Up in the Air, the latest George Clooney film, is only the third movie I’ve reviewed on this blog, and the only common thread they share is that they all deal with philosophical issues, albeit in completely different ways with totally different themes.
Man on Wire was a documentary about a truly extraordinary, eccentric and uniquely talented human being. It’s hard to imagine we will ever see another Philippe Petit – certainly what he did was a once-in-a-lifetime event.
Watchmen was a fantasy comic-book movie that captured an entire era, specifically the cold war, and consequently brought to the screen the contradictions that many of us, on the outside at least, find in the American psyche.
Up in the Air is an existentialist movie for our time, and, even though it is marketed as a romantic-comedy, anyone expecting it to be a typical feel-good movie that promotes happily-ever-after scenarios will be disappointed. It is uplifting, I believe, but not in the way many people will expect. It has had good reviews, at least in this country, and deservedly so in my opinion.
Firstly, I cannot over-emphasise how well-written this movie is. When I ran a writing course, I told my students that good writing is transparent. Even in a novel, I contend that no one notices good writing, they only notice bad writing. The reader should be so engaged in the story and the characters, that the writing becomes a transparent medium.
Well, in a movie the writing is even more transparent, because it comes out of the mouths of actors or is seen through the direction of the director. To give an example, there is a scene in this movie where two different people get two different reactions from the same person in the same scenario. This scene could easily have appeared contrived and unconvincing, but it was completely believable, because all the characters were so well written. But, as far as the audience is concerned, all credit goes to the actors, and that’s what I mean when I say the writing is transparent.
Now, I know that, according to the internet, part of this movie is unscripted and they used real people (non-actors) who had been laid off, but their participation is seamless. And, paradoxically, it’s the script-writing that allows this to happen invisibly.
Personally, I felt some resonances with this movie, because, when I was in America in 2001/2, I was living the same type of life as the protagonist (George Clooney’s Ryan Bingham): living in hotels and flying or driving around the country. No, I wasn’t a high-flying executive or a hatchet-man; just an ordinary bloke working in a foreign country, so I had no home so to speak. I also wrote half a novel during that period, which, in retrospect, I find quite incredible, as I now struggle to write at all, even though I live alone and no longer hold a full time job. I digress and indulge – two unpardonable sins – so let me get back to my theme.
The movie opens with a montage of people being sacked (fired) with a voice-over of Clooney explaining his job. This cuts to the core of the movie for me: what do we live for? For many people their job defines them – it is their identity, in their own eyes and the eyes of their society. So cutting off someone’s job is like cutting off their life – it’s humiliating at the very least, suicidally depressing at worst and life-changing at best.
The movie doesn’t explore these various scenarios, just hints at them, but that’s all it needs to do. A story puts you in the picture - makes you empathise - otherwise it doesn’t work as a story. So sitting in the cinema, we all identify with these people, feel their pain, their humiliation, their sense of betrayal and their sense of failure. It’s done very succinctly – the movie doesn’t dwell on the consequences – it hits us where it hurts then leave us to contemplate. Just how important is your job to you? Is it just a meal ticket or does it define who you are?
In another sub-plot or 2 or 3, the movie explores relationships and family. So in one film all the existential questions concerning 21st Century living are asked. Getting married, having kids, bringing up the next generation – is that what it’s all about? There’s no definitive answer; the question is left hanging because it’s entirely up to the individual.
Recently (last month) Stephen Law tackled the Meaning of Life question from a humanist perspective. Basically he was defending the position against those who claim that there is no meaning to life without religion, specifically, without God. God doesn’t get a mention in this movie, but that’s not surprising; God rarely gets a mention in the best of fiction. In a recent post of my own (Jesus’ Philosophy) I reviewed Don Cupitt’s book on that very topic, and Cupitt makes the observation that it was the introduction of the novel that brought humanist morality into ordinary discourse. And he’s right: one rarely finds a story where God provides the answer to a moral dilemma – the characters are left to work it out for themselves, and we would be hugely disappointed if that wasn’t the case.
In one scene in the movie, Bingham tells a teary-eyed middle-aged man that he can finally follow the dream he gave up in his youth of becoming a pastry chef or something similar. Existential psychology, if not existential philosophy, emphasises the importance of authenticity – it’s what all artists strive for - it’s about being honest to one’s self. How many of us fail to follow the dream and instead follow the path of least resistance, which is to do what is expected of us by our family, our church, our society or our spouse.
For most of us, finding meaning in our life has very little to do with God, even those of us who believe in a god, because it’s something internal not external. Viktor Frankl, in his autobiographical book about Auschwitz (Man's Search for Meaning), contends that there are 3 ways we find meaning in our life: through a project, through a relationship and through adversity. This movie, with no detour to a war zone or prison camp, hints at all three. Yet it’s in the context of relationships that the real questions are asked.
On Stephen’s blog, another blogger wrote a response which was drenched in cynicism – effectively saying that anyone seeking meaning, in a metaphysical sense, is delusional. And that Stephen’s criteria about what constitutes a ‘meaningful’ life was purely subjective. I challenged this guy by saying: ‘I don’t believe you’; everyone seeks meaning in their life, through their work or their art or their relationships, but, in particular, through relationships.
At the end of one’s life, I would suggest that one would judge it on how many lives one touched and how meaningfully they touched them; all other criteria would pale by comparison. To quote one of my favourite quotes from Eastern antiquity: If you want to judge the true worth of a person, observe the effects they have on other people’s lives.
Saturday, 6 February 2010
Sunday, 24 January 2010
Interview with David Kilcullen; expert on Afghanistan and counter-insurgency
Anyone who thinks that there are simplistic solutions to the crisis in Afghanistan and Pakistan, should listen to this interview.
Kilcullen also provides some background on the Iraqi conflict, especially from the perspective of the US State Department.
I thought it was very informative what he had to say about Indonesia (and SE Asia in general) towards the end of the interview.
Most quotable quote: “We need to get out of the business of invading other people’s countries just because there are terrorist cells there [though] I would never say never.”
Kilcullen also provides some background on the Iraqi conflict, especially from the perspective of the US State Department.
I thought it was very informative what he had to say about Indonesia (and SE Asia in general) towards the end of the interview.
Most quotable quote: “We need to get out of the business of invading other people’s countries just because there are terrorist cells there [though] I would never say never.”
Sunday, 17 January 2010
Quantum Entanglement; nature’s great tease
I’ve just read the best book on the history of quantum mechanics that I’ve come across, called The Age of Entanglement, subtitled When Quantum Physics was Reborn, by Louisa Gilder. It’s an even more extraordinary achievement when one discovers that it’s Gilder’s first book, yet one is not surprised to learn it had an 8 year gestation. It’s hard to imagine a better researched book in this field.
Gilder takes an unusual approach, where she creates conversations between key players, as she portrays them, using letters and anecdotal references by the protagonists. She explains how she does this, by way of example, in a preface titled A Note To The Reader, so as not to mislead us that these little scenarios were actually recorded. Sometimes she quotes straight from letters.
When I taught a fiction-writing course early last year, someone asked me is biography fiction or non-fiction? My answer was that as soon as you add dialogue, unless it’s been recorded, it becomes fiction. An example is Schindler’s Ark by Thomas Keneally, who explained that he wrote it as a novel because ‘that is his craft’. In the case of Gilder’s book, I would call these scenarios quasi-fictional. The point is that they work very well, whether they be fictional or not, in giving flesh to the characters as well as the ideas they were exploring.
She provides an insight into these people and their interactions, at a level of perspicuity, that one rarely sees. In particular, she provides an insight into their personal philosophies and prejudices that drove their explorations and their arguments. The heart of the book is Bell’s Theorem or Bell’s Inequality, which I’ve written about before (refer Quantum Mechanical Philosophy, Jul.09). She starts the book off like a Hollywood movie, by providing an excellent exposition of Bell’s Theorem for laypeople (first revealed in 1964) then jumping back in time to the very birth of quantum mechanics (1900) when Planck coined the term, h, (now known as Planck’s constant) to satisfactorily explain black body radiation. Proceeding from this point, Gilder follows the whole story and its amazing cast of characters right up to 2005.
In between there were 2 world wars, a number of Nobel Prizes, the construction of some very expensive particle accelerators and a cold war, which all played their parts in the narrative.
David Mermin, a solid state physicist at Cornell gave the best exposition of Bell’s Theorem to non-physicists, for which the great communicator, Richard Feynman, gave him the ultimate accolade by telling him that he had achieved what Feynman himself had been attempting to achieve yet failed to realise.
Bell’s Theorem, in essence, makes predictions about entangled particles. Entangled particles counter-intuitively suggest action-at-a-distance occurring simultaneously, contradicting everything else we know about reality, otherwise known as ‘classical physics’. Classical physics includes relativity theory which states that nothing, including communication between distinct objects, can occur faster than the speed of light. This is called ‘locality’. Entanglement, which is what Bell’s Theorem entails, suggests the opposite, which we call ‘non-locality’.
