Monday, June 25, 2018


Charles Krauthammer Was an Independent Thinker in an Age of Blind Partisanship

We live in an era of blind partisanship, when it is expected that a person must strictly adhere to a given party line or else be ostracized: you are either to the right or to the left and woe to the person who dares to be an independent thinker.

Charles Krauthammer, who passed away on June 21 at the age of 68, defied the norm and did not conform to partisan politics: he criticized President Barack Obama for--among other things--his Mideast policy, but he also called President Trump a "moral disgrace" for not immediately condemning the racist, white supremacist rally at Charlottesville.

Krauthammer, who won the Pulitzer Prize in 1987, wrote commentaries that defy simple labels, as Adam Bernstein noted in Krauthammer's Washington Post obituary:
He initially defined himself as a liberal Cold Warrior, a Democrat who embraced anti-communist as well as New Deal and Great Society programs that aided the most vulnerable. His support for the robust use of American military power gradually left him alienated from the Democratic Party, however, and he found ideological succor in neoconservatism, identifying with writer Irving Kristol's definition of its adherents as onetime liberals who have been "mugged by reality."
There are many examples of Krauthammer's crisp writing and his distinct perspective. In a September 25, 2006 column titled Everyone's Jewish, Krauthammer started with a light-hearted tone but then made some serious points:
Krauthammer's Law: Everyone is Jewish until proven otherwise. I've had a fairly good run with this one. First, it turns out that John Kerry--windsurfing, French-speaking, Beacon Hill aristocrat--had two Jewish grandparents. Then Hillary Clinton--methodical Methodist--unearths a Jewish stepgrandfather in time for her run as New York senator...

For all its tongue-in-cheek irony, Krauthammer's Law works because when I say "everyone," I don't mean everyone you know personally. Depending on the history and ethnicity of your neighborhood and social circles, there may be no one you know who is Jewish. But if "everyone" means anyone that you've heard of in public life, the law works for two reasons. Ever since the Jews were allowed out of the ghetto and into European society at the dawning of the Enlightenment, they have peopled the arts and sciences, politics, and history in astonishing disproportion to their numbers.

There are 13 million Jews in the world, one-fifth of 1 percent of the world's population. Yet 20 percent of Nobel Prize winners are Jewish, a staggering hundredfold surplus of renown and genius. This is similarly true for a myriad of other "everyones"--the household names in music, literature, mathematics, physics, finance, industry, design, comedy, film and, as the doors opened, even politics.

But it is not just Jewish excellence at work here. There is a dark side to these past centuries of Jewish emancipation and achievement--an unrelenting history of persecution. The result is the other more somber and poignant reason for the Jewishness of public figures being discovered late and with surprise: concealment. 
In a January 29, 2015 column titled Do We Really Mean "Never Again"?, Krauthammer noted the "bitter irony" that in the wake of the 70th anniversary of the liberation of Auschwitz it was obvious that anti-Semitism was alive and well in Europe. Krauthammer lamented that the real issues were (1) Jew-hatred is the norm, not exception, throughout European history and (2) while it took Hitler and his followers years to massacre six million Jews, the state of Israel and her more than six million Jews face the dire prospect of annihilation by just one nuclear weapon:
The rise of European anti-Semitism is, in reality, just a return to the norm. For a millennium, virulent Jew-hatred--persecution, expulsions, massacres--was the norm in Europe until the shame of the Holocaust created a temporary anomaly wherein anti-Semitism became socially unacceptable.

The hiatus is over. Jew-hatred is back, recapitulating the past with impressive zeal. Italians protesting Gaza handed out leaflets calling for a boycott of Jewish merchants. As in the 1930s. A widely popular French comedian has introduced a variant of the Nazi salute. In Berlin, Gaza brought out a mob chanting, "Jew, Jew, cowardly pig, come out and fight alone!" Berlin, mind you.

European anti-Semitism is not a Jewish problem, however. It's a European problem, a stain, a disease of which Europe is congenitally unable to rid itself.

