Nonlinear Nabokov

Updated on Monday, April 28, 2008 by R.A. DiDio

In his Letters to a Young Poet, Rainer Maria Rilke wrote most achingly of the need, for those so called, to write...

ask yourself in the most silent hour of your night: must I write? Dig into yourself for a deep answer. And if this answer rings out in assent, if you meet this solemn question with a strong, simple "I must," then build your life in accordance with this necessity;

Vladimir Nabokov - a pre-eminent author of the 20th century, Russian emigre, butterfly expert, author of Lolita - built his life according to Rilke's mandate.

But he shuffled while he wrote.

Nabokov's writing method typically included composing on index cards. Quirkily, he would shuffle these cards daily, allowing him to see different paths to take by looking at the story unfolding in different ways.

This non-linearity in structure was also matched by a non-linearity in focus: he often wrote the middle of the story last.

At several thousand index cards per book, this produces a lot of different paths.

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Prescience and Spice and Everything Nice

There is prediction, and there is prognostication.  And, once in a great while, there is true prescience.

Consider the case of J.C.R. Licklider - a seminal figure of whom, until recently, I had never heard. On reading about him, I am staggered by his dead-on prescience in predicting the ultimate power of social connections via the internet - back in 1960. His Man-Computer Symbiosis has to be read to be believed. In it he touches on the obvious: the need for speed, memory, robust programming languages, and effective I/O.  But he goes much deeper, brilliantly identifying memory and its organization (which leads to necessary "searchability") as necessary developments before the symbiosis can happen:

Man-computer symbiosis is an expected development in cooperative interaction between men and electronic computers. It will involve very close coupling between the human and the electronic members of the partnership. The main aims are 1) to let computers facilitate formulative thinking as they now facilitate the solution of formulated problems, and 2) to enable men and computers to cooperate in making decisions and controlling complex situations without inflexible dependence on predetermined programs...Prerequisites for the achievement of the effective, cooperative association include developments in computer time sharing, in memory components, in memory organization, in programming languages, and in input and output equipment.

And note the reference to emergent behavior: to enable men and computers to cooperate in making decisions and controlling complex situations without inflexible dependence on predetermined programs.

Man-Computer Symbiosis reminds me of one of my favorite sci-fi books, although pigeonholing it into that genre doesn't do justice to Last and First Men: A Story of the Near and Far Future, by Olaf Stapledon. Here Stapledon predicts the fate of mankind from Stapledon's present (1930) through the next two billion years, during which mankind evolves through

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ODE to Dark Matter

Dark Matter may account for the large-scale structures being mapped by HubbleMy dream job: working at The Perimeter Institute in Waterloo, Ontario. The latest from this "autonomous" center for theoretical physics is a Teaching tool for Dark Matter - a DVD, Teaching guide, and downloadable activities. The 30-minute video is embedded in this post and is definitely worth watching.

Even though there is now some agreement that Dark Matter has been observed (see my earlier post on this topic), there is still much debate about its reality. For an interesting take on matters dark, consider the position of artist/author Anton Sevcik, who, in a private e-mail to me some time ago suggested that

On a really simplistic level, I'm wondering if we've over theorized the subatomic realm, creating too many particles to explain too few things. Just because something is tiny, we seem to presuppose it can only have one property, so we've created a particle for every property. The reason I'm thinking about this is the dark matter myth. I say myth, because dark is a particularly uncomfortable word to anglo saxons, suggesting evil (say, film noir), and anything inexplicable seems by its nature unsettling to our minds.

Sevcik has since expanded on this theme, and I highly recommend The Fallibility of Perception on his View From the Studio blog.

While we're getting all literary here, a web search for Dark Matter poetry yields way too many hits to be a coincidence, and indeed suggests something dark, impenetrable, and slightly creepy, (if not necessarily "evil") at play in the universe. For example, look no further than Musicman's free verse:

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Aphorismically Consistent

Oscar Wilde Action FigureOne of the wonderful things about words and sentences is the ability to create paradoxical statements that are more clever than they are troubling. No, verbal paradoxes aren't typically offensive in the same way that mathematical ones are. Mathematical statements are usually not labeled "paradoxical;" instead, they are described as contradictions, or, even worse, inconsistent statements. (Try to think of a paradoxical mathematical statement that isn't a contradiction - go ahead, I dare you)

Mathematical inconsistencies are often nasty, unwanted, theorem-killers, and their presence is usually a sign of things gone awry. Actually, inconsistency and/or incompleteness is built into all of the mathematics we do - sort of. After all, Gödel showed that mathematics cannot be both consistent and complete.

Ahh, but words are a different story. Words are the atoms of sentences, and if somehow the sentence doesn't make "sense", well, consider metal atoms that are frozen into a glassy state, but in fact want to be in a nice, regular matrix. These metallic glasses are then "inconsistencies."

