Mathematics is Art: Make No Apology

"Ikebana" by Tim Fadden

Recently, the following provocatively simple set of questions was added to an earlier post describing Jackson Pollock and fractals - one of a series of posts that debate whether technology & mathematics -produced art can actually be ART:

why does the mathematics have to be producing art? why can't the mathematics be art itself? would that actually solve any of the problems discussed here.

This question is from Jonathan "Fish" Fisher - co-winner of the 2005 Duke poetry award. Fish has posted a number of interesting comments and questions, adding his voice to the dialogue of whether or not art can be produced using mathematics and technology. He recently posted his Poem For Benoit Mandelbrot, A Connoisseur of Chaos, a moving poem that ends that concludes with his own awareness of the beauty and mystery of mathematical forms and structure via Mandelbrot's fractals:

Briefly I taste the salt sting
Of equations I'll never understand,
But a wave of awe
Sweeps me up as if divine
Artistry had finally
Conformed to a function of
Some rigid geometry.

Can any man be more than an artist?

I am always heartened when a non-mathematician senses the beauty of mathematics, which Fish makes evident in his poem, and his suggestive question: why can't the mathematics be art itself?

There are mathematicians who will go into full rapture mode when describing the beauty, in their eyes, of mathematics. This is especially true when they describe mathematical proofs that are considered "elegant" - proofs whose logical path leads inexorably from axiom to conclusion using an economy of steps, with leaps to other areas of mathematics hitherto unrelated, demonstrating a dizzying web of connections among the farthest reaches of mathematics.

This view is typified by G.H. Hardy, an early-mid-20th-century British number theorist, and the author of A Mathematician's Apology, his 1941 memoir and a book that should be read by all mathematicians. Hardy writes...

In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.

But what about beauty? And where is the art? Hardy lived in a world of pure thought and number - far-removed from the real world earthiness of mathematical modeling, and just as far from the computer-produced display of impossibly intricate fractals. Yet for him, it is the essence of pattern - not, as we've seen, a pattern in space such as a fractal pattern, but a pattern of abstraction and logic that is the substrate of mathematics, and it is there that beauty can, and MUST be found:

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

For Hardy, mathematics is surely art. To those who still aren't convinced, and who would claim that only mathematicians can see the "beauty," hence it is not art, isn't this an argument similar to those who can't see the landscape in an abstract painting, or who can't hear a melody in the serial music of Schoenberg?

Applying some logic here, mathematics must be art because it has an art-essence that is independent of the observer. If you don't see it, it must be there.

Stanislaw Lem: The Passing of a Deep Spirit

Stanislaw Lem, the great Polish "science fiction" writer died on March 27, 2006, at the age of 85. Two of Lem's works have played a role in the Chaos and Fractals course, and I describe the connection below. First, though, must be a tribute to this extraordinary writer.

Even though I know many who read, or have read a great deal of science fiction, I know very few who have read any of Lem's works. This is very odd, given that Lems' works have been translated into over 40 languages, with an estimated 27 million sold. (Some do read and prosper: Will Wright, the creator of the wildly popular SimCity simultaion game credits Lem's The Cyberiad as inspiration. )

With sci-fi readers (in the U.S., at least) not paying attention, what hope is there for more readership of this essential 20th-century author who is usually listed as I wrote above - a science -fiction writer, only without the quotes.

It has always been unfortunate that Lem's works are described as science fiction. This is itself a fiction. Lem - a brilliant scientist, writer, and thinker - told wonderful tales with an unnerving mixture of darkness, humor, philosophy, and theology that just happened to be placed deep in space, or inside a computer. While the location and time period of his stories are essential to their plots, Lem's stories are often more relevant to our current time and place because of his ability to paint rich characters in situations that are paradoxically both imaginable and impossibly strange.

Lem's life as a scientist and writer growing up in Poland, through Nazi occupation and Soviet rule, is much of the reason for his chosen genre, as described in the Times of London obituary -

He began to write fiction, his first works being in the tradition of socialist realism acceptable to the authorities. But he graduated to literary "fantasies", which he succeeded in hoodwinking the humourless and dogma-bound authorities into believing were innocuous, though they were in fact highly subversive and satirical.