Gilder’s abridged version of Mermin’s exposition is lengthy and difficult to summarise, but, by the use of tables, she manages to convey how Bell’s Theorem defies common sense, and that’s the really important bit to understand. Quantum mechanics defies what our expectations are, and Bell’s great contribution to quantum physics was that his famous Inequality puts the conundrum into a succinct and testable formula.
Most people know that Bohr and Einstein were key players and philosophical antagonists over quantum theory. The general view is that Bohr ultimately won the argument, and was further justified by the successful verification of Bell’s Theorem, while Einstein was consigned to history as having discovered two of the most important theories in physics (the special and general theories of relativity) but stubbornly rejected the most empirically successful theory of all time, quantum mechanics. Gilder’s book provides a subtle but significantly different perspective. Whilst she portrays Einstein as unapologetically stubborn, he played a far greater role in the development of quantum theory than popular history tends to grant him. In particular, it could be argued that he understood the significance of Bell’s Theorem many decades before Bell actually conceived it.
Correspondence, referenced by Gilder, suggests that Schrodinger’s famous Cat thought experiment originally arose from a suggestion by Einstein, only Einstein envisaged a box containing explosives that were both exploded and un-exploded at the same time. Einstein also supported De Broglie at a time when everyone else ignored him, and he acknowledged that de Broglie had ‘lifted a corner of the great veil’.
Curiously, the cover of her book contains 3 medallion-like photographic portraits, in decreasing size: Albert Einstein, Erwin Schrodinger and Louis de Broglie; all quantum mechanic heretics. Gilder could have easily included David Bohm and John Bell as well, if that was her theme.
Why heretics? Because they all challenged the Copenhagen interpretation of quantum mechanics, led by Bohr and Heisenberg, and which remains the ‘conventional’ interpretation to this day, even though the inherent conundrum of entanglement remains its greatest enigma.
It was Bohr who apparently said that anyone who claims they understand quantum mechanics doesn’t comprehend it at all, or words to that effect. When we come across something that is new to us, that we don’t readily understand, the brain looks for an already known context in which to place it. In an essay I wrote on Epistemology (July 2008) I made the point that we only understand new knowledge when we incorporate it into existing knowledge. The best example is when we look up a word in a dictionary – it’s always explained by using words that we already know. I also pointed out that this plays a role in storytelling where we are continuously incorporating new knowledge into existing knowledge as the story progresses. Without this innate human cognitive ability we’d give up on a story after the first page.
Well the trap with quantum mechanics is that we attempt to understand it in the context of what we already know, when, really, we can’t. It’s only when you understand the mystery of quantum mechanics that you can truly say: I understand it. In other words, when you finally understand what can’t be known, or can’t be predicted, as we generally do with so-called ‘classical physics’. Quantum mechanics obeys different rules, and when you appreciate that they don’t meet our normal ‘cause and effect’ expectations, then you are on the track of appreciating the conundrum. It’s a great credit to Gilder that she conveys this aspect of quantum physics, both in theory and in experiment, better than any other writer I’ve read.
Some thumbnail sketches based on Gilder’s research are worth relaying. She consistently portrays Neils Bohr as a charismatic leader who dominated as much by personality as by intellect. People loved him, but, consequently, found it difficult to oppose him, is the impression that she gives. The great and famous exception was Einstein, who truly did have a mind of his own, but also Wolfgang Pauli, who was famously known to be the most critical critic of any physicist.
John Wheeler, who in the latter part of the 20th Century, became Bohr’s greatest champion said of his early days with Bohr: “Nothing has done more to convince me that there once existed friends of mankind with the human wisdom of Confucius and Buddha, Jesus and Pericles, Erasmus and Lincoln, than walks and talks under the beech trees of Klampenborg Forest with Neils Bohr.” Could there be any greater praise?
Einstein wrote of Max Planck: “an utterly honest man who thinks of others rather than himself. He has, however, one fault: he is clumsy in finding his way about foreign trains of thought.” As for Lorentz, with whom he was corresponding with at the same time as Planck, he found him “astonishingly profound… I admire this man as no other, I would say I love him.”
Much later in the story, Gilder relates an account of how a 75 year-old Planck made a personal presentation to Hitler, attempting to explain how his dismissal of Jewish scientists from academic positions would have disastrous consequences for Germany. Apparently, he barely opened his mouth before he was given a severe dressing-down by the dictator and told where to go. Nevertheless, the story supports Einstein’s appraisal of the man from a generation earlier.
Gilder doesn’t provide a detailed portrait of Paul Dirac or P.A.M. Dirac, as he’s often better-known, but we know he was a very reserved and eccentric individual, whose mathematical prowess effectively forecast the existence of anti-matter. The Dirac equation is no less significantly prophetic than Einstein’s famous equation, E=mc2.
Wolfgang Pauli’s great contribution to physics was the famous Pauli exclusion principle, which I learnt in high school, and provides the explanation as to why atoms don’t all collapse in on each other, and, why, when you touch something you don’t sink into it. He also predicted the existence of the neutrino. Pauli’s personal life went into a steep decline in the 1930s when he suffered from chronic depression and alcoholism. His life turned around after he met Carl Jung and became a lifelong friend. ‘In two years of Jung’s personal analysis and friendship, Pauli shed his depression. In 1934 he met and married Franca Bertram, who would be his companion for the rest of his life.’
This friendship with Jung led to a contradiction in the light of our 21st Century sensibilities, according to Gilder:
’Pauli could tell Bohr to “shut up” and Einstein that his ideas were “actually not stupid”… But in the words of Franca Pauli, “the extremely rational thinker subjected himself to total dependence on Jung’s magical personality.”’
Schrodinger is as well known for his libertine attitude towards sexual relationships as he is for his famous equation. His own wife became the mistress of Schrodinger’s close friend and mathematician, Hermann Weil, whilst Schrodinger had a string of mistresses. But the identity of his lover-companion, when he was famously convalescing from tuberculosis in an Alpine resort in Arosa and conjured up the wave equations that bear his name, is still unknown to this day.
When Schrodinger died in 1961, Max Born (another Nobel Prize winner in the history of quantum mechanics) wrote the following eulogy:
“His private life seemed strange to bourgeois people like ourselves. But all this does not matter. He was a most loveable person, independent, amusing, temperamental, kind, and generous, and he had a most perfect and efficient brain.”
It was Born who turned Schrodinger’s equations into a probability function that every quantum theorist uses to this day. Born was a regular correspondent with Einstein, but is now almost as famously known in pop culture as being grandfather to Australian songstress, Olivia Newton John (not mentioned in Gilder’s book).
Gilder provides a relatively detailed and bitter-sweet history of the relationship between David Bohm and J. Robert Oppenheimer, both affected in adverse ways by the cold war and McCarthy’s ‘House Un-American Activities Committee’.
I personally identify with Gilder’s portrait of Bohm more than I anticipated, not because of his brilliance or his courage, but because of his apparent neurotic disposition and insecurity and his almost naïve honesty.
Gilder has obviously accessed transcripts of his interrogation, where he repeatedly declined to answer questions “on the ground that it might incriminate and degrade me, and also, I think it infringes on my rights as guaranteed by the First Amendment.”
When he was eventually asked if he belonged to a political party, he finally said, “Yes, I am. I would say ‘Yes’ to that question.”
This raised everyone’s interest, naturally, but when he followed up the next question, “What party or association is that?” he said, “I would say definitely that I voted for the Democratic ticket.” ‘The representative from Missouri’, who asked the question, must have been truly pissed off when he pointed out that that wasn’t what he meant. To which Bohm said, in all honesty no doubt, “How does one become a member of the Democratic Pary?”
Bohm lost his career, his income, his status and everything else at a time when he should have been at the peak of his academic abilities. Even Einstein’s letter of recommendation couldn’t get him a position at the University of Manchester and he eventually went to Sao Paulo in Brasil, though he never felt at home there. Gilder sets one of her quasi-fictional scenarios in a bar, when Feynman was visiting Brasil and socialising with Bohm, deliberately juxtaposing the two personalities. She portrays Bohm as not being jealous of Feynman’s mind, but being jealous of his easy confidence in a foreign country and his sex-appeal to women. That’s the David Bohm I can identify with at a similar age.
Bohm eventually migrated to England where he lived for the rest of his life. I don’t believe he ever returned to America, though I can’t be sure how true that is. I do know he became a close friend to the Dalai Lama, because the Dalai Lama mentions their friendship in one of his many autobiographies.
According to Gilder, it’s unclear if Bohm ever forgave Oppenheimer for ‘selling out’ his friend, Bernard Peters, both of whom hero-worshipped Oppenheimer. Certainly, at the time that Oppenheimer ‘outed’ Peters as a ‘crazy red’, Bohm felt that he had betrayed him.
Bohm made a joke of the House Un-American Activities Committee based on the famous logic conundrum postulated by Bertrand Russell: “If the barber is the man who shaves all men who do not shave themselves, who shaves the barber?” Bohm’s version: “Congress should appoint a committee to investigate all committees that do not investigate themselves.”