From the Jewish point of view, European anti-Semitism is a sideshow. The story of European Jewry is over. It died at Auschwitz. Europe's place as the center and fulcrum of the Jewish world has been inherited by Israel. Not only is it the first independent Jewish commonwealth in 2,000 years. It is, also for the first time in 2,000 years, the largest Jewish community on the planet.

The threat to the Jewish future lies not in Europe but in the Muslim Middle East, today the heart of global anti-Semitism, a veritable factory of anti-Jewish literature, films, blood libels and calls for violence, indeed for another genocide.

The founding charter of Hamas calls not just for the eradication of Israel but for the killing of Jews everywhere. Hezbollah chief Hassan Nasrallah welcomes Jewish emigration to Israel-because it makes the killing easier: "If Jews all gather in Israel, it will save us the trouble of going after them worldwide." And, of course, Iran openly declares as its sacred mission the annihilation of Israel...

Former Iranian president Ali Akbar Hashemi Rafsanjani, known as a moderate, once characterized tiny Israel as a one-bomb country. He acknowledged Israel’s deterrent capacity but noted the asymmetry: "Application of an atomic bomb would not leave anything in Israel, but the same thing would just produce damages in the Muslim world." Result? Israel eradicated, Islam vindicated. So much for deterrence.

And even if deterrence worked with Tehran, that's not where the story ends. Iran's very acquisition of nukes would set off a nuclear arms race with half a dozen Muslim countries from Turkey to Egypt to the Gulf states--in the most unstable part of the world. A place where you wake up in the morning to find a pro-American Yemeni government overthrown by rebels whose slogan is "God is Great. Death to America. Death to Israel. Damn the Jews. Power to Islam."

The idea that some kind of six-sided deterrence would work in this roiling cauldron of instability the way it did in the frozen bipolarity of the Cold War is simply ridiculous.

The Iranian bomb is a national security issue, an alliance issue and a regional Middle East issue. But it is also a uniquely Jewish issue because of Israel's situation as the only state on earth overtly threatened with extinction, facing a potential nuclear power overtly threatening that extinction.

On the 70th anniversary of Auschwitz, mourning dead Jews is easy. And, forgive me, cheap. Want to truly honor the dead? Show solidarity with the living--Israel and its 6 million Jews. Make "never again" more than an empty phrase. It took Nazi Germany seven years to kill 6 million Jews. It would take a nuclear Iran one day.
Krauthammer deftly wove together the history of European and Middle Eastern anti-Semitism in that column, like a boxer nimbly throwing jabs that hit the target--but he also concluded with a knockout punch that hammered home the main point and that knockout punch bears repeating for anyone who does not understand what is at stake for Israel vis a vis Iran: "It took Nazi Germany seven years to kill 6 million Jews. It would take a nuclear Iran one day."

Krauthammer used words to entertain, to enlighten and to inspire. His allegiance was to independent thought, not a particular ideology or political party. That kind of voice is rare, always needed, and will be particularly missed in our era.


Thursday, November 30, 2017


Seeing Light in the Darkest Times

November 9 was the 79th anniversary of the beginning of Kristallnacht (German for "Night of Crystal" but usually translated in this context as "Night of the Broken Glass"), a two day state-sanctioned pogrom in Nazi Germany, German-occupied Austria and German-occupied Sudetenland during which over 260 synagogues were burned to the ground, nearly 100 Jews were killed and as many as 30,000 Jews were sent to concentration camps. Nazi Germany then imposed a one billion Reichsmark fine (equivalent to $400 million in U.S. dollars at the time) on the Jewish community to make sure that the Jewish people--not German-owned insurance companies--paid the economic price for all of the destroyed Jewish properties/businesses.

