Monday, April 17, 2006

Math and art, strange bedfellows

This is pretty cool:
and rumor
But how about a
Rare, geeky form of poetry?

THAT'S exactly what happened after Gregory K. Pincus, a screenwriter and aspiring children's book author in Los Angeles, wrote a post on his GottaBook blog ( two weeks ago inviting readers to write "Fibs," six-line poems that used a mathematical progression known as the Fibonacci sequence to dictate the number of syllables in each line.

Within a few days, Mr. Pincus, 41, had received about 30 responses, a large portion of them Fibonacci poems. Most of them were from friends or relatives or people who regularly read his blog, which focuses on children's literature.
There is often an intriguing overlap between mathematical and dramatic theories. My favorite example is the Golden Section; a colleague of mine named Doug Adams once wrote a fascinating article on film music which included an intriguing discourse on the theory:
There exists a theory known as the rule of the Golden Section. Roughly paraphrased, this theory states that just under two-thirds (0.618034... and so on) of the way through anything there is some significant occurrence. The idea is that those things which humans naturally find appealing or stereotypically beautiful are most likely to adhere to these guidelines. Much of nature adheres to this rule. Many flowers have their largest leaves about two-thirds of the way up their total height. Multiply a human's height by .618 and you'll often find the waist. The eyes are approximately two-thirds of the way up the human face, the heart two-thirds of the way up the torso. Human-made art often follows these rules as well. Debussy was a strong believer in the Golden Section and structured his works accordingly. Stravinsky's "Rite of Spring" has some elements of the GS in its construction. "Alien"'s climatic cat-and-mouse chase begins at roughly around this ratio, as does "Star Wars"' trench battle.
In practically every writing course I've ever taken, mention was made of something similar in terms of the structure of whatever piece of writing you were focused on. For example, the Joseph Campbell model of screenwriting (which has been nearly beaten to death in the years since Star Wars first opened... thanks a lot, George) posits nine steps in the hero's journey:
  1. The ordinary world.
  2. The call to action.
  3. Refusal of the call.
  4. Crossing the threshold.
  5. Tests, allies and enemies.
  6. Ordeal.
  7. Reward.
  8. The road back.
  9. Return and resurrection.
You'll note that two-thirds of the way through this list is "ordeal," which typically takes the form of a plot twist that changes the hero's goal -- the token damsel getting kidnapped by the bad guy, for example, thus giving the hero a new emotional investment in achieving his objective. (This device is also commonly referred to as the "third-act ticking clock," and was satirized hilariously in South Park: Bigger, Longer and Uncut.) The rhythm of certain styles of poetry -- cinquains and sonnets, for example -- follow this idea. Basic rules of composition for art and photography emphasize a one-thirds/two-thirds standard for filling the frame. And the musicians amongst you are already aware that typical 32-bar (AABA) song structure usually places the bridge about two-thirds of the way through the song.

Anyway, the point of all this is that this rule, ingrained as it is in typical perceptions of art and aesthetics, can be of great help to you in terms of the construction of your work, be it written, visual or auditory. If anything, it's a good jumping-off point. Not all works of art adhere to this rule, of course, but a lot of fun can be had in the manipulation of the rules... once you learn them, that is.

As an extension of that, I’ve found, more often than not, that exploring the strictures of math and science can in fact reveal new elements in aesthetics. Arthur Koestler's The Act of Creation has many such passages that illustrate how one could inform the other. Mathematics, as Bertrand Russell pointed out, is entirely theoretical, and like any other man-made system of thought it’s subject to the same fallibility, and flexibility, as art.

Now I want someone to come up with a way to turn Occam's Razor into, say, a cell phone ad.


Veronica said...

Great article, as always. I've learned more from reading your blog than I did in my entire senior year.

I love what you write about. And I love how you write.

Gregory K. said...

The sad truth is that we're more likely to see "The Occam by Gilette" than anything else.

Thanks for the link. And good article, too!

Jason Comerford said...

Thanks for the kind comments, folks.

Captain Mike said...

I think it all sucks, personally.

Jason Comerford said...

I love the smell of candor in the morning!

Stuart said...

You need to be careful in discussing the relation of aesthetics to the Golden Mean. Much bullshit has been written and little of it stands up to scientific scrutiny (navel heights when tested are not .618 of a person's height - see Martin Gardner's writings and Mario Livio's book ). The golden mean is equal to (the square root of 5 plus 1 ) divided by 2, due to the square root of 5, the golden mean is an irrational number and has an infinite expansion. I think the application of Occams Razor in this case would dispense with the Golden Mean and instead concentrate on the role of 2/3 in aesthetics and simple integer ratios generally