Missing Information and the W(hole) at the Center
A parable: Two friends decide to write a book on how chaos theory might apply in daily life. They divide the book into seven chapters, each explaining part of the theory and exploring its implications. For the next few months, they work away, busily sending each other drafts and notes until they realize they have left something out. Chaos theory is about being unable to predict and control. It’s about never being able to make a complete description. It’s about something scientists have called “the missing information!”
So where will they put the missing information? There’s not enough room in the universe, let alone in a book, for everything missing. How on Earth will they tell people that once they’ve read this book the most important things will be the bits left out?
Then our friends remember the irrational numbers –one of the emblems of chaos. Irrational numbers find their own spaces, even when the number line is totally full. “We’d better make an irrational chapter,” they decide, so here it is!
Paradoxes and koans take us to the edges of logical, rational, ordered thought. They cause our minds to run in loops and perform iterations of logic as we try to find a way out of the problem. Yet there can be no resolution from within the context in which they are framed. Koans tell us something is missing, something is incomplete about our concept of reality. Yet the very fact we think up such paradoxes in the first place means we are bigger than the conceptual systems we create. They tell us that ‘we‘ are the missing information we’ve been seeking!
Koans confront our desire to partition the world into dualities, to place concepts into convenient categories and then draw boundaries around them. By taking us to the edge of such thinking, they create the mental chaos necessary for creativity in which the mind shifts and self-reorganizes its perception of reality.
You can never round off an irrational number without leaving something out. The something you have left out is a hole in your information. At the same time, those dots at the end of the irrational number—the dots in the title of this chapter—are like stepping stones on a trail that leads to the whole of the system, to the hidden feedback loops, to all the little butterflies out there. Those dots of missing information are, in other words, a symbol for the whole, which we can never take account of…
When Edward Lorenz discovered that his second weather prediction didn’t match his first, his problem was missing information. Rounding off to just three decimal places instead of six resulted in a completely different picture. Chaos theorists have been quick to point out that, both in principle and practice, there will always be missing information, a limitation to our knowledge, a hole in the data. Our data-gathering abilities can never be sufficiently extensive to know all there is to know about a complex system like the weather, let alone the world. For one thing, in a complex system there is no clear division between one “part” of it and another, which alone makes getting “all” the information impossible. For another thing, our act of trying to obtain the information, just our presence, perturbs a system in unpredictable ways.
Here is a koan: If chaos theory tells us about the missing information, isn’t it also telling us that it is not the whole story? Chaos theory is science and all science is subject to change. In fifty years, time, the theory will probably look very different from the way it does today. But does that mean that the issue of missing information might somehow be resolved? Possibly, but very unlikely. Paradox and limitation appear inherent to our human thinking and existence. Whether chaos theory changes or disappears, it seems pretty certain that there’ll always be a (w)hole of some important sort at the center of all our ideas.
Koan: You can’t put the whole in your pocket and the reason is that your pocket is part of the whole. Therefore it has a hole in it.
In prior lessons, we’ve seen how the dimensions of space and time fractalize and look very different when viewed through the prism of chaos. Now we hold chaos itself up to reality and find an overlooked dimension revealed there: mystery. In fact, chaos’s most timeless lesson may be that it reenchants us with mystery.
It reminds us that amid the glitter and excitement of our expanding scientific knowledge we had forgotten about the unknowable that beats inside of all we know… Chaos makes a link to the experience that appears in the gaps of koans, poetic ironies, metaphors, and other self-similar and -different forms… and to the feeling that appeared in our hearts when we first saw earth from space.
We have been critical of Western technological societies in this book, which means that we, as authors, have created a koan. We happen to live on different continents, and without the inventive power of an industrial society, we would not have the computers, faxes, Internet, and transatlantic aircraft we used to write this book. Revolving now within this koan, having availed ourselves of the technology, our criticism remains. If we have been hard on our own times it is because we have recoiled from the arrogance it often displays, its great desire to control human nature and the material world, its lust for constant progress, and its condescending attitude toward civilizations it classifies as primitive, underdeveloped, or backward.