Minnesota Supreme Court Justice David Stras' family experienced the horrors of Kristallnacht firsthand; his grandfather--who was 14 years old at the time--saw Jewish stores being looted, Jewish books being burned in bonfires in the street and signs declaring "Kill the Jews." Stras' great-grandfather was sent to Dachau, the Nazis' first concentration camp. Stras recently wrote an article for The Wall Street Journal about his family's experiences during Kristallnacht specifically and the Holocaust in general. Stras noted that four years ago, for the first time, he spoke publicly about what happened to his family during the Holocaust and how his grandfather narrowly survived Auschwitz. Stras explained that his grandfather never lost his faith in humanity:

My grandfather had the uncommon gift of being able to see the light of human generosity in the midst of near-total darkness...
Only after years researching their stories and reflecting on their lives do I understand the message my grandparents had tried to impart--one of hope and gratitude, not bitterness or pity. As my grandfather said in a memorial service speech in 1979, we remember those who "lost their freedom, the freedom of us and the freedom of mankind." He emphasized that "we, the survivors, have to let the world know that we will never again allow another Holocaust" and told the audience that "you, and you alone, have the responsibility to speak up for our fallen relatives and friends."
My grandparents always said they were the lucky ones, and that they were left on earth to speak for those who had perished. Their guidepost was humanity, not indulgence in their own sorrow and suffering.
The human capacity to do evil and inflict suffering is terrifying and tragic but the human capacity to endure, survive and retain compassion/hope despite suffering is inspirational.

Here is a link to the entire article (subscription required): My Grandparents Saw Light, Even After the Dark of Kristallnacht

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Tuesday, November 14, 2017


Perfectionism, Despair and Meaning

The October 16, 2017 edition of The Wall Street Journal contains a book review by Emily Esfahani Smith entitled "Redefining a Well-Lived Life." Smith offers her take on Iddo Landau's Finding Meaning in an Imperfect World. Landau, a philosophy professor at Haifa University in Israel, seeks to understand why the rates for suicide, depression and alienation have been rising for quite some time. Smith notes that much research on this subject has concluded that despair is the primary reason that so many people decide that their lives are meaningless and she adds that Landau concludes that the issue is not so much that people's lives lack meaning but rather--in Smith's words--that people "have distorted ideas about what a meaningful life actually is."

Landau ticks off several arguments that are commonly made to prove that life is meaningless: (1) Nothing that we do individually matters because we are tiny specks in a vast universe; (2) We will be forgotten soon after we die; (3) Everything that we do and everything that we value will ultimately decay or be destroyed.

Landau asserts that the crucial flaw in each of these arguments is the idea that the only valuable life is a perfect one: "According to this presupposition, meaningful lives must include some perfection or excellence or some rare and difficult achievements." Smith powerfully amplifies this point: "Does the life of a child with Down syndrome have less value than the life of a healthy child? Is a retail clerk leading a less meaningful life than, say, Elon Musk? A perfectionist would have to say yes and yes. But Mr. Landau wisely points out that it's cruel to hold ourselves or others to this standard for meaning, because it neglects life's inherent worth."

In The Good Inclination and the Bad Inclination, I quoted David Holzel's take on perfectionism/trying to always do the right thing: "If one is overly righteous, one is likely to become suicidal." Perfectionism sounds noble but it can have pernicious effects on the mind and soul, because perfection is not attainable--and the fact that perfection is unttainable can easily transform a noble pursuit into a race toward oblivion.

I have always admired perfectionists and I have always strived for perfection but perfectionism seems to be a trap that leads not to excellence but to suffering. How does one ramp down the pursuit of perfection without sacrificing the competitive edge/edginess that seems to be necessary to achieve greatness? One point of view is that the world is not bifurcated into successes/failures but rather learners/nonlearners and that the value of new experiences is not defined by always winning but rather by always learning. For several years I have tried to embrace and embody this approach but it is not easy to tame the fires of perfectionism after they have been lit and after they have swelled to massive proportions. Kobe Bryant once declared that he was "not with" the idea of it is OK to fall short of your goals as long as you tried your best. I admire and identify with Bryant's determination and relentlessness but I wonder if this way of thinking is healthy.

My Mom has always emphasized to me that success is not defined by material goods or accomplishments but rather by service to others. During times when the vicissitudes of life have buffeted my mind and soul, she consistently told me that the path to healing involved focusing less on myself/my goals and more on helping others.

I see the wisdom in this way of reframing one's thinking but it is not so easy to rewire one's brain.

Smith's book review offers a simple conclusion that could have been written by my Mom: "Holding your child's hand, volunteering in your community, doing your job, appreciating the beauty around you--these are the wellsprings of meaning all of us can tap."

