Buckminster Wolfram

Writing or speaking clearly may be harder then you think. (I wrote this in August of 2002, after finishing Stephen Wolfram’s book, “A New Kind of Science”.)


Once upon a time, the world was a simple place, a place of myth and of math. Some said that an ethereal craftsman had made it all from a handful of basic forms. Others, that it had made itself, after a fashion, through an unplanned eternity of randomness. And although it was certainly filled with an unimaginable variety of things, some like plants or animals, and others like rocks or stars, most were certain that behind it all lay a simplicity of form and a certainty of method. But because those things were not evident, they told stories to explain it all to one another. They gave their stories names, and by naming them, gave them life. In time, their stories grew strong roots to anchor themselves in the rich ground of their understanding, and they grew branches to lift their followers closer to the light that illuminated that understanding.

The two trees grew across a stream from one another, each confident in its ability to provide for its leaves everything that they might need to grow strong and to prosper. It supplied nutrients from the ground upon which it grew, and spread itself high and broad to be certain that each leaf could get enough light as well.

Then, one day a squirrel named Buckminster Wolfram happened by. He’d been watching the two trees for some time, and had always been bothered by something that he could never quite explain. This morning, at sunrise, however, he finally understood what it was that had so bothered him, and he went to ask the trees about it.

“Tree of Myth,” he asked quietly, afraid of disturbing the first tree’s slumber.

The tree looked down at little Bucky, and wondered why he wasn’t climbing its branches, as were several other squirrels that day.

“Are you the only tree of your kind?” Bucky asked, paying especial attention to his enunciation, lest the great tree not understand what he had said.

“Certainly not,” the Tree of Myth replied. “Why would you think that?”

The squirrel looked out from the shade of the tree. “It’s just that the world is such a big place, and you are rooted here, in the middle of the shade that you make so well.”

The tree swayed in the breeze for a while before answering. “But why,” it asked at length, “should that be a problem?”

The squirrel climbed to a low branch and sat beside a leaf. “Well,” Bucky told him, “I know that this leaf gets nutrients from the ground below you, and light from the sun above, but your trunk is shaded by the leaves, and your roots are buried in the ground. Neither can get any light.”

“Silly squirrel,” laughed the tree, “the leaves send some of what they have made from combining the nutrients and the light to those parts of me. They are well fed. But you asked about other trees, not about my trunk and roots.”

Bucky hopped off the branch. “That is correct, wise old tree. Yet, if your trunk and roots know of the sun only what the leaves tell them, and the leaves only know of the ground what your roots tell them, how do any of them know what is real? How do they know if it is the truth that shines on those leaves, rather than some false light such as the moon? Or that it is the earth that you are planted in, and not a pot?”

“That,” the Tree of Myth said gravely, “is something that they must take on faith. But why did you ask about other trees?”

“Only this,” the squirrel said, looking up at the great tree, and squinting at the sparks of light slipping past its leaves. “If there were other trees of Myth, then just as yours, their trunks and roots would not know the light directly. But if you were close enough to see one another, if your roots and leaves were close enough to tangle, then perhaps they could learn from the wisdom of your neighbor tree.”

“Perhaps so,” said the tree, “but how would that solve the problem you have come here to pose?”

The squirrel considered the tree’s answer for a time, and then turned to go. “I think that you are right,” he said, looking back. “I believe I will ask the Tree of Math.”

And with that, Bucky scurried off towards the other great tree. When he was halfway there, perched upon a shapely rock amid the stream, he paused to look back, and noticed how much alike the two trees really were. Then, he looked at his distorted reflection in the rippled water for a moment and continued on towards the Tree of Math.

“Pardon me,” Bucky said politely, “but I was just speaking with the Tree of Myth, and I have a question to ask of you.”

Although the two trees looked so alike at a distance, when Bucky stood in the shade of this tree, he could see the ways in which they were different. For while the Tree of Myth was cloaked in endless variation, the tree of math was made from shapes and textures that seemed to repeat themselves in one way or another.

“Speak up!” the tree said after a time. “I’ve lost your voice amid the rustle of my leaves.”

“I said,” the squirrel called out, much louder this time, “I have a question for you.”

The Tree of Math didn’t so much sway in the breeze as vibrate from it, and it made a low howl, of the kind that would be at home in a graveyard. “Yes?” the tree said at last.

“How do your leaves know whether the ground exists, and how do your roots know that the sun exists? I asked the Tree of Myth, and he said that it was a matter of faith.”

The tree laughed heartily. “I’m not surprised,” it said. “After all, that it the basis for his existence.”

Bucky tried to climb the tree’s truck, but became dizzy from the repeating texture of its bark. “I see,” he said amiably. “And what is the basis for your own existence?”

“Why, proofs, of course!” exclaimed the tree happily. “To get from one part of me to another, all you need to do is to select a set of theorems and apply the right rules in the right order.”

The squirrel looked up at the tree. “Does that mean,” he said carefully, “that there are no others like you? That you are the only Math tree in the world?”

“Well,” the tree said, “I’m certainly the only one that I know of. Is that a problem?”