But of all the characters, John Bell is the one about whom I knew the least, and yet he is the principal character in Gilder’s narrative, because he was not only able to grasp the essential character of quantum mechanics but to quantify it in a way that could be verified. I won’t go into the long story of how it evolved from the Einstein-Podolsky-Rosen (EPR) conjecture, except to say that Gilder covers it extremely well.
What I did find interesting was that after Bell presented his Inequality, the people who wanted to confirm it were not supported or encouraged on either side of the Atlantic. It was considered a career-stopper, and Bell himself, even discouraged up-and-coming physicists from pursuing it. That all changed, of course, when results finally came out.
After reading Gilder’s account, I went back to the interview that Paul Davies had with Bell (The Ghost in the Atom, 1986) after the famous Alain Aspect experiment had confirmed Bell’s Inequality.
Bell is critical of the conventional Copenhagen interpretation because he argues where do you draw the line between the quantum world and the classical world when you make your ‘observation’. Is it at the equipment, or is it in the optic nerve going to your brain, or is it at the neuron in the brain itself. He’s deliberately mocking the view that ‘consciousness’ is the cause of the ‘collapse’ of the quantum wave function.
In the interview he makes specific references to de Broglie and Bohm. Gilder, I noticed, sourced the same material.
“One of the things that I specifically wanted to do was to see whether there was any real objection to this idea put forward long ago by de Broglie and Bohm that you could give a completely realistic account of all quantum phenomena. De Broglie had done that in 1927, and was laughed out of court in a way that I now regard as disgraceful, because his arguments were trampled on. Bohm resurrected that theory in 1952, and was rather ignored. I thought that the theory of Bohm and de Broglie was in all ways equivalent to quantum mechanics for experimental purposes, but nevertheless it was realistic and unambiguous. But it did have the remarkable feature of action-at-a-distance. You could see that when something happened at one point there were consequences immediately over the whole of space unrestricted by the velocity of light.”
Perhaps that should be the last word in this dissertation, but I would like to point out, that, according to Gilder, Einstein made the exact same observation in 1927, when he tried to comprehend the double-slit experiment in terms of Schrodinger’s waves.
Gilder takes an unusual approach, where she creates conversations between key players, as she portrays them, using letters and anecdotal references by the protagonists. She explains how she does this, by way of example, in a preface titled A Note To The Reader, so as not to mislead us that these little scenarios were actually recorded. Sometimes she quotes straight from letters.
When I taught a fiction-writing course early last year, someone asked me is biography fiction or non-fiction? My answer was that as soon as you add dialogue, unless it’s been recorded, it becomes fiction. An example is Schindler’s Ark by Thomas Keneally, who explained that he wrote it as a novel because ‘that is his craft’. In the case of Gilder’s book, I would call these scenarios quasi-fictional. The point is that they work very well, whether they be fictional or not, in giving flesh to the characters as well as the ideas they were exploring.
She provides an insight into these people and their interactions, at a level of perspicuity, that one rarely sees. In particular, she provides an insight into their personal philosophies and prejudices that drove their explorations and their arguments. The heart of the book is Bell’s Theorem or Bell’s Inequality, which I’ve written about before (refer Quantum Mechanical Philosophy, Jul.09). She starts the book off like a Hollywood movie, by providing an excellent exposition of Bell’s Theorem for laypeople (first revealed in 1964) then jumping back in time to the very birth of quantum mechanics (1900) when Planck coined the term, h, (now known as Planck’s constant) to satisfactorily explain black body radiation. Proceeding from this point, Gilder follows the whole story and its amazing cast of characters right up to 2005.
In between there were 2 world wars, a number of Nobel Prizes, the construction of some very expensive particle accelerators and a cold war, which all played their parts in the narrative.
David Mermin, a solid state physicist at Cornell gave the best exposition of Bell’s Theorem to non-physicists, for which the great communicator, Richard Feynman, gave him the ultimate accolade by telling him that he had achieved what Feynman himself had been attempting to achieve yet failed to realise.
Bell’s Theorem, in essence, makes predictions about entangled particles. Entangled particles counter-intuitively suggest action-at-a-distance occurring simultaneously, contradicting everything else we know about reality, otherwise known as ‘classical physics’. Classical physics includes relativity theory which states that nothing, including communication between distinct objects, can occur faster than the speed of light. This is called ‘locality’. Entanglement, which is what Bell’s Theorem entails, suggests the opposite, which we call ‘non-locality’.
Gilder’s abridged version of Mermin’s exposition is lengthy and difficult to summarise, but, by the use of tables, she manages to convey how Bell’s Theorem defies common sense, and that’s the really important bit to understand. Quantum mechanics defies what our expectations are, and Bell’s great contribution to quantum physics was that his famous Inequality puts the conundrum into a succinct and testable formula.
Most people know that Bohr and Einstein were key players and philosophical antagonists over quantum theory. The general view is that Bohr ultimately won the argument, and was further justified by the successful verification of Bell’s Theorem, while Einstein was consigned to history as having discovered two of the most important theories in physics (the special and general theories of relativity) but stubbornly rejected the most empirically successful theory of all time, quantum mechanics. Gilder’s book provides a subtle but significantly different perspective. Whilst she portrays Einstein as unapologetically stubborn, he played a far greater role in the development of quantum theory than popular history tends to grant him. In particular, it could be argued that he understood the significance of Bell’s Theorem many decades before Bell actually conceived it.
Correspondence, referenced by Gilder, suggests that Schrodinger’s famous Cat thought experiment originally arose from a suggestion by Einstein, only Einstein envisaged a box containing explosives that were both exploded and un-exploded at the same time. Einstein also supported De Broglie at a time when everyone else ignored him, and he acknowledged that de Broglie had ‘lifted a corner of the great veil’.
Curiously, the cover of her book contains 3 medallion-like photographic portraits, in decreasing size: Albert Einstein, Erwin Schrodinger and Louis de Broglie; all quantum mechanic heretics. Gilder could have easily included David Bohm and John Bell as well, if that was her theme.
Why heretics? Because they all challenged the Copenhagen interpretation of quantum mechanics, led by Bohr and Heisenberg, and which remains the ‘conventional’ interpretation to this day, even though the inherent conundrum of entanglement remains its greatest enigma.
It was Bohr who apparently said that anyone who claims they understand quantum mechanics doesn’t comprehend it at all, or words to that effect. When we come across something that is new to us, that we don’t readily understand, the brain looks for an already known context in which to place it. In an essay I wrote on Epistemology (July 2008) I made the point that we only understand new knowledge when we incorporate it into existing knowledge. The best example is when we look up a word in a dictionary – it’s always explained by using words that we already know. I also pointed out that this plays a role in storytelling where we are continuously incorporating new knowledge into existing knowledge as the story progresses. Without this innate human cognitive ability we’d give up on a story after the first page.
Well the trap with quantum mechanics is that we attempt to understand it in the context of what we already know, when, really, we can’t. It’s only when you understand the mystery of quantum mechanics that you can truly say: I understand it. In other words, when you finally understand what can’t be known, or can’t be predicted, as we generally do with so-called ‘classical physics’. Quantum mechanics obeys different rules, and when you appreciate that they don’t meet our normal ‘cause and effect’ expectations, then you are on the track of appreciating the conundrum. It’s a great credit to Gilder that she conveys this aspect of quantum physics, both in theory and in experiment, better than any other writer I’ve read.
Some thumbnail sketches based on Gilder’s research are worth relaying. She consistently portrays Neils Bohr as a charismatic leader who dominated as much by personality as by intellect. People loved him, but, consequently, found it difficult to oppose him, is the impression that she gives. The great and famous exception was Einstein, who truly did have a mind of his own, but also Wolfgang Pauli, who was famously known to be the most critical critic of any physicist.
John Wheeler, who in the latter part of the 20th Century, became Bohr’s greatest champion said of his early days with Bohr: “Nothing has done more to convince me that there once existed friends of mankind with the human wisdom of Confucius and Buddha, Jesus and Pericles, Erasmus and Lincoln, than walks and talks under the beech trees of Klampenborg Forest with Neils Bohr.” Could there be any greater praise?
Einstein wrote of Max Planck: “an utterly honest man who thinks of others rather than himself. He has, however, one fault: he is clumsy in finding his way about foreign trains of thought.” As for Lorentz, with whom he was corresponding with at the same time as Planck, he found him “astonishingly profound… I admire this man as no other, I would say I love him.”
Much later in the story, Gilder relates an account of how a 75 year-old Planck made a personal presentation to Hitler, attempting to explain how his dismissal of Jewish scientists from academic positions would have disastrous consequences for Germany. Apparently, he barely opened his mouth before he was given a severe dressing-down by the dictator and told where to go. Nevertheless, the story supports Einstein’s appraisal of the man from a generation earlier.
Gilder doesn’t provide a detailed portrait of Paul Dirac or P.A.M. Dirac, as he’s often better-known, but we know he was a very reserved and eccentric individual, whose mathematical prowess effectively forecast the existence of anti-matter. The Dirac equation is no less significantly prophetic than Einstein’s famous equation, E=mc2.