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Sunday, November 12, 2017


Prince's Versatility and Influence

Prince's untimely death is still difficult to accept for those who appreciate his rare genius and who mourn for the loss of the great music he never had the opportunity to create because his life was cut short. Prince's combination of productivity, creativity, ingenuity and high-level multi-instrument proficiency may never be seen again.

Rob Sheffield recently wrote an insightful tribute to Prince and the enduring influence of his 1999 album. Sheffield notes that many artists from diverse genres influenced Prince but he took music to another level:
But as any of these artists probably would have conceded, Prince topped them all, creating his own kind of nonstop erotic cabaret. Instead of just overdubbing instruments to replicate a live band, he built the tracks around a colossal synth pulse, which made 1999 one of the decade's most influential productions. "Little Red Corvette" became such a massive pop hit, it's easy to overlook how radical it sounded at the time. All through the song, you can hear the machines puff and hiss, as if Prince's engines are overheating, with his studio as a Frankenstein lab full of sparks flying everywhere. It's sleek on the surface, but the rhythm track keeps sputtering and threatening to blow up. It's the sonic equivalent of George Lucas' breakthrough in the original Star Wars movie--he figured out that the way to make droids look real was to make them dusty and dented, as if they'd gotten banged around on the job.
Joe Levy's May 4, 2016 remembrance of Prince takes an even broader view: "As with so many visionary artists, there was a period in Prince's career--almost all of the 1980s--when he seemed able to look around corners, when his music seemed to live in the future, and then assemble that future around us."

Levy observes that the divorce of Prince's parents when Prince was around eight years old had a lasting influence on the budding music superstar: "...his domestic exiles created longing and anger that played out in his career: He would build a community in his music and his band, but then cut off band members whenever he felt it necessary; he would most often record albums by himself. He was the only one he could count on. 'What if everybody around me split?' he said to Rolling Stone in 1990. 'Then I'd be left with only me, and I'd have to fend for me. That's why I have to protect me.'"

Prince's ability to play multiple instruments was largely the result of intensive self-education. After Warner Brothers signed him to his first recording deal in 1977 when Prince was 19 years old, the label intended for Earth, Wind and Fire's Maurice White to produce Prince's first album but Prince immediately shut down that plan: "Nobody is producing my album," Prince declared, and then he proceeded to prove that he was more than capable of handling those duties. Levy reports that Lenny Waronker, Warners' A&R chief at the time, was suitably impressed. Waronker recalled, "He put down a guitar track and got it right. Then he put down the drums--wow. You could just tell--the guitar was locked in, the timing was good, you could tell it was easy for him."

Prince then embarked on a staggering outburst of musical creativity, as recounted by Levy:
Prince began work on his fifth album, 1999, in early 1982. He was 23 years old and entering a golden period: For the next three years, it seemed like every waking moment yielded a song, and every song was a hit. He now had three groups: his own band, the Revolution; the Time; and a trio of women in lingerie he called Vanity 6. Before long, he would also be creating music for percussionist Sheila E. He was ceaseless, sometimes working for three days straight without sleep. "Do I have to eat?" he mused in Rolling Stone in 1985. "I wish I didn't have to eat."

By the end of 1985, he had made 15 albums in seven years--seven under his own name; three by the Time; two from Sheila E., and one each from Vanity 6, Apollonia 6 and the Family. Those albums generated 13 Top 20 hits on the Billboard Hot 100. The Minneapolis sound--that synth-driven blend of funk, pop and rock which Prince pioneered--was everywhere, especially after Jimmy Jam and Terry Lewis, whom Prince had fired from the Time, began producing a string of hits for artists like the S.O.S. Band, Klymaxx and Janet Jackson. Then there were the Prince songs that became huge hits for Chaka Khan ("I Feel for You," 1984), Sheena Easton ("Sugar Walls," 1984), and the Bangles ("Manic Monday," 1986).
Prince had gone after all this, but on his own terms. No one would have predicted that he'd break through with singles about the End Times or a sexually voracious woman, or that he could increase the power of his burgeoning fame by refusing to do interviews. Yet that's exactly what happened with 1999.
Prince's career peaked in 1984, when he became the only artist other than the Beatles to simultaneously have the number one album, number one single and number one movie in the United States. That feat is obviously a tall order to match commercially or artistically but Prince remained relevant as a song writer, musician and live performer until the day he died, inspiring a wide array of artists to push the boundaries of their creativity.


