to different "schools").

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Derivative writers seem versatile because they imitate many others, past and present. Artistic originality has only its own self to copy.

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Nabokov clearly not only possessed talent and originality but he had a quite keen awareness of the extent of his talent and originality; this is a characteristic feature of genius: while people of lesser talent are often clueless about how their skills compare to those of other people and people of average/slightly above average talent have understandable doubts about their capacity to compete with the truly gifted, geniuses generally possess extreme self assurance--to the point of sounding megalomaniacal or even delusional if their public accomplishments do not measure up to their seemingly grossly inflated opinions about themselves. The great architect Frank Lloyd Wright once declared, "Early in life I had to choose between an honest arrogance and a hypocritical humility. I chose honest arrogance and have seen no occasion to change."

Wright's statement is similar to World Chess Champion Bobby Fischer's reply after being asked who is the greatest chess player: "It's nice to be modest, but it would be stupid if I did not tell the truth. It is Fischer."

Albert Einstein's self confidence went even further than Wright's or Fischer's. Einstein's Theory of Relativity was not confirmed until Sir Arthur Eddington made his famous eclipse observations proving that gravity bends light in the manner that Einstein predicted but Einstein never doubted that his conception of how the universe works is not only correct but also the most elegant way for nature to function. Asked what he would have thought if Eddington's experiment had not confirmed the Theory of Relativity, Einstein replied, "Then I would have felt sorry for the Dear Lord. The theory is correct." Einstein thought that he knew better than God--or at least as much as God--about how the laws of nature should work in terms of mathematical elegance, beauty and simplicity!

There can be a thin line between confidence and self-delusion. The tremendous self confidence possessed by Wright, Fischer and Einstein does not seem delusional to us now because each of those men proved himself to be arguably the greatest practitioner of his craft--but what about George Ohr? Was he a confident genius, a delusional eccentric or some combination of both? Should he be defined by his own descriptions of his abilities, by what his contemporaries thought of him or by the high esteem with which his art is now viewed? Which perspective is true, which perspective is most accurate? If Einstein had lived in an era during which it was not possible to experimentally confirm the Theory of Relativity but he insisted that despite his status as a lowly patent clerk he had glimpsed into the mind of God would it have been correct to view Einstein as a genius or a madman?

I suspect that anyone who ranks well above the 99th percentile in a given endeavor--whether that field is architecture, chess, physics, basketball, writing or anything else--truly believes that he is the best in the world, if not the greatest of all-time. Of course, there can really only be one person who is truly the greatest. Disregarding the difficulty--if not impossibility--of proving who is in fact the greatest, if only one person actually is the greatest are the other nine people who rank in the top 10 delusional for thinking that they are the greatest? Or is that kind of thinking, that perspective about oneself, an essential personality trait for anyone who is trying to scale the very highest of heights?

George Ohr: "The Mad Potter of Biloxi"

"Mozart died a pauper/Heine lived in dread/Foster died in Bellevue/Homer begged for bread/Genius pays off handsomely--/After you are dead"--Yip Harburg

"When I am gone, my work will be praised, honored, and cherished. It will come."--George Ohr

Imagine being the very best at what you do, an innovative trendsetter with boundless energy and creativity. That may sound wonderful but often the Faustian "bargain" that comes with such a tremendous gift is that the rest of the world does not recognize your greatness until long after you have died--Vincent Van Gogh sold just one canvas before he killed himself at the age of 37, yet more than a century after his death one biographer rightly declared that Van Gogh "produced an incredible number of masterpieces that will continue 'living' for the rest of human history."

You have most likely never heard of George Ohr. When he died of throat cancer at the age of 60 in 1918 he was considered--by the few people who even knew who he was--to be a flamboyant eccentric. More than 7000 pieces of pottery that Ohr lovingly created languished in crates stored in the garage of an auto repair shop run by his sons in his native Biloxi, Mississippi. If not for a chance encounter between a New Jersey antiques dealer named James Carpenter and Ohr's son Ojo it is likely that the world would never have known about Ohr's distinctive works.

Although Ohr was mocked during his lifetime and had trouble selling his pottery even to his few admirers, Ohr had boundless confidence. When he set up his wares, Ohr proudly posted a sign that read, "'Greatest' art potter on Earth. 'You' prove it contrary." In a 1901 interview, Ohr acknowledged his lack of commercial success by lamenting "I have a notion...that I am a mistake" but his prescient prediction from that same interview indicates that he knew that the "mistake" was really the lack of insight shown by his contemporaries: "When I am gone, my work will be praised, honored, and cherished. It will come." In his shop, Ohr hung a hand-lettered sign with the Latin phrase Magnus opus, nulli secundus/optimus cognito, ergo sum! (A masterpiece, second to none/The best, therefore, I am!).

How thin is the line between being a genius who is celebrated during his lifetime and a genius who is not recognized as such until long after his death? Consider that Albert Einstein--whose name has become synonymous with the word genius--worked six days a week for seven years as a patent clerk because he could not obtain a full time academic position. During his spare time, Einstein wrote five papers that completely revolutionized the way that we perceive the universe--and yet even after the "annus mirabilis" (miracle year) of 1905 in which Einstein composed and published those papers it took until 1908 before Einstein became a full professor. Wouldn't you love to eavesdrop on some of those job interviews? "We're sorry, Herr Einstein, but you just are not quite qualified to teach at our institution." What must Einstein have thought after being rejected numerous times by people who had just a fraction of his intelligence? A quote from a letter that Einstein wrote during this frustrating period provides a glimpse of how he perceived the academics who refused to hire him: "From now on I’ll no longer turn to such people, and will instead attack them mercilessly in the journals, as they deserve. No wonder little by little one becomes a misanthrope."

Although Einstein had to suffer slings and arrows from many fools, he eventually achieved the fame and respect that he deserved, which provided him what he most wanted--the opportunity to work on his theories in solitude, undisturbed by the rest of the world. The huge advantage that Einstein enjoyed over Van Gogh and Ohr is that it became possible to experimentally verify some of the fantastic theoretical predictions that Einstein made in his 1905 papers; when Arthur Eddington's 1919 eclipse observations confirmed Einstein's assertion that gravity bends light Einstein instantly became a figure of worldwide renown not only in the scientific community but among the general public. Sadly, such instant verification of genius does not exist in the literary or artistic fields.