Wolfgang Pauli’s great contribution to physics was the famous Pauli exclusion principle, which I learnt in high school, and provides the explanation as to why atoms don’t all collapse in on each other, and, why, when you touch something you don’t sink into it. He also predicted the existence of the neutrino. Pauli’s personal life went into a steep decline in the 1930s when he suffered from chronic depression and alcoholism. His life turned around after he met Carl Jung and became a lifelong friend. ‘In two years of Jung’s personal analysis and friendship, Pauli shed his depression. In 1934 he met and married Franca Bertram, who would be his companion for the rest of his life.’
This friendship with Jung led to a contradiction in the light of our 21st Century sensibilities, according to Gilder:
’Pauli could tell Bohr to “shut up” and Einstein that his ideas were “actually not stupid”… But in the words of Franca Pauli, “the extremely rational thinker subjected himself to total dependence on Jung’s magical personality.”’
Schrodinger is as well known for his libertine attitude towards sexual relationships as he is for his famous equation. His own wife became the mistress of Schrodinger’s close friend and mathematician, Hermann Weil, whilst Schrodinger had a string of mistresses. But the identity of his lover-companion, when he was famously convalescing from tuberculosis in an Alpine resort in Arosa and conjured up the wave equations that bear his name, is still unknown to this day.
When Schrodinger died in 1961, Max Born (another Nobel Prize winner in the history of quantum mechanics) wrote the following eulogy:
“His private life seemed strange to bourgeois people like ourselves. But all this does not matter. He was a most loveable person, independent, amusing, temperamental, kind, and generous, and he had a most perfect and efficient brain.”
It was Born who turned Schrodinger’s equations into a probability function that every quantum theorist uses to this day. Born was a regular correspondent with Einstein, but is now almost as famously known in pop culture as being grandfather to Australian songstress, Olivia Newton John (not mentioned in Gilder’s book).
Gilder provides a relatively detailed and bitter-sweet history of the relationship between David Bohm and J. Robert Oppenheimer, both affected in adverse ways by the cold war and McCarthy’s ‘House Un-American Activities Committee’.
I personally identify with Gilder’s portrait of Bohm more than I anticipated, not because of his brilliance or his courage, but because of his apparent neurotic disposition and insecurity and his almost naïve honesty.
Gilder has obviously accessed transcripts of his interrogation, where he repeatedly declined to answer questions “on the ground that it might incriminate and degrade me, and also, I think it infringes on my rights as guaranteed by the First Amendment.”
When he was eventually asked if he belonged to a political party, he finally said, “Yes, I am. I would say ‘Yes’ to that question.”
This raised everyone’s interest, naturally, but when he followed up the next question, “What party or association is that?” he said, “I would say definitely that I voted for the Democratic ticket.” ‘The representative from Missouri’, who asked the question, must have been truly pissed off when he pointed out that that wasn’t what he meant. To which Bohm said, in all honesty no doubt, “How does one become a member of the Democratic Pary?”
Bohm lost his career, his income, his status and everything else at a time when he should have been at the peak of his academic abilities. Even Einstein’s letter of recommendation couldn’t get him a position at the University of Manchester and he eventually went to Sao Paulo in Brasil, though he never felt at home there. Gilder sets one of her quasi-fictional scenarios in a bar, when Feynman was visiting Brasil and socialising with Bohm, deliberately juxtaposing the two personalities. She portrays Bohm as not being jealous of Feynman’s mind, but being jealous of his easy confidence in a foreign country and his sex-appeal to women. That’s the David Bohm I can identify with at a similar age.
Bohm eventually migrated to England where he lived for the rest of his life. I don’t believe he ever returned to America, though I can’t be sure how true that is. I do know he became a close friend to the Dalai Lama, because the Dalai Lama mentions their friendship in one of his many autobiographies.
According to Gilder, it’s unclear if Bohm ever forgave Oppenheimer for ‘selling out’ his friend, Bernard Peters, both of whom hero-worshipped Oppenheimer. Certainly, at the time that Oppenheimer ‘outed’ Peters as a ‘crazy red’, Bohm felt that he had betrayed him.
Bohm made a joke of the House Un-American Activities Committee based on the famous logic conundrum postulated by Bertrand Russell: “If the barber is the man who shaves all men who do not shave themselves, who shaves the barber?” Bohm’s version: “Congress should appoint a committee to investigate all committees that do not investigate themselves.”
But of all the characters, John Bell is the one about whom I knew the least, and yet he is the principal character in Gilder’s narrative, because he was not only able to grasp the essential character of quantum mechanics but to quantify it in a way that could be verified. I won’t go into the long story of how it evolved from the Einstein-Podolsky-Rosen (EPR) conjecture, except to say that Gilder covers it extremely well.
What I did find interesting was that after Bell presented his Inequality, the people who wanted to confirm it were not supported or encouraged on either side of the Atlantic. It was considered a career-stopper, and Bell himself, even discouraged up-and-coming physicists from pursuing it. That all changed, of course, when results finally came out.
After reading Gilder’s account, I went back to the interview that Paul Davies had with Bell (The Ghost in the Atom, 1986) after the famous Alain Aspect experiment had confirmed Bell’s Inequality.
Bell is critical of the conventional Copenhagen interpretation because he argues where do you draw the line between the quantum world and the classical world when you make your ‘observation’. Is it at the equipment, or is it in the optic nerve going to your brain, or is it at the neuron in the brain itself. He’s deliberately mocking the view that ‘consciousness’ is the cause of the ‘collapse’ of the quantum wave function.
In the interview he makes specific references to de Broglie and Bohm. Gilder, I noticed, sourced the same material.
“One of the things that I specifically wanted to do was to see whether there was any real objection to this idea put forward long ago by de Broglie and Bohm that you could give a completely realistic account of all quantum phenomena. De Broglie had done that in 1927, and was laughed out of court in a way that I now regard as disgraceful, because his arguments were trampled on. Bohm resurrected that theory in 1952, and was rather ignored. I thought that the theory of Bohm and de Broglie was in all ways equivalent to quantum mechanics for experimental purposes, but nevertheless it was realistic and unambiguous. But it did have the remarkable feature of action-at-a-distance. You could see that when something happened at one point there were consequences immediately over the whole of space unrestricted by the velocity of light.”
Perhaps that should be the last word in this dissertation, but I would like to point out, that, according to Gilder, Einstein made the exact same observation in 1927, when he tried to comprehend the double-slit experiment in terms of Schrodinger’s waves.
Monday, 4 January 2010
Jesus' philosophy
Normally, I wouldn’t look twice at a book with the title, Jesus & Philosophy, but when the author’s name is Don Cupitt, that changes everything. In September last year, I reviewed his book, Above Us Only Sky (under a post titled The Existential God) which is effectively a manifesto on the ‘religion of ordinary life’ to use his own words.
Cupitt takes a very scholarly approach to his topic, referencing The Gospel of Jesus, which arose from the ‘Jesus Seminar’ (1985 to 1995). And, in fact, Cupitt dedicates the book to the seminar’s founder, Robert W. Funk. He also references a document called ‘Q’. For those, like myself, who’ve never heard of Q, I quote Cupitt himself:
“Q, it should be said in parenthesis here, is the term used by Gospel critics to describe a hypothetical sayings-Gospel, written somewhere between the years 50 and 70 CE, and drawn upon extensively by both Matthew and Luke.”
Cupitt is a most unusual theologian in that he has all but disassembled orthodox Christian theology, and he now sees himself more as a philosopher. The overarching thesis of his book, is that Jesus was the first humanist. From anyone else, this could be dismissed as liberal-theological claptrap, but Cupitt is not anyone else; he commands you to take him seriously by the simple merit of his erudition and his lack of academic pretension or arrogance. You don’t have to agree with him but you can’t dismiss him as a ratbag either.
Many people, these days, even question whether Jesus ever existed. Stephen Law, has posed the question more than once on his blog, but, besides provoking intelligent debate, he’s merely revealed how little we actually know. Cupitt doesn’t even raise this question; he assumes that there was an historical Jesus in the same way that we assume there was an historical Buddha, who, like Jesus, kept no records of his teachings. In fact, Cupitt makes this very same comparison. He argues that Jesus’ sayings, like the Buddha’s, would have been remembered orally before anyone wrote them down, and later narratives were attached to them, which became the gospels we know today. He doesn’t question that the biblical stories are fictional, but he believes that behind them was a real person, whose teachings have been perverted by the long history of the Church. He doesn’t use that term, but I do, because it’s what I’ve long believed. The distortion, if not the perversion, was started by Paul, who is the single most responsible person for the concept of Jesus as saviour or messiah that we have today.
.
I actually disagree with Stephen Law’s thesis, and I’ve contended it on his blog, because a completely fictional Jesus doesn’t make a lot of sense to me. If you are going to create a fictional saviour (who is a Deity) then why make him a mortal first and why make him a complete failure, which he was. On the other hand, deifying a mortal after their death at the hands of their enemy, to become a saviour for an oppressed people, makes a lot of sense. A failure in mortal flesh becomes a messiah in a future kingdom beyond death.