Thursday, September 7, 2017


Mental Toughness

What is mental toughness? There is no simple answer and indeed there is not even just one answer. Pondering this question sent my mind racing in many directions, but one recurring thought/memory is Michael Jordan's "What is Love?" commercial. Jordan concluded, "Love is playing every game as if it's your last." Jordan never took games or even plays off, because he knew that there might be someone in the stands who had never seen him play and he wanted that person to see him at his very best.

To me, that video is a powerful testament to the intense devotion required to become the greatest practitioner of your craft (whether or not you believe Jordan is the greatest basketball player ever is not the point; he displayed the focus and the traits that are essential to challenge for that number one spot). Watching that video still evokes strong feelings in me--but my Mom was unmoved the first time she saw it. "That's not what love is," she declared. She says that love is about human relationships--about caring so much about another person that you sacrifice to make that person happy, to make that person's life better. My Mom felt that the commercial was about winning a game and winning a game is not what defines love to her.

Both perspectives are valid. Jordan's video is a testament to one kind of love but my Mom is correct that there are other kinds of love as well: parent-child, husband-wife, sibling-sibling. The Jordan commercial does not deny other kinds of love or minimize the importance of human relationships; it speaks to the power of love to inspire a person to achieve greatness.

So, what is love? Love means different things in different contexts.

What is mental toughness? Mental toughness is not defined/proven by fame or glory. I recently heard a broadcaster extolling the mental toughness that Emmitt Smith once displayed when he led the Dallas Cowboys to victory despite having a separated shoulder--and there is no doubt that this took great mental toughness. But is Smith tougher than my Grandma Ida, who fought cancer for almost five years and who never lost her optimism and her zest for life even as the cancer drained the life out of her body?

Mental toughness is doing what has to be done--doing the right thing, the life-affirming thing--no matter the odds.

Life can be bitterly cruel. It is easy to complain or to give up but perhaps it is helpful to understand that life is not only about "winning" but also about personal growth. Alexander Solzhenitsyn survived being imprisoned--buried alive might be a more accurate description--in what he later called the Gulag Archipelago but he did not curse his fate or those who oppressed him. Instead, he said, "Bless you prison, bless you for being in my life. For there, lying upon the rotting prison straw, I came to realize that the object of life is not prosperity as we are made to believe, but the maturity of the human soul."

Mental toughness is facing down a totalitarian regime bent on destroying individuality and individuals. Solzhenitsyn did this and his writings lay bare the horrors of living under Communist rule and the flaws inherent in building a society around the Communist philosophy. Later, Natan Sharansky was arrested by the Soviet government, convicted on trumped up charges of being a spy and sentenced to 13 years in prison, including solitary confinement and hard labor; the Communist regime literally and figuratively sought to bury Sharansky alive in a hole so deep that he would be mentally, psychologically and physically destroyed. Instead, after he was sentenced he defiantly declared, "To the court I have nothing to say--to my wife and the Jewish people I say 'Next Year in Jerusalem.'"

Sharansky, a master level chess player, played chess games against himself to maintain his sanity when he was in solitary confinement. After nine years, the Soviets finally set him free in an exchange of prisoners in Berlin. Sharansky's Soviet tormentors ordered him to walk straight across a bridge, but instead Sharansky defiantly marched to freedom in zig zag fashion. Sharansky later recalled what his Communist captors had first told him when he arrived in prison: "This is the end of the Zionist movement and you will never get out alive." Instead, the Berlin Wall fell just a few years after Sharansky zig zagged his way to freedom in that city and, as Sharansky said with justifiable pride, "There is no KGB, there is no communism and more than a million former Soviet Jews are free and in Israel. It is a very triumphant feeling."

Mental toughness is maintaining sanity despite having a brain that is wired so differently than other people's brains that one is perceived to be--and may feel like--an alien. Alexander Grothendieck has been called the greatest mathematician of the 20th century but he spent his last years in seclusion, unwilling or unable to function in society the way that people are expected to function.