I first read Lem in 1983, when my best friend, Eric Törnqvist, gave me a copy of Solaris as a birthday gift and demanded that I read it. To this day it remains not just the greatest "science fiction" that I have ever read, but one of the best books I have ever read. It is a book in which there is no action of the type usually associated with a sci-fi stories. Instead, Solaris chronicles centuries of observation of a liquid planet and its seemingly non-descript moons, a planet that may be sentient, and may be malicious. With this simple idea , an idea that seems to present little opportunity for

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Sometimes a Great Notion: Turbulence and Ken Kesey

I recently began re-reading Sometimes a Great Notion, Ken Kesey's monumental second novel published in 1964, and one of my favorite books. Even though I read it over 20 years ago, I still remember many of the most famous scenes. More remarkable, perhaps, is the fact that I vividly recall the haunting descriptions of the Pacific northwest so magically captured by Kesey.

When I read about the chaotic aspects of turbulence, especially as described by James Gleick in Chaos: Making a New Science, I am always reminded of Great Notion's opening passage:

Along the western slopes of the Oregon Coastal Range ... come look: the hysterical crashing of tributaries as they merge into the Wakonda Auga River. ... The first little washes flashing like thick rushing winds through sheep sorrel and clover, ghost fern and nettle, sheering, cutting ... forming branches. Then, through bearberry and salmonberry, blueberry and blackberry, the branches crashing into creek, into streams. Finally, in the foothills, through tamarack and sugar pine, shittim bark and silver spruce -- and the green and blue mosaic of Douglas fir -- the actual river falls 500 feet ... and look: opens out upon the fields."

Many others feel the same way as I do about Great Notion. In a 1997 survey, the Seattle Post-Intelligencer published a list of the 12 Essential Northwest Books. Sometimes a Great Notion was #1, after being named the top book by over 1/3rd of the participants.

According to Kesey (who died in 2001), "I think 'Sometimes a Great Notion' is the best thing I'll ever write...Writing it was much different from 'Cuckoo's Nest,' which often seemed like filling in the blanks. 'Notion,' to my mind, is a great piece of work. People sometimes ask me why I don't write something like that again and I reply that I simply can't. I can't keep all that in my head at once anymore. Why, on 'Notion,' I used to work 30 hours at a stretch -- you've got to have youth to do that."

I don't know how the book fares on re-reading, 20 years after my initial reading. Maybe one must also "have youth" to really embrace the novel's sprawling, non-linear, 627 page narrative. I do know, however, that I will always be mesmerized by the "the hysterical crashing of tributaries as they merge into the Wakonda Auga River..."

Causality, Murder Novels, and Determinism

File this under books that might appear on the reading list of a future course in Chaos and Fractals...

A fascinating idea for a book: Stephen Kern's A Cultural History of Causality: Science, Murder Novels, and Systems of Thought" looks at changing views of causality through time - as played out in murder novels and scientific theories.

Kern is attempting to follow changes in societal explanations for the causes of aberrant human behavior - in this case murder. He juxtaposes this with the increasing refinement in scientific models of causation.

Given our umbrella for this course of "modeling/prediction/understanding", Kern's study touches on determinism, anti-determinism, and free will - perfect material to muck up our already chaotic understanding of the limits of predicting human behavior.

You can read the source of Kern's ideas for the study in his own words by clicking here.

Notes on Two Bradbury Stories

Originally posted by Tom Plick

At the end of "A Sound of Thunder," I was amazed at the slightness of the changes that occurred because of Eckels' killing the butterfly. The English language was spelled differently, but still pronounced the same way. Everyone who had existed "before" the trip still existed afterward. (Think of that old conceit in the movies, where someone's parents never meet, and so the person is never born.) It boggles my mind that such small changes are all that take place over thousands of millennia.

I read another of Bradbury's stories in grade school, entitled "All Summer In a Day." It is about a group of kids in an underground society on Venus; they live underground to avoid the constant rains. The rain only stops every seven years, for an hour at a time. The kids in this one class are skeptical about the outdoors, except for a frail little girl named Margot, who has known the wonders of nature and misses them dearly. When the teacher prepares the kids to go outside during the brief window, the kids hatch a plan against Margot.

I won't spoil it for you - you can read the story by clicking here. (It's about four pages.) I will tell you that years later, I am still turning it over in my head, pondering its true meaning.