Bucky backed away from the tree, just to be on the safe side. After all, he didn’t know how his next question might affect the old tree. “I think it might be,” he said, certain that he was now a safe distance. “The Tree of Myth told me that there were others like himself. Then, on my way here, when I was halfway between you, it seemed that there were many similarities between the shapes made by Myth and Math. And since there are other trees of Myth, I must wonder whether there are other trees of Math.”

“If there are,” the tree said gruffly, annoyed at the squirrel’s brashness, “I certainly don’t know about them.”

Bucky put some more distance between himself and the tree before yelling his final question. “But how could you? Have you traveled, as I can?”

The Tree of Math shook from crown to ground. “I know there are no others because none of my theorems have led me there, and there are no other theorems.”

“We’ll see,” Bucky said to himself, “we’ll see.”

Cracking the Nut

In his long-awaited book, “A New Kind of Science,” Stephen Wolfram makes the startling suggestion that all of the astounding technology and engineering that we have built on what we know of math and physics represents only a special case, and that there is an unexplored realm far larger than what has so far been explored. Well, he didn’t really say that, but it’s how I have interpreted what he said.

The world, according to math and physics, is like a vast edifice constructed on the solid footing of simple laws. According to these laws, there are eternal truths, simple patterns and relationships, at the heart of everything. To use these laws, as the Tree of Math explained, you begin with a set of theorems, and then apply them to the data.

So, for example, the paths of the moons and planets might be described by a simple equation. To predict where a planet would be at some point in the future, then, you apply the rules of gravitation to things you know about its mass, position and motion. That was how Isaac Newton saw it, anyway. And unless you looked really closely, it worked. Since his time, however, we’ve learned to look a great deal closer, and discovered in the process that the motion of our moon isn’t quite as simple as Sir Isaac had supposed. Instead of tracing the pure curve laid out by Newton’s gravitational equation, its orbit wobbles around within a range of possible places, and the area that its orbit might take it through can be called its attractor. Unfortunately, that’s about the best we could do, because its actual path seemed beyond prediction.

The subtle randomness in the moon’s actual path, like the randomness in a heartbeat or pretty much anything else, was therefore a nut caught in the jaws of math and physics, a nut that refused to crack. Many solutions were proposed, many sources of this randomness were suggested, but because it was still random, math and physics were powerless to do more than be vague about the details of these patterns.

Wolfram had a different idea, one with far-ranging implications. But because the basis for his way of seeing and working with the problem was different than what had come before, he needed to first construct a new tree, as it were, before revealing the fruit that it might bear. That is why his book is so long, and why it took so long for him to create it.

In a way, the comparison that Wolfram draws between the traditional math and physics and the basis for his new kind of science is like the difference between nouny and verby languages.

English, like many other languages, is built on the idea that things are the most basic elements of communication. The words we use in English to represent things are called nouns. To say something about one of these nouns, we act on it with a verb. And because actions are represented by the verbs, the things we refer to with nouns are passive on their own. Speaking in the language of physics, then, the Earth is a noun, and gravity is a verb that acts on it. Without the action supplied by the verb, in this case Newton’s force of gravity, the noun we inhabit would not move.

In contrast, there are also many verby languages, such as Native American cultural languages. Here, the active principal, the verb, is the most basic element of communication. Motion and activity are expressed through things represented by nouns, but because they are the basis of all else, there is no such thing as a static noun. This difference in language reveals a much more pervasive difference in how the world is understood, and how those using each variety of communication interact with the world.

What Stephen Wolfram has done is suggest that the basis for traditional math and physics, static things being acted upon by sets of rules, is like living in a nouny world. His new kind of science, however, is founded on the active basis that he describes in terms of simple programs; in other words, verbs.

It was something that inventor and futurist Buckminster Fuller had recognized many years earlier, and had expressed in the simple phrase, “I seem to be a verb.” Of course, Fuller was living in a nouny English world, but his ideas transcended that space, and many people were baffled by what and how he wrote.

Using a computer to explore the world he saw, Wolfram discovered that some simple programs produced extremely complex behavior, yet the sorts of rules that traditional math and physics applied to static objects could not describe it. He had discovered a place that could not be explored using the current methods of math and physics.

The question he has posed for the rest of us is this: “What awaits?”

Beyond Words

While most people will probably choose to explore the scientific implications of Wolfram’s work, I would like to take a different approach and look at how his insights can benefit those people who use language to communicate. Much has been written about the effects of language on culture, but there remain many areas in which communication is thwarted by the distinction between nouny and verby worldviews. I would like to suggest that the world, as seen by Stephen Wolfram and Buckminster Fuller, when taken together, might offer some solutions to this problem.

Returning briefly to the tale with which I began, the squirrel’s Tree of Math represents the prevailing static world of objects acted on by rules, which in language is the nouny langscape. It is a well-wrought, self-consistent universe defined by the sets of rules brought to bear on the objects within it. Similarly, the internal world that is developed along with a nouny language is a robust universe capable of exploring and describing everything within its scope. But, as the squirrel suggested, there is more world than there is tree. Something else is therefore needed to enable us to explore that world.

