Sunday, December 19, 2010

Imagination

In the late 1970's, a wonderful magazine, Omni, was first published. I saved every issue of it for the first few years or so. I moved the heavy boxes of magazines wherever I went until I finally tired of it and gave them to a used book store.

The first issues were marvelous with fine science fiction stories, and fantastic art work. What I loved the most were the articles on the interesting edge of real science. I discovered the Rubik's Cube and its brilliant mathematician creator in the pages of Omni about a year before they were in stores. When the cubes hit the shelves, I promptly bought one and tortured myself trying to solve it. I could solve to the point of one cube being out of place - so close! My husband was equally intrigued but he eventually solved the puzzle by purchasing a book that demonstrated the sequence of steps required to solve. He memorized the steps, then wowed everyone with how "smart" he was. (I never did entirely solve Rubik's cube. Like a chicken, there is just so far my logic can travel in certain directions.)

I read a small but wonderful Omni article about the Game of Life, an exercise the really big computer wizards at the time, with access to Cray computers, used to "race" their computers. Life is played on a grid. Each cell that is On, (contains a dot), is living. Each On cell with one or no neighbors dies in the next generation. If an On cell has four or more neighbors, it dies in the next generation. An On cell with two or three neighbors survives. An Off cell with three On neighbors turns On in the next generation. It starts with several dots you randomly place on a grid, then you map the generations according to the simple rules of On or Off. It theoretically replicates the engine of generations of evolution, creating new shapes, some going extinct, some replicating themselves, some blinking on and off across the generations. For something so simple, it is fascinating, as Spock would say. I played this game on engineering grid paper for years, and sometimes I will still graph out several generations while killing time. Computers are accessible to everyman now, and any one can play the Game of Life online. Game of Life.

I first read about fractals in Omni magazine. It was many years before I saw that word in print again. The Omni article explained that by using fractal mathematics, a coastline could be more accurately measured. Of course, I had no clear idea why that was so, but the shapes generated by fractal mathematics were intriguing and beautiful. I intuitively understood that fractals were closer to natural patterning, and was intrigued to learn many years later that Jackson Pollock's paintings have fractal properties within them. This week on the local PBS channel, a program of the discovery of the mathematics of fractals, the development, and the eventual acceptance of fractal geometry as a genuine branch of mathematics. It includes a layman's explanation of fractals, and some real world applications.

Benoit Mandelbrot, building on the earlier work of others, is the man who brought fractals to the world. He explained that he fell in love with geometry while a school boy, and soon realized he could visualize the formulas. I thought of Einstein's ability to imagine what he would see if he could travel the speed of light. I do not believe the human race needs alien intervention to progress. We do not need to reverse engineer crashed alien spaceships to discover new sciences. We have been given everything we need to progress within our own imagination. The right minds ask the right questions in the right timing. Though Benoit Mandelbrot had the theory well in hand, it was not until he went to work at IBM, with access to the power of computers to rapidly compute the infinite iterations of mathematical replications that fractal geometry came into its own.

Cosmic timing.

1 comment:

cyberkit said...

While I now find fractals and chaos/string theory fascinating, in school I was a charter member of the I hate Euclid club. I'll leave the heavy lifting to others and just enjoy the show.

The most fun I ever had with a Rubik's cube involved a large hammer!

Both my train of thought and learning curve are fractals. Oh! Look! A chicken!