About this blog

  • In Shakespeare's The Tempest, Prospero, Duke of Milan, is ousted by his brother and exiled to an island. With the help of a friend, Prospero manages to take with him his beloved library.

    Prospero, like his creator, lived in a time when boundaries between disciplines were not as rigid as they are today. Prospero's books would have dealt with the cosmos—spiritual and material, inner and outer—as a whole.

    In this blog, I try to do the same. I'm not Prospero, just a student rummaging through his library and writing in the margins. Prospero's Books is a blog about seeing the world as a whole, by looking at

    • signs, especially the relationships between signifiers and what they signify
    • stories, especially big-picture stories, such as myths and the works of Dante, Shakespeare, and Joyce
    • systems, especially complex, nonlinear systems
    • spirit, especially as understood by the Christian and Western esoteric traditions

    Welcome! Please join the conversation.

    —Kenneth W. Davis

    (Note: Although I admire Peter Greenaway's film Prospero's Books, this blog is not directly about that film. )

    Who, and Some of What, I Am

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21 posts categorized "Fractals"

05 May 2008

Shakespeare behind Bars

Shakesbehindbars Last month, in my "Shakespeare, Systems, and Intertextuality" course, I showed Hank Rogerson and Jilann Spitzmiller's film Shakespeare behind Bars, a 93-minute documentary on a production of The Tempest by inmates in Kentucky's Luther Luckett prison. Four observations:

  • A prison, by definition, is a "closed system," increasing in entropy unless it can draw energy from outside. The introduction of The Tempest into the lives of the cast brings such energy, allowing for growth.
  • The production process shown in the film is a remarkable example of how living systems grow and evolve by moving from organization through disorganization to reorganization. (The very word tempest suggests the necessary slip into chaos, and "chaos theory" can be said to have been born in Lorenz's study of complex weather systems.)
  • With so little to distract them, the cast members--during several months of production--study and "live" their roles at a depth I've never seen before, in students or in actors. Shakespeare's fractal complexity constantly repays this effort.
  • As the cast members perform a play that centers on forgiveness and redemption, they collectively and individually struggle with those issues in their own lives.

Shakespeare behind Bars is one of the best half-dozen Shakespeare films I've ever seen. I recommend it highly.

17 January 2008

A twenty-first-century Shakespeare?

Angels_in_america Scott Malia, at The Shakespeare Blog, writes:

While Shakespeare appreciation might be near universal among writers, it begs the question of comparison. Who among today’s writers is what might be considered the twenty first century answer to him?

His initial suggestion: TV and film writer Aaron Sorkin--a great candidate. Over at The Shakespeare Teacher, Bill and his readers suggest others.

In my Conversations with Shakespeare course, I lead students through half a dozen of Shakespeare's plays, as well as later works in explicit "conversation" with them: Stoppard's Rosencrantz and Guildenstern Are Dead, Smiley's A Thousand Acres, Cesaire's A Tempest, Gaiman's Sandman treatment of A Midsummer Night's Dream, and others. The course ends with a play that I find the most "Shakespearean" of recent dramas: Tony Kushner's Angels in America. My students always find lots of ways that Angels is in implicit, if not explicit, conversation with the Bard.

So Kushner's my candidate--not in the quantity of his output, but in his almost unique ability (among many others) to give his subjects both cosmic and fractal dimensions. If you haven't read or seen the play, do so (especially the amazing HBO film of it), and see if you agree.

24 October 2007

Intricate beauty born out of chaos

Earthfr Karmen, at Chaotic Utopia, has posted one of her best-ever "Friday Fractals," an Earth-like planet she has formed by plugging a just-right seed number into a fractal formula. She writes:

As I toyed with the different settings, I couldn’t help notice how such intricate beauty was born out of chaos. Now, I could be speaking of the fractal, or of our planet. I’ll let you decide.

(Please check out the video she has posted, of the fractal Earth being formed.)

24 September 2007

"Equiknot"

Equiknot My friend Karmen, at Chaotic Utopia, has posted, as last week's Friday Fractal, a beautiful piece inspired by both the autumnal equinox and ancient Celtic art, especially the "Celtic knot." Be sure to see it both still and animated.

18 September 2007

Whence beautiful complexity?

Boxfittingprn At Gallery of Computation is a gallery of art works, by Jared Tarbell, that are uniquely generated by computer programs as you watch. They are stunning examples of a new level of artistic creation in which the artist does not create just one instance of beauty but instead creates a generative program that can produce infinite instances of beauty.