Also if Jesus is completely fictional, who was the original author? The logical answer is Paul, but records of Jesus precede Paul, so Paul must have known he was fictional, if that was the case. I’m not an expert in this area, but Cupitt is not the first person to make a distinction between a Jesus who took on the Church of his day and stood up for the outcast and disenfranchised in his society, and Paul’s version, who both knew and prophesied that he was the ‘Son of God’. H.G. Wells in his encyclopedic book, The Outline of History (written after WWI), remarks similarly on a discontinuity in the Jesus story as we know it.
But all this speculation is secondary, though not irrelevant, to Cupitt’s core thesis. Cupitt creates a simple imagery concerning the two conflicting strands of morality, theistic and humanistic, as being vertical and horizontal. The vertical strand comes straight from God or Heaven, which makes it an unassailable authority, and the horizontal strand stems from the human ‘heart’.
His argument, in essence, is that Jesus’ teachings, when analysed, appealed to the heart, not to God’s authority, and, in this respect, he had more in common with Buddha and Confucius than to Moses or Abraham or David. In fact, more than once, Cupitt likens Jesus to an Eastern sage (his words) who drew together a group of disciples, and through examples and teachings, taught a simple philosophy, not only of reciprocity, but of forgiveness.
In fact, Cupitt contends that reciprocity was not Jesus’ core teaching, and, even in his Preface, before he gets into the body of his text, he quotes from the ‘Gospel of Jesus’ to make his point: “If you do good to those who do good to you, what merit is there in that?” (Gospel of Jesus, 7.4; Q/Luke 7.33). Cupitt argues that one of Jesus’ most salient messages was to break the cycle of violence that afflicts all of humanity, and which we see, ironically, most prominently demonstrated in modern day Palestine.
Cupitt uses the term 'ressentiment' to convey this peculiar human affliction: the inability to let go of a grievance, especially when it involves a loved one, but also when it involves more amorphous forms of identity, like nation or race or creed (see my post on Evil, Oct. 07). According to Cuppit, “Jesus says: ‘Don’t let yourself be provoked into ressentiment by the prosperity of the wicked. Instead, be magnanimous, and teach yourself to see in it the grace of God, giving them time to repent. Too many people who have seen the blood of the innocent crying out for vengeance have allowed themselves to develop the revolting belief in a sadistic and vengeful God.’” (Cupitt doesn’t give a reference for this ‘saying’, however.)
I don’t necessarily agree with Cupitt’s conclusion that Jesus is the historical ‘hinge’ from the vertical strand to the horizontal strand, which is the case he makes over 90 odd pages. I think there have been others, notably Gautama Siddhartha (Buddha) and Confucius, who were arguably just as secular as Jesus was, and preceded him by 500 years, though their spheres of influence were geographically distinct from Jesus’.
Obviously, I haven’t covered all of Cupitt’s thesis, including references to Plato and Kant, and the historical relationship between the vertical and horizontal strands of morality. He makes compelling arguments that Jesus has long been misrepresented by the Church, in particular, that Jesus challenged his society’s dependence on dogmatic religious laws.
One interesting point Cupitt makes, almost as a side issue, is that it was the introduction of the novel that brought humanist morality into intellectual discourse. Novels, and their modern derivatives in film and television, have invariably portrayed moral issues as being inter-human not God-human. As Cupitt remarks, you will go a long way before you will find a novel that portrays morality as being God-given. Even so-called religious writers, like Graham Greene and Morris West, were always analysing morality through human interaction (Greene was a master of the moral dilemma) and if God entered one of their narratives, ‘He’ was an intellectual concept, not a character in the story.
There is one aspect of Jesus that Cupitt doesn’t address, and it’s the fact that so many Christians claim to have a personal relationship with him. This, of course, is not isolated to Jesus. I know people who claim to have a personal relationship with Quan Yin (the Buddhist Goddess of Mercy) and others claim a relationship with the Madonna and others with Allah and others with Yahweh and so on. So what is all this? This phenomena, so widespread, has fascinated me all my life, and the simple answer is that it’s a projection. There is nothing judgmental in this hypothesis. My reasoning is that for every individual, the projection is unique. Everyone who believes in this inner Jesus has their own specific version of him. I don’t knock this, but, as I’ve said before, the Deity someone believes in says more about them than it says about the Deity. If this Deity represents all that is potentially good in humanity then there is no greater aspiration.
In the beginning of Cupitt’s book, even before the Preface, he presents William Blake’s poem, The Divine Image. In particular, I like the last verse, which could sum up Cupitt’s humanist thesis.
And all must love the human form,
In heathen, Turk, or Jew;
Where Mercy, Love, & Pity dwell
There God is dwelling too.
In other words, God represents the feeling we have for all of humanity, which is not only subjective, but covers every possible attribute. If you believe in a vengeful, judgmental God, then you might not have a high opinion of humanity, but if you believe in a forgiving and loving God, then maybe that’s where your heart lies. As for those who claim God is both, then I can only assume they are as schizoid in their relationships as their Deity is.
Cupitt takes a very scholarly approach to his topic, referencing The Gospel of Jesus, which arose from the ‘Jesus Seminar’ (1985 to 1995). And, in fact, Cupitt dedicates the book to the seminar’s founder, Robert W. Funk. He also references a document called ‘Q’. For those, like myself, who’ve never heard of Q, I quote Cupitt himself:
“Q, it should be said in parenthesis here, is the term used by Gospel critics to describe a hypothetical sayings-Gospel, written somewhere between the years 50 and 70 CE, and drawn upon extensively by both Matthew and Luke.”
Cupitt is a most unusual theologian in that he has all but disassembled orthodox Christian theology, and he now sees himself more as a philosopher. The overarching thesis of his book, is that Jesus was the first humanist. From anyone else, this could be dismissed as liberal-theological claptrap, but Cupitt is not anyone else; he commands you to take him seriously by the simple merit of his erudition and his lack of academic pretension or arrogance. You don’t have to agree with him but you can’t dismiss him as a ratbag either.
Many people, these days, even question whether Jesus ever existed. Stephen Law, has posed the question more than once on his blog, but, besides provoking intelligent debate, he’s merely revealed how little we actually know. Cupitt doesn’t even raise this question; he assumes that there was an historical Jesus in the same way that we assume there was an historical Buddha, who, like Jesus, kept no records of his teachings. In fact, Cupitt makes this very same comparison. He argues that Jesus’ sayings, like the Buddha’s, would have been remembered orally before anyone wrote them down, and later narratives were attached to them, which became the gospels we know today. He doesn’t question that the biblical stories are fictional, but he believes that behind them was a real person, whose teachings have been perverted by the long history of the Church. He doesn’t use that term, but I do, because it’s what I’ve long believed. The distortion, if not the perversion, was started by Paul, who is the single most responsible person for the concept of Jesus as saviour or messiah that we have today.
.
I actually disagree with Stephen Law’s thesis, and I’ve contended it on his blog, because a completely fictional Jesus doesn’t make a lot of sense to me. If you are going to create a fictional saviour (who is a Deity) then why make him a mortal first and why make him a complete failure, which he was. On the other hand, deifying a mortal after their death at the hands of their enemy, to become a saviour for an oppressed people, makes a lot of sense. A failure in mortal flesh becomes a messiah in a future kingdom beyond death.
Also if Jesus is completely fictional, who was the original author? The logical answer is Paul, but records of Jesus precede Paul, so Paul must have known he was fictional, if that was the case. I’m not an expert in this area, but Cupitt is not the first person to make a distinction between a Jesus who took on the Church of his day and stood up for the outcast and disenfranchised in his society, and Paul’s version, who both knew and prophesied that he was the ‘Son of God’. H.G. Wells in his encyclopedic book, The Outline of History (written after WWI), remarks similarly on a discontinuity in the Jesus story as we know it.
But all this speculation is secondary, though not irrelevant, to Cupitt’s core thesis. Cupitt creates a simple imagery concerning the two conflicting strands of morality, theistic and humanistic, as being vertical and horizontal. The vertical strand comes straight from God or Heaven, which makes it an unassailable authority, and the horizontal strand stems from the human ‘heart’.
His argument, in essence, is that Jesus’ teachings, when analysed, appealed to the heart, not to God’s authority, and, in this respect, he had more in common with Buddha and Confucius than to Moses or Abraham or David. In fact, more than once, Cupitt likens Jesus to an Eastern sage (his words) who drew together a group of disciples, and through examples and teachings, taught a simple philosophy, not only of reciprocity, but of forgiveness.
In fact, Cupitt contends that reciprocity was not Jesus’ core teaching, and, even in his Preface, before he gets into the body of his text, he quotes from the ‘Gospel of Jesus’ to make his point: “If you do good to those who do good to you, what merit is there in that?” (Gospel of Jesus, 7.4; Q/Luke 7.33). Cupitt argues that one of Jesus’ most salient messages was to break the cycle of violence that afflicts all of humanity, and which we see, ironically, most prominently demonstrated in modern day Palestine.