Most of all, we are concerned with our society’s obsession with the known and its woeful neglect of the dimension of mystery. It is quite right that we should be amazed at our own achievements, our triumphant technology, our science, the power of our computers, but what we don’t know may be sufficiently powerful to overturn in a moment our entire existence and certified knowledge.
We often joke that someone has a “blind spot,” without necessarily realizing that each one of us literally possesses a blind place, an absolute gap in our information-gathering abilities, in the retina of the eye. The retina is packed with visual receptors, except for one tiny region where the nerve connections from those receptors gather together and form the optic nerve. When we look out at the world, there is always a tiny piece of missing information that the brain is constantly filling in so that vision appears to be uniform.
Think of missing information as the trickster of chaos theory. We imagine that we’ve got everything tied up and accounted for and then the trickster appears to turn things upside down and leap across all our nice convenient boundaries. Like the clown in a medieval court, the trickster is always at our elbow to remind us of our limitations.
It is probably not a coincidence —or maybe it’s a fractal coincidence— that in the ancient Tarot deck, the card for the trickster, the Fool, the figure with the cap and bells, is also the Tarot’s emblem for the whole. The Fool is foolishness or madness, but also spirit. He is the perfected spirit of man approaching the One, the zero that contains all things but is nothing—the mysterious undefinable chaos.
Missing information reminds us that our great achievements are always limited and that one of the most favorable hexagrams in the I Ching, the book of changes, is hexagram 15, Modesty. Modesty is hard to come by in our Western civilization, where we take pride in completeness.
We want complete scientific theories. Our stories always have to have an ending; music must move toward its final resolutions; until recently, paintings were always bounded within frames. In the Arab world, by contrast, music, art, and storytelling flow on forever without the need for an attainable end point. Although the Sherpas of Tibet like to climb mountains, out of respect to the gods they usually refrain from standing on the peak itself. Imagine a Western climber who didn’t have his photograph taken with his foot dominating the summit. Such a person would be considered mediocre and his journey incomplete.
Perhaps at a deep level our reluctance to embrace the missing information has something to do with our anxiety about ‘death‘—the ultimate missing information, the ultimate unknown that makes all knowledge shrink to nothing. But chaos theory provides a different outlook. Chaos tells us that the missing information is the window to the whole. In the pit of uncertainty looms our access to creative possibilities.
Everything we have said about missing information and the provisional nature of the concepts we project onto the world obviously must also apply to the metaphor that this book has made of chaos theory. Both the metaphor and the theory from which it came are ways of seeing. A theory is a mental projection onto the infinite complexity of nature—one that emphasizes certain nuances within the flux. The physicist David Bohm liked to point out that the words “theory” and “theater” came from the same Greek root, “to see.” For Bohm, a scientific or a philosophical theory was a “theater of the mind.”
A theory is of necessity provisional. It’s an abstraction from a much wider context that includes nature, society, and individual life. The context from which theories are born is itself always changing. So theories work well for a time, then seem to get stuck, no matter how much we attempt to modify them, until creative chaos—or whatever else we may call it—causes the mind to come up with a new theatrical production.
But no matter how provocative or insightful, metaphors, theories, concepts, and knowledge can take us only so far. To live sanely and deeply we need something else, a special sort of awareness. Yet as soon as we sense the lack, we immediately ask, “Where does this something else come from? How am I going to grasp it, own it, make use of it in my life?” And so the circuit begins again.
We jump too quickly from the openness of the question to the need for its resolution. But what if what we are seeking doesn’t lie in any answer but at the center of the question, in the very depths of the missing information? Rather than ending this book with a summing up, some definitive statement about life and chaos theory, perhaps we should be simply asking a question.
What question shall we ask?