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The Green Lantern and Quantum Poetry

A recent book of poetry by A. Van Jordan titled Quantum Lyrics has received a lot of favorable press. From the publisher's (AP Norton) site:

This provocative, ambitious collection explores the intersection of the infinite world of physics with the perplexities of the human condition.

For more on Van Jordan, including how he came to include physics in his latest works, see his interview in nat creole.magazine.

I am very interested in Jordan's work for a number of reasons:

a. I am a sucker for all things quantum. The idea of poetry with a quantum flavor, or poetry trying to describe quantum theory, seems to be the most natural fit in a world that appears highly unnatural because of quantum theory

b. Einstein is heavily featured. QL contains a set of poems about Albert as he "wrestles with his marital infidelities as he both reinvents physics and becomes a pioneer in race relations" (Read some excerpts here.)

d. How can I not react to the fractal reference by Linda Gregerson in the following review?

"The superheroes of DC Comics meet the Nobel laureates of particle physics: Charlie Chaplin meets Albert Einstein, who gives shelter to Marian Anderson when no hotel in Princeton will have her; the fractal repetitions of branching twig and leaf vein haunt the son of a father who did or did not teach him cruelty to women: all fuel for the sustained nuclear reaction of Quantum Lyrics. A. Van Jordan's is one of the most capacious, deep-structural imaginations in American poetry today. These poems are radioactive."

c. The Green Lantern is mentioned. Along with The Flash, this was my favorite comic growing up. I could recite Hal Jordan's Lantern Oath by the time I was 6:

In Brightest Day, In Darkest Night
No evil shall escape my sight
Let those who worship evil's might
Beware my power - Green Lantern's light

Which always has been poetry to me...

Check out Perry Crowe's LA Citybeat article on the very upsetting changes to Green Lantern over the years.

The Art of Biography - Einstein and Goethe

I recently read an interesting review by J. Parini in the May 11, 2007 Chronicle of Love, Life, Goethe: Lessons of the Imagination From the Great German Poet by John Armstrong. According to Parini, Armstong's approach is non-chronological, instead focusing on different thematic "nodes" in Goethe's life. This style of biography is remarkably similar to that of Jürgen Neffe in his recently translated Einstein: An Autobiography. Unlike Isaacson's best-seller Einstein: His Life and Universe, Neffe presents Einsteins's life prismatically in chapters that go over the same events, but with different emphases. (See my review of Isaacson and Neffe)

Here's Panini writing about Armstrong's Goethe:

In the case of Goethe, there were many observers, and the factual record is not much in doubt. Hardly anyone crossed his path who did not feel compelled to record an impression. And so biographers have a wealth of material, some of it quite marvelous. Armstrong plucks the choicest bits from that vast record, but refuses to narrate the life in conventional terms. Instead, he picks 10 key words and gathers his work around those nodes: Luck, Love, Power, Art, War, Friendship, Nature, Peace, Happiness, Death. There is an underpinning of chronology here, as one might expect; but the timeline is folded back upon itself, even discarded for long stretches as Armstrong lunges into meditations on the meaning of the life itself in the context of those seminal words.

The image of "timeline folding back upon itself" is a wonderful way of describing this biography of connected "nodes."  Panini goes on to describe the effect of reading such a biography...

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Poetry, Space-time, and Entropy

Plotkin's Entropy by Donna Bellas. See text for info. With the amazing success of Isaacson's bio of Einstein, and the translation and release in the US of Neffe's uniquely-German bio, Einstein is certainly in the air. Not as much as 100 years ago, when he was perhaps the most famous person in the world, but nevertheless many are reading, and writing poetic about Albert.

From Bernhardt Blumenthal, a colleague at La Salle who is a Rilke scholar and poet (and in his spare time chair of the Dept. of Foreign Languages & Literatures and the Master's Program in Central & Eastern European Studies) describes Einstein's influence on his latest work:

...my latest poem, Schwere Seelen, (Heavy Souls), which just appeared last week in a German literary periodical plays on Einstein's General Relativity. The souls, heavy with love and suffering, warp reality and pass over the space-time curve through hyper-space into another universe--one without entropy. The female lover, incidentally, transits space escaping on a light beam exiting a black hole (thus faster than our conventional absolute speed of light) and rescues the beloved from his entropic situation.

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As the World Turns - Foucault's Eco

Feb. 3rd marked the 156th anniversary of Léon Foucault's demonstration that the earth revolved on its axis. The experiment was brilliantly simple: let a large pendulum swing back and forth over the course of a day, with a sharp tip hanging off of the pendulum bob making patterns in a bed of sand below it. As the pendulum bob moves back and fort in a vertical plane the earth rotates beneath it, and this rotation can be measured by the marks in the sand. (For a nice intro to Foucault's Pendulum, check out the scriptographic booklet on the subject at the California Academy of Sciences.)