Cupitt uses the term 'ressentiment' to convey this peculiar human affliction: the inability to let go of a grievance, especially when it involves a loved one, but also when it involves more amorphous forms of identity, like nation or race or creed (see my post on Evil, Oct. 07). According to Cuppit, “Jesus says: ‘Don’t let yourself be provoked into ressentiment by the prosperity of the wicked. Instead, be magnanimous, and teach yourself to see in it the grace of God, giving them time to repent. Too many people who have seen the blood of the innocent crying out for vengeance have allowed themselves to develop the revolting belief in a sadistic and vengeful God.’” (Cupitt doesn’t give a reference for this ‘saying’, however.)
I don’t necessarily agree with Cupitt’s conclusion that Jesus is the historical ‘hinge’ from the vertical strand to the horizontal strand, which is the case he makes over 90 odd pages. I think there have been others, notably Gautama Siddhartha (Buddha) and Confucius, who were arguably just as secular as Jesus was, and preceded him by 500 years, though their spheres of influence were geographically distinct from Jesus’.
Obviously, I haven’t covered all of Cupitt’s thesis, including references to Plato and Kant, and the historical relationship between the vertical and horizontal strands of morality. He makes compelling arguments that Jesus has long been misrepresented by the Church, in particular, that Jesus challenged his society’s dependence on dogmatic religious laws.
One interesting point Cupitt makes, almost as a side issue, is that it was the introduction of the novel that brought humanist morality into intellectual discourse. Novels, and their modern derivatives in film and television, have invariably portrayed moral issues as being inter-human not God-human. As Cupitt remarks, you will go a long way before you will find a novel that portrays morality as being God-given. Even so-called religious writers, like Graham Greene and Morris West, were always analysing morality through human interaction (Greene was a master of the moral dilemma) and if God entered one of their narratives, ‘He’ was an intellectual concept, not a character in the story.
There is one aspect of Jesus that Cupitt doesn’t address, and it’s the fact that so many Christians claim to have a personal relationship with him. This, of course, is not isolated to Jesus. I know people who claim to have a personal relationship with Quan Yin (the Buddhist Goddess of Mercy) and others claim a relationship with the Madonna and others with Allah and others with Yahweh and so on. So what is all this? This phenomena, so widespread, has fascinated me all my life, and the simple answer is that it’s a projection. There is nothing judgmental in this hypothesis. My reasoning is that for every individual, the projection is unique. Everyone who believes in this inner Jesus has their own specific version of him. I don’t knock this, but, as I’ve said before, the Deity someone believes in says more about them than it says about the Deity. If this Deity represents all that is potentially good in humanity then there is no greater aspiration.
In the beginning of Cupitt’s book, even before the Preface, he presents William Blake’s poem, The Divine Image. In particular, I like the last verse, which could sum up Cupitt’s humanist thesis.
And all must love the human form,
In heathen, Turk, or Jew;
Where Mercy, Love, & Pity dwell
There God is dwelling too.
In other words, God represents the feeling we have for all of humanity, which is not only subjective, but covers every possible attribute. If you believe in a vengeful, judgmental God, then you might not have a high opinion of humanity, but if you believe in a forgiving and loving God, then maybe that’s where your heart lies. As for those who claim God is both, then I can only assume they are as schizoid in their relationships as their Deity is.
Friday, 1 January 2010
Stieg Larsson’s The Girl with the Dragon Tattoo
I don’t normally review novels, but, to be honest, I don’t read a lot of them either, which is an incredible admission for a want-to-be author to make (actually, I’m a real author, just not a very successful one). Most of my reading is non-fiction, at least 90%, and when given a choice between a novel or a non-fiction book, I’ll invariably end up with the latter. There are always a stack of unread books in front of me, which are all non-fiction.
The Girl with the Dragon Tattoo was an exception – this was a book I had to read – simply because I’d heard so much about it. It’s the first in a trilogy by Stieg Larsson, who unfortunately died before they became monstrously successful. The first won a Galaxy British Books award for the ‘Crime Thriller of the Year 2009’. I’m not sure if it has the same status in America as it has in the rest of the world, but, if it hasn’t, I expect that would change if the movie went international.
Larsson was not much younger than me, and was a journalist and editor-in-chief of Expo from 1999. He died in 2004, only 50 years old, just after he delivered all three manuscripts to his Swedish publisher. As a first novel, I’m extraordinarily impressed, and, from my own experience of publishing my first novel at a similar age, I suspect he must have been practicing the art of fiction well beforehand. Very few journalists make the jump from non-fiction to fiction (refer my post on Storytelling, Jul.09) even though the craft of creating easy-to-read yet meaningful and emotively charged prose is well hone. It’s a big leap from writing stories about real people and real events to imaginary scenarios populated by fictional yet believable characters. The craft of writing engaging dialogue looks deceptively simple, yet it can stump the most practiced wordsmith if they’ve never attempted it before.
Larsson has two protagonists, one middle-aged male and one mid-twenties female, who are opposites in almost every respect except intelligence. Mikael Blomkvist could easily be an alter-ego for Larsson, as he’s a financial investigative journalist who jointly runs a magazine with his ‘occasional lover’, Erika Berger, but, being an author myself, I don’t necessarily jump to such obvious conclusions. When people see an actor in a role on the screen, they often assume that that is what he or she must be like in real life, yet that’s the actor’s job: to make you believe the screen persona is a real person. Well, we authors have to create the same illusion – we are all magicians in that sense. There’s no doubt that Larsson used his inside-knowledge in developing his story and background for his character, but the personality of Blomkvist may be quite different to Larsson. In fact, there is no reason not to assume that his other protagonist, albeit a different age, sex and occupation, may be closer in personality to its creator. Having said that, Lisbeth Salander (who is the girl with the dragon tattoo) is a dysfunctional personality, possibly with a variant of Asberger’s that makes one pause. The point is that she’s just as well drawn as Blomkvist, perhaps even better.
My point is that authors, myself included, often create characters who have characteristics that we wish we had but know we haven’t. Blomkvist is an easy-going, tolerant person with liberal views, who charms the pants off women, but has an incisive mind that sees through deception. Larsson may have had these qualities or some of these qualities and added others. We all do this to our protagonists.
One of the strengths of this book is that, whilst it entertains in a way that we expect thrillers to, it exhibits a social conscience with a strong feminist subtext. There are 4 parts, comprising 29 chapters, bookended with a prologue and epilogue. Each part has its own title page, and they all contain a statistic concerning violence against women in Sweden. I will quote the last one in the book, on the title page for Part 4, Hostile Takeover:
“92% of women in Sweden who have been subjected to sexual assault have not reported the most recent violent incident to the Police.”
One of the things I personally like about this book is that it challenges our natural tendency to judge people by appearances. Larsson does this with Salander all through the book, where people continually misjudge her, and, all through her fictional life, she’s been undervalued and written off as a ‘retard’ and social misfit.
As a young person growing up, two of the most influential people in my life were eccentrics, both women, one my own age and one 2 generations older. This has made me more tolerant and less judgemental than most people I know. To this extent I can identify with Blomkvist. It’s one of the resonances I felt most strongly in this novel.
Larsson is a very good writer on all fronts. It is halfway through the book (comprising over 500 pages, approx. 150,000 words long) before anything truly dramatic happens on the page. Beforehand we have lots of mystery and lots of intrigue, but not a lot of action or real suspense. It’s a great credit to Larsson that he keeps you engaged for that entire time (it’s a genuine page-turner) without resorting to mini-climaxes. Dan Brown could learn a lot from Stieg Larsson. Brown is a master of riddles, but Larsson’s writing has a depth, both in characterisation and subtext, that’s way over Brown’s head.
There’s nothing much else to say – I’m yet to read the other two in the series. I assume they are self-contained stories with the same protagonists. One is naturally interested in how their relationship develops, both professionally and personally. I often believe that what raises one novel above another is the psychological believability of the characters, to coin my own phrase. Last year I reviewed the film, Watchmen (Oct. 09), a movie based on a graphic novel, but it was the depth of characterisation, along with its substantial subtext, that lifted it above the expected norm for comic-book movies. The Girl with the Dragon Tattoo is in a similar class of fiction. I don’t judge books or films by their genre; I judge them, primarily, by how well-written they are – it’s probably the criterion we all use, but we’re not consciously aware of.
Friday, 25 December 2009
The Origins of Mathematics
Note the plural in the title, because the mathematics we use today comes from a number of different sources, geographically and culturally. We have a very Eurocentric outlook on mathematics that belies its global heritage.