"My first impression was that he had been transported from an advanced alien civilization in order to speed up our intellectual evolution," Marvin Jay Greenberg, professor emeritus of mathematics at the University of California at Santa Cruz, said about meeting Grothendieck during Grothendieck's prime.

According to Kaja Perina (in an article published in the July/August 2017 issue of Psychology Today), "Thinking styles lie on a continuum. On one end is mechanistic, rule-based thinking, which is epitomized in minds that gravitate to math, science, engineering, and tech-heavy skill-sets. Mechanistic cognition is bottom-up, concerned with the laws of nature and with objects as they exist in the world, and stands in contrast to mentalistic thinking. Mentalistic cognition exists to decode and engage with the minds of others, both interpersonally and in terms of larger social forces. It is more holistic (top-down) and humanistic, concerned, broadly speaking, with people, not with things. This mind-set makes loose, sometimes self-referential inferences about reality. If  'hypermentalistic,' too much meaning will be ascribed to events: All coincidences are meaningful and all events are interconnected."

Perina argues that, in this view of thinking styles, autism is an extreme form of mechanistic thinking, while extreme mentalistic thinking is typified by "psychotic disorders, characterized by false beliefs in the sentience of inanimate objects and delusions about the self and others."

In other words, the racing thoughts and the ability to see/make unusual mental connections that made Grothendieck a mathematical genius also pushed him to the brink of insanity (at least in terms of how insanity is defined by the majority of people who consider themselves sane and who run the world on a day to day basis).

Being a genius might sound like fun in theory but living day to day in this world as a genius is a major challenge. Frank Herbert's depiction of Alia in Dune--and how her pre-birth exposure to all of the collective wisdom of her ancestors made her both powerful and an "abomination"--is a very apt metaphor for the struggle a genius faces in controlling/managing the thoughts/wisdom/visions that bless (or afflict) at all hours of day and night.

You may think that Grothendieck was weak because he withdrew from society--but I think that he actually showed a kind of mental toughness that most people will never understand or appreciate. He made immense contributions to society while battling against the way that his mind functioned. It could be argued that World Chess Champion Bobby Fischer faced a similar inner struggle and that Fischer also made immense contributions to the art and science of chess before he too found it necessary to seclude himself from the world.

What is mental toughness? Sometimes, just surviving day to day requires tremendous mental toughness, depending on the internal and external circumstances that a person faces.

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Monday, January 16, 2017


Dr. Martin Luther King, Jr.'s Mountaintop Speech

As we celebrate the life and legacy of Dr. Martin Luther King, Jr. today, we remember what an eloquent and powerful orator he was. His speeches tingle the spine, elevate one's thoughts and touch one's heart. While "I Have a Dream" is probably his most famous speech, Dr. King's "I've Been to the Mountaintop" speech--delivered the day before he was assassinated--synthesized history, prophecy and a call to action in a striking manner. Dr. King's passionate belief in the power of non-violence to effect social change gave him the faith and courage to state that his people would reach the Promised Land even if his life were cut short.

Dr. King declared that if he had been blessed with the choice of living at any time in recorded history he would have chosen this very moment:

Strangely enough, I would turn to the Almighty, and say, "If you allow me to live just a few years in the second half of the 20th century, I will be happy."

Now that's a strange statement to make, because the world is all messed up. The nation is sick. Trouble is in the land; confusion all around. That's a strange statement. But I know, somehow, that only when it is dark enough can you see the stars. And I see God working in this period of the twentieth century in a way that men, in some strange way, are responding.
Dr. King concluded with this breathtaking testament of his faith and courage:
Like anybody, I would like to live a long life. Longevity has its place. But I'm not concerned about that now. I just want to do God's will. And He's allowed me to go up to the mountain. And I've looked over. And I've seen the Promised Land. I may not get there with you. But I want you to know tonight, that we, as a people, will get to the promised land!

And so I'm happy, tonight.

I'm not worried about anything.

I'm not fearing any man!

Mine eyes have seen the glory of the coming of the Lord!!

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Thursday, August 25, 2016


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--'."

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