Foucault did not stop with simply showing that the earth rotates. He was able to predict how fast the pendulum would appear to rotate because of the fact that the rate at which the marks carve out a pattern depends on the latitude of the pendulum. So, for example, at one of the poles the earth will spin once in 24 hours, while at the equator the earth does not spin with respect to the plane of the pendulum. Anywhere in between the amount of time it takes for the pendulum to make one complete rotation is given by

T = 24/sin L

Here T is the time for the pendulum to return to its original position (in hours), and L is the latitude at which the experiment is carried out.

The pendulum demonstration was a huge success, showing as it did in a very simple way what could not be felt by earthly inhabitants - the rotation of the earth they were standing on. (It was also a majestic demonstration, being conducted in the the Panthéon in Paris.) The fact that Foucault could actually predict the exact timing of the rotation made him akin to the explorers who mesmerized remote villagers with abilities to predict eclipses, and he achieved physics rock-star status - maybe the most until Einstein.

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Prediction, Fiction, and Science Policy: The Jurassic Park Syndrome

Michael Crichton needs to visit an ER for an arrogancectomy...

It's amazing to me how global warming is now accepted as fact, when not too long ago it was still being described as possibly a climate condition that appears, and has appeared, from time to time in the course of the lifespan of the earth.  There now seems to be an article every week in the major press about the latest discoveries confirming a warming trend that does not appear to be part of some grand cycle through earth's history.  This has led several countries and continents  to proclaim global warming to be the BIGGEST threat to humanity in the not-so-long term, enacting legislation and controls that will stem the tide of further warming.  

The U.S. is not one of them, of course.  Hopefully, this sad state of affairs will begin to change with the  new makeup of Congress.   If so, it will be those who aren't fans of Michael Crichton that may make the difference.

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Smilla's Sense of Mathematics

The quotes from G. H. Hardy in the previous post are well known - in mathematical circles at least. Their succinctness is a hallmark of Hardy's desired economy of words in mathematical proofs.

Hardy was a number-theorist, and it seems appropriate to follow up the posting of his quotes on the beauty of mathematics with a very interesting fictional passage about the nature of numbers, and the connection with human life.

The following passage is from Smilla's Sense of Snow, a 1992 novel by Danish author Peter Høeg. A strange mystery that involves a child's murder and an eery trip to Greenland, Smilla is a fascinating heroine, at home in the worlds of mathematics, intrigue, and, obviously, snow...

Do you know what the foundation of mathematics is? ... The foundation of mathematics is numbers. If anyone asked me what makes me truly happy, I would say: numbers. Snow and ice and numbers. And do you know why?

Because the number system is like human life. First you have the natural numbers. The ones that are whole and positive. The numbers of a small child. But human consciousness expands. The child discovers a sense of longing, and do you know what the mathematical expression is for longing?

The negative numbers. The formalization of the feeling that you are missing something.And human consciousness expands and grows even more, and the child discovers the in-between spaces. Between stones, between pieces of moss on the stones, between people. And between numbers. And do you know what that leads to? It leads to fractions. Whole numbers plus fractions produce rational numbers. And human consciousness doesn't stop there. It wants to go beyond reason. It adds an operation as absurd as the extraction of roots. And produces irrational numbers.

It's a form of madness. Because the irrational numbers are infinite. They can't be written down. They force human consciousness out beyond the limits. And by adding irrational numbers to rational numbers, you get real numbers.

It doesn't stop. It never stops. Because now, on the spot, we expand the real numbers with imaginary square roots of negative numbers. These are the numbers we can't picture, numbers that normal human consciousness cannot comprehend. And when we add the imaginary numbers to the real numbers, we have the complex number system. The first number system in which it's possible to explain satisfactorily the crystal formation of ice. It's like a vast, open landscape. The horizons. You head towards them and they keep receding.

Greenland icecap. Photo by Evert Wesker.Luckily for all of us, the madness hasn't stopped. The complex number system is essential to fractals, and forms the mathematical plasma in which algorithms for determining the Mandelbrot set are calculated. This set is like a vast, open landscape with horizons replaced by fractal basin boundaries. As you head towards them, they don't recede. Rather, they get more complex. Without complex numbers, then, we'd be living in world bereft of color and self-similarity - an uninteresting world of snow.

Notes - Thanks to Sharon Armstrong, of La Salle's Psych department, for reminding me of Smilla's mathematical musings...Julia Ormond played Smilla in the movie version. Click here for a film clip of the mathematics scene...And be sure to try this excellent fractal basin applet.