Speakers of verby languages, on the other hand, can easily explore this realm, but they may find themselves at a disadvantage when faced with some aspects of the nouny world. This is because the foundations of the two worlds rest on different understandings of what the world is and how we relate to it. To a person whose world is alive, for example, treating it as if it were not is nearly incomprehensible, and vice versa.

By providing a way for people living in the nouny universe of traditional math and physics to understand a verby way of seeing, Wolfram introduces the possibility of bridging the gap, and creating a new, more inclusive worldview that encompasses both nouny and verby perspectives. This is not to say that either one is fully right or wrong, any more than the world is made exclusively of Yin or Yang. Rather, the two compliment one another, and each holds within it the seed of the other.

Buckminster Fuller spent his life showing the world another way of seeing, and in so doing developed a wealth of innovative ideas and inventions. Some of these have proved invaluable, while other were more profound in how they approached a given problem than in how they solved it. In the spirit of Fuller’s way of addressing problems, then, let us take a look at the effects of creating a new kind of langscape, one neither nouny, nor verby, yet both as well.

So, what would a language, and therefore a worldview, be like if it was neither wholly nouny, nor wholly verby? Surely the choice must be one of logical exclusivity, with the selection of either one negating that of the other, mustn’t it? But wait a moment, before answering that question, because even the way it is posed reveals the assumptions of a nouny world. As written, the question posits two alternatives, and asks which one is to be acted upon by the enlivening quality of truth. Pick either one, and other must be relegated to falsity. But then, where does that leave us? What are we to use as the basis for our language, and for the basis of the worldview it supports?

Clearly, there must be either a change made to our understanding of nouns and verbs — things and actions, or we must adopt some new kind of model, within which these concepts can peacefully coexist. The spirit of Fuller would suggest the latter.

What then, would such a language be like, and what kind of a world would thinking in it build around us? Where do we even begin? Since the attributes associated with nouns and verbs have gotten in our way, then it might be useful to take a step back and look at the source of those attributes, and whether they exist in a form that does not require words.

To do this, we must first consider the origin of the thoughts that are associated with words, and that brings us face-to-face with the nature of awareness, and of consciousness. In other words, what is it that has the thoughts that get encoded as language?

Even among humans, not all communication is conveyed through languages constructed of words. One easy example of this is body language, including the detailed interpretations developed under the name Neuro-Linguistic Programming, or NLP. There is ample communication among animals as well. How far afield you take this argument is not as important as accepting the idea that not all language requires words. If we accept the premise that even our own communication comes from a source that does not require language, then it is that source where we must begin.

Say then, that I am such a being possessed of the need to communicate, and that that which is to be communicated exists in a form that is not yet encoded into the words of a language. Unless I am able to transfer this information directly to the equivalent aspect of another individual, perhaps by using some form of psi, it must first be encoded through a language understood by both parties. It is at this moment that our concept of language intrudes, and it is also when our choice of a language becomes crucial, for the use of either kind will alter the message.

Our current choices appear to be either nouny or verby, and both will alter the essence of the message. This is because the filter through which it is transmitted imparts a flavor of its own, and causes many unintentional assumptions to be added to the message as well.

One of the things that Wolfram discovered was that with a simple program that produces complex behavior, it is possible to emulate the behavior of any other simple program. If his simple programs are like verby languages, it should be possible to express both the content and the context of a message as it would be understood in a nouny language, through careful use of a verby one. Doing this may not be simple, but it is possible. But is the reverse also possible? In other words, can the content and the context of a verby message be expressed through careful use of a nouny language as well? Numerous papers suggest that it can. Therefore, if you think of nouny and verby languages as Yin and Yang, the small spot of the complementary color in each part represents this ability to emulate the other.

Perhaps, then, some averbal language exists within us that can be made to express ideas in the form of nouny and verby languages. Within this averbal context then, the special added meanings layered on by nouny and verby languages do not exist, leaving only the pure essence of that which was to be communicated.

But, like the Tree of Myth asked the squirrel, how does this solve our problem?

One way is that by knowing how a message is distorted, the recipient can remove the distortion to reveal the intended message. Encryption and decryption are used for this purpose everywhere. However, not all methods of encoding preserve the entire original message. A good example of this is the JPEG format for pictures. This method of encoding an image discards some information that is deemed unnecessary to the recognition of the decoded picture. Because it is not important to preserve every detail of an image to convey the idea expressed in it, this is usually an acceptable trade-off. It could not be used, however, if there was special meaning associated with each pixel in the image.

So how important is the accurate preservation of the averbal message encoded in either kind of language? Since both linguistic encoding schemes distort the message and even add possibly unrelated context to it, I suspect that we can handle some amount of degradation and still understand what the sender meant.

Therefore, knowing how our languages distort reality is a useful way to enable us to strip away the distortions. Implementing this, however, will require a new kind of language instruction, and there would have to be two varieties of it as well. In such a class, the student would learn about the distortions imposed by both kinds of language, and how to remove it from what is said by a speaker of the other kind. I suspect, though, that there would be considerable resistance to such instruction, because it requires each student to accept the existence of a bit of unintended error in their understanding of the world, something that is threatening to some worldviews.

…of course, I might be wrong.

Copyright 2007 P. Orin Zack


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