Fractals, Hammers and Other Tools: an Oldie but Goodie
"Fractint" was one of the first computer programs I encountered that blew my mind. (It's still out there on the Internet. Download one if you want to try it.)
Fractint generates fractals. Fractals are mathematical formulae that express complex realities with elegant simplicity. Before computers, you had to have a mathematician's mind to grasp the relationships expressed by fractals. Computers enabled those relationships to be represented pictorially. Fractint lets you generate images of fractals, then cycle through them in thousands of colors. The vision of a fractal in action is stunning.
Fractals often resemble natural objects. Simple formulae using recursion generate images that look like branching trees, clouds, coastlines, or fern leaves. Seeing those images on a computer changed how I saw the natural world. The computer generated a different framework for looking at and comprehending the "real" world.
Fractals are self-similar at all scales. If you magnify a section of a fractal, then magnify a section of the section, each one looks similar, like nested wooden dolls. You can keep magnifying smaller and smaller pieces until the image on your monitor is part of something so big that, if you spread it out, it would stretch from the sun to the orbit of Jupiter.
My wife, who is not a geek, looks up now as we walk through a forest or watch clouds move through the sky and says, "Fractals."
Computers are programming us to see things in their own image, teaching our minds as well as our mouse-clicking hands how to use them.
Fractint also taught me that intellectual property, as we have known it, is over.
The concept of an "author" who owned "a work" was invented by the printing press. The printing press fixed words in text and created an illusion of permanence, of something solid "out there." Students are still surprised to learn that Shakespeare did not care to preserve his plays for future generations. "Writing for future generations" was a conceit thinkable only after we had fully internalized the world of text and thought of books as artifacts that would last.
Fractint was built by "the Stone Soup Group," programmers who worked collaboratively online. Some of their names are known, but many are anonymous. A collective wrote the program, just as monasteries in the middle ages created illuminated manuscripts without a thought for the name of an "author" or owner of the "intellectual property."
Cultural artifacts like laws (copyrights, patents) are tools too. The shape of those tools is determined by our information systems. After we use them a while, we forget that, and they become part of the background noise of our lives.
Fractals are a metaphor not only for what I see "out there" but also for what I observe within myself. Every decade or so, I discover myself in transition to another developmental stage. Each stage includes and transcends everything that came before. My psyche is self-similar at all scales, just like a fractal.
Civilizations too go through developmental transitions, and they too include and transcend everything that came before.
Back to tools.
It is said in the consulting business that "to the person with only a hammer, every problem looks like a nail." Our tools structure our perception and frame our possibilities for action.
I asked a number of engineers what tools they commonly use. All but one said "computer" first. Some added T-square, or architect's rule, or drafting board. Only one said pencils, although everybody uses them. Nobody said "words."
We only notice the new tools in our kit, like computers. Those we were given by prior generations disappear into the background. I notice that most people mean by the word "technology" the technology that has been invented since they were children.
The evolution of tools and the hands that hold them or the minds that think them is a cultural process. It's a chicken-and-egg kind of thing. Did we build more complex bridges and buildings because we had better tools, or did tools evolve that enabled us to build better bridges and buildings?
Computers simulate what we call "reality" but that "reality" in fact consists of nested levels of symbols. If it were a mathematical formula, it would look like this: Digital images => printed texts => writing => spoken words. They are all artifacts, nested in levels of abstraction that are self-similar at all scales.
Before human beings spoke, the artifacts or tools generated by language did not exist. We call those tools ideas, concepts, mental models. They are the building blocks of our maps of reality. Because they are modular, we can connect words and ideas in an infinite number of ways and build more ideas, more elaborate frameworks or architectures that enable us to build everything from bridges to religions.
Like speech, writing, and print, the computer is a tool that shapes our perceptions into forms the computer can use. If we are to bring our ideas to the computer, they must be expressed in language the computer understands.
To the person with a hammer, everything looks like a nail. To human beings who use speech, the only ideas we can think are ideas we can express in words. In a civilization transformed by interaction through networked computers, we will think only thoughts that can be simulated or manipulated by the worldwide network that mediates communication and the flow of information.
The world looks to me like fractals because Fractint taught me to perceive the world as fractals. Engineers will build the kind of infrastructure that networked computers teach and enable them to see and think. The physical structures of civilization will be determined by how computers think.
Everything is a flowing, the Greek philosopher Heraclitus said. If only he'd had a PC and a program like Fractint! Then he could have seen that flowing in thousands of colors, fractals of unimaginable simplicity and complexity, self-similar at all scales.
I bet it would have blown his mind.
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