I came across a small, well-presented volume in my local bookshop: The Bedside Book of Algebra by Michael Willers, a Canadian high school teacher of my vintage, going by the pop-cultural references he sprinkles throughout. When I thumbed through it, my first impression was that it contained nothing I didn’t already know, but I liked the presentation and I realised that it gave a history of mathematics as well as an exposition. It would be an excellent book for anyone wanting a grasp of high school mathematics, as it covers most topics, except calculus and matrices. The presentation is excellent, as he delivers his topics in 2 page bites, and provides examples that are easy to follow. I read it from cover to cover, and learnt a few new things as well as reacquainting myself with old friends like Pascal’s triangle. In fact, Willers revealed a few things about Pascal’s triangle that I didn’t know, like its relationship with the Fibonacci sequence and its generation of fractal patterns using a ‘tiling’ algorithm developed by Polish mathematician, Waclaw Sierpinski in 1915.
I already knew that the Chinese had discovered Pascal’s triangle some 500 years before Pascal (11th Century, Jia Xian), but I didn’t know that the earliest known reference was from an Indian mathematician, Varahamihira, in the 6th Century, or that it appeared in 10th Century Persia, thanks to Al-Karaji. (Blaise Pascal lived 1623-1662.)
Fibonacci (1170-1250) is most famously remembered for the arithmetic sequence that bears his name and also the ‘Golden Ratio’, which can be generated from the sequence. Both the Fibonacci sequence and the Golden Ratio can be found in nature – for example, flower petals are invariably a Fibonacci number and the height of a person’s navel to their height is supposedly the Golden Ratio, but I’m unsure if that is true or just wistful thinking on the part of renaissance artists. Because the Fibonacci sequence is derived by the sum of the previous 2 numbers in the sequence, there are some natural events that follow that rule, like the unchecked population growth of rabbits (that is provided as an example in Willers’ book) and was apparently the original example that Fibonacci used to introduce it.
But we all owe Fibonacci a great debt, because it was he who introduced the Hindu-Arabic numeral system to the Western world in a popular format that has made life so much easier for accountants, engineers, economists, mathematical students and anyone who has ever had to deal with numbers, which is all of us. When I was a child I was told that we used ‘Arabic’ numerals, and I only learned recently that they originated in India. The 7th Century Indian mathematician, Brahmagupta, formulated the first known mathematical concepts that treated zero as a number as well as a place holder (to paraphrase Willers).
Zero and negative numbers were treated with suspicion by the ancient Greeks and Romans, as they preferred geometrical over arithmetical analysis. Because there were no negative areas or negative volumes, the idea of a negative number was considered ‘absurd’. (I have to admit I had the same problem with ‘imaginary’ numbers, when I first encountered them, but I’m getting off the track, and I’ll return to imaginary numbers later.) Likewise, there was no place for a number that represented nothing, but once one introduces negative numbers, zero becomes inevitable, because a negative plus a positive of the same amount must give zero. But zero as a place holder is even more important, because it facilitates all arithmetical computations. As Willer says, imagine trying to do basic arithmetic with Roman numerals, let alone anything esoteric.
Willers quotes Pierre-Simon Laplace (1749-1827): “It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.”
Willers is the first author I’ve read who makes a genuine attempt to give the Indians and the Persians their due credit for our mathematical heritage. Like the Chinese, the Indians discovered Pythagoras’s triangle before the Pythagoreans, though many people believe Pythagoras actually learnt it from the Babylonians. The Indians also investigated the square route of 2, as well as π (pi), around the same time as the ancient Greeks. In the middle ages, a succession of Indian scholars worked on quadratic equations.
But it is Brahmagupta (598-670), who lived in northwestern India (now Pakistan), to whom Willers devotes one of his 2-page treatises, because he argues that Brahmagupta had the biggest influence on Western mathematics. He lists Brahmagupta’s 14 laws, all dealing with the arithmetic ‘rules’ applicable to zero and negative numbers that, in modern times, we all learn in our childhood.
Willers also gives special attention to two Islamic mathematicians, Al-Khwarizmi (born around 780) and Omar Khayam (1048-1122). Al-Khwarizmi came from Khwarezm (present-day Uzbekistan) and worked in the ‘House of Wisdom’ (see below). He gave us two of our most common mathematical terms: algebra and algorithm. Algebra came from the title of a book he wrote, Hisab Al-jabr w’Al-Muqabala, derived from the word, ‘Al-jabr’. Significantly, he developed methods for deriving the roots of quadratic equations.
The word, algorithm, also comes from the title of a book, Algoritmi de Numero Indorum, which is a Latin translation of one of Al-Khwarizmi’s Arabic texts, now lost. And, according to Willers, algorithm ‘means a number of steps or instructions to be followed.’ Of course, this word is now associated with computer programmes (software). This modern incarnation began with Alan Turing’s famous ‘thought experiment’ of a ‘Universal Turing machine’, as the first iconic example of the modern use of algorithm, which is literally a set of instructions, otherwise known as ‘code’. All modern computers are universal Turing machines, by the way, so it’s much more than a thought experiment now, and algorithms are the code, or software, that drives them.
Omar Khayam is probably better known as a poet, from his authorship of The Rubaiyat, a collection of 600 quatrains (4 line poems). But he also authored a number of books on mathematics, including Treatise on Demonstration of Problems of Algebra (1070), in which he solves cubic equations geometrically by intersecting conic sections with a plane. If one cuts a cone with a plane it describes a curve on the plane. Depending on the angle of the plane with the cone, one can get a circle, an ellipse, a parabola, or, using two cones, two mirror hyperbolae. In another text, that Khayam references, but has since been lost, he writes about Pascal’s triangle, though, obviously, he called it something else.
Omar Khayam provides the best quote in Willers’ book, taken from the above text:
The majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes.
As Willers points out, Plato’s academy closed in 529 and Fibonacci came on the scene in Pisa at the end of the 12th Century, and it wasn’t until the renaissance that Western science, art and philosophy really gained the ascendancy again. The interim period is known colloquially as the ‘dark ages’, because knowledge and scientific progress seemed to stagnate. As Willers says: “From that point [the closure of Plato’s Academy] until the thirteenth century the mathematical centre of the world was in the East.”
According to Willers, The House of Wisdom was established in Baghdad by Harun Al-Rashid (763-809) and translated works from Persia, Greece and India. It was a centre for education in humanities and sciences until it was destroyed by the Mongols in 1258. Without this Islamic connection over that period, the Greek and Roman knowledge in the sciences, philosophy, mathematics and literature, which, today, we consider to be our Western heritage, may have been lost.
As well as providing this historical context, in more detail than I can render here, and that most of us don’t even know about, Willers gives us excellent exposition on a number of topics: permutations and combinations, probability theory, logarithms, trigonometry, quadratics, complex algebra, the binomial theorem, and others.
He treats all these exemplarily, but I would like to say something about complex arithmetic and imaginary numbers, because it was a personal stumbling block for me, and, in hindsight, it shouldn’t have been. The set of imaginary numbers contains only one number, i, which is the square route of -1 (some texts say the set contains 2 numbers, i and –i, but, being pedantic, I beg to differ). Now all through my childhood, the square route of -1 was considered an impossibility like dividing by zero. So when someone finally came up with i, I believed I’d been conned – it was a convenience, invented to overcome a conundrum, and, from my perspective, it should have remained an impossibility. Part of the problem, as Willers points out, is that it’s called an ‘imaginary’ number, when it’s just as real as any other number, and I think that’s a very good point.
When one thinks that the Pythagoreans had serious problems accepting irrational numbers, and then the Greek and Roman mathematicians who followed them, had conceptual issues with zero and negative numbers, the concept of i is no different. It’s a number and it opens up an entirely new world in mathematics that includes fractals, the famous Mandelbrot set and quantum mechanics. If one doesn’t explain complex numbers using the complex plane (or Argand diagram) then it won’t make sense, but if one does, everything falls into place. In particular, multiplying by i rotates any graph on the plane through 90 degrees (a right angle), and by i2 (-1) by 180 degrees. In an ordinary number line with positive numbers running right and negative numbers running left, multiplying a positive number by -1 rotates the number through the origin (0) by 180 degrees to its negative equivalent. If you have an i axis running vertically through 0 then multiplying a number by i just rotates it by 90 degrees (half way). If you draw the graph it makes perfect sense.
Imaginary numbers, like multiple dimensions, demonstrate that the mathematical world can go places that the physical world doesn’t necessarily follow, yet these esoteric mathematical entities can have applications in the real world that we don’t anticipate at the time of their discovery. Reimann’s geometry giving us Einstein’s General Theory of Relativity and imaginary numbers giving us the key to quantum mechanics are two cases in point, both barely a century ago.
I’m one of those who sees mathematics as an abstract territory that only an intelligent species can navigate. Personally, I would like to think that we are not the only ones in the universe who can, and maybe there is at least one other species somewhere who can navigate even further than we can. It’s a sobering yet tantalising thought.
Addendum: I've since written an exposition on imaginary numbers and the complex plane, for those who are interested.