The fact that the each piece of artwork emerges from very simple rules makes the artist not less significant but more significant: not every set of simple rules produces something interesting, not to mention beautiful. If we glory in the infinitely complex beauty of Tarbell's work, how much more should we glory in the infinitely complex beauty of our universe, from subatomic particles, to us, to galaxies.

Whether we posit a creator behind that beautiful complexity (Freemasons refer to "the Great Architect of the Universe"), posit (with Tillich) a "ground of being" from which complex beauty can arise, or posit our universe as one particularly interesting instance among an infinite number of existing universes, the fact of our existence and the existence of beauty around us is surely worthy of adoration and gratitude.

(To see Tarbell's works, go to the Gallery of Computation. As words appear in the white space, try moving your cursor among them, clicking on them if you wish. Or click on "Thumbnail Gallery" to see a visual index. When you see a work you like, click on it. When you arrive at its page, you'll see a large static image of just one manifestation of the work. But don't stop there. Click on "Small," "Medium," or "Large" below the image and watch a unique art object evolve. Experiment with the sizes to learn which work best on your computer.)

(Thanks to Seed magazine for the lead.)

23 July 2007

A life-shape reconfigured

Poster_from_wikipedia Last week, I was pleased to find in Philip Davis's Shakespeare Thinking (see What I've Been Reading, in the right column) the juxtaposition of two of the major themes of this blog--Shakespeare's work, and theories of complex, nonlinear systems:

Shakespeare seems intuitively to love what these days we would call a Mandelbrot fractal: a generated self-symmetry working through varied recursion, like the two sets of twins in A Comedy of Errors or the two sets of lovers in A Midsummer Night's Dream; a life-shape reconfigured within ever smaller sub-divisions of itself; a part thus containing within itself almost to bursting-point the fundamental pattern of its larger whole (17).

02 June 2007

Fractal fundamentals

Pbf Several times on this blog, among my posts on fractals, I've linked you to Chaotic Utopia, and Karmen's amazing Friday Fractals, both recent and less recent. This week, she has published the clearest explanation of fractal geometry I've ever read.

It's a hands-on explanation, requiring a sheet of paper and a few minutes of your time. Please have a look.

25 May 2007

Trying to teach that she was one

Snowflake_from_wikipedia In The Elixir and the Stone (see What I've Been Reading), Baigent and Leigh quote at length from the  novelist Thomas Mann as a twentieth-century artist influenced by Hermeticism. Because I am fascinated by unity of the cosmos, and by the fractals and other patterns that occur throughout art and nature, at all scales, I was struck by this passage from Mann's Felix Krull:

The interdependent whirling and circling, this convolution of gases into heavenly bodies, this burning, flaming, freezing, exploding, pulverizing, this plunging and spreading, bred out of Nothingness and awaking Nothingness--which would perhaps have preferred to remain asleep and was waiting to fall asleep again--all this was Being, known also as Nature, and everywhere in everything it was one. I was not to doubt that all Being, Nature itself, constituted a unitary system from the simplest inorganic element to Life at its  liveliest, to the woman with the shapely arm and to the figure of Hermes. Our human brain, our flesh and bones, these were mosaics made up of the same elementary particles as stars and star dust and the dark clouds hanging in the frigid wastes of interstellar space. Life, which had been called forth from Being, just as Being had been from Nothingness--Life, this fine flower of Being--consisted of the same raw material as inanimate Nature. It had nothing new to show that belonged to it alone. One could not even say it was unambiguously distinguishable from simple Being. The boundary line between it and the inanimate world was indistinct. Plant cells aided by sunlight possessed the power of transforming the raw materials of the mineral kingdom so that it came to life in them. Thus the spontaneous generative power of the green leaf provided an example of the emergence of the organic from the inorganic. Nor was the opposite process lacking, as in the formation of stones from silicic acid of animal origin. Future cliffs were composed in the depths of the sea out of the skeletons of tiny creatures. In the crystallization of liquids with the illusory appearance of life, Nature was quite evidently playfully crossing the line from one domain into the other. Always when Nature produced the deceptive appearance of the organic in the inorganic--in sulphur flowers, for instance, or ice ferns--she was trying to teach that she was one (Baigent and Leigh 314-15).

20 April 2007

Pushing the limits of human vision and imagination

Science_in_silico Seed magazine has posted a fascinating and beautiful video about science as done on computers. Lee Billings's introduction:

Computer simulations and visualizations are performing the thought experiments of the 21st century and pushing the limits of human vision and imagination.

05 March 2007

MandelSwarm

Zooms "Watch two thousand particles swarm towards the boundary of the Mandelbrot Set."

(Thanks to JJ Ventrella for the toy, and to Karmen at Chaotic Utopia for telling us about it.)

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