I came across a small, well-presented volume in my local bookshop: The Bedside Book of Algebra by Michael Willers, a Canadian high school teacher of my vintage, going by the pop-cultural references he sprinkles throughout. When I thumbed through it, my first impression was that it contained nothing I didn’t already know, but I liked the presentation and I realised that it gave a history of mathematics as well as an exposition. It would be an excellent book for anyone wanting a grasp of high school mathematics, as it covers most topics, except calculus and matrices. The presentation is excellent, as he delivers his topics in 2 page bites, and provides examples that are easy to follow. I read it from cover to cover, and learnt a few new things as well as reacquainting myself with old friends like Pascal’s triangle. In fact, Willers revealed a few things about Pascal’s triangle that I didn’t know, like its relationship with the Fibonacci sequence and its generation of fractal patterns using a ‘tiling’ algorithm developed by Polish mathematician, Waclaw Sierpinski in 1915.
I already knew that the Chinese had discovered Pascal’s triangle some 500 years before Pascal (11th Century, Jia Xian), but I didn’t know that the earliest known reference was from an Indian mathematician, Varahamihira, in the 6th Century, or that it appeared in 10th Century Persia, thanks to Al-Karaji. (Blaise Pascal lived 1623-1662.)
Fibonacci (1170-1250) is most famously remembered for the arithmetic sequence that bears his name and also the ‘Golden Ratio’, which can be generated from the sequence. Both the Fibonacci sequence and the Golden Ratio can be found in nature – for example, flower petals are invariably a Fibonacci number and the height of a person’s navel to their height is supposedly the Golden Ratio, but I’m unsure if that is true or just wistful thinking on the part of renaissance artists. Because the Fibonacci sequence is derived by the sum of the previous 2 numbers in the sequence, there are some natural events that follow that rule, like the unchecked population growth of rabbits (that is provided as an example in Willers’ book) and was apparently the original example that Fibonacci used to introduce it.
But we all owe Fibonacci a great debt, because it was he who introduced the Hindu-Arabic numeral system to the Western world in a popular format that has made life so much easier for accountants, engineers, economists, mathematical students and anyone who has ever had to deal with numbers, which is all of us. When I was a child I was told that we used ‘Arabic’ numerals, and I only learned recently that they originated in India. The 7th Century Indian mathematician, Brahmagupta, formulated the first known mathematical concepts that treated zero as a number as well as a place holder (to paraphrase Willers).
Zero and negative numbers were treated with suspicion by the ancient Greeks and Romans, as they preferred geometrical over arithmetical analysis. Because there were no negative areas or negative volumes, the idea of a negative number was considered ‘absurd’. (I have to admit I had the same problem with ‘imaginary’ numbers, when I first encountered them, but I’m getting off the track, and I’ll return to imaginary numbers later.) Likewise, there was no place for a number that represented nothing, but once one introduces negative numbers, zero becomes inevitable, because a negative plus a positive of the same amount must give zero. But zero as a place holder is even more important, because it facilitates all arithmetical computations. As Willer says, imagine trying to do basic arithmetic with Roman numerals, let alone anything esoteric.
Willers quotes Pierre-Simon Laplace (1749-1827): “It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit.”
Willers is the first author I’ve read who makes a genuine attempt to give the Indians and the Persians their due credit for our mathematical heritage. Like the Chinese, the Indians discovered Pythagoras’s triangle before the Pythagoreans, though many people believe Pythagoras actually learnt it from the Babylonians. The Indians also investigated the square route of 2, as well as π (pi), around the same time as the ancient Greeks. In the middle ages, a succession of Indian scholars worked on quadratic equations.
But it is Brahmagupta (598-670), who lived in northwestern India (now Pakistan), to whom Willers devotes one of his 2-page treatises, because he argues that Brahmagupta had the biggest influence on Western mathematics. He lists Brahmagupta’s 14 laws, all dealing with the arithmetic ‘rules’ applicable to zero and negative numbers that, in modern times, we all learn in our childhood.
Willers also gives special attention to two Islamic mathematicians, Al-Khwarizmi (born around 780) and Omar Khayam (1048-1122). Al-Khwarizmi came from Khwarezm (present-day Uzbekistan) and worked in the ‘House of Wisdom’ (see below). He gave us two of our most common mathematical terms: algebra and algorithm. Algebra came from the title of a book he wrote, Hisab Al-jabr w’Al-Muqabala, derived from the word, ‘Al-jabr’. Significantly, he developed methods for deriving the roots of quadratic equations.
The word, algorithm, also comes from the title of a book, Algoritmi de Numero Indorum, which is a Latin translation of one of Al-Khwarizmi’s Arabic texts, now lost. And, according to Willers, algorithm ‘means a number of steps or instructions to be followed.’ Of course, this word is now associated with computer programmes (software). This modern incarnation began with Alan Turing’s famous ‘thought experiment’ of a ‘Universal Turing machine’, as the first iconic example of the modern use of algorithm, which is literally a set of instructions, otherwise known as ‘code’. All modern computers are universal Turing machines, by the way, so it’s much more than a thought experiment now, and algorithms are the code, or software, that drives them.
Omar Khayam is probably better known as a poet, from his authorship of The Rubaiyat, a collection of 600 quatrains (4 line poems). But he also authored a number of books on mathematics, including Treatise on Demonstration of Problems of Algebra (1070), in which he solves cubic equations geometrically by intersecting conic sections with a plane. If one cuts a cone with a plane it describes a curve on the plane. Depending on the angle of the plane with the cone, one can get a circle, an ellipse, a parabola, or, using two cones, two mirror hyperbolae. In another text, that Khayam references, but has since been lost, he writes about Pascal’s triangle, though, obviously, he called it something else.
Omar Khayam provides the best quote in Willers’ book, taken from the above text:
The majority of people who imitate philosophers confuse the true with the false, and they do nothing but deceive and pretend knowledge, and they do not use what they know of the sciences except for base and material purposes.
As Willers points out, Plato’s academy closed in 529 and Fibonacci came on the scene in Pisa at the end of the 12th Century, and it wasn’t until the renaissance that Western science, art and philosophy really gained the ascendancy again. The interim period is known colloquially as the ‘dark ages’, because knowledge and scientific progress seemed to stagnate. As Willers says: “From that point [the closure of Plato’s Academy] until the thirteenth century the mathematical centre of the world was in the East.”
According to Willers, The House of Wisdom was established in Baghdad by Harun Al-Rashid (763-809) and translated works from Persia, Greece and India. It was a centre for education in humanities and sciences until it was destroyed by the Mongols in 1258. Without this Islamic connection over that period, the Greek and Roman knowledge in the sciences, philosophy, mathematics and literature, which, today, we consider to be our Western heritage, may have been lost.
As well as providing this historical context, in more detail than I can render here, and that most of us don’t even know about, Willers gives us excellent exposition on a number of topics: permutations and combinations, probability theory, logarithms, trigonometry, quadratics, complex algebra, the binomial theorem, and others.
He treats all these exemplarily, but I would like to say something about complex arithmetic and imaginary numbers, because it was a personal stumbling block for me, and, in hindsight, it shouldn’t have been. The set of imaginary numbers contains only one number, i, which is the square route of -1 (some texts say the set contains 2 numbers, i and –i, but, being pedantic, I beg to differ). Now all through my childhood, the square route of -1 was considered an impossibility like dividing by zero. So when someone finally came up with i, I believed I’d been conned – it was a convenience, invented to overcome a conundrum, and, from my perspective, it should have remained an impossibility. Part of the problem, as Willers points out, is that it’s called an ‘imaginary’ number, when it’s just as real as any other number, and I think that’s a very good point.
When one thinks that the Pythagoreans had serious problems accepting irrational numbers, and then the Greek and Roman mathematicians who followed them, had conceptual issues with zero and negative numbers, the concept of i is no different. It’s a number and it opens up an entirely new world in mathematics that includes fractals, the famous Mandelbrot set and quantum mechanics. If one doesn’t explain complex numbers using the complex plane (or Argand diagram) then it won’t make sense, but if one does, everything falls into place. In particular, multiplying by i rotates any graph on the plane through 90 degrees (a right angle), and by i2 (-1) by 180 degrees. In an ordinary number line with positive numbers running right and negative numbers running left, multiplying a positive number by -1 rotates the number through the origin (0) by 180 degrees to its negative equivalent. If you have an i axis running vertically through 0 then multiplying a number by i just rotates it by 90 degrees (half way). If you draw the graph it makes perfect sense.
Imaginary numbers, like multiple dimensions, demonstrate that the mathematical world can go places that the physical world doesn’t necessarily follow, yet these esoteric mathematical entities can have applications in the real world that we don’t anticipate at the time of their discovery. Reimann’s geometry giving us Einstein’s General Theory of Relativity and imaginary numbers giving us the key to quantum mechanics are two cases in point, both barely a century ago.
I’m one of those who sees mathematics as an abstract territory that only an intelligent species can navigate. Personally, I would like to think that we are not the only ones in the universe who can, and maybe there is at least one other species somewhere who can navigate even further than we can. It’s a sobering yet tantalising thought.
Addendum: I've since written an exposition on imaginary numbers and the complex plane, for those